diff --git a/__init__.py b/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/ampullary.pdf b/ampullary.pdf index f85b166..f1aa6d3 100644 Binary files a/ampullary.pdf and b/ampullary.pdf differ diff --git a/ampullary.png b/ampullary.png deleted file mode 100644 index 8ee4509..0000000 Binary files a/ampullary.png and /dev/null differ diff --git a/cells_suscept.pdf b/cells_suscept.pdf index af7d897..fea1195 100644 Binary files a/cells_suscept.pdf and b/cells_suscept.pdf differ diff --git a/cells_suscept.png b/cells_suscept.png deleted file mode 100644 index cb58dba..0000000 Binary files a/cells_suscept.png and /dev/null differ diff --git a/cells_suscept_high_CV.pdf b/cells_suscept_high_CV.pdf index 1989a6c..e322303 100644 Binary files a/cells_suscept_high_CV.pdf and b/cells_suscept_high_CV.pdf differ diff --git a/cells_suscept_high_CV.png b/cells_suscept_high_CV.png deleted file mode 100644 index 693f17f..0000000 Binary files a/cells_suscept_high_CV.png and /dev/null differ diff --git a/data_overview_mod.pdf b/data_overview_mod.pdf index 9d27092..9f99801 100644 Binary files a/data_overview_mod.pdf and b/data_overview_mod.pdf differ diff --git a/data_overview_mod.png b/data_overview_mod.png deleted file mode 100644 index ec24f6f..0000000 Binary files a/data_overview_mod.png and /dev/null differ diff --git a/flowchart.pdf b/flowchart.pdf index 2715452..34c0a39 100644 Binary files a/flowchart.pdf and b/flowchart.pdf differ diff --git a/flowchart.png b/flowchart.png deleted file mode 100644 index 9bd3459..0000000 Binary files a/flowchart.png and /dev/null differ diff --git a/model_and_data.pdf b/model_and_data.pdf index db6c70c..d8383bb 100644 Binary files a/model_and_data.pdf and b/model_and_data.pdf differ diff --git a/model_and_data.png b/model_and_data.png deleted file mode 100644 index 5132756..0000000 Binary files a/model_and_data.png and /dev/null differ diff --git a/model_and_data.py b/model_and_data.py index 82044f6..fe87065 100644 --- a/model_and_data.py +++ b/model_and_data.py @@ -114,7 +114,7 @@ def model_and_data2(eod_metrice=False, width=0.005, nffts=['whole'], powers=[1], ] nrs_s = [3, 4, 8, 9] #, 10, 11 c = 2.5 - cs = ['$c=%.1f$' % c + '$\,\%$', '$c=0\,\%$'] + cs = ['$c=%.1f$' % c + r'\,\%', r'$c=0$\,\%'] titles = ['Model\n$N=11$', 'Model\n' + '$N=10^6$', 'Model\,(' + label_noise_name().lower() + ')' + '\n' + '$N=11$', 'Model\,(' + label_noise_name().lower() + ')' + '\n' + '$N=10^6$' diff --git a/model_full.pdf b/model_full.pdf index 16ca0ae..aa4fd70 100644 Binary files a/model_full.pdf and b/model_full.pdf differ diff --git a/model_full.png b/model_full.png deleted file mode 100644 index 4a350bf..0000000 Binary files a/model_full.png and /dev/null differ diff --git a/motivation.pdf b/motivation.pdf index ff2a1ee..de2c362 100644 Binary files a/motivation.pdf and b/motivation.pdf differ diff --git a/motivation.png b/motivation.png deleted file mode 100644 index 914ea4e..0000000 Binary files a/motivation.png and /dev/null differ diff --git a/motivation_stim.png b/motivation_stim.png deleted file mode 100644 index 6892f79..0000000 Binary files a/motivation_stim.png and /dev/null differ diff --git a/nonlin_regime.pdf b/nonlin_regime.pdf index 4f0e45d..3872648 100644 Binary files a/nonlin_regime.pdf and b/nonlin_regime.pdf differ diff --git a/nonlin_regime.png b/nonlin_regime.png deleted file mode 100644 index 3e27854..0000000 Binary files a/nonlin_regime.png and /dev/null differ diff --git a/nonlin_regime.py b/nonlin_regime.py index be07c02..3054521 100644 --- a/nonlin_regime.py +++ b/nonlin_regime.py @@ -220,9 +220,9 @@ def plt_stim_nonlin(arrays_st, axe_all, axes, c_nn, c_nrs, colors_array_here, gr else: spines = '' plt_stim_saturation(0, [], [am * 100], axe, colors_array_here, i, - c_nn, ['Contrast [$\%$]'], time, + c_nn, [r'Contrast [\%]'], time, xlim=xlim, lw=1, spines=spines) # np.array(arrays_sp)*1000 - #beat_here = r'$\rm{Contrast}=%s$' % (int(np.round(c_nrs[c_nn]))) + '$\%$' # +'$' + #beat_here = r'$\rm{Contrast}=%s$' % (int(np.round(c_nrs[c_nn]))) + r'\%' # +'$' beat_here = f'$\\rm{{Contrast}}={c_nrs[c_nn]:.2g}\\%$' title_name = beat_here # fish + '\n' + +c1+c2#twobeat_cond(big=True, double=True,cond=False) axe.text(1, 1.1, title_name, va='bottom', ha='right', @@ -405,6 +405,7 @@ def plt_amplitudes_for_contrasts(c_nrs_orig, cell_here, freq1, freq2, grid_down, labels = [label_deltaf1(), label_deltaf2(), label_sum(), label_diff(), label_fbasename_small()] # ax_u1.legend(ncol = 4, loc = (0,1.2)) + plt_single_trace([], ax_u1, frame_cell_orig, freq1, freq2, scores=np.array(scores)[index], labels=np.array(labels)[index], colors=np.array(colors)[index], @@ -434,7 +435,7 @@ def plt_amplitudes_for_contrasts(c_nrs_orig, cell_here, freq1, freq2, grid_down, # ax_u1.plot([c_nr, c_nr], [0, 435], color='black', linewidth=0.8, clip_on=False) ylim = ax_u1.get_ylim() ax_u1.set_ylim(0, ylim[-1]) - ax_u1.set_xlabel('Contrast [$\%$]') + ax_u1.set_xlabel(r'Contrast [\%]') ax_u1.set_ylabel('Amplitude [Hz]') return ax_u1, c_dist_recalc, c_nrs, color0, color01, color012, color01_2, color02, eodf, f_counter, frame_cell, frame_cell_orig, freq1, freq2, i, sampling diff --git a/plot_chi2.pdf b/plot_chi2.pdf index 0abfcdb..b9b034a 100644 Binary files a/plot_chi2.pdf and b/plot_chi2.pdf differ diff --git a/plot_chi2.png b/plot_chi2.png deleted file mode 100644 index 5d2f7da..0000000 Binary files a/plot_chi2.png and /dev/null differ diff --git a/plotstyle.py b/plotstyle.py index a605578..c583d00 100644 --- a/plotstyle.py +++ b/plotstyle.py @@ -101,8 +101,7 @@ def plot_style(ns=__main__): compression=6, fonttype=3, stripfonts=False) grid_params(grid=False, axis='both', which='major', **ns.lsGrid) labels_params(labelformat='{label} [{unit}]', labelsize='medium', labelweight='normal', - labelcolor='axes', labelpad=8, - xlabellocation='center', ylabellocation='center') + labelcolor='axes', labelpad=8) legend_params(fontsize='small', frameon=False, borderpad=0, handlelength=1.5, handletextpad=0.5, numpoints=1, scatterpoints=1, labelspacing=0.5, columnspacing=0.5) diff --git a/references.bib.bak b/references.bib.bak deleted file mode 100644 index 76cb8fc..0000000 --- a/references.bib.bak +++ /dev/null @@ -1,7003 +0,0 @@ -% Encoding: UTF-8 - 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The difference frequency between the signals sets the frequency of the beat. A field study in the electric fish Apteronotus rostratus showed the behavioral relevance of very high difference frequencies. Contrary to expectations from previous studies, our electrophysiological data show strong responses of p-type electroreceptor afferents whenever the difference frequency approaches integer multiples (mistuned octaves) of the fish’s own electric field frequency (carrier). Mathematical reasoning and simulations show that common approaches to extract amplitude modulations, such as Hilbert transform or half-wave rectification, are not sufficient to explain the responses at carrier octaves. Instead, half-wave rectification needs to be smoothed out, for example by a cubic function. Because electroreceptive afferents share many properties with auditory nerve fibers, these mechanisms may underly the human perception of beats at mistuned octaves as described by Ohm and Helmholtz.} -} - -@article{Barayeu2024, - title={Bursts boost nonlinear encoding in electroreceptor afferents}, - author={Barayeu, Alexandra and Schlungbaum, Maria and Lindner, Benjamin and Grewe, Jan and Benda, Jan}, - journal={bioRxiv}, - pages={2024--06}, - year={2024}, - publisher={Cold Spring Harbor Laboratory} -} - -@Article{Barber2000, - Title = {{The importance of stable schooling: do familiar sticklebacks stick together?}}, - Author = {Barber, Iain and Ruxton, Graeme D}, - Journal = ProcRSocLondBBiolSci, - Year = {2000}, - Number = {1439}, - Pages = {151-155}, - Volume = {267}, - - Doi = {10.1098/rspb.2000.0980}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - -@article{Barlow1957, - title={{Change of organization in the receptive fields of the cat's retina during dark adaptation}}, - author={Barlow, HB and Fitzhugh, Roo and Kuffler, SW}, - journal={The Journal of Physiology}, - volume={137}, - number={3}, - pages={338}, - year={1957}, - publisher={Wiley-Blackwell} -} - -@InCollection{Barlow1961, - Title = {{Possible principles underlying the transformation of sensory messages.}}, - Author = {H. 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Bastian}, - Journal = JCompPhysiolA, - Year = {1993}, - Pages = {409-423}, - Volume = {172} -} - - -@Article{Bastian1993b, - Title = {Commisural neurons of the electrosensory lateral line lob of \textit{Apteronotus leptorhynchus}: morphological and physiological characteristics.}, - Author = {J. Bastian and J. Courtright and J. Crawford}, - Journal = JCompPhysiolA, - Year = {1993}, - Pages = {257-274}, - Volume = {173} -} - -@Article{Bastian1995, - Title = {Pyramidal-cell plasticity in weakly electric fish: a mechanism for attenuating responses to reafferent electrosensory inputs.}, - Author = {J. Bastian}, - Journal = JCompPhysiolA, - Year = {1995}, - Pages = {63-78}, - Volume = {176} -} - - - -@Article{Bastian1996a, - Title = {{Plasticity in an Electrosensory System. I. General Features of a Dynamic Sensory Filter.}}, - Author = {Joseph Bastian}, - Journal = {Journal of Neurophysiology}, - Year = {1996}, - Number = {4}, - Pages = {2483-2496}, - Volume = {76} -} - -@Article{Bastian1996b, - Title = {{Plasticity in an Electrosensory System. II. Postsynaptic Events Associated With a Dynamic Sensory Filter.}}, - Author = {Joseph Bastian}, - Journal = {Journal of Neurophysiology}, - Year = {1996}, - Number = {4}, - Pages = {2497-2507}, - Volume = {76} -} - -@Article{Bastian1998, - Title = {{Modulation of Calcium-Dependent Postsynaptic Depression Contributes to an Adaptive Sensory Filter.}}, - Author = {Joseph Bastian}, - Journal = {Journal of Neurophysiology}, - Year = {1998}, - Pages = {3352-3355}, - Volume = {80} -} - -@Article{Bastian2001, - Title = {Dentritic Modulation of Burst-Like Firing in Sensory Neurons.}, - Author = {Joseph Bastian and Jerry Nguyenkim}, - Journal = {Journal of Neurophysiology}, - Year = {2001}, - Number = {1}, - Pages = {10-22}, - Volume = {85} -} -@article{Bastian2002, - title={Receptive field organization determines pyramidal cell stimulus-encoding capability and spatial stimulus selectivity}, - author={Bastian, Joseph and Chacron, Maurice J and Maler, Leonard}, - journal={Journal of Neuroscience}, - volume={22}, - number={11}, - pages={4577--4590}, - year={2002}, - publisher={Soc Neuroscience} -} - -@Article{Bastian2004, - title={Plastic and nonplastic pyramidal cells perform unique roles in a network capable of adaptive redundancy reduction}, - author={Bastian, Joseph and Chacron, Maurice J and Maler, Leonard}, - journal={Neuron}, - volume={41}, - number={5}, - pages={767--779}, - year={2004}, - publisher={Elsevier} -} - -@article{Batra1989, - title={Temporal coding of envelopes and their interaural delays in the inferior colliculus of the unanesthetized rabbit}, - author={Batra, R and Kuwada, S and Stanford, TR}, - journal={Journal of Neurophysiology}, - volume={61}, - number={2}, - pages={257--268}, - year={1989} -} - -@Article{Behrend1977, - Title = {Processing information carried in a high frequency wave: properties of cerebellar units in a high frequency electric fish.}, - Author = {Konstantin Behrend}, - Journal = JCompPhysiol, - Year = {1977}, - Pages = {357-371}, - Volume = {118} -} - -@article{Beiran2018, - title={Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations}, - author={Beiran, Manuel and Kruscha, Alexandra and Benda, Jan and Lindner, Benjamin}, - journal={Journal of Computational Neuroscience}, - volume={44}, - pages={189--202}, - year={2018}, - publisher={Springer} -} - -@article{Beiran2018coding, - title={Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations}, - author={Beiran, Manuel and Kruscha, Alexandra and Benda, Jan and Lindner, Benjamin}, - journal={Journal of Computational Neuroscience}, - volume={44}, - pages={189--202}, - year={2018}, - publisher={Springer} -} - -@ARTICLE{Belbenoit1970, - AUTHOR = {Pierre Belbenoit}, - TITLE = {Conditionnement instrumental de l'\'electroperception des objets chez \textit{Gnathonemus petersii} ({Mormyridae}, {Teleostei}, {Pisces}).}, - JOURNAL = {Z vergl Physiol}, - YEAR = {1970}, - VOLUME = {67}, - PAGES = {192--204} -} - -@ARTICLE{Bell1976, - AUTHOR = {C. C. Bell and J. Bradbury and C. J. Russell}, - TITLE = {The electric organ of a mormyrid as a current and voltage source.}, - JOURNAL = JCompPhysiol, - YEAR = {1976}, - VOLUME = {110}, - PAGES = {65--88} -} - - -@ARTICLE{Benda2005, - AUTHOR = {Jan Benda and Andr\'e Longtin and Leonard Maler}, - TITLE = {Spike-frequency adaptation separates transient communication signals from background oscillations.}, - YEAR = {2005}, - JOURNAL = {Journal of Neuroscience}, - VOLUME = {25}, - NUMBER = {9}, - PAGES = {2312--2321} } - - -@ARTICLE{Benda2006, - AUTHOR = {Jan Benda and Andr\'e Longtin and Leonard Maler}, - TITLE = {A synchronization-desynchronization code for natural communication signals.}, - YEAR = {2006}, - JOURNAL = Neuron, - VOLUME = {52}, - PAGES = {347--358} } - -@ARTICLE{Benda2010, - AUTHOR = {Jan Benda and Leonard Maler and Andr\'e Longtin}, - TITLE = {Linear versus Nonlinear Signal Transmission in Neuron Models - with Adaptation-Currents or Dynamic Thresholds.}, - YEAR = {2010}, - JOURNAL = {Journal of Neurophysiology}, - VOLUME = {104}, - PAGES = {2806-2820} } - -@incollection{Benda2013, - author = {Benda, Jan and Grewe, Jan and Krahe, R{\~A}ƒ{\^A}ƒ{\~A}‚{\^A}ƒ{\~A}ƒ{\^A}‚{\~A}‚{\^A}¼diger}, - booktitle = {Animal Communication and Noise}, - doi = {10.1007/978-3-642-41494-7_12}, - editor = {Brumm, Henrik}, - isbn = {978-3-642-41493-0}, - language = {English}, - pages = {331-372}, - publisher = {Springer Berlin Heidelberg}, - refid = {876}, - series = {Animal Signals and Communication}, - timestamp = {2014.02.03}, - title = {Neural Noise in Electrocommunication: From Burden to Benefits}, - url = {http://dx.doi.org/10.1007/978-3-642-41494-7_12}, - volume = {2}, - year = {2013}, - bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-642-41494-7_12}} - -@incollection{Benda2020, - title={The physics of electrosensory worlds.}, - author={Benda, Jan}, - editor={Fritsch, B. and Bleckmann, H}, - volume={7}, - pages={228--254}, - year={2020}, - publisher={Elsevier, Academic Press}, - booktitle={The senses: a comprehensive reference} -} - -@article{Benda2021, - title={Neural adaptation}, - author={Benda, Jan}, - journal={Current Biology}, - volume={31}, - number={3}, - pages={R110--R116}, - year={2021}, - publisher={Elsevier} -} - -@ARTICLE{Bennett1970, - AUTHOR = {Michael V. L. Bennett}, - TITLE = {Comparative physiology: electric organs.}, - JOURNAL = AnnuRevPhysiol, - YEAR = {1970}, - VOLUME = {32}, - PAGES = {471--528} -} - -@ARTICLE{Bennett1971, - AUTHOR = {Michael V. L. Bennett}, - TITLE = {Electroreception.}, - JOURNAL = {Fish Physiology}, - YEAR = {1971}, - VOLUME = {5}, - PAGES = {493--574} -} - -@Article{Berdahl2018, - author = {Berdahl, Andrew M. and Kao, Albert B. and Flack, Andrea and Westley, Peter A. H. and Codling, Edward A. and Couzin, Iain D. and Dell, Anthony I. and Biro, Dora}, - title = {Collective animal navigation and migratory culture: from theoretical models to empirical evidence}, - journal = PhilTransRSocLondBBiolSci, - year = {2018}, - volume = {373}, - pages = {20170009}, - doi = {10.1098/rstb.2017.0009} -} - -@Article{Berman1995, - title={Inositol 1, 4, 5-trisphosphate receptor localization in the brain of a weakly electric fish (\textit{Apteronotus leptorhynchus}) with emphasis on the electrosensory system}, - author={Berman, Neil J and Hincke, Maxwell T and Maler, Leonard}, - journal={Journal of comparative neurology}, - volume={361}, - number={3}, - pages={512--524}, - year={1995}, - publisher={Wiley Online Library} -} - -@article{Berman1998inhibition, - title={Inhibition evoked from primary afferents in the electrosensory lateral line lobe of the weakly electric fish \textit{(Apteronotus leptorhynchus)}.}, - author={Berman, Neil J and Maler, Leonard}, - journal={Journal of Neurophysiology}, - volume={80}, - number={6}, - pages={3173--3196}, - year={1998} -} - -@article{Berman1999, - title={Neural architecture of the electrosensory lateral line lobe: adaptations for coincidence detection, a sensory searchlight and frequency-dependent adaptive filtering}, - author={Berman, Neil J and Maler, Leonard}, - journal={Journal of Experimental Biology}, - volume={202}, - number={10}, - pages={1243--1253}, - year={1999}, - publisher={The Company of Biologists Ltd} -} - -@Article{Betsch2004, - Title = {The world from a cat{'}s perspective --- statistics of natural videos.}, - Author = {Belinda Y. Betsch and Wolfgang Einh\"auser and Konrad P. K\"ording and Peter K\"onig}, - Journal = BiolCybern, - Year = {2004}, - Pages = {41-50}, - Volume = {90} -} - -@Article{Bilde2007, - Title = {Survival benefits select for group living in a social spider despite reproductive costs}, - Author = {Bilde, T. and Coates, K. S. and Birkhofer, K. and Bird, T. and Maklakov, A. A. and Lubin, Y. and Avil\'es, L.}, - Journal = JEvolBiol, - Year = {2007}, - Number = {6}, - Pages = {2412-2426}, - Volume = {20}, - - Abstract = {Abstract The evolution of cooperation requires benefits of group living to exceed costs. Hence, some components of fitness are expected to increase with increasing group size, whereas others may decrease because of competition among group members. The social spiders provide an excellent system to investigate the costs and benefits of group living: they occur in groups of various sizes and individuals are relatively short-lived, therefore life history traits and Lifetime Reproductive Success (LRS) can be estimated as a function of group size. Sociality in spiders has originated repeatedly in phylogenetically distant families and appears to be accompanied by a transition to a system of continuous intra-colony mating and extreme inbreeding. The benefits of group living in such systems should therefore be substantial. We investigated the effect of group size on fitness components of reproduction and survival in the social spider Stegodyphus dumicola in two populations in Namibia. In both populations, the major benefit of group living was improved survival of colonies and late-instar juveniles with increasing colony size. By contrast, female fecundity, female body size and early juvenile survival decreased with increasing group size. Mean individual fitness, estimated as LRS and calculated from five components of reproduction and survival, was maximized for intermediate- to large-sized colonies. Group living in these spiders thus entails a net reproductive cost, presumably because of an increase in intra-colony competition with group size. This cost is traded off against survival benefits at the colony level, which appear to be the major factor favouring group living. In the field, many colonies occur at smaller size than expected from the fitness curve, suggesting ecological or life history constraints on colony persistence which results in a transient population of relatively small colonies.}, - Doi = {10.1111/j.1420-9101.2007.01407.x}, - Keywords = {cooperation, fitness components, lifetime reproductive success, multilevel selection, social spiders, Stegodyphus dumicola}, - Owner = {raab}, - Timestamp = {2020.01.21} -} - -@article{Birmingham1999, - title={Encoding of muscle movement on two time scales by a sensory neuron that switches between spiking and bursting modes}, - author={Birmingham, JT and Szuts, ZB and Abbott, LF and Marder, Eve}, - journal={Journal of Neurophysiology}, - volume={82}, - number={5}, - pages={2786--2797}, - year={1999}, - publisher={American Physiological Society Bethesda, MD} -} - -@ARTICLE{Black1970, - AUTHOR = {Patricia Black-Cleworth}, - TITLE = {The Role of electrical discharges in the non-reproductive social behaviour of \textit{Gymnotus carapo} ({Gymnotidae}, {Pisces}).}, - JOURNAL = {Animal Behaviour Monographs}, - YEAR = {1970}, - VOLUME = {3}, - PAGES = {1--78} -} - -@Article{Bleckmann1993, - Title = {The responses of peripheral and central mechanosensory lateral line units of weakly electric fish to moving objects.}, - Author = {H. Bleckmann and R. Zelick}, - Journal = JCompPhysiolA, - Year = {1993}, - Pages = {115-128}, - Volume = {172} -} - -@ARTICLE{Bleckmann2009, - AUTHOR = {Horst Bleckmann and Randy Zelick}, - TITLE = {Lateral line system of fish.}, - YEAR = {2009}, - JOURNAL = {Integrative Zoology}, - VOLUME = {4}, - PAGES = {13--25} } - -@Article{Blumstein2001, - Title = {Yellow-Footed Rock-Wallaby Group Size Effects Reflect A Trade-Off}, - Author = {Blumstein, Daniel T. and Daniel, Janice C. and Evans, Christopher S.}, - Journal = {Ethology}, - Year = {2001}, - Number = {7}, - Pages = {655-664}, - Volume = {107}, - Owner = {raab}, - Timestamp = {2020.01.21} -} - -@Article{Boerlin2013, - Title = {Predictive Coding of Dynamical Variables in Balanced Spiking Networks.}, - Author = {Martin Boerlin and Christian K. Machens and Sophie Den\`eve}, - Journal = {PLoS Computational Biology}, - Year = {2013}, - Number = {11}, - Pages = {e1003258}, - Volume = {9} -} - -@Article{Bol2011, - Title = {Frequency-Tuned Cerebellar Channels and Burst Induced {LTD} Lead to the Cancellation of Redundant Sensory Inputs.}, - Author = {Kieran Bol and Gary Marsat and Eric Harvey-Girard and Andr\'e Longtin and Leonard Maler}, - Journal = JNeurosci, - Year = {2011}, - Number = {30}, - Pages = {11028-11038}, - Volume = {31} -} - -@Article{Bol2013, - Title = {Modeling cancellation of periodic inputs with burst-{STDP} and feedback.}, - Author = {K. Bol and G. Marsat and J.F. Mejias and L. Maler and A. Longtin}, - Journal = NeuralNetw, - Year = {2013}, - Pages = {120-133}, - Volume = {47} -} - -@Article{Borst1999, - author = {Borst, A. and Theunissen, F.E.}, - journal = {Nature Neurosci.}, - keywords = {Information, Information Theory, neural code, review, theory}, - number = {11}, - owner = {grewe}, - pages = {947--957}, - refid = {216}, - timestamp = {2008.09.26}, - title = {Information theory and neural coding}, - volume = {2}, - year = {1999}} - -@Book{Bradbury2011, - Title = {Principles of animal communication}, - Author = {Bradbury, JW and Vehrencamp, SL}, - Publisher = {Sinauer}, - Year = {2011}, - - Address = {Sunderland}, - Edition = {2nd} -} - -@Article{Bratton1990, - Title = {Descending Control of Electroreception. {II.} Properties of Nucleus Praeeminentialis Neurons Projecting Directly to the Electrosensory Lateral Line Lobe.}, - Author = {Bradford Bratton and Joseph Bastian}, - Journal = JNeurosci, - Year = {1990}, - Number = {4}, - Pages = {1241-1253}, - Volume = {10} -} - - -@Article{Bretschneider1985, - Title = {Functioning of catfish electroreceptors: fractional order filtering and non-linearity.}, - Author = {F. Bretschneider and J.R. De Weille and J.F.L. Klis}, - Journal = CompBiochemPhysiol, - Year = {1985}, - Number = {2}, - Pages = {191-198}, - Volume = {80A} -} - -@incollection{Briand2016, - title={Taste perception and integration}, - author={Briand, Lo{\"\i}c and Salles, Christian}, - booktitle={Flavor}, - pages={101--119}, - year={2016}, - publisher={Elsevier} -} - -@Article{Brincat2004, - title={Underlying principles of visual shape selectivity in posterior inferotemporal cortex}, - author={Brincat, Scott L and Connor, Charles E}, - journal={Nature Neuroscience}, - volume={7}, - number={8}, - pages={880--886}, - year={2004}, - publisher={Nature Publishing Group US New York} -} - -@article{Brownell1990, - title={Outer hair cell electromotility and otoacoustic emissions}, - author={Brownell, William E}, - journal={Ear Hearing}, - volume={11}, - number={2}, - pages={82}, - year={1990}, - publisher={NIH Public Access} - } - -@ARTICLE{Budelli2000, - AUTHOR = {Ruben Budelli and Angel A. Caputi}, - TITLE = {The electric image in weakly electric fish: perception of objects of complex impedance.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2000}, - VOLUME = {203}, - PAGES = {481--492} -} - -@ARTICLE{Budelli2002, - AUTHOR = {R. Budelli and A. Caputi and L. Gomez and D. Rother and K. Grant}, - TITLE = {The electric image of \textit{Gnathonemus petersii}.}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2002}, - VOLUME = {96}, - PAGES = {421--429} -} - -@ARTICLE{Bullock1969, - AUTHOR = {Theodore H. Bullock}, - TITLE = {Species differences in effect of electroreceptor input on electric organ pacemakers and other aspects of behavior i -n electric fish.}, - JOURNAL = BrainBehavEvol, - YEAR = {1969}, - VOLUME = {2}, - PAGES = {85--118} -} - -@article{Bullock1970, - author = {Bullock, TH}, - journal = JGenPhysiol, - number = {5}, - pages = {565--584}, - title = {The reliability of neurons.}, - volume = {55}, - year = {1970} -} - -@Article{Bullock1972a, - Title = {The jamming avoidance response of high frequency electric fish. {I.} General Features.}, - Author = {Bullock, Th H and Hamstra, RH and Scheich, H}, - Journal = JCompPhysiol, - Year = {1972}, - Number = {1}, - Pages = {1--22}, - Volume = {77} -} - -@Article{Bullock1972b, - Title = {The jamming avoidance response of high frequency electric fish. {II.} {Quantitative} aspects.}, - Author = {Bullock, TH and H, RH and Scheich, H}, - Journal = JCompPhysiol, - Year = {1972}, - Number = {1}, - Pages = {23--48}, - Volume = {77} -} - -@ARTICLE{Bullock1972General, - AUTHOR = {Theodore H. Bullock and Robert H. Hamstra, Jr. and Henning Scheich}, - TITLE = {The jamming avoidance response of high frequency electric fish {I.} General features.}, - JOURNAL = JCompPhysiol, - YEAR = {1972}, - VOLUME = {77}, - PAGES = {1--22} -} - -@Article{Bullock1982, - Title = {Evolution of electroreception.}, - Author = {T.H. Bullock and R.G. Northcutt and D.A. Bodznick}, - Journal = TINS, - Year = {1982}, - Pages = {50-53}, - Volume = {5} -} - -@ARTICLE{Bullock1983, - AUTHOR = {T. H. Bullock and D. A. Bodznick and R. G. Northcutt}, - TITLE = {The phylogenetic distribution of electroreception: evidence for convergent evolution of a primitive vertebrate sense modality.}, - YEAR = {1983}, - JOURNAL = BrainResRev, - VOLUME = {6}, - PAGES = {25--46} } - -@book{Bullock2006, - title={Electroreception}, - author={Bullock, Theodore Holmes and Hopkins, Carl D and Fay, Richard R}, - volume={21}, - year={2006}, - publisher={Springer Science \& Business Media} -} - -@ARTICLE{Burham1969, - AUTHOR = {E. G. Burham and W. B. Huckaby and R. Gowdy and B. Burns}, - TITLE = {Microvolt electric signals from fishes and the environment.}, - JOURNAL = Science, - YEAR = {1969}, - VOLUME = {164}, - PAGES = {965--968} -} - -@article{Bushdid2014, - title={Humans can discriminate more than 1 trillion olfactory stimuli}, - author={Bushdid, Caroline and Magnasco, Marcelo O and Vosshall, Leslie B and Keller, Andreas}, - journal={Science}, - volume={343}, - number={6177}, - pages={1370--1372}, - year={2014}, - publisher={American Association for the Advancement of Science} -} - -@article{Cai1996, - title={Temporal patterns of the responses of auditory-nerve fibers to low-frequency tones}, - author={Cai, Yidao and Geisler, C Daniel}, - journal={Hearing Research}, - volume={96}, - number={1-2}, - pages={83--93}, - year={1996}, - publisher={Elsevier} -} - -@article{Caldwell1978, - title={New properties of rabbit retinal ganglion cells.}, - author={Caldwell, JH and Daw, NW}, - journal={The Journal of Physiology}, - volume={276}, - number={1}, - pages={257--276}, - year={1978}, - publisher={Wiley Online Library} -} - -@ARTICLE{Capurro1997, - AUTHOR = {A. Capurro and M. Reyes-Parada and D. Olazabal and R. Perrone and R. Silveira and O. Macadar}, - TITLE = {Aggressive behavior and jamming avoidance response in the weakly electric fish \textit{Gymnotus carapo}: effects of {3,4-Methylenedioxymethamphetamine} ({MDMA}).}, - JOURNAL = {Comp Biochem Physiol}, - YEAR = {1997}, - VOLUME = {188A}, - PAGES = {831--840} -} - -@ARTICLE{Caputi1998, - AUTHOR = {Angel A. Caputi and R. Budelli and K. Grant and C. C. Bell}, - TITLE = {The electric image in weakly electric fish: physical images of resistive objects in \textit{Gnathonemus petersii}.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2000}, - VOLUME = {203}, - PAGES = {481--492} -} - - -@ARTICLE{Caputi1998Brachy, - AUTHOR = {A. A. Caputi and A. C. Silva and O. Macadar}, - TITLE = {The electric organ discharge of \textit{Brachyhypopomus pinnicaudatus}. The effects of environmental variables on waveform generation.}, - JOURNAL = BrainBehavEvol, - YEAR = {1998}, - VOLUME = {52}, - PAGES = {148--158} -} - - -@ARTICLE{Caputi1999, - AUTHOR = {A. A. Caputi}, - TITLE = {The electric organ discharge of pulse gymnotiforms: the transformation of a simple -impulse into a complex spatiotemporal electromotor pattern.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1999}, - VOLUME = {202}, - PAGES = {1229--1241} -} - -@ARTICLE{Caputi2006, - AUTHOR = {A. A. Caputi and R. Budelli}, - TITLE = {Peripheral electrosensory imaging by weakly electric fish.}, - JOURNAL = JCompPhysiolA, - YEAR = {2006}, - VOLUME = {192}, - PAGES = {587--600} -} - -@ARTICLE{Caputi2008, - AUTHOR = {\'Angel A. Caputi and Mar\'ia E. Castell\'o and Pedro A. Aguilera and Carolina Pereira and Javier Nogueira and Alejo Rodr\'iguez-Cattaneo and Carolina Lezcano}, - TITLE = {Active electroreception in \textit{Gymnotus omari}: imaging, object discrimination, and early processing of actively generated signals.}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2008}, - VOLUME = {102}, - PAGES = {256--271} -} - -@article{Cariani2001, - title={Temporal coding of sensory information in the brain}, - author={Cariani, Peter A}, - journal={Acoustical Science and Technology}, - volume={22}, - number={2}, - pages={77--84}, - year={2001}, - publisher={ACOUSTICAL SOCIETY OF JAPAN} -} - -@ARTICLE{Carlson2000, - AUTHOR = {Bruce A. Carlson and Carls D. Hopkins and Peter Thomas}, - TITLE = {Androgen correlates of socially induced changes in the electric organ discharge waveform of a mormyrid fish.}, - JOURNAL = HormBehav, - YEAR = {2000}, - VOLUME = {38}, - PAGES = {177--186} -} - - - - - -@ARTICLE{Carlson2002, - AUTHOR = {Bruce A. Carlson}, - TITLE = {Electric signaling behavior and the mechanisms of electric organ discharge production in mormyrid fish.}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2002}, - VOLUME = {96}, - PAGES = {405--419} -} - -@ARTICLE{Carlson2011, - AUTHOR = {Bruce A. Carlson and Saad M. Hasan and Michael Hollmann and Derek B. Miller and Luke J. Harmon and Matthew E. Arnegard}, - TITLE = {Brain evolution triggers increased diversification of electric fishes.}, - JOURNAL = Science, - YEAR = {2011}, - VOLUME = {332}, - PAGES = {583--586} -} - - -@Article{Carlson2013, - Title = {From Sequence to Spike to Spark: Evo-devo-neuroethology of Electric Communication Mormyrid Fishes.}, - Author = {Bruce A Carlson and Jason R. Gallant}, - Journal = JNeuroGenetics, - Year = {2013}, - Number = {3}, - Pages = {106-129}, - Volume = {27} -} - -@Article{Carr1982, - Title = {Peripheral organization and central projections of the electrosensory nerves in gymnotiform fish.}, - Author = {C. E. Carr and L. Maler and E. Sas}, - Journal = {Journal of Comparative Neurology}, - Year = {1982}, - Pages = {139--153}, - Volume = {211} -} - -@Article{Carr1986, - title={Electroreception in gymnotiform fish: central anatomy and physiology}, - author={Carr, CE}, - journal={Electroreception}, - pages={319--373}, - year={1986}, - publisher={John Wiley} -} - -@article{Carriot2017, - title={Envelope statistics of self-motion signals experienced by human subjects during everyday activities: Implications for vestibular processing}, - author={Carriot, J{\'e}rome and Jamali, Mohsen and Cullen, Kathleen E and Chacron, Maurice J}, - journal={PLoS One}, - volume={12}, - number={6}, - pages={e0178664}, - year={2017}, - publisher={Public Library of Science San Francisco, CA USA} -} - -@ARTICLE{Castello2000, - AUTHOR = {Mar\'ia E. Castell\'o and Pedro A. Aguilera and Omar Trujillo-Cen\'oz and Angel A. Caputi}, - TITLE = {Electroreception in \textit{Gymnotus carapo}: pre-receptor processing and the distribution of electroreceptor types.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2000}, - VOLUME = {203}, - PAGES = {3279--3287} -} - -@Article{Catania2014, - Title = {The shocking predatory strike of the electric eel}, - Author = {Catania, KC}, - Journal = Science, - Year = {2014}, - Number = {6214}, - Pages = {1231--1234}, - Volume = {346} -} - -@Article{Catania2015a, - Title = {Electric eels use high-voltage to track fast-moving prey}, - Author = {Catania, KC}, - Journal = NatCommun, - Year = {2015}, - Pages = {8638}, - Volume = {6} -} - -@Article{Cattaneo1981, - title={Patterns in the discharge of simple and complex visual cortical cells}, - author={Cattaneo, A and Maffei, L and Morrone, Concetta}, - journal={Proceedings of the Royal Society of London. Series B. Biological sciences}, - volume={212}, - number={1188}, - pages={279--297}, - year={1981}, - publisher={The Royal Society London} -} - -@Article{Cavigelli1999, - Title = {Behavioural patterns associated with faecal cortisol levels in free-ranging female ring-tailed lemurs, {Lemur catta}}, - Author = {Sonia A. Cavigelli}, - Journal = AnimBehav, - Year = {1999}, - Number = {4}, - Pages = {935 - 944}, - Volume = {57}, - - Abstract = {The study of physiological stress and its context in free-ranging animals provides a means for understanding the challenges found in the natural habitat. Patterns of physiological stress in free-ranging animals have yet to be well characterized. Methodological difficulties in measuring physiological responses in the natural habitat have limited this area of research. In this research, physiological stress in free-ranging ring-tailed lemurs,Lemur catta, was estimated using a steroid-extraction method to measure cortisol levels from female faeces. Ten females were observed across two social groups in southwestern Madagascar during a 5-month period including portions of the annual wet and dry seasons. I used behavioural measures to estimate predation threat, food accessibility and individual dominance status, to determine whether these variables predict faecal cortisol levels. Faecal cortisol levels were relatively high during two distinct periods: one period coincided with late gestation and the other period corresponded with the end of the dry season, when high-intensity antipredatory behaviour and estimates of feeding effort were elevated. In addition, faecal cortisol measures were significantly correlated with dominance indices: high-index individuals had high cortisol values, and low-index individuals had low cortisol values. These results suggest that faecal cortisol measures can be used to assess seasonal and individual differences in adrenal activity in this lemurid primate, and that this measure could provide a means for quantifying physiological stress in free-ranging animals.}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - -@article{Chacron2000, - title={Suprathreshold stochastic firing dynamics with memory in {P-type} electroreceptors}, - author={Chacron, Maurice J and Longtin, Andr{\'e} and St-Hilaire, Martin and Maler, Len}, - journal={Physical Review Letters}, - volume={85}, - number={7}, - pages={1576}, - year={2000}, - publisher={APS} -} - -@article{Chacron2001, - title={Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli}, - author={Chacron, Maurice J and Longtin, Andre and Maler, Leonard}, - journal={Journal of Neuroscience}, - volume={21}, - number={14}, - pages={5328--5343}, - year={2001}, - publisher={Soc Neuroscience} -} - -@Article{Chacron2004, - title={To burst or not to burst?}, - author={Chacron, Maurice J and Longtin, Andr{\'e} and Maler, Leonard}, - journal={Journal of Computational Neuroscience}, - volume={17}, - pages={127--136}, - year={2004}, - publisher={Springer} -} - -@Article{Chacron2005, - title={Electroreceptor neuron dynamics shape information transmission}, - author={Chacron, Maurice J and Maler, Leonard and Bastian, Joseph}, - journal={Nature Neuroscience}, - volume={8}, - number={5}, - pages={673--678}, - year={2005}, - publisher={Nature Publishing Group US New York} -} - -@Article{Chacron2006, - title={Nonlinear information processing in a model sensory system}, - author={Chacron, Maurice J}, - journal={Journal of Neurophysiology}, - volume={95}, - number={5}, - pages={2933--2946}, - year={2006}, - publisher={American Physiological Society} -} - -@Article{Chagnaud2008, - Title = {Receptive field organization of electrosensory neurons in the paddlefish (\textit{Polyodon spathula}.}, - Author = {B.P. Chagnaud and L.A. Wilkens and M.H. Hofmann}, - Journal = JPhysiol, - Year = {2008}, - Pages = {246-255}, - Volume = {102} -} - -@article{Chakravarthy2018, - title={Burst spinal cord stimulation: review of preclinical studies and comments on clinical outcomes}, - author={Chakravarthy, Krishnan and Kent, Alexander R and Raza, Adil and Xing, Fang and Kinfe, Thomas M}, - journal={Neuromodulation: Technology at the Neural Interface}, - volume={21}, - number={5}, - pages={431--439}, - year={2018}, - publisher={Elsevier} -} - -@Article{Chan2005, - title={{Ca2+} current--driven nonlinear amplification by the mammalian cochlea in vitro}, - author={Chan, Dylan K and Hudspeth, AJ}, - journal={Nature Neuroscience}, - volume={8}, - number={2}, - pages={149--155}, - year={2005}, - publisher={Nature Publishing Group US New York} -} - -@Article{Chapman1995, - Title = {Ecological constraints on group size: an analysis of spider monkey and chimpanzee subgroups}, - Author = {Chapman, C. and Chapman, L. and Wrangham, R.}, - Journal = BehavEcolSociobiol, - Year = {1995}, - Number = {59}, - Volume = {36}, - Owner = {raab}, - Timestamp = {2020.01.30} -} - -@Article{Charpentier2005, - Title = {Constraints on control: factors influencing reproductive success in male mandrills ({Mandrillus sphinx})}, - Author = {Charpentier, Marie and Peignot, Patricia and Hossaert-McKey, Martine and Gimenez, Olivier and Setchell, Joanna M. and Wickings, E. Jean}, - Journal = BehavEcol, - Year = {2005}, - Number = {3}, - Pages = {614-623}, - Volume = {16}, - - Owner = {raab}, - Timestamp = {2020.01.23} -} - -@ARTICLE{Chen2005, - AUTHOR = {Ling Chen and Jonathan L. House and R\"udiger Krahe and Mark E. Nelson}, - TITLE = {Modeling signal and background components of electrosensory scenes.}, - JOURNAL = JCompPhysiolA, - YEAR = {2005}, - VOLUME = {191}, - PAGES = {331--345} -} - -@article{Cherry1953, - title={Some experiments on the recognition of speech, with one and with two ears}, - author={Cherry, E Colin}, - journal={The Journal of the Acoustical Society of America}, - volume={25}, - number={5}, - pages={975--979}, - year={1953}, - publisher={acoustical society of America} -} - -@Article{Chikkerur2010, - Title = {What and where: {A Bayesian} inference theory of attention.}, - Author = {Sharat Chikkerur and Thomas Serre and Cheston Tan and Tomaso Poggio}, - Journal = VisionRes, - Year = {2010}, - Pages = {2233-2247}, - Volume = {50} -} - -@Article{Chivers1995, - Title = {Familiarity and shoal cohesion in fathead minnows ({Pimephales promelas}): implications for antipredator behaviour}, - Author = {Douglas P. Chivers and Grant E. Brown and R. Jan F. Smith}, - Journal = {Can J Zool}, - Year = {1995}, - Pages = {955-960}, - Volume = {73}, - - Doi = {https://doi.org/10.1139/z95-111}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - -@article{Chocholle1957, - title={About the sensation of beats between two tones whose frequencies are nearly in a simple ratio}, - author={Chocholle, R and Legouix, JP}, - journal={The Journal of the Acoustical Society of America}, - volume={29}, - number={6}, - pages={750--750}, - year={1957}, - publisher={Acoustical Society of America} -} - -@ARTICLE{Clarke2020, - AUTHOR = {Shelby B. Clarke and Lauren J. Chapman and R\"udiger Krahe}, - TITLE = {The effect of normoxia exposure on hypoxia tolerance and sensory sampling in a swamp-dwelling mormyrid fish.}, - JOURNAL = {Comp Biochem Physiol A}, - YEAR = {2020}, - VOLUME = {240}, - PAGES = {110586} -} - -@article{Clevert2015, - title={{Fast and accurate deep network learning by exponential linear units (ELUs)}}, - author={Clevert, DjorkArn{\'e} and Unterthiner, Thomas and Hochreiter, Sepp}, - journal={arXiv preprint arXiv:1511.07289}, - year={2015} -} - -@Article{Clutton-Brock1999, - Title = {Predation, group size and mortality in a cooperative mongoose, {Suricata suricatta}}, - Author = {Clutton-Brock, T. H. and Gaynor, D. and McIlrath, G. M. and Maccoll, A. D. C. and Kansky, R. and Chadwick, P. and Manser, M. and Skinner, J. D. and Brotherton, P. N. M.}, - Journal = {J Anim Ecol}, - Year = {1999}, - Number = {4}, - Pages = {672-683}, - Volume = {68}, - Keywords = {cooperative breeding, demography, mammals, mortality}, - Owner = {raab}, - Timestamp = {2020.01.21} -} - -@ARTICLE{Coates1954, - AUTHOR = {C. W. Coates}, - TITLE = {Activity in electrogenic organs of knifefishes}, - JOURNAL = Science, - YEAR = {1954}, - VOLUME = {120}, - PAGES = {845--846} -} - -@Article{Collin2012, - Title = {The Neuroecology of Cartilaginous Fishes: Sensory Strategies for Survival.}, - Author = {Shaun P. Collin}, - Journal = BrainBehavEvol, - Year = {2012}, - Pages = {80-96}, - Volume = {80} -} - - -@Article{Cote1995, - Title = {Parasitism and group size in social animals: a meta-analysis}, - Author = {Isabelle M. C\^ot\'e and Robert Poulinb}, - Journal = BehavEcol, - Year = {1995}, - Pages = {159-165}, - Volume = {6}, - - Doi = {https://doi.org/10.1093/beheco/6.2.159}, - Owner = {raab}, - Timestamp = {2020.01.30} -} - -@ARTICLE{Cox2004, - AUTHOR = {C. Cox-Fernandes and J. Podos and J. G. Lundberg}, - TITLE = {Amazonian ecology: tributaries enhance the diversity of electric fishes.}, - JOURNAL = Science, - YEAR = {2004}, - VOLUME = {305}, - PAGES = {1960--1962} -} - -@INCOLLECTION{Crampton2006, - TITLE = {Evolution of electric signal diversity in gymnotiform fishes. {I. Phylogenetic} systematics, ecology and biogeography.}, - AUTHOR = {W. G. R. Crampton and J. S. Albert}, - Year = {2006}, - Pages = {647--696}, - BOOKTITLE = {Communication in fishes}, - EDITOR = {F. Ladich and S. P. Collin and P. Moller and B. G. Kapoor}, - PUBLISHER = {Science Publishers}, - ADDRESS = {Enfield, N.H.} -} - -@INCOLLECTION{Crampton2011, - TITLE = {An ecological perspective on diversity and distributions.}, - AUTHOR = {W. G. R. Crampton}, - BOOKTITLE = {Historical biogeography of neotropical freshwater fishes.}, - PUBLISHER = {University of California Press}, - YEAR = {2011}, - ADDRESS = {California}, - EDITOR = {J. S. Albert and R. Reis}, - PAGES = {165--189} -} - -@Article{Crampton2013, - Title = {Proximate and ultimate causes of signal diversity in the electric fish {Gymnotus}.}, - Author = {W.G.R. Crampton and A. Rodriguez-Catt\'aneo and N.R. Lovejoy and A.A. Caputi}, - Journal = {Journal of Experimental Biology}, - Year = {2013}, - Pages = {2523-2541}, - Volume = {216} -} - -@Article{Creel1996, - Title = {Social stress and dominance}, - Author = {S. Creel and N. Marusha Creel and S. Monfort}, - Journal = {Nature}, - Year = {1996}, - Pages = {212}, - Volume = {379}, - - Doi = {https://doi.org/10.1038/379212a0}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - - -@Article{Crick1984, - Title = {Function of the thalamic reticular complex: the searchlight hypothesis.}, - Author = {Francis Crick}, - Journal = {Proceedings of the National Academy of Sciences}, - Year = {1984}, - Pages = {4586--4590}, - Volume = {81} -} - -@ARTICLE{Crook2004, - AUTHOR = {David A. Crook}, - TITLE = {Is the home range concept compatible with the movements of two species of lowland river fish?}, - JOURNAL = JAnimEcol, - YEAR = {2004}, - VOLUME = {73}, - PAGES = {353--366} -} - -@article{Csicsvari1998, - title={Reliability and state dependence of pyramidal cell--interneuron synapses in the hippocampus: an ensemble approach in the behaving rat}, - author={Csicsvari, Jozsef and Hirase, Hajime and Czurko, Andras and Buzs{\'a}ki, Gy{\"o}rgy}, - journal={Neuron}, - volume={21}, - number={1}, - pages={179--189}, - year={1998}, - publisher={Elsevier} -} - -@Article{Cuadrado1987, - Title = {The Cytoarchitecture of the {Torus Semicircularis} in the Teleost \textit{Barbus meridionalis}.}, - Author = {M.I. Cuadrado}, - Journal = {Journal of Morphology}, - Year = {1987}, - Pages = {233-245}, - Volume = {191} -} - -@Article{Cuadrado1992, - Title = {Neuropeptides and Monoamines in the {Torus Semicircularis} of the Carp ({Cyprinus carpio}).}, - Author = {M. Isabel Cuadrado and Rafael Cove{\~n}as and G\'erard Tramu}, - Journal = BrainResBull, - Year = {1992} -} - -@Article{Cunningham2004, - title={A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro}, - author={Cunningham, Mark O and Whittington, Miles A and Bibbig, Andrea and Roopun, Anita and LeBeau, Fiona EN and Vogt, Angelika and Monyer, Hannah and Buhl, Eberhard H and Traub, Roger D}, - journal={Proceedings of the National Academy of Sciences}, - volume={101}, - number={18}, - pages={7152--7157}, - year={2004}, - publisher={National Acad Sciences} -} - - -@Article{Cunningham2017, - title={{Measuring nonlinear signal combination using EEG}}, - author={Cunningham, Darren GM and Baker, Daniel H and Peirce, Jonathan W}, - journal={Journal of Vision}, - volume={17}, - number={5}, - pages={10--10}, - year={2017}, - publisher={The Association for Research in Vision and Ophthalmology} -} - -@Article{Cvikel2015, - Title = {On-board recordings reveal no jamming avoidance in wild bats}, - Author = {Cvikel, Noam and Levin, Eran and Hurme, Edward and Borissov, Ivailo and Boonman, Arjan and Amichai, Eran and Yovel, Yossi}, - Journal = {Proc. R. Soc. B}, - Year = {2015}, - Number = {1798}, - Volume = {282}, - - Doi = {10.1098/rspb.2014.2274}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@Article{Dalton2000, - title={The merging of the senses: integration of subthreshold taste and smell}, - author={Dalton, P and Doolittle, N and Nagata, H and Breslin, PAS}, - journal={Nature Neuroscience}, - volume={3}, - number={5}, - pages={431--432}, - year={2000}, - publisher={Nature Publishing Group} -} - -@article{Dau1997, - title={{Modeling auditory processing of amplitude modulation. I. Detection and masking with narrow-band carriers}}, - author={Dau, Torsten and Kollmeier, Birger and Kohlrausch, Armin}, - journal={The Journal of the Acoustical Society of America}, - volume={102}, - number={5}, - pages={2892--2905}, - year={1997}, - publisher={Acoustical Society of America} -} - -@ARTICLE{Dawson2018, - AUTHOR = {D. R. Dawson and W. M. Koster}, - TITLE = {Habitat use and movements of Australian grayling (\textit{Prototroctes maraena}) in a Victorian coastal stream.}, - JOURNAL = {Marine and Freshwater Research}, - YEAR = {2018}, - VOLUME = {69}, - PAGES = {1259--1267} -} - -@Article{Deemyad2013, - Title = {Serotonin selectively enhances perception and sensory neural response to stimuli generated by same sex conspecifics.}, - Author = {Tara Deemyad and Michael G. Metzen and Yingzhou Pan and Maurice J. Chacron}, - Journal = {Proceedings of the National Academy of Sciences}, - Year = {2013}, - Number = {48}, - Pages = {19609-19614}, - Volume = {110} -} - -@article{Delgutte1990, - title={Two-tone rate suppression in auditory-nerve fibers: Dependence on suppressor frequency and level}, - author={Delgutte, Bertrand}, - journal={Hearing Research}, - volume={49}, - number={1-3}, - pages={225--246}, - year={1990}, - publisher={Elsevier} -} - -@Article{Dell2014, - Title = {Automated image-based tracking and its application in ecology}, - Author = {Anthony I. Dell and John A. Bender and Kristin Branson and Iain D. Couzin and Gonzalo G. de Polavieja and Lucas P.J.J. Noldus and Alfonso P\'erez-Escudero and Pietro Perona and Andrew D. Straw and Martin Wikelski and Ulrich Brose}, - Journal = TIEE, - Year = {2014}, - Number = {7}, - Pages = {417 - 428}, - Volume = {29}, - Keywords = {behavior, bio-logging, ecological interactions, tracking, automated image-based tracking}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@article{DeMorgan1864, - title={On the beats of imperfect consonances}, - author={De Morgan, Augustus}, - journal={Transactions of the Cambridge Philosophical Society}, - volume={10}, - pages={129}, - year={1864} -} - -@article{DeSantana2013, -author = {de Santana, Carlos David and Vari, Richard P.}, -doi = {10.1111/zoj.12022}, -journal = {Zoological Journal of the Linnean Society}, -number = {3}, -pages = {564--596}, -title = {{Brown ghost electric fishes of the \textit{Apteronotus leptorhynchus} species-group (Ostariophysi, Gymnotiformes); monophyly, major clades, and revision}}, -volume = {168}, -year = {2013} -} - -@ARTICLE{DeSantana2019, - AUTHOR = {C. David de Santana and W. G. R. Crampton and Casey B. Dillman and Renata G. Frederico and Mark H. Sabaj and Rapha\"el Covain and Jonathan Ready and Jansen Zuanon and Renildo R. de Oliveira and Raimundo N. Mendes-J\'unior and Douglas A. Bastos and Tulio F. Teixeira and Jan Mol and Willian Ohara and Nat\'alia Castro e Castro and Luiz A. Peixoto and Cleusa Nagamachi and Leandro Sousa and Luciano F. A. Montag and Frank Ribeiro and Joseph C. Waddell and Nivaldo M. Piorsky and Richard P. Vari and Wolmar B. Wosiacki}, - TITLE = {Unexpected species diversity in electric eels with a description of the strongest living bioelectricity generator.}, - JOURNAL = NatCommun, - YEAR = {2019}, - VOLUME = {10}, - PAGES = {4000} -} - -@Article{Destexhe1993, - title={Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons}, - author={Destexhe, Alain and Babloyantz, Agnessa and Sejnowski, Terrence J}, - journal={Biophysical Journal}, - volume={65}, - number={4}, - pages={1538--1552}, - year={1993}, - publisher={Elsevier} -} - -@article{DeValois1982, - title={Spatial frequency selectivity of cells in macaque visual cortex}, - author={De Valois, Russell L and Albrecht, Duane G and Thorell, Lisa G}, - journal={Vision Research}, - volume={22}, - number={5}, - pages={545--559}, - year={1982}, - publisher={Pergamon} -} - -@Article{DeWeille1983, - Title = {Electrosensory information processing by lateral-line lobe neurons of catfish investigated by means of white noise cross-correlation.}, - Author = {J.R. De Weille}, - Journal = CompBiochemPhysiol, - Year = {1983}, - Number = {3}, - Pages = {677-680}, - Volume = {74A} -} - -@Article{DeWoody2000, - Title = {Genetic monogamy and biparental care in an externally fertilizing fish, the largemouth bass ({Micropterus salmoides})}, - Author = {J. Andrew DeWoody and Dean E. Fletcher and S. David Wilkins and William S. Nelson and John C. Avise}, - Journal = ProcRSocLondBBiolSci, - Year = {2000}, - Pages = {2431 - 2437}, - Volume = {267}, - - Doi = {10.1098/rspb.2000.1302}, - Owner = {raab}, - Timestamp = {2020.01.30} -} - -@article{Doiron2002, - title={Ghostbursting: a novel neuronal burst mechanism}, - author={Doiron, Brent and Laing, Carlo and Longtin, Andr{\'e} and Maler, Leonard}, - journal={Journal of Computational Neuroscience}, - volume={12}, - pages={5--25}, - year={2002}, - publisher={Springer} -} - -@Article{Dong1995, - Title = {Statistics of natural time varying-images.}, - Author = {Dawei W Dong and Joseph J Atick}, - Journal = Network, - Year = {1995}, - Pages = {345-358}, - Volume = {6} -} - -@article{Dunlap1998, - author = {Dunlap, KD and Thomas, P and Zakon, HH}, - journal = JCompPhysiolA, - number = {1}, - pages = {77--86}, - title = {{Diversity of sexual dimorphism in - electrocommunication signals and its androgen - regulation in a genus of electric fish, - \textit{Apteronotus}.}}, - volume = {183}, - year = {1998} -} - -@ARTICLE{Dunlap2000, - AUTHOR = {Kent D. Dunlap and G. T. Smith and A. Yekta}, - TITLE = {Temperature Dependence of Electrocommunication Signals and Their Underlying Neural Rhythms in the Weakly Electric Fish, \textit{Apteronotus leptorhynchus}.}, - JOURNAL = BrainBehavEvol, - YEAR = {2000}, - VOLUME = {55}, - PAGES = {152--162} -} - -@Article{Dunlap2002, - AUTHOR = {K. D. Dunlap and L. M. Oliveri}, - TITLE = {Retreat site selection and social organization in captive electric fish, \textit{Apteronotus leptorhynchus}.}, - JOURNAL = {Journal of Comparative Physiology A}, - YEAR = {2002}, - VOLUME = {188}, - PAGES = {469--477} -} - -@ARTICLE{Dunlap2003a, - AUTHOR = {K. D. Dunlap and J. Larkins-Ford}, - TITLE = {Production of aggressive electrocommunication signals to progressively realistic social stimuli in male \textit{Apteronotus leptorhynchus}.}, - YEAR = {2003}, - JOURNAL = {Ethology}, - VOLUME = {109}, - PAGES = {243--258} } - -@ARTICLE{Dunlap2003b, - AUTHOR = {K. D. Dunlap and J. Larkins-Ford}, - TITLE = {Diversity in the structure of electrocommunication signals within a genus of electric fish, \textit{Apteronotus}.}, - YEAR = {2003}, - JOURNAL = JCompPhysiolA, - VOLUME = {189}, - PAGES = {153--161} } - -@article{Dux2006, - title={Isolation of a central bottleneck of information processing with time-resolved {fMRI}}, - author={Dux, Paul E and Ivanoff, Jason and Asplund, Christopher L and Marois, Ren{\'e}}, - journal={Neuron}, - volume={52}, - number={6}, - pages={1109--1120}, - year={2006}, - publisher={Elsevier} -} - -@ARTICLE{Dye1987, - AUTHOR = {John Dye}, - TITLE = {Dynamics and stimulus-dependence of pacemaker control during behavioral modulations in the weakly electric fish, \textit{Apteronotus}.}, - JOURNAL = JCompPhysiolA, - YEAR = {1987}, - VOLUME = {161}, - PAGES = {175--185} -} - -@article{Edwards2010, - title={{Association of the \textit{OCA2} polymorphism His615Arg with melanin content in east Asian populations: further evidence of convergent evolution of skin pigmentation}}, - author={Edwards, Melissa and Bigham, Abigail and Tan, Jinze and Li, Shilin and Gozdzik, Agnes and Ross, Kendra and Jin, Li and Parra, Esteban J}, - journal={PLoS Genetics}, - volume={6}, - number={3}, - pages={e1000867}, - year={2010}, - publisher={Public Library of Science San Francisco, USA} -} - - -@Article{Eeuwes2008, - Title = {{Behavioural relevance of AC and DC in prey detection by the brown bullhead, Ameiurus nebulosus.}}, - Author = {Lonneke B.M. Eeuwes and Robert C. Peters and Franklin Bretschneider}, - Journal = AnimBiol, - Year = {2008}, - Pages = {321-336}, - Volume = {58} -} - -@article{Ott2020, - title={Modeling the Heterogeneity of Electrosensory Afferents in Electric Fish}, - author={Ott, Alexander}, - year={2020}, - journal = {Unpublished master thesis}, - volume = {Eberhard Karls Universit\"at T\"ubingen} -} - -@article{Egerland2020, - title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, - author={Egerland, Christoph H}, - year={2021}, - journal = {Unpublished master thesis}, - volume = {Humboldt-Universität zu Berlin} -} - -phdthesis{Egerland2020, - author={Egerland, Christoph H}, - title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, - school = {Humboldt-Universität zu Berlin},% - year = {2021}, - note = {unpublished master thesis} -} - -article{Egerland2020, - author={Egerland, Christoph H}, - year = {2021}, - title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, -} - -@article{Eggermont1993, - title={Wiener and Volterra analyses applied to the auditory system}, - author={Eggermont, Jos J}, - journal={Hearing Research}, - volume={66}, - number={2}, - pages={177--201}, - year={1993}, - publisher={Elsevier} -} - -@article{Eggermont1996, - title={Burst-firing sharpens frequency-tuning in primary auditory cortex.}, - author={Eggermont, Jos J and Smith, Geoff M}, - journal={Neuroreport}, - volume={7}, - number={3}, - pages={753--757}, - year={1996} -} - -@Article{Egner2010, - Title = {Expectation and Surprise Determine Neural Population Responses int the Ventral Visual Stream.}, - Author = {Tobias Egner and Jim M. Monti and Christopher Summerfield}, - Journal = JNeurosci, - Year = {2010}, - Number = {49}, - Pages = {16601-16608}, - Volume = {30} -} - -@Article{Egnor2016, - Title = {Computational Analysis of Behavior.}, - Author = {S. E. Roian Egnor and Kristin Branson}, - Journal = AnnuRevNeurosci, - Year = {2016}, - Pages = {217-36}, - Volume = {39}, - - Doi = {10.1146/annurev-neuro-070815-013845}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@article{Elfwing2018, - title={Sigmoid-weighted linear units for neural network function approximation in reinforcement learning}, - author={Elfwing, Stefan and Uchibe, Eiji and Doya, Kenji}, - journal={Neural Networks}, - volume={107}, - pages={3--11}, - year={2018}, - publisher={Elsevier} -} - -@ARTICLE{Emde1990, - AUTHOR = {Gerhard von der Emde}, - TITLE = {Discrimination of objects through electrolocation in the weakly electric fish, \textit{Gnathonemus petersii}.}, - JOURNAL = JCompPhysiolA, - YEAR = {1990}, - VOLUME = {167}, - PAGES = {413--421} -} - -@ARTICLE{Emde1992, - AUTHOR = {Gerhard von der Emde and Thomas Ringer}, - TITLE = {Electrolocation of capacitive objects in four species of pulse-type weakly electric fish.}, - JOURNAL = {Ethology}, - YEAR = {1992}, - VOLUME = {91}, - PAGES = {326--338} -} - -@ARTICLE{Emde1993, - AUTHOR = {Gerhard von der Emde}, - TITLE = {The sensing of electrical capacitances by weakly electric mormyrid fish: effects of water conductivity.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1993}, - VOLUME = {181}, - PAGES = {157--173} -} - -@ARTICLE{Emde1994, - AUTHOR = {G. von der Emde and B. Ronacher}, - TITLE = {Perception of electric properties of objects in electrolocating weakly electric fish: two-dimensional similarity scaling reveals a {City-Block} metric.}, - JOURNAL = JCompPhysiolA, - YEAR = {1994}, - VOLUME = {175}, - PAGES = {801--812} -} - -@ARTICLE{Emde1998, - AUTHOR = {Gerhard von der Emde}, - TITLE = {Capacitance detection in the wave-type electric fish \textit{Eigenmannia} during active electrolocation.}, - JOURNAL = JCompPhysiolA, - YEAR = {1998}, - VOLUME = {182}, - PAGES = {217--224} -} - -@ARTICLE{Emde1998Distance, - AUTHOR = {Gerhard von der Emde and Stephan Schwarz and Leonel Gomez and Ruben Budelli and Kirsty Grant}, - TITLE = {Electric fish measure distance in the dark.}, - JOURNAL = Nature, - YEAR = {1998}, - VOLUME = {395}, - PAGES = {890--894} -} - -@INCOLLECTION{Emde2001, - TITLE = {Electric fields and electroreception: how electrosensory fish perceive their environment.}, - AUTHOR = {Gerhard von der Emde}, - PAGES = {313--329}, - BOOKTITLE = {Ecology of sensing}, - PUBLISHER = {Springer}, - ADDRESS = {Berlin, Heidelberg}, - YEAR = {2001}, - EDITOR = {Friedrich G. Barth and Axel Schmid} -} - - -@ARTICLE{Emde2006, - AUTHOR = {Gerhard von der Emde}, - TITLE = {Non-visual environmental imaging and object detection through active electrolocation in weakly electric fish.}, - JOURNAL = JCompPhysiolA, - YEAR = {2006}, - VOLUME = {192}, - PAGES = {601--612} -} - -@ARTICLE{Emde2010Signalling, - AUTHOR = {Gerhard von der Emde}, - TITLE = {Electrolocation of capacitive objects in four species of pulse-type weakly electric fish {II}. electric signalling behaviour.}, - JOURNAL = Ethology, - YEAR = {1992}, - VOLUME = {92}, - PAGES = {177--192} -} - -@Article{Engelmann2010, - Title = {Coding of stimuli by ampullary afferents in \textit{Gnathonemus petersii}.}, - Author = {J. Engelmann and S. Gertz and J. Goulet and A. Schuh and G. von der Emde}, - Journal = {Journal of Neurophysiology}, - Year = {2010}, - - Month = {Oct}, - Number = {4}, - Pages = {1955--1968}, - Volume = {104}, - - Abstract = {Weakly electric fish use electroreception for both active and passive electrolocation and for electrocommunication. While both active and passive electrolocation systems are prominent in weakly electric Mormyriform fishes, knowledge of their passive electrolocation ability is still scarce. To better estimate the contribution of passive electric sensing to the orientation toward electric stimuli in weakly electric fishes, we investigated frequency tuning applying classical input-output characterization and stimulus reconstruction methods to reveal the encoding capabilities of ampullary receptor afferents. Ampullary receptor afferents were most sensitive (threshold: 40 μV/cm) at low frequencies (<10 Hz) and appear to be tuned to a mix of amplitude and slope of the input signals. The low-frequency tuning was corroborated by behavioral experiments, but behavioral thresholds were one order of magnitude higher. The integration of simultaneously recorded afferents of similar frequency-tuning resulted in strongly enhanced signal-to-noise ratios and increased mutual information rates but did not increase the range of frequencies detectable by the system. Theoretically the neuronal integration of input from receptors experiencing opposite polarities of a stimulus (left and right side of the fish) was shown to enhance encoding of such stimuli, including an increase of bandwidth. Covariance and coherence analysis showed that spiking of ampullary afferents is sufficiently explained by the spike-triggered average, i.e., receptors respond to a single linear feature of the stimulus. Our data support the notion of a division of labor of the active and passive electrosensory systems in weakly electric fishes based on frequency tuning. Future experiments will address the role of central convergence of ampullary input that we expect to lead to higher sensitivity and encoding power of the system.}, - Institution = {University of Bonn, Institute for Zoology, Neuroethology-Sensory Ecology, Bonn, Germany. Jacob.Engelmann@uni-bielefeld.de}, - Keywords = {Action Potentials; Animals; Electric Fish; Electric Stimulation; Female; Hair Cells, Ampulla; Male; Neurons, Afferent; Random Allocation}, - Timestamp = {2011.10.12} -} - -@ARTICLE{Enger1968, - AUTHOR = {Per S. Enger and Thomas Szabo}, - TITLE = {Effect of temperature on the discharge rates of the electric organ of some gymnotids.}, - JOURNAL = CompBiochemPhysiol, - YEAR = {1968}, - VOLUME = {27}, - PAGES = {625--627} -} - -@Article{Engh2002, - Title = {Reproductive skew among males in a female-dominated mammalian society}, - Author = {Engh, Anne L. and Funk, Stephan M. and Horn, Russell C. Van and Scribner, Kim T. and Bruford, Michael W. and Libants, Scot and Szykman, Micaela and Smale, Laura and Holekamp, Kay E.}, - Journal = BehavEcol, - Year = {2002}, - Number = {2}, - Pages = {193-200}, - Volume = {13}, - - Owner = {raab}, - Timestamp = {2020.01.23} -} - -@Article{Engler2000, - Title = {Spontaneous modulations of the electric organ discharge in the weakly electric fish, \textit{Apteronotus leptorhynchus}: a biophysical and behavioral analysis}, - Author = {Engler, G. and Fogarty, C.M. and Banks, J.R. and Zupanc, G.K.H.}, - Journal = {Journal of Comparative Physiology}, - Year = {2000}, - Number = {7}, - Pages = {645--660}, - Volume = {186}, - Owner = {raab}, - Timestamp = {2017.05.04} -} - -@Article{Engler2001, - Title = {Differential production of chirping behavior evoked by electrical stimulation of the weakly electric fish, \textit{Apteronotus leptorhynchus}.}, - Author = {Engler, G and Zupanc, G K}, - Journal = {Journal of Comparative Physiology A}, - Year = {2001}, - Number = {9}, - Pages = {747--756}, - Volume = {187} -} - -@ARTICLE{Escamilla2019, - AUTHOR = {Carolina Escamilla-Pinilla and Jos\'e Iv\'an Mojica and Jorge Molina}, - TITLE = {Spatial and temporal distribution of \textit{Gymnorhamphichthys rondoni} ({Gymnotiformes}: {Rhamphichthyidae}) in a long-term study of an Amazonian terra firme stream, {Leticia} - {Colombia}.}, - JOURNAL = {Neotropical Ichtyology}, - YEAR = {2019}, - VOLUME = {17}, - PAGES = {e190006} -} - -@article{Evans1972, - title={The frequency response and other properties of single fibres in the guinea-pig cochlear nerve}, - author={Evans, EF1331164}, - journal={The Journal of Physiology}, - volume={226}, - number={1}, - pages={263--287}, - year={1972}, - publisher={Wiley Online Library} -} - -@incollection{Evans1981, - title={The dynamic range problem: place and time coding at the level of cochlear nerve and nucleus}, - author={Evans, EF}, - booktitle={Neuronal Mechanisms of Hearing}, - pages={69--85}, - year={1981}, - publisher={Springer} -} - -@article{Ewert2000, - title={Characterizing frequency selectivity for envelope fluctuations}, - author={Ewert, Stephan D and Dau, Torsten}, - journal={The Journal of the Acoustical Society of America}, - volume={108}, - number={3}, - pages={1181--1196}, - year={2000}, - publisher={Acoustical Society of America} -} - -@ARTICLE{Fechler2013, - AUTHOR = {Katharina Fechler and Gerhard von der Emde}, - TITLE = {Figure–ground separation during active electrolocation in the weakly electric fish, \textit{Gnathonemus petersii}.}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2013}, - VOLUME = {107}, - PAGES = {72--83} -} - -@Article{Fenske2006, - Title = {Top-down facilitation of visual object recognition: object-based and context-based contributions.}, - Author = {Mark J. Fenske and Elissa Aminoff and Nurit Gronau and Moshe Bar}, - Journal = ProgBrainRes, - Year = {2006}, - Pages = {3-21}, - Volume = {155} -} - -@Article{Fernald2014, - Title = {Communication about social status}, - Author = {Russell D Fernald}, - Journal = CurrOpinNeurobiol, - Year = {2014}, - Note = {SI: Communication and language}, - Pages = {1 - 4}, - Volume = {28}, - - Abstract = {Dominance hierarchies are ubiquitous in social species and serve to organize social systems. Social and sexual status is communicated directly among animals via sensory systems evolved in the particular species. Such signals may be chemical, visual, auditory, postural or a combination of signals. In most species, status is initially established through physical conflict between individuals that leads to ritualized conflict or threats, reducing possibly dangerous results of fighting. Many of the status signals contain other information, as in some bird species that communicate both the size of their group and their individual rank vocally. Recent studies have shown that scent signaling among hyenas of east Africa is unique, being produced by fermentative, odor producing bacteria residing in the scent glands.}, - Owner = {raab}, - Timestamp = {2020.01.23}, -} - -@ARTICLE{Ferraris2017, - AUTHOR = {Ferraris, Jr., C. J. and C. D. de Santana and R. P. 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Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/fα, where the power α depends on the spike initiation mechanism. For conductance-based models, α = 1, and the prefactor C depends solely on the average firing rate and a spike {\textquotedblleft}slope factor,{\textquotedblright} which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the {\textquotedblleft}exponential integrate-and-fire neuron,{\textquotedblright} as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.}, - issn = {0270-6474}, - journal = {Journal of Neuroscience} -} - -@ARTICLE{Franchina1998, - AUTHOR = {C. R. Franchina and P. K. Stoddard}, - TITLE = {Plasticity of the electric organ discharge waveform of the electric fish \textit{Brachyhypopomus pinnicaudatus} {I.} Quantification of day-night changes.}, - JOURNAL = JCompPhysiolA, - YEAR = {1998}, - VOLUME = {183}, - PAGES = {759--768} -} - -@Article{Freeman2013, - Title = {A functional and perceptual signature of the second visual area in primates.}, - Author = {Jeremy Freeman and Corey M. Ziemba and David H. Heeger and Eero P. Simoncelli and J. Anthony Movshon}, - Journal = {Nature Neuroscience}, - Year = {2013}, - Number = {7}, - Pages = {doi:10.1038/nn.3402.}, - Volume = {16} -} - -@article{French1973, - title={Measuring the Wiener kernels of a non-linear system using the fast {Fourier} transform algorithm}, - author={French, AS and Butz, EG}, - journal={International Journal of Control}, - volume={17}, - number={3}, - pages={529--539}, - year={1973}, - publisher={Taylor \& Francis} -} - -@article{French1976, - title={Practical nonlinear system analysis by {Wiener} kernel estimation in the frequency domain}, - author={French, AS}, - journal={Biological Cybernetics}, - volume={24}, - number={2}, - pages={111--119}, - year={1976}, - publisher={Springer} -} - -@article{Marmarelis1999, - title={Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor}, - author={Marmarelis, Vasilis Z and Juusola, Mikko and French, Andrew S}, - journal={Annals of biomedical engineering}, - volume={27}, - pages={391--402}, - year={1999}, - publisher={Springer} -} - -@Article{Freund2002, - Title = {Behavioral Stochastic Resonance: How the Noise from a Daphnia Swarm Enhances Individual Prey Capture by Juvenile Paddlefish.}, - Author = {Jan A. Freund and Lutz Schimanski-Geier and Beatrix Beisner and Alexander Neiman and David F. Russell and Tatyana Yakusheva and Frank Moss}, - Journal = JTheorBiol, - Year = {2002} -} - -@Article{Friard2016, - Title = {{BORIS}: a free, versatile open-source event-logging software for video/audio coding and live observations}, - Author = {Friard, Olivier and Gamba, Marco}, - Journal = {Methods in Ecology and Evolution}, - Year = {2016}, - Number = {11}, - Pages = {1325-1330}, - Volume = {7} -} - -@ARTICLE{Friedman1996, - AUTHOR = {M. A. Friedman and C. D. Hopkins}, - TITLE = {Tracking individual mormyrid electric fish in the field using electric organ discharge waveforms.}, - JOURNAL = AnimBehav, - YEAR = {1996}, - VOLUME = {51}, - PAGES = {391--407} -} - -@Article{Froudarakis2014, - Title = {Population code in mouse {V1} facilitates readout of natural scenes through increased sparseness.}, - Author = {Emmanouil Froudarakis and Philipp Berens and Alexander S Ecker and R James Cotton and Fabian H Sinz and Dimitri Yatsenko and Peter Saggau and Matthias Bethge and Andreas S Tolias}, - Journal = {Nature Neuroscience}, - Year = {2014}, - Pages = {doi:10.1038/nn.3707}, - Volume = {Advance online publication} -} - -@ARTICLE{Fugere2010, - AUTHOR = {Vincent Fug\`ere and R\"udiger Krahe}, - TITLE = {Electric signals and species recognition in the wave-type gymnotiform fish \textit{Apteronotus leptorhynchus}.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2010}, - VOLUME = {213}, - PAGES = {225--236} -} - -@ARTICLE{Fugere2011, - AUTHOR = {Vincent Fug\`ere and Hernan Ortega and R\"udiger Krahe}, - TITLE = {Electrical signalling of dominance in a wild population of electric fish.}, - JOURNAL = BiolLett, - YEAR = {2011}, - VOLUME = {7}, - PAGES = {197--200} -} - -@ARTICLE{Fujita2010, - AUTHOR = {Kazuhisa Fujita and Yoshiki Kashimori}, - TITLE = {Modeling the electric image produced by objects with complex impedance in weakly electric fish.}, - JOURNAL = BiolCybern, - YEAR = {2010}, - VOLUME = {103}, - PAGES = {105--118} -} - -@ARTICLE{Fujita2019, - AUTHOR = {Kazuhisa Fujita and Yoshiki Kashimori}, - TITLE = {Representation of object’s shape by multiple electric images in electrolocation.}, - JOURNAL = BiolCybern, - YEAR = {2019}, - VOLUME = {113}, - PAGES = {239--255} -} - -@article{Fukutomi2020, - title={A history of corollary discharge: contributions of mormyrid weakly electric fish}, - author={Fukutomi, Matasaburo and Carlson, Bruce A}, - journal={Frontiers in Integrative Neuroscience}, - volume={14}, - pages={42}, - year={2020}, - publisher={Frontiers Media SA} -} - -@Article{Furutsu1963, - title={On the statistical theory of electromagnetic waves in a fluctuating medium}, - author={Furutsu, Koichi}, - journal={Journal of Research of the National Bureau of Standards}, - volume={67}, - pages={303--323}, - year={1963} -} - -@Article{Gabbiani1996, - title={From stimulus encoding to feature extraction in weakly electric fish}, - author={Gabbiani, Fabrizio and Metzner, Walter and Wessel, Ralf and Koch, Christof}, - journal={Nature}, - volume={384}, - number={6609}, - pages={564--567}, - year={1996}, - publisher={Nature Publishing Group UK London} -} - -@Article{Gabbiani1999, - title={Encoding and processing of sensory information in neuronal spike trains}, - author={Gabbiani, Fabrizio and Metzner, W}, - journal={Journal of Experimental Biology}, - volume={202}, - number={10}, - pages={1267--1279}, - year={1999}, - publisher={The Company of Biologists Ltd} -} - -@ARTICLE{Gavassa2012, - AUTHOR = {Sat Gavassa and Ana C. Silva and Emmanuel Gonzalez and Philip K. Stoddard}, - TITLE = {Signal modulation as a mechanism for handicap disposal.}, - JOURNAL = AnimBehav, - YEAR = {2012}, - VOLUME = {83}, - PAGES = {935--944} -} - -@Article{Geffen1996, - Title = {Size, Life-History Traits, and Social Organization in the {Canidae}: A Reevaluation}, - Author = {Geffen, Eli and Gompper, Matthew E. and Gittleman, John L. and Luh, Hang-Kwang and MacDonald, David W. and Wayne, Robert K.}, - Journal = {The American Naturalist}, - Year = {1996}, - Number = {1}, - Pages = {140-160}, - Volume = {147}, - Owner = {raab}, - Timestamp = {2020.01.30}, -} - -@Article{Geisler2008, - Title = {Visual perception and the statistical properties of natural scenes.}, - Author = {Wilson S. Geisler}, - Journal = AnnuRevPsychol, - Year = {2008} -} - -@Article{Gershman2012, - Title = {Multistability and Perceptual Inference.}, - Author = {Samuel J. Gersham and Edward Vul and Joshua B. 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Mainen}, - TITLE = {Big behavioral data: psychology, ethology and the foundations of neuroscience.}, - JOURNAL = {Nature Neuroscience}, - YEAR = {2014}, - VOLUME = {17}, - PAGES = {1455--1462} -} - -@Article{Goris2014, - Title = {Partitioning neuronal variability.}, - Author = {Robbe L T Goris and J Anthony Movshon and Eero P Simoncelli}, - Journal = {Nature Neuroscience}, - Year = {2014}, - Pages = {doi:10.1038/nn.3711}, - Volume = {Advanced online publication} -} - -@ARTICLE{Gottwald2017, - AUTHOR = {Martin Gottwald and Raya A. Bott and Gerhard von der Emde}, - TITLE = {Estimation of distance and electric impedance of capacitive objects in the weakly electric fish \textit{Gnathonemus petersii}.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2017}, - VOLUME = {220}, - PAGES = {3142--3153} -} - -@ARTICLE{Gottwald2018, - AUTHOR = {Martin Gottwald and Neha Singh and Andr\'e Haubrich and Sophia Regett and Gerhard von der Emde}, - TITLE = {Electric-color sensing in weakly electric fish suggests color perception as a sensory concept beyond vision.}, - JOURNAL = CurrBiol, - YEAR = {2018}, - VOLUME = {220}, - PAGES = {3142--3153} -} - -@article{Gollisch2010, - title={Eye smarter than scientists believed: neural computations in circuits of the retina}, - author={Gollisch, Tim and Meister, Markus}, - journal={Neuron}, - volume={65}, - number={2}, - pages={150--164}, - year={2010}, - publisher={Elsevier} -} - -@ARTICLE{Graff1992, - AUTHOR = {Christian Graff and Bernd Kramer}, - TITLE = {Trained weakly-electric fishes \textit{Pollimyrus isidori} and \textit{Gnathonemus petersii} {(Mormyridae, Teleostei)} discriminate between waveforms of electric pulse discharges.}, - JOURNAL = {Ethology}, - YEAR = {1992}, - VOLUME = {90}, - PAGES = {279--292} -} - -@article{Grahn2012, - title={Neural mechanisms of rhythm perception: current findings and future perspectives}, - author={Grahn, Jessica A}, - journal={Topics in Cognitive Science}, - volume={4}, - number={4}, - pages={585--606}, - year={2012}, - publisher={Wiley Online Library} -} - -@Article{Grewe2017, - Title = {Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons}, - Author = {Grewe, Jan and Kruscha, Alexandra and Lindner, Benjamin and Benda, Jan}, - Journal = {Proceedings of the National Academy of Sciences}, - Year = {2017}, - Number = {10}, - Pages = {E1977-E1985}, - Volume = {114} -} - -@Article{Gross2002, - title={Genealogy of the “grandmother cell”}, - author={Gross, Charles G}, - journal={The Neuroscientist}, - volume={8}, - number={5}, - pages={512--518}, - year={2002}, - publisher={Sage Publications Sage CA: Thousand Oaks, CA} -} - -@article{Gussin2007, - title={Limits of linear rate coding of dynamic stimuli by electroreceptor afferents}, - author={Gussin, Daniel and Benda, Jan and Maler, Leonard}, - journal={Journal of Neurophysiology}, - volume={97}, - number={4}, - pages={2917--2929}, - year={2007} -} - -@Article{Hagedorn1985, - Title = {Court and spark: electric signals in the courtship and mating of gymnotoid fish}, - Author = {Hagedorn, Mary and Walter Heiligenberg}, - Journal = AnimBehav, - Year = {1985}, - Number = {1}, - Pages = {254 - 265}, - Volume = {33}, - - Doi = {http://doi.org/10.1016/S0003-3472(85)80139-1}, - Owner = {raab}, - Timestamp = {2017.04.27}, - Url = {http://www.sciencedirect.com/science/article/pii/S0003347285801391} -} - -@ARTICLE{Hagedorn1985Hypopomus, - AUTHOR = {Mary Hagedorn and Catherine Carr}, - TITLE = {Single electrocytes produce a sexually dimorphic signal in {South American} electric fish, \textit{Hypopomus occidentalis} {(Gymnotiformes, Hypopomidae)}.}, - JOURNAL = JCompPhysiolA, - YEAR = {1985}, - VOLUME = {156}, - PAGES = {511--523} -} - - -@Article{Hagedorn1988, - Title = {Ecology and behavior of a pulse-type electric fish, \textit{Hypopomus occidentalis} {(Gymnotiformes, Hypopomidae)}, in a fresh-water stream in {Panama}.}, - Author = {Mary Hagedorn}, - Journal = {Copeia}, - Year = {1988}, - Number = {2}, - Pages = {324-335}, - Volume = {1988} -} - -@Article{Hager1991, - Title = {Safety in numbers: shoal size choice by minnows under predatory threat}, - Author = {Hager, M.C. and Helfman, G.S.}, - Journal = BehavEcolSociobiol, - Year = {1991}, - Number = {4}, - Pages = {271-276}, - Volume = {29}, - - Doi = {https://doi.org/10.1007/BF00163984}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - -@article{Haggard2023, - title={Coding of object location by heterogeneous neural populations with spatially dependent correlations in weakly electric fish}, - author={Haggard, Myriah and Chacron, Maurice J}, - journal={PLOS Computational Biology}, - volume={19}, - number={3}, - pages={e1010938}, - year={2023}, - publisher={Public Library of Science San Francisco, CA USA} -} - -@ARTICLE{Hagiwara1963, - AUTHOR = {S. Hagiwara and H. Morita}, - TITLE = {Coding mechanisms of electroreceptor fibers in some electric fish.}, - JOURNAL = {Journal of Neurophysiology}, - YEAR = {1963}, - VOLUME = {26}, - PAGES = {551--567} -} - -@ARTICLE{Harder1964, - AUTHOR = {Wilhelm Harder and Alfred Schief and Hartmut Uhlemann}, - TITLE = {{Zur Funktion des Elektrischen Organs von \textit{Gnathonemus petersii} (Gthr. 1862) (Mormyriformes, Teleostei)}.}, - JOURNAL = {Zeitschrift f\'ur vergleichende Physiologie}, - YEAR = {1964}, - VOLUME = {48}, - PAGES = {302--331} -} - -@article{Hartmann1979, - title={Detection of amplitude modulation}, - author={Hartmann, WM}, - journal={The Journal of the Acoustical Society of America}, - volume={65}, - number={S1}, - pages={S59--S59}, - year={1979}, - publisher={Acoustical Society of America} -} - -@Article{Harvey-Girard2013, - Title = {Expression of the Cannabinoid {CB1} Receptor in the Gymnotiform Fish Brain and Its Implications for the Organization of the Telleost Pallium.}, - Author = {Erik Harvey-Girard and Ana C.C. Giassi and William Ellis and Leonard Maler}, - Journal = {Journal of Comparative Neurology}, - Year = {2013}, - Pages = {949-975}, - Volume = {521} -} - -@ARTICLE{Harvey2010, - AUTHOR = {Erik Harvey-Girard and Jessica Tweedle and Joel Ironstone and Martin Cuddy and William Ellis and Leonard Maler}, - TITLE = {Long-Term recognition memory of individual conspecifics is associated with telencephalic expression of {Egr-1} in the electric fish \textit{Apteronotus leptorhynchus}.}, - JOURNAL = {Journal of Comparative Neurology}, - YEAR = {2010}, - VOLUME = {518}, - PAGES = {2666--2692} -} - -@Article{Harvey2013, - Title = {Dendritic {SK.} Channels convert {NMDA-R-dependent LTD} to burst timing-dependent plasticity}, - Author = {Eric Harvey-Girard and Leonard Maler}, - Journal = {Journal of Neurophysiology}, - Year = {2013}, - Pages = {2689-2703}, - Volume = {110} -} - -@Article{Hass2002, - Title = {Anti-predator benefits of group living in white-nosed coatis {(Nasua narica)}}, - Author = {Hass, Christine C. -and Valenzuela, David}, - Journal = BehavEcolSociobiol, - Year = {2002}, - Number = {6}, - Pages = {570--578}, - Volume = {51}, - Day = {01}, - Doi = {10.1007/s00265-002-0463-5}, - Owner = {raab}, - Timestamp = {2020.01.21}, - Url = {https://doi.org/10.1007/s00265-002-0463-5} -} - -@Article{Hawken1996, - title={Temporal-frequency selectivity in monkey visual cortex}, - author={Hawken, MJ and Shapley, Robert M and Grosof, DH}, - journal={Visual neuroscience}, - volume={13}, - number={3}, - pages={477--492}, - year={1996}, - publisher={Cambridge University Press} -} - - -@article{Haykin2005, - title={The cocktail party problem}, - author={Haykin, Simon and Chen, Zhe}, - journal={Neural Computation}, - volume={17}, - number={9}, - pages={1875--1902}, - year={2005}, - publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…} -} - -@article{Heil2015, - title={Basic response properties of auditory nerve fibers: a review}, - author={Heil, Peter and Peterson, Adam J}, - journal={Cell and tissue research}, - volume={361}, - pages={129--158}, - year={2015}, - publisher={Springer} -} - - -@article{Heil2016, - title={Spike timing in auditory-nerve fibers during spontaneous activity and phase locking}, - author={Heil, Peter and Peterson, Adam J}, - journal={Synapse}, - volume={71}, - number={1}, - pages={5--36}, - year={2017}, - publisher={Wiley Online Library} -} - -@ARTICLE{Heiligenberg1973, - AUTHOR = {Walter Heiligenberg}, - TITLE = {Electrolocation of objects in the electric fish \textit{Eigenmannia} ({Rhamphichthyidae}, {Gymnotoidei}).}, - JOURNAL = JCompPhysiol, - YEAR = {1973}, - VOLUME = {87}, - PAGES = {137--164} -} - -@ARTICLE{Heiligenberg1975, - AUTHOR = {Walter Heiligenberg}, - TITLE = {Theoretical and experimental approaches to spatial aspects of electrolocation.}, - JOURNAL = JCompPhysiol, - YEAR = {1975}, - VOLUME = {103}, - PAGES = {247--272} -} - -@ARTICLE{Heiligenberg1976, - AUTHOR = {Walter Heiligenberg}, - TITLE = {Electrolocation and jamming avoidance in the mormyrid fish \textit{Brienomyrus}.}, - JOURNAL = JCompPhysiol, - YEAR = {1976}, - VOLUME = {109}, - PAGES = {357--372} -} - -@ARTICLE{Heiligenberg1978, - AUTHOR = {Walter Heiligenberg and Richard A. Altes}, - TITLE = {Phase sensitivity in electrorecption}, - JOURNAL = Science, - YEAR = {1978}, - VOLUME = {199}, - PAGES = {1001--1003} -} - - -@article{Heiligenberg1981, - title={How electroreceptors encode {JAR}-eliciting stimulus regimes: reading trajectories in a phase-amplitude plane}, - author={Heiligenberg, Walter and Partridge, Brian L}, - journal={Journal of Comparative Physiology}, - volume={142}, - pages={295--308}, - year={1981}, - publisher={Springer} -} - - -@Article{Heiligenberg1982, - title={Labelling of electroreceptive afferents in a gymnotoid fish by intracellular injection of {HRP}: the mystery of multiple maps}, - author={Heiligenberg, Walter and Dye, John}, - journal={Journal of Comparative Physiology}, - volume={148}, - pages={287--296}, - year={1982}, - publisher={Springer} -} - - -@book{Heiligenberg1991, - title={Neural nets in electric fish}, - author={Heiligenberg, Walter}, - year={1991}, - publisher={MIT press Cambridge, MA} -} - -@ARTICLE{Heiligenberg1996, - AUTHOR = {W. Heiligenberg and W. Metzner and C. J. H. Wong and C. H. Keller}, - TITLE = {Motor control of the jamming avoidance response of \textit{Apteronotus leptorhynchus}: evolutionary changes of a behavior and its neuronal substrates.}, - JOURNAL = JCompPhysiolA, - YEAR = {1996}, - VOLUME = {179}, - PAGES = {653--674} -} - - -@book{Helmholtz2009, - title={On the sensations of tone as a physiological basis for the theory of music}, - author={Helmholtz, Hermann LF}, - year={1875}, - publisher={Cambridge University Press} -} - - -@article{Hendrycks2016, - title={Gaussian error linear units {(gelus)}}, - author={Hendrycks, Dan and Gimpel, Kevin}, - journal={arXiv preprint arXiv:1606.08415}, - year={2016} -} - - -@Article{Hennig2004, - Title = {Processing of auditory information in insects.}, - Author = {R. M. Hennig and A. Franz and A. Stumpner}, - Journal = MicroscResTech, - Year = {2004}, - Pages = {351--374}, - Volume = {63} -} - -@article{Henninger2017, - title={Court and spark in the wild: communication at the limits of sensation}, - author={Henninger, J{\"o}rg and Kirschbaum, Frank and Grewe, Jan and Krahe, Ruediger and Benda, Jan}, - journal={bioRxiv:114249}, - year={2017}, - publisher={Cold Spring Harbor Laboratory}, - elocation-id = {114249}, - year = {2017}, - doi = {10.1101/114249}, - abstract = {Sensory systems evolve in the ecological niches each species is occupying. Accordingly, the tuning of sensory neurons is expected to be adapted to the statistics of natural stimuli. For an unbiased quantification of sensory scenes we tracked natural communication behavior of the weakly electric fish Apteronotus rostratus in their Neotropical rainforest habitat with high spatio-temporal resolution over several days. In the context of courtship and aggression we observed large quantities of electrocommunication signals. Echo responses and acknowledgment signals clearly demonstrated the behavioral relevance of these signals. The known tuning properties of peripheral electrosensory neurons suggest, however, that they are barely activated by these obviously relevant signals. Frequencies of courtship signals are clearly mismatched with the frequency tuning of neuronal population activity. Our results emphasize the importance of quantifying sensory scenes derived from freely behaving animals in their natural habitats for understanding the evolution and function of neural systems.}, - URL = {https://www.biorxiv.org/content/early/2017/08/12/114249}, - eprint = {https://www.biorxiv.org/content/early/2017/08/12/114249.full.pdf}, - journal = {bioRxiv} -} - - -@Article{Henninger2018, - Title = {Statistics of natural communication signals observed in the wild identify important yet neglected stimulus regimes in weakly electric fish.}, - Author = {J\"org Henninger and R\"udiger Krahe and Frank Kirschbaum and Jan Grewe and Jan Benda}, - Journal = {Journal of Neuroscience}, - Year = {2018}, - Pages = {5456--5465}, - Volume = {38} -} - -@Article{Henninger2020, - Title = {Tracking activity patterns of a multispecies community of gymnotiform weakly electric fish in their neotropical habitat without tagging}, - Author = {Henninger, J{\"o}rg and Krahe, R{\"u}diger and Sinz, Fabian and Benda, Jan}, - Journal = {Journal of Experimental Biology}, - Year = {2020}, - Volume = {223}, - - Abstract = {Field studies on freely behaving animals commonly require tagging and often are focused on single species. Weakly electric fish generate a species- and individual-specific electric organ discharge (EOD) and therefore provide a unique opportunity for individual tracking without tagging. Here, we present and test tracking algorithms based on recordings with submerged electrode arrays. Harmonic structures extracted from power spectra provide fish identity. Localization of fish based on weighted averages of their EOD amplitudes is found to be more robust than fitting a dipole model. We apply these techniques to monitor a community of three species, \textit{Apteronotus rostratus}, Eigenmannia humboldtii and Sternopygus dariensis, in their natural habitat in Dari{\'e}n, Panama. We found consistent upstream movements after sunset followed by downstream movements in the second half of the night. Extrapolations of these movements and estimates of fish density obtained from additional transect data suggest that some fish cover at least several hundreds of meters of the stream per night. Most fish, including E. humboldtii, were traversing the electrode array solitarily. From in situ measurements of the decay of the EOD amplitude with distance of individual animals, we estimated that fish can detect conspecifics at distances of up to 2 m. Our recordings also emphasize the complexity of natural electrosensory scenes resulting from the interactions of the EODs of different species. Electrode arrays thus provide an unprecedented window into the so-far hidden nocturnal activities of multispecies communities of weakly electric fish at an unmatched level of detail.}, - Pages = {jeb206342}, - Owner = {raab}, - Publisher = {The Company of Biologists Ltd}, - Timestamp = {2020.02.11} -} - -@article{Henry2017, - title={What can we learn about beat perception by comparing brain signals and stimulus envelopes?}, - author={Henry, Molly J and Herrmann, Bj{\"o}rn and Grahn, Jessica A}, - journal={PLoS One}, - volume={12}, - number={2}, - pages={e0172454}, - year={2017}, - publisher={Public Library of Science San Francisco, CA USA} -} - -@article{Hind1967, - title={Coding of information pertaining to paired low-frequency tones in single auditory nerve fibers of the squirrel monkey.}, - author={Hind, JOSEPH E and Anderson, DAVID J and Brugge, JOHN F and Rose, JERZY E}, - journal={Journal of Neurophysiology}, - volume={30}, - number={4}, - pages={794--816}, - year={1967} -} - - -@Article{Hirabayashi2014, - Title = {Computational principles of microcircuits for visual object processing in the macaque temporal cortex.}, - Author = {Toshiyuki Hirabayashi and Yasushi Miyashita}, - Journal = TINS, - Year = {2014}, - Number = {3}, - Pages = {178-187}, - Volume = {37} -} - -@Article{Hladnik2023, - AUTHOR = {T. C. Hladnik and J. Grewe}, - TITLE = {Receptive field sizes and neuronal encoding bandwidth are constrained by axonal conduction delays}, - JOURNAL = {PLoS Computational Biology}, - YEAR = {2023}, - NUMBER = {19}, - VOLUME = {8}, - Doi = {https://doi.org/ -10.1371/journal.pcbi.1010871} -} - -@Article{Hodgkin1952, - Title = {A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve.}, - Author = {A. L. Hodgkin and A. F. Huxley}, - Journal = JPhysiol, - Year = {1952}, - Pages = {500--544}, - Volume = {117} -} - -@Article{Hofmann2008, - Title = {Response properties of electrosensory units in the midbrain tectum of the paddlefish {(Polyodon spathula Walbaum)}.}, - Author = {M.H. Hofmann and S.N. Jung and U. Siebenaller and M. Prei{\ss}ner and B.P. Chagnaud and L.A. Wilkens}, - Journal = {Journal of Experimental Biology}, - Year = {2008}, - Pages = {773-779}, - Volume = {211} -} - -@ARTICLE{Hofmann2013, - AUTHOR = {Volker Hofmann and Juan I. Sanguinetti-Scheck and Leonel G\'omez-Sena and Jacob Engelmann}, - TITLE = {From static electric images to electric flow: Towards dynamic perceptual cues -in active electroreception.}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2013}, - VOLUME = {107}, - PAGES = {95--106} -} - -@ARTICLE{Hofmann2017, - AUTHOR = {Volker Hofmann and Juan I. Sanguinetti-Scheck and Leonel G\'omez-Sena and Jacob Engelmann}, - TITLE = {Flow as a basis for a novel distance cue in freely behaving electric fish.}, - JOURNAL = JNeurosci, - YEAR = {2017}, - VOLUME = {37}, - PAGES = {302--312} -} - -@Article{Hojesjo1998, - Title = {The importance of being familiar: individual recognition and social behavior in sea trout {(Salmo trutta)}}, - Author = {H\"ojesj\"o, Johan and Johnsson, J\"orgen I. and Petersson, Erik and J\"arvi, Torbj\"orn}, - Journal = BehavEcol, - Year = {1998}, - Number = {5}, - Pages = {445-451}, - Volume = {9}, - - Doi = {https://doi.org/10.1093/beheco/9.5.445}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - - -@ARTICLE{Hopkins1972, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Sex differences in electric signaling in an electric fish.}, - JOURNAL = Science, - YEAR = {1972}, - VOLUME = {176}, - PAGES = {1035--1037} -} - -@ARTICLE{Hopkins1974Eigen, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Electric communication: functions in the social behavior of \textit{Eigenmannia virescens}.}, - JOURNAL = {Behavior}, - YEAR = {1974}, - VOLUME = {50}, - PAGES = {270--304} -} - -@ARTICLE{Hopkins1974Sterno, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Electric communication in the reproductive behavior of \textit{Sternopygus macrurus} {(Gymnotoidei)}.}, - JOURNAL = {Zeitschrift für Tierpsychologie}, - YEAR = {1974}, - VOLUME = {35}, - PAGES = {518--535} -} - -@ARTICLE{Hopkins1976, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Stimulus filtering and electroreception: tuberous electroreceptors in three species of gymnotoid fish.}, - JOURNAL = {Journal of Comparative Physiology}, - YEAR = {1976}, - VOLUME = {111}, - PAGES = {171--207} -} - -@ARTICLE{Hopkins1978, - AUTHOR = {Carl D. Hopkins and Walter F. Heiligenberg}, - TITLE = {Evolutionary designs for electric signals and electroreceptors in gymnotoid fishes of {Surinam}.}, - JOURNAL = BehavEcolSociobiol, - YEAR = {1978}, - VOLUME = {3}, - PAGES = {113--134} -} - -@ARTICLE{Hopkins1980, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Evolution of electric communication channels of mormyrids.}, - JOURNAL = BehavEcolSociobiol, - YEAR = {1980}, - VOLUME = {7}, - PAGES = {1--13} -} - -@ARTICLE{Hopkins1981, - AUTHOR = {Carl D. Hopkins and Andrew H. Bass}, - TITLE = {Temporal coding of species recognition signals in an electric fish.}, - JOURNAL = Science, - YEAR = {1981}, - VOLUME = {212}, - PAGES = {85--87} -} - -@ARTICLE{Hopkins1986Temporal, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Temporal strucuture of non-propagated electric communication signals.}, - JOURNAL = BrainBehavEvol, - YEAR = {1986}, - VOLUME = {28}, - PAGES = {43--59} -} - -@ARTICLE{Hopkins1986Time, - AUTHOR = {Carl D. Hopkins and G. W. Max Westby}, - TITLE = {Time domain processing of electric organ discharge waveforms by pulse-type electric fish.}, - JOURNAL = BrainBehavEvol, - YEAR = {1986}, - VOLUME = {29}, - PAGES = {77--104} -} - -@ARTICLE{Hopkins1990, - AUTHOR = {Carl D. Hopkins and Nathaniel C. Comfort and Joseph Bastian and Andreas H. Bass}, - TITLE = {Functional analysis of sexual dimorphism in an electric fish, \textit{Hypopomus pinnicaudatus}, order {Gymnotiformes}.}, - JOURNAL = BrainBehavEvol, - YEAR = {1990}, - VOLUME = {35}, - PAGES = {350--367} -} - -@ARTICLE{Hopkins1999, - AUTHOR = {Carl D. Hopkins}, - TITLE = {Design features for electric communication.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1999}, - VOLUME = {202}, - PAGES = {1217--128} -} - -@ARTICLE{Hoshimiya1980, - AUTHOR = {N. Hoshimiya and K. Shogen and T. Matsuo and S. Chichibu}, - TITLE = {The \textit{Apteronotus} {EOD} field: waveform and {EOD} field simulation}, - JOURNAL = JCompPhysiol, - YEAR = {1980}, - VOLUME = {135}, - PAGES = {283--290} -} - -@Article{Hosoya2005, - Title = {Dynamic predictive coding by the retina.}, - Author = {Toshihiko Hosoya and Stephen A. Baccus and Markus Meister}, - Journal = Nature, - Year = {2005}, - Pages = {71-77}, - Volume = {436} -} - -@ARTICLE{Howard1988, - AUTHOR = {J. Howard and A. J. Hudspeth}, - TITLE = {Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell.}, - YEAR = {1988}, - JOURNAL = {Neuron}, - VOLUME = {1}, - PAGES = {189--199} } - -@Article{Hubel1959, - title={Receptive fields of single neurones in the cat's striate cortex}, - author={Hubel, David H and Wiesel, Torsten N}, - journal={The Journal of Physiology}, - volume={148}, - number={3}, - pages={574}, - year={1959}, - publisher={Wiley-Blackwell} -} - -@article{Hubel1962, - title={Receptive fields, binocular interaction and functional architecture in the cat's visual cortex}, - author={Hubel, David H and Wiesel, Torsten N}, - journal={The Journal of Physiology}, - volume={160}, - number={1}, - pages={106}, - year={1962}, - publisher={Wiley-Blackwell} -} - -@article{Hubel1965, - title={Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat}, - author={Hubel, David H and Wiesel, Torsten N}, - journal={Journal of Neurophysiology}, - volume={28}, - number={2}, - pages={229--289}, - year={1965} -} - -@article{Hudspeth1988kinetic, - title={{Kinetic analysis of voltage-and ion-dependent conductances in saccular hair cells of the bull-frog, Rana catesbeiana.}}, - author={Hudspeth, AJ and Lewis, RS}, - journal={The Journal of Physiology}, - volume={400}, - number={1}, - pages={237--274}, - year={1988}, - publisher={Wiley Online Library} -} - -@article{Hudspeth1988model, - title={A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, {Rana catesbeiana}.}, - author={Hudspeth, AJ and Lewis, RS}, - journal={J Physiol}, - volume={400}, - number={1}, - pages={275--297}, - year={1988}, - publisher={Wiley Online Library} -} - -@Article{Huetz2011, - Title = {Neural codes in the thalamocortical auditory system: from artificial stimuli to communication sounds.}, - Author = {Chlo\'e Huetz and Boris Gour\'evitch and Jean-Marc Edeline}, - Journal = HearRes, - Year = {2011}, - Pages = {147-158}, - Volume = {271} -} - -@Article{Hughey2018, - Title = {Challenges and solutions for studying collective animal behaviour in the wild}, - Author = {Hughey, Lacey F. and Hein, Andrew M. and Strandburg-Peshkin, Ariana and Jensen, Frants H.}, - Journal = PhilTransRSocLondBBiolSci, - Year = {2018}, - Number = {1746}, - Volume = {373}, - - Doi = {10.1098/rstb.2017.0005}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@article{Hunter2007, - title={Matplotlib: A 2D graphics environment}, - author={Hunter, John D}, - journal={Computing in science \& engineering}, - volume={9}, - number={3}, - pages={90--95}, - year={2007}, - publisher={IEEE Computer Society} -} - -@Article{Hupe2008, - Title = {Electrocommunication signals in free swimming brown ghost knifefish, \textit{Apteronotus leptorhynchus}}, - Author = {Ginette Hup\'e and John Lewis}, - Journal = {Journal of Experimental Biology}, - Year = {2008}, - Pages = {1657-67}, - Volume = {211}, - - Doi = {10.1242/jeb.013516}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@ARTICLE{Hupe2008DF, - AUTHOR = {Ginette J. Hup\'e and John E. Lewis and Jan Benda}, - TITLE = {The effect of difference frequency on electrocommunication: chirp production and encoding in a species of weakly electric fish, \textit{Apteronotus leptorhynchus}.}, - YEAR = {2008}, - JOURNAL = {Journal of Physiology-Paris}, - VOLUME = {102}, - NUMBER = {4--6}, - PAGES = {164--172} } - -@Article{Izhikevich2000, - title={Neural excitability, spiking and bursting}, - author={Izhikevich, Eugene M}, - journal={International Journal of Bifurcation and Chaos}, - volume={10}, - number={06}, - pages={1171--1266}, - year={2000}, - publisher={World Scientific} -} - -@book{Izhikevich2007, - title={Dynamical systems in neuroscience}, - author={Izhikevich, Eugene M}, - year={2007}, - publisher={MIT press} -} - -@Article{Janson1985, - Title = {Aggresive competition and individual food consumption in wild brown capuchin monkeys ({Cebus apella})}, - Author = {Janson, Charles}, - Journal = BehavEcolSociobiol, - Year = {1985}, - Number = {2}, - Pages = {125--138}, - Volume = {18}, - - Abstract = {The impact of aggresive competition on food intake at all the resources used is analysed for every member of a group of brown capuchin monkeys (Cebus apella) in the Manu National Park, Peru, where they live in groups of 8--14 animals. An individual's food intake at a given tree was affected independently both by its domirance rank (Fig. 1) and by how much aggression it received (Table 5). Food intake was not strongly affected by body size when dominance rank was held constant by partial correlation. At food sources where high rates of fighting occurred, an individual's food intake depended more on its domirance status than on the rate of aggression it received (Fig. 2). However, food intake at resources where rates of fighting were low depended mostly on the rate of aggression received. When aggression over food was absent, the food intakes of dominants and subordinates were equal. Dominants had significantly greater total energy intake (20.5{\%} more) than did subordinates, even though more than one third of their diet came from food sources where little or no fighting occurred (Fig. 3). Energy intake was also significantly greater for individuals that received little aggression. The only adult that emigrated from the rescue_local_eod study group was the individua with the lowest energy intake. Competition for food within groups was more than ten times as intense as competition between brown capuchin groups.}, - Day = {01}, - Doi = {10.1007/BF00299041}, - Owner = {raab}, - Timestamp = {2020.01.21}, - Url = {https://doi.org/10.1007/BF00299041} -} - -@article{Janson2022, - title={Motive-modulated attentional orienting: Implicit power motive predicts attentional avoidance of signals of interpersonal dominance.}, - author={Janson, Kevin T and K{\"o}llner, Martin G and Khalaidovski, Ksenia and P{\"u}lschen, Lea-Sarah and Rudnaya, Alexandra and Stamm, Laura and Schultheiss, Oliver C}, - journal={Motivation Science}, - volume={8}, - number={1}, - pages={56}, - year={2022}, - publisher={Educational Publishing Foundation} -} - -@Article{Jason1990, - Title = {Ecological consequences of individual spatial choice in foraging groups of brown capuchin monkeys, {Cebus apella}}, - Author = {Charles H. Janson}, - Journal = AnimBehav, - Year = {1990}, - Number = {5}, - Pages = {922 - 934}, - Volume = {40}, - - Abstract = {Individuals in a foraging group of brown capuchin monkeys choose different spatial positions relative to the rest of the group. An individual's choice of spatial positiion affects its foraging success and perceived predation risk (as measured by vigilance behaviour). The two most dominant group members preferred to forage where their expected forwaging success was greatest. Juveniles chose to forage where their perceived predation risk was least, not where they would achieve the highest foraging success. The positions used by non-dominant adults neither maximized foraging success nor minimized predation risk. It is likely that subordinate adults accept spatial positions with suboptimal ecological consequences to avoid the costs of frequent confrontations with the dominant members of the group over foraging sites in poreferred positions.}, - Doi = {https://doi.org/10.1016/S0003-3472(05)80994-7}, - Owner = {raab}, - Timestamp = {2020.01.21}, - Url = {http://www.sciencedirect.com/science/article/pii/S0003347205809947} -} - -@Article{Jazayeri2006, - Title = {Optimal representation of sensory information by neural populations.}, - Author = {Mehrdad Jazayeri and J Anthony Movshon}, - Journal = {Nature Neuroscience}, - Year = {2006}, - Number = {5}, - Pages = {690-696}, - Volume = {9} -} - -@article{Joris1992, - title={Responses to amplitude-modulated tones in the auditory nerve of the cat}, - author={Joris, Philip X and Yin, Tom CT}, - journal={The Journal of the Acoustical Society of America}, - volume={91}, - number={1}, - pages={215--232}, - year={1992}, - publisher={Acoustical Society of America} -} - -@article{Joris2004, - title={Neural processing of amplitude-modulated sounds}, - author={Joris, PX and Schreiner, CE and Rees, A}, - journal={Physiological Reviews}, - volume={84}, - number={2}, - pages={541--577}, - year={2004} -} - -@article{Juergens1999, - title={{Visual stimulation elicits locked and induced gamma oscillations in monkey intracortical-and {EEG-potentials}, but not in human {EEG}}}, - author={Juergens, Egbert and Guettler, Andreas and Eckhorn, Reinhard}, - journal={Experimental Brain Research}, - volume={129}, - pages={247--259}, - year={1999}, - publisher={Springer} -} - -@article{Julicher2001, - title={Physical basis of two-tone interference in hearing}, - author={J{\"u}licher, Frank and Andor, Daniel and Duke, Thomas}, - journal={Proceedings of the National Academy of Sciences}, - volume={98}, - number={16}, - pages={9080--9085}, - year={2001}, - publisher={National Acad Sciences} -} - -@Article{Jun2013, - Title = {Real-Time Localization of Moving Dipole Sources for Tracking Multiple Free-Swimming Weakly Electric Fish}, - Author = {Jun, James Jaeyoon and Longtin, Andr\'e and Maler, Leonard}, - Journal = PLOSOne, - Year = {2013}, - Number = {6}, - Pages = {1-14}, - Volume = {8}, - Doi = {10.1371/journal.pone.0066596}, - Owner = {raab}, - Publisher = {Public Library of Science}, - Timestamp = {2020.02.11}, - Url = {https://doi.org/10.1371/journal.pone.0066596} -} - -@ARTICLE{Jun2014, - AUTHOR = {James J. Jun and Andr\'e Longtin and Leonard Maler}, - TITLE = {Enhanced sensory sampling precedes spef-initiated locomotion in an electric fish.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2014}, - VOLUME = {217}, - PAGES = {3615--3628} -} - -@INCOLLECTION{Kalmijn1974, - TITLE = {The detection of electric fields from inanimate and animate sources other than electric organs.}, - AUTHOR = {A. J. Kalmijn}, - Year = {1974}, - Pages = {148--194}, - BOOKTITLE = {Electroreceptors and other specialized receptors in lower vertrebrates}, - EDITOR = {A. Fessard}, - PUBLISHER = {Springer}, - ADDRESS = {Heidelberg} -} - -@book{Kandel2000, - title={Principles of neural science}, - author={Kandel, Eric R and Schwartz, James H and Jessell, Thomas M and Siegelbaum, Steven and Hudspeth, A James and Mack, Sarah and others}, - volume={4}, - year={2000}, - publisher={McGraw-hill New York} -} - -@Article{Kappeler2008, - Title = {The lemur syndrome unresolved: extreme male reproductive skew in sifakas ({Propithecus verreauxi}), a sexually monomorphic primate with female dominance}, - Author = {Kappeler, Peter M. -and Sch{\"a}ffler, Livia}, - Journal = BehavEcolSociobiol, - Year = {2008}, - Number = {6}, - Pages = {1007--1015}, - Volume = {62}, - Day = {01}, - Doi = {10.1007/s00265-007-0528-6}, - Owner = {raab}, - Timestamp = {2020.01.23}, - Url = {https://doi.org/10.1007/s00265-007-0528-6} -} - -@Article{Karri2020, - title={Spinal cord stimulation for chronic pain syndromes: a review of considerations in practice management}, - author={Karri, Jay and Joshi, Mihir and Polson, George and Tang, Tuan and Maxwell, Lee and Orhurhu, Vwaire and Deer, Timothy and Abd-Elsayed, Alaa}, - journal={Pain Physician}, - volume={23}, - number={6}, - pages={599}, - year={2020}, - publisher={American Society of Interventional Pain Physician} -} - -@article{Kashimori1996, - title={Model of P-and {T-electroreceptors} of weakly electric fish}, - author={Kashimori, Yoshiki and Goto, Mituyuki and Kambara, Takeshi}, - journal={Biophysical Journal}, - volume={70}, - number={6}, - pages={2513--2526}, - year={1996}, - publisher={Elsevier} -} - -@ARTICLE{Kelly2008, - AUTHOR = {Marc Kelly and David Babineau and Andr\'e Longtin and John E. Lewis}, - TITLE = {Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs.}, - JOURNAL = BiolCybern, - YEAR = {2008}, - VOLUME = {98}, - PAGES = {479--490} -} - -@Article{Kemp1978, - title={Stimulated acoustic emissions from within the human auditory system}, - author={Kemp, David T}, - journal={The Journal of the Acoustical Society of America}, - volume={64}, - number={5}, - pages={1386--1391}, - year={1978}, - publisher={Acoustical Society of America} -} - -@Article{Kern2005, - Title = {Function of a Fly Motion-Sensitive Neuron Matches Eye Movements during Free Flight.}, - Author = {Roland Kern and J. H. van Hateren and Christian Michaelis and Jens Peter Lindemann and Martin Egelhaaf}, - Journal = PLoSBiol, - Year = {2005}, - Pages = {e171}, - Volume = {3} -} - -@Article{Kerth2003, - Title = {Information Transfer about Roosts in Female Bechstein's Bats: An Experimental Field Study}, - Author = {Gerald Kerth and Karsten Reckardt}, - Journal = {Proceedings: Biological Sciences}, - Year = {2003}, - Number = {1514}, - Pages = {511-515}, - Volume = {270}, - - Doi = {10.2307/3558892}, - Owner = {raab}, - Timestamp = {2020.01.30} -} - -@Article{Khanbabaie2010, - title={Kinetics of fast short-term depression are matched to spike train statistics to reduce noise}, - author={Khanbabaie, Reza and Nesse, William H and Longtin, Andre and Maler, Leonard}, - journal={Journal of Neurophysiology}, - volume={103}, - number={6}, - pages={3337--3348}, - year={2010}, - publisher={American Physiological Society Bethesda, MD} -} - -@article{Khanna1989, - title={Spectral characteristics of the responses of primary auditory-nerve fibers to amplitude-modulated signals}, - author={Khanna, SM and Teich, MC}, - journal={Hearing Research}, - volume={39}, - number={1-2}, - pages={143--157}, - year={1989}, - publisher={Elsevier} -} - -@Article{Khosravi-Hashemi2014, - Title = {Motion processing across multiple topographic maps in the electrosensory system.}, - Author = {Navid Khosravi-Hashemi and Maurice J. Chacron}, - Journal = PhysiolRep, - Year = {2014}, - Number = {3}, - Pages = {e00253}, - Volume = {2} -} - -@article{King2019, - title={Accounting for masking of frequency modulation by amplitude modulation with the modulation filter-bank concept}, - author={King, Andrew and Varnet, L{\'e}o and Lorenzi, Christian}, - journal={The Journal of the Acoustical Society of America}, - volume={145}, - number={4}, - pages={2277--2293}, - year={2019}, - publisher={AIP Publishing} -} - -@ARTICLE{Kirschbaum1983, - AUTHOR = {F. Kirschbaum}, - TITLE = {Myogenic electric organ precedes the neurogenic organ in apteronotid fish.}, - JOURNAL = {Naturwissenschaften}, - YEAR = {1983}, - VOLUME = {70}, - PAGES = {205--207} -} - -@Article{Kirschbaum2002, - Title = {Reproductive strategies and developmental aspects in mormyrid and gymnotiform fishes}, - Author = {Frank Kirschbaum and Christian Schugardt}, - Journal = {Journal of Physiology-Paris}, - Year = {2002}, - Number = {5}, - Pages = {557 - 566}, - Volume = {96}, - Doi = {https://doi.org/10.1016/S0928-4257(03)00011-1}, - Keywords = {Reproductive strategies, Mormyrids, Gymnotiforms, Fecundity, Cyclical reproduction}, - Owner = {raab}, - Timestamp = {2020.02.11}, - Url = {http://www.sciencedirect.com/science/article/pii/S0928425703000111} -} - -@article{Kiskinis2018, - title={{All-optical electrophysiology for high-throughput functional characterization of a human iPSC-derived motor neuron model of ALS}}, - author={Kiskinis, Evangelos and Kralj, Joel M and Zou, Peng and Weinstein, Eli N and Zhang, Hongkang and Tsioras, Konstantinos and Wiskow, Ole and Ortega, J Alberto and Eggan, Kevin and Cohen, Adam E}, - journal={Stem Cell Reports}, - volume={10}, - number={6}, - pages={1991--2004}, - year={2018}, - publisher={Elsevier} -} - -@ARTICLE{Knight1972a, - AUTHOR = {Bruce W. Knight}, - TITLE = {Dynamics of Encoding in a Population of Neurons.}, - YEAR = {1972}, - JOURNAL = {The Journal of General Physiology}, - VOLUME = {59}, - PAGES = {734--766} } - -@article{Knudsen1974, - author = {Knudsen, EI}, - journal = {Journal of Comparative Physiology}, - number = {4}, - pages = {333--353}, - publisher = {Springer}, - title = {Behavioral thresholds to electric signals in high - frequency electric fish}, - volume = {91}, - year = {1974} -} - -@article{Knudsen1975, - author = {Knudsen, EI}, - journal = {Journal of Comparative Physiology}, - number = {2}, - pages = {103--118}, - publisher = {Springer}, - title = {Spatial aspects of the electric fields generated by - weakly electric fish}, - volume = {99}, - year = {1975} -} - -@Article{Knudsen1976a, - Title = {Midbrain Responses to Electroreceptive Input in Catfish - Evidence of Orientation Preferences and Somatotopic Organization.}, - Author = {Eric I. Knudsen}, - Journal = JCompPhysiol, - Year = {1976}, - Pages = {51-67}, - Volume = {106} -} - -@Article{Knudsen1976b, - Title = {Midbrain Units in Catfish: Response Properties to Electroreceptive Input.}, - Author = {Eric I. Knudsen}, - Journal = JCompPhysiol, - Year = {1976}, - Pages = {315-335}, - Volume = {109} -} - -@Article{Knudsen1978, - Title = {Funcitonal Organization in Electroreceptive Midbrain of the Catfish.}, - Author = {Eric I. Knudsen}, - Journal = {Journal of Neurophysiology}, - Year = {1978}, - Number = {2}, - Pages = {350-364}, - Volume = {41} -} - -@article{Knudsen2007, - title={Fundamental components of attention}, - author={Knudsen, Eric I}, - journal={Annual Review of Neuroscience}, - volume={30}, - pages={57--78}, - year={2007}, - publisher={Annual Reviews} -} - -@Article{Koelsch2005, - title={Towards a neural basis of music perception}, - author={Koelsch, Stefan and Siebel, Walter A}, - journal={Trends in Cognitive Sciences}, - volume={9}, - number={12}, - pages={578--584}, - year={2005}, - publisher={Elsevier} -} - - - -@article{Koenig1876, - title={{LI. On the simultaneous sounding of two notes}}, - author={K{\"o}nig, Rudolph}, - journal={The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, - volume={1}, - number={6}, - pages={417--446}, - year={1876}, - publisher={Taylor \& Francis} -} - -@article{Koenig1881, - title={Ueber den Ursprung der St{\"o}sse und Stosst{\"o}ne bei harmonischen Intervallen}, - author={Koenig, Rudolph}, - journal={Annalen der Physik}, - volume={248}, - number={3}, - pages={335--349}, - year={1881}, - publisher={Wiley Online Library} -} - -@Article{Koerding2004, - Title = {How Are Complex Cell Properties Adapted to the Statistics of Natural Stimuli?}, - Author = {Konrad P. K\"ording and Christoph Kayser and Wolfgang Einh\"auser and Peter K\"onig}, - Journal = {Journal of Neurophysiology}, - Year = {2004}, - Pages = {206-212}, - Volume = {91} -} - -@article{Koch1995, - title={Do neurons have a voltage or a current threshold for action potential initiation?}, - author={Koch, Christof and Bernander, {\"O}jvind and Douglas, Rodney J}, - journal={Journal of computational neuroscience}, - volume={2}, - pages={63--82}, - year={1995}, - publisher={Springer} -} - -@ARTICLE{Kolodziejski2005, - AUTHOR = {Johanna A. Kolodziejski and Brian S. Nelson and G. Troy Smith}, - TITLE = {Sex and species differences in neuromodulatory input to a premotor nucleus: a comparative study of substance {P} and communication behavior in weakly electric fish.}, - JOURNAL = {J Neuro Biol}, - YEAR = {2005}, - VOLUME = {62}, - PAGES = {299--315} -} - -@article{Koppl1997, - title={Phase locking to high frequencies in the auditory nerve and cochlear nucleus magnocellularis of the barn owl, {Tyto alba}}, - author={K{\"o}ppl, Christine}, - journal={Journal of Neuroscience}, - volume={17}, - number={9}, - pages={3312--3321}, - year={1997} -} - -@Article{Korstjens2006, - Title = {Time as a constraint on group size in spider monkeys}, - Author = {Korstjens, Amanda H. -and Verhoeckx, Ingrid Lugo -and Dunbar, Robin I. M.}, - Journal = BehavEcolSociobiol, - Year = {2006}, - Number = {5}, - Pages = {683}, - Volume = {60}, - - Abstract = {An animal can only survive in a given habitat if it has enough time to find, process and digest food whilst avoiding predation. The time it has for food acquisition is affected by the vegetation and competition with conspecifics, which depends on aggregation tendencies. We used the relationships between time allocations, on the one hand, and climatic variables (as a proxy for habitat quality) and group size, on the other, to develop a model that predicts maximum ecologically tolerable group size at different locations for spider monkeys. Spider monkeys are particularly interesting because the social communities often split up into small units. Temperature variation and rainfall variation were the rescue_local_eod determinants of time budgets. Community size and average annual rainfall determined party size. The model correctly predicted presence or absence of spider monkeys at 78--83{\%} of 217 New World forest sites. Within the geographical range of the species, this time budget model predicted the presence of spider monkeys better than a model based directly on climate variables. Predicted community and party sizes were significantly larger at sites where spider monkeys are present than at sites where they are absent. As required by the model, predicted maximum community sizes were significantly larger than observed community sizes. Moving time showed a U-shaped relationship with party size, which suggests that moving time is the factor that keeps spider monkey communities from travelling together in a tight group.}, - Day = {20}, - Doi = {10.1007/s00265-006-0212-2}, - Owner = {raab}, - Timestamp = {2020.01.21}, - Url = {https://doi.org/10.1007/s00265-006-0212-2} -} - -@article{Kozmik2008, - title={Assembly of the cnidarian camera-type eye from vertebrate-like components}, - author={Kozmik, Zbynek and Ruzickova, Jana and Jonasova, Kristyna and Matsumoto, Yoshifumi and Vopalensky, Pavel and Kozmikova, Iryna and Strnad, Hynek and Kawamura, Shoji and Piatigorsky, Joram and Paces, Vaclav and others}, - journal={Proceedings of the National Academy of Sciences}, - volume={105}, - number={26}, - pages={8989--8993}, - year={2008}, - publisher={National Acad Sciences} -} - - - -@Article{Krahe2004, - Title = {Burst firing in sensory systems.}, - Author = {R\"udiger Krahe and Fabrizio Gabbiani}, - Journal = {Nature Reviews Neuroscience}, - Year = {2004}, - Month = {Jan}, - Number = {1}, - Pages = {13--23}, - Volume = {5}, - DOI = {10.1038/nrn1296}, - File = {:Krahe_Gabbiani_{Nature Neuroscience}Rev_.pdf:PDF}, - Institution = {Beckman Institute for Advanced Science and Technology and Department of Molecular and Integrative Physiology, University of Illinois at Urbana/Champaign, 405 North Mathews Avenue, Urbana, Illinois 61801, USA.}, - Keywords = {Action Potentials; Animals; Brain; Humans; Nerve Net; Neurons; Neurons, Afferent}, - Pii = {nrn1296}, - Pmid = {14661065}, - Refid = {731}, - Timestamp = {2011.06.14}, - URL = {http://dx.doi.org/10.1038/nrn1296} -} - -@Article{Krahe2008, - title={Temporal processing across multiple topographic maps in the electrosensory system}, - author={Krahe, Rudiger and Bastian, Joseph and Chacron, Maurice J}, - journal={Journal of Neurophysiology}, - volume={100}, - number={2}, - pages={852--867}, - year={2008}, - publisher={American Physiological Society} -} - -@Article{Krahe2014, - Title = {Neural maps in the electrosensory system of weakly elcectric fish.}, - Author = {R\"udiger Krahe and Leonard Maler}, - Journal = {Current Opinion in Neurobiology}, - Year = {2014}, - Pages = {13-21}, - Volume = {24} -} - - - -@incollection{Kramer1981, -title = {Species specificity of electric organ discharges in a sympatric group of gymnotoid fish from {Manaus} ({Amazonas}).}, -editor = {T. Szabó and G. Czéh}, -booktitle = {Sensory physiology of aquatic lower vertebrates}, -publisher = {Pergamon}, -pages = {195-219}, -year = {1981}, -isbn = {978-0-08-027352-5}, -doi = {https://doi.org/10.1016/B978-0-08-027352-5.50018-5}, -url = {https://www.sciencedirect.com/science/article/pii/B9780080273525500185}, -author = {Bernd Kramer and Frank Kirschbaum and Hubert Markl}, -abstract = {SUMMARY -We collected weakly electric gymnotoid fish in the vicinity of Manaus, Amazonas, in the Solimoes river (white water). We tried to find out whether Electric Organ Discharges (EODs) are species specific which is essential for their presumed role in recognition of conspecifics and reproductive isolation. We considered at least 43 valid sympatric species, some of them unnamed. All of these displayed stable EOD waveform patterns, most of them clearly distinct from the other species' EODs. Eleven species are of the pulse EOD type, 32 of the wave EOD type (one of the latter is intermediate). The EODs of pulse species were analysed (1) by EOD repetition rate at rest (variation from 1 Hz to 60 Hz), (2) by Fourier amplitude spectrum analysis of single EODs (Fig. 1; in these spectra, frequencies of peak amplitude ranged up to 2300 Hz). There was a significant, positive correlation between both parameters (Fig. 2). Identification of pairs of species with similar EODs by these parameters does not appear to be possible because of inter-individual EOD variations. In wave species there is conclusive evidence that EOD fundamental frequencies (= repetition rate of a complete EOD period) do not allow species identification: twenty-eight wave species displayed EOD fundamental frequencies from 300 to 1800 Hz (Fig. 3). This yields a hypothetical frequency band of 0.09 octave to signal species identity; the actual value of EOD frequency variations in Eigenmannia is much greater (1.2 octaves). Seven species of the family Apteronotidae displayed a new signal type: the main energy of the signal was contained in higher harmonics, and not at the fundamental frequencies (Figs. 6 and 7). For all wave species there was a significant, positive correlation between their dominant frequency (= the strongest signal component) and harmonic content of their EOD although individual species deviated considerably from what was predicted by the regression line (Fig. 8). Thus separation of species was greatly improved compared to the criterion of fundamental frequency (Fig. 3) but still appeared insufficient in a number of cases. Therefore, in both wave and pulse species still other parameters must be involved in recognition of conspecifics.} -} - -@ARTICLE{Kramer1988, - AUTHOR = {Bernd Kramer and B. Otto}, - TITLE = {Female discharges are more electrifying: spontaneous preference in the electric fish, \textit{Eigenmannia} ({Gymnotiformes}, {Teleostei}).}, - JOURNAL = BehavEcolSociobiol, - YEAR = {1988}, - VOLUME = {23}, - PAGES = {55--60} -} - -@ARTICLE{Kramer1999, - AUTHOR = {Bernd Kramer}, - TITLE = {Waveform discrimination, phase sensitivity and jamming avoidance in a wave-type electric fish.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1999}, - VOLUME = {202}, - PAGES = {1387--1398} -} - -@article{Krishna2000, - title={Auditory temporal processing: responses to sinusoidally amplitude-modulated tones in the inferior colliculus}, - author={Krishna, B Suresh and Semple, Malcolm N}, - journal={Journal of Neurophysiology}, - volume={84}, - number={1}, - pages={255--273}, - year={2000} -} - -@article{Kubo1957, - title={Statistical-mechanical theory of irreversible processes. {I}. General theory and simple applications to magnetic and conduction problems}, - author={Kubo, Ryogo}, - journal={Journal of the physical society of Japan}, - volume={12}, - number={6}, - pages={570--586}, - year={1957}, - publisher={The Physical Society of Japan} -} - -@article{Kujawa1995, - title={{Time-varying alterations in the {f2- f1 DPOAE} response to continuous primary stimulation {I}: Response characterization and contribution of the olivocochlear efferents}}, - author={Kujawa, SG and Fallon, M and Bobbin, RP}, - journal={Hearing Research}, - volume={85}, - number={1-2}, - pages={142--154}, - year={1995}, - publisher={Elsevier} -} - -@inproceedings{Kunkel2010, - title={A reassessment of the simultaneous dynamic range of the human visual system}, - author={Kunkel, Timo and Reinhard, Erik}, - booktitle={Proceedings of the 7th symposium on applied perception in graphics and visualization}, - pages={17--24}, - year={2010} -} - -@article{Lamore1986, - title={Envelope detection of amplitude-modulated high-frequency sinusoidal signals by skin mechanoreceptors}, - author={Lamore, PJJ and Muijser, H and Keemink, CJ}, - journal={The Journal of the Acoustical Society of America}, - volume={79}, - number={4}, - pages={1082--1085}, - year={1986}, - publisher={Acoustical Society of America} -} - -@Article{Land1977, - title={The retinex theory of color vision}, - author={Land, Edwin H}, - journal={Scientific american}, - volume={237}, - number={6}, - pages={108--129}, - year={1977}, - publisher={JSTOR} -} - -@article{Langley1996, - title={Linear filtering precedes nonlinear processing in early vision}, - author={Langley, K and Fleet, DJ and Hibbard, PB}, - journal={Current Biology}, - volume={6}, - number={7}, - pages={891--896}, - year={1996}, - publisher={Elsevier} -} - -@Article{Larson2014, - Title = {Serotonin modulates electrosensory processing and behavior via {5-HT2-like} receptors.}, - Author = {E.A. Larson and M.G. Metzen and M.J. Chacron}, - Journal = Neuroscience, - Year = {2014}, - Volume = {in press} -} - -@Article{Laughlin1981, - Title = {A simple coding procedure enhances a neuron's information capacity.}, - Author = {S. B. Laughlin}, - Journal = {Zeitschrift für Naturforschung}, - Year = {1981}, - Pages = {910--912}, - Volume = {36C} -} - -@Article{Lavoue2000, - Title = {Phylogenetic Relationships of Mormyrid Electric Fishes ({Mormyridae; Teleostei}) Inferred from Cytochrome b Sequences}, - Author = {S\'ebastien Lavou\'e and R\'emy Bigorne and Guillaume Lecointre and Jean-Fran{\c c}ois Agn\`ese}, - Journal = {Molecular Phylogenetics and Evolution}, - Year = {2000}, - Number = {1}, - Pages = {1 - 10}, - Volume = {14}, - Doi = {https://doi.org/10.1006/mpev.1999.0687}, - Keywords = {Mormyridae, electric fish, phylogeny, cytochrome , electric organ.}, - Owner = {raab}, - Timestamp = {2020.02.11}, - Url = {http://www.sciencedirect.com/science/article/pii/S1055790399906875} -} - -@article{Lavoue2012, - title={Comparable ages for the independent origins of electrogenesis in {African and South American} weakly electric fishes}, - author={Lavou{\'e}, S{\'e}bastien and Miya, Masaki and Arnegard, Matthew E and Sullivan, John P and Hopkins, Carl D and Nishida, Mutsumi}, - journal={PLoS One}, - volume={7}, - number={5}, - pages={e36287}, - year={2012}, - publisher={Public Library of Science San Francisco, USA} -} - -@Article{Lee2003, - Title = {Hierarchical {Bayesian} inference in the visual cortex.}, - Author = {Tai Sing Lee and David Mumford}, - Journal = JOSA, - Year = {2003}, - Number = {7}, - Pages = {1434-1448}, - Volume = {20} -} - -@article{Leek2001, - title={Adaptive procedures in psychophysical research}, - author={Leek, Marjorie R}, - journal={Perception \rm{\&} \textit{Psychophysics}}, - volume={63}, - number={8}, - pages={1279--1292}, - year={2001}, - publisher={Springer} -} - -@Article{Lewicki2002, - Title = {Efficient coding of natural sounds.}, - Author = {Michael S. Lewicki}, - Journal = {Nature Neuroscience}, - Year = {2002}, - Number = {4}, - Pages = {356-363}, - Volume = {5} -} - -@Article{Lewicki2014, - Title = {Scene analysis in the natural environment.}, - Author = {Michael S. Lewicki and Bruno A. Olshausen and Annemarie Surlykke and Cynthia F. Moss}, - Journal = FrontPsychol, - Year = {2014}, - Pages = {1--21}, - Volume = {5} -} - -@Article{Liberman1982, - title={Single-neuron labeling in the cat auditory nerve}, - author={Liberman, MC}, - journal={Science}, - volume={216}, - number={4551}, - pages={1239--1241}, - year={1982}, - publisher={American Association for the Advancement of Science} -} - - -@Article{Lindner2022, - title={Fluctuation-dissipation relations for spiking neurons}, - author={Lindner, Benjamin}, - journal={Physical Review Letters}, - volume={129}, - number={19}, - pages={198101}, - year={2022}, - publisher={APS} -} - - - - -@article{Lisman1997, - title={Bursts as a unit of neural information: making unreliable synapses reliable}, - author={Lisman, John E}, - journal={Trends in Neurosciences}, - volume={20}, - number={1}, - pages={38--43}, - year={1997}, - publisher={Elsevier} -} - -@ARTICLE{Lissmann1951, - AUTHOR = {H. W. Lissmann}, - TITLE = {Continous electrical signals from the tail of a fish, \textit{Gymnarchus niloticus} Cuv.}, - YEAR = {1951}, - JOURNAL = Nature, - VOLUME = {167}, - PAGES = {201--202} } - -@ARTICLE{Lissmann1958Function, - AUTHOR = {H. W. Lissmann}, - TITLE = {On the function and evolution of electric organs in fish.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1958}, - VOLUME = {35}, - PAGES = {156--191} -} - -@ARTICLE{Lissmann1958Mechanism, - AUTHOR = {H. W. Lissmann and K. E. Machin}, - TITLE = {The mechanism of object location in \textit{Gymnarchus niloticus} and similar fish.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {1958}, - VOLUME = {35}, - PAGES = {451--486} -} - -@ARTICLE{Lissmann1965, - AUTHOR = {Hans W. Lissmann and Hosrt O. Schwassmann}, - TITLE = {Activity rhythm of an electric fish, \textit{Gymnorhamphichtys hypostomus}, Ellis.}, - JOURNAL = {Z vergl Physiol}, - YEAR = {1965}, - VOLUME = {51}, - PAGES = {153--171} -} - -@Article{Litwin-Kumar2012, - Title = {The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity.}, - Author = {Ashok Litwin-Kumar and Maurice J. Chacron and Brent Doiron}, - Journal = {PLoS Computational Biology}, - Year = {2012}, - Number = {9}, - Pages = {e1002667}, - Volume = {8} -} - -@Article{Lochmann2011, - Title = {Neural processing as causal inference.}, - Author = {Timm Lochmann and Sophie Deneve}, - Journal = CurrOpinNeurobiol, - Year = {2011}, - Pages = {774-781}, - Volume = {21} -} - -@article{Longtin1993, - title={Stochastic resonance in neuron models}, - author={Longtin, Andr{\'e}}, - journal={Journal of statistical physics}, - volume={70}, - pages={309--327}, - year={1993}, - publisher={Springer} -} - -@Article{Longtin1996, - title={Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors}, - author={Longtin, Andre and Hinzer, Karin}, - journal={Neural Computation}, - volume={8}, - number={2}, - pages={215--255}, - year={1996}, - publisher={MIT Press} -} - -@article{Longtin2008, - title={Neural dynamics of envelope coding}, - author={Longtin, Andr{\'e} and Middleton, Jason W and Cieniak, Jakub and Maler, Leonard}, - journal={Mathematical Biosciences}, - volume={214}, - number={1-2}, - pages={87--99}, - year={2008}, - publisher={Elsevier} -} - -@article{Lonsbury1990, - title={The clinical utility of distortion-product otoacoustic emissions.}, - author={Lonsbury-Martin, Brenda L and Martin, Glen K}, - journal={Ear Hearing}, - volume={11}, - number={2}, - pages={144--154}, - year={1990} -} - -@ARTICLE{Machnik2008, - AUTHOR = {Peter Machnik and Bernd Kramer}, - TITLE = {Female choice by electric pulse duration: attractiveness of the males' communication signal assessed by female bulldog fish, \textit{Marcusenius pongolensis} {(Mormyridae, Teleostei)}.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2008}, - VOLUME = {211}, - PAGES = {1969--1977} -} - -@ARTICLE{MacIver2010, - AUTHOR = {Malcolm A. MacIver and Neelesh A. Patankar and Anup A. Shirgaonkar}, - TITLE = {Energy-information trade-offs between movement and sensing.}, - JOURNAL = {PLoS Computational Biology}, - YEAR = {2010}, - VOLUME = {6}, - PAGES = {e1000769} -} - -@Article{Madhav2018, - Title = {High-resolution behavioral mapping of electric fishes in Amazonian habitats}, - Author = {Manu S. Madhav and Ravikrishnan P. Jayakumar and Alican Demir and Sarah A. Stamper and Eric S. Fortune and Noah J. Cowan}, - Journal = {Scientific Reports}, - Year = {2018}, - Number = {5830}, - Volume = {8}, - - Doi = {https://doi.org/10.1038/s41598-018-24035-5}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - -@article{Maier2008, - title={Integration of bimodal looming signals through neuronal coherence in the temporal lobe}, - author={Maier, Joost X and Chandrasekaran, Chandramouli and Ghazanfar, Asif A}, - journal={Current Biology}, - volume={18}, - number={13}, - pages={963--968}, - year={2008}, - publisher={Elsevier} -} - - -@Article{Maler1974, - Title = {Differential projections of Ordinary Lateral Line Receptors and Electroreceptors in the Gymnotic Fish, {\textit{Apteronotus (Sternarchus) albifrons}}.}, - Author = {L. Maler and T. Finger and H.J. Karten}, - Journal = {Journal of Comparative Neurology}, - Year = {1974}, - Pages = {363-382}, - Volume = {158} -} - -@Article{Maler1979, - Title = {The Posterior Lateral Line Lobe of Certain Gymnotoid Fish: Quantitative Light Microscopy.}, - Author = {Leonard Maler}, - Journal = {Journal of Comparative Neurology}, - Year = {1979}, - Pages = {323-364}, - Volume = {183} -} - -@ARTICLE{Maler2009a, - AUTHOR = {Leonard Maler}, - TITLE = {Receptive field organization across multiple electrosensory maps. {I}. Columnar organization and estimation of receptive field size.}, - YEAR = {2009}, - JOURNAL = {Journal of Comparative Neurology}, - VOLUME = {516}, - PAGES = {376--393} } - -@article{Malone2010, - title={Temporal codes for amplitude contrast in auditory cortex}, - author={Malone, Brian J and Scott, Brian H and Semple, Malcolm N}, - journal={Journal of Neuroscience}, - volume={30}, - number={2}, - pages={767--784}, - year={2010}, - publisher={Soc Neuroscience} -} - - -@Article{Manley1990, - title={Peripheral auditory processing in the bobtail lizard {Tiliqua rugosa}: {I}. Frequency tuning of auditory-nerve fibres}, - author={Manley, Geoffrey A and K{\"o}ppl, Christine and Johnstone, Brian M}, - journal={Journal of Comparative Physiology A}, - volume={167}, - pages={89--99}, - year={1990}, - publisher={Springer} -} - -@article{Margolskee2002, - title={Molecular mechanisms of bitter and sweet taste transduction}, - author={Margolskee, Robert F}, - journal={Journal of Biological Chemistry}, - volume={277}, - number={1}, - pages={1--4}, - year={2002}, - publisher={ASBMB} -} - -@Article{Markham2015, - Title = {Optimal group size in a highly social mammal}, - Author = {Markham, A. Catherine and Gesquiere, Laurence R. and Alberts, Susan C. and Altmann, Jeanne}, - Journal = {{Proceedings of the National Academy of Sciences}}, - Year = {2015}, - Number = {48}, - Pages = {14882--14887}, - Volume = {112}, - - Abstract = {What are the costs and benefits for animals living in groups of different sizes? Balancing the trade-offs between within-group competition (which favors smaller groups) and between-group competition (which favors larger groups) suggests that intermediate-sized groups may be best, yet empirical support for this prediction has largely been lacking. Using long-term data on wild baboons, we provide novel evidence that individuals living in intermediate-sized groups have energetically optimal space-use strategies and lower glucocorticoid (stress hormone) concentrations than individuals in either large or small groups. Our results offer new insight into the costs and benefits of group living.Group size is an important trait of social animals, affecting how individuals allocate time and use space, and influencing both an individual{\textquoteright}s fitness and the collective, cooperative behaviors of the group as a whole. Here we tested predictions motivated by the ecological constraints model of group size, examining the effects of group size on ranging patterns and adult female glucocorticoid (stress hormone) concentrations in five social groups of wild baboons (Papio cynocephalus) over an 11-y period. Strikingly, we found evidence that intermediate-sized groups have energetically optimal space-use strategies; both large and small groups experience ranging disadvantages, in contrast to the commonly reported positive linear relationship between group size and home range area and daily travel distance, which depict a disadvantage only in large groups. Specifically, we observed a U-shaped relationship between group size and home range area, average daily distance traveled, evenness of space use within the home range, and glucocorticoid concentrations. We propose that a likely explanation for these U-shaped patterns is that large, socially dominant groups are constrained by within-group competition, whereas small, socially subordinate groups are constrained by between-group competition and predation pressures. Overall, our results provide testable hypotheses for evaluating group-size constraints in other group-living species, in which the costs of intra- and intergroup competition vary as a function of group size.}, - Doi = {10.1073/{Proceedings of the National Academy of Sciences}.1517794112}, - Owner = {raab}, - Publisher = {National Academy of Sciences}, - Timestamp = {2020.01.21}, - Url = {https://www.{Proceedings of the National Academy of Sciences}.org/content/112/48/14882} -} - -@Article{Markham2016, - Title = {Energetics of Sensing and Communication in Electric Fish: A Blessing and a Curse in the {Anthropocene}?}, - Author = {Michael R. Markham and Yue Ban and Austin G. McCauley and Rosalie Maltby}, - Journal = IntegrCompBiol, - Year = {2016}, - Number = {5}, - Pages = {889-900}, - Volume = {56} -} - -@Article{Markham2017, - Title = {Costs and benefits of group living in primates: an energetic perspective}, - Author = {A. Catherine Markham and Laurence R. Gesquiere}, - Journal = PhilTransRSocLondBBiolSci, - Year = {2017}, - Volume = {372}, - - Doi = {http://doi.org/10.1098/rstb.2016.0239}, - Owner = {raab}, - Timestamp = {2020.01.21} -} - -@Article{Marquez2013a, - Title = {Distribution of Muscarinic Acetylcholine Receptor {mRNA} in the Brain of the Weakly Electric Fish \textit{Apteronotus leptorhynchus}.}, - Author = {Brenda Toscano-M\'arquez and Robert J. Dunn and R\"udiger Krahe}, - Journal = {Journal of Comparative Neurology}, - Year = {2013}, - Pages = {1054-1072}, - Volume = {521} -} - -@Article{Marquez2013b, - Title = {Neuromodulation of early electrosensory processing in gymnotiform weakly electric fish.}, - Author = {Brenda Toscano-M\'arquez and R\"udiger Krahe and Maurice J. Chacron}, - Journal = {Journal of Experimental Biology}, - Year = {2013}, - Pages = {2442-2450}, - Volume = {216} -} - -@ARTICLE{Marrero1991, - AUTHOR = {C. Marrero and D. C. Taphorn}, - TITLE = {Notas sobre la historia natural y la distribuicion de los peces {Gymnotiformes} em la cuenca del {Rio Apure} y otros rios de la {Orinoquia}.}, - JOURNAL = {Biollania}, - YEAR = {1991}, - VOLUME = {8}, - PAGES = {123--142} -} - - - -@Article{Marsat2010burst, - title={The structure and size of sensory bursts encode stimulus information but only size affects behavior}, - author={Marsat, Gary and Pollack, Gerald S}, - journal={Journal of Comparative Physiology A}, - volume={196}, - pages={315--320}, - year={2010}, - publisher={Springer} -} - -@Article{Marsat2012a, - Title = {Cellular and circuit properties supporting different sensory coding strategies in electric fish and other systems.}, - Author = {Gary Marsat and Andr\'e Longtin and Leonard Maler}, - Journal = CurrOpinNeurobiol, - Year = {2012}, - Pages = {1-7}, - Volume = {22} -} - -@Article{Marsat2012b, - Title = {Preparing for the unpredictable: adaptive feedback enhances the response to unexpected communication signals.}, - Author = {Gary Marsat and Leonard Maler}, - Journal = {Journal of Neurophysiology}, - Year = {2012}, - Pages = {1241-1246}, - Volume = {107} -} - -@article{Marsat2012bursting, - title={Bursting neurons and ultrasound avoidance in crickets}, - author={Marsat, Gary and Pollack, Gerald S}, - journal={Frontiers in Neuroscience}, - volume={6}, - pages={95}, - year={2012}, - publisher={Frontiers Research Foundation} -} - - -@Article{Mathis2018, - Title = {{DeepLabCut}: markerless pose estimation of user-defined body parts with deep learning}, - Author = {Alexander Mathis and Pranav Mamidanna and Kevin M. Cury and Taiga Abe and Venkatesh N. Murthy and Mackenzie Weygandt Mathis and Matthias Bethge}, - Journal = {Nature Neuroscience}, - Year = {2018}, - Pages = {1281-1289}, - Volume = {21}, - - Doi = {https://doi.org/10.1038/s41593-018-0209-y}, - Owner = {raab}, - Timestamp = {2020.02.11} -} - - -@ARTICLE{Matias2015, - AUTHOR = {Paulo Matias and Jan Frans Willem Slaets and Reynaldo Daniel Pinto}, - TITLE = {Individual discrimination of freely swimming pulse-type electric fish from electrode array recordings.}, - JOURNAL = {Neurocomputing}, - YEAR = {2015}, - VOLUME = {153}, - PAGES = {191--198} -} - -@Article{McAdams1999, - Title = {Effects of attention on orientation-tuning functions of - single neurons in macaque cortical area {V4}.}, - Author = {C. J. McAdams and J. H. Maunsell}, - Journal = JNeurosci, - Year = {1999}, - Pages = {431--441}, - Volume = {19} -} - -@ARTICLE{McAnelly2000, - AUTHOR = {M. Lynne McAnelly and Harold H. Zakon}, - TITLE = {Coregulation of voltage-dependent kinetics of {Na$^+$} and {K$^+$} currents in electric organ.}, - JOURNAL = JNeurosci, - YEAR = {2000}, - VOLUME = {20}, - PAGES = {3408--3414} -} - -@Article{McCreery1977, - Title = {Two Types of Electroreceptive Lateral Lemniscal Neurons of the Lateral Line Lobe of the Catfish {Ictalurus nebulosus}; Connections from the Lateral Line Nerve and Steady-State Frequency Response Characteristics.}, - Author = {Douglas B. McCreery}, - Journal = JCompPhysiol, - Year = {1977}, - Pages = {317-339}, - Volume = {113} -} - -@article{Mcdermott2009, - title={The cocktail party problem}, - author={McDermott, Josh H}, - journal={Current Biology}, - volume={19}, - number={22}, - pages={R1024--R1027}, - year={2009}, - publisher={Elsevier} -} - -@Article{McGillivray2012, - Title = {Parallel Coding of First- and Second-Order Stimulus Attributes by Midbrain Electrosensory Neurons.}, - Author = {Patrick McGillivray and Katrin Vonderschen and Eric S. Fortune and Maurice J. Chacron}, - Journal = JNeurosci, - Year = {2012}, - Number = {16}, - Pages = {5510-5524}, - Volume = {32} -} - -@ARTICLE{McGregor1992, - AUTHOR = {Peter K. McGregor and G. W. Max Westby}, - TITLE = {Discrimination of individually charactersitic electric organ discharges by a weakly electric fish.}, - JOURNAL = AnimBehav, - YEAR = {1992}, - VOLUME = {43}, - PAGES = {977--986} -} - -@ARTICLE{McKibben1993, - AUTHOR = {J. R. McKibben and C. D. Hopkins and D. D. Yager}, - TITLE = {Directional sensitivity of tuberous electroreceptors: polarity preferences and frequency tuning.}, - JOURNAL = JCompPhysiolA, - YEAR = {1993}, - VOLUME = {173}, - PAGES = {415--424} -} - -@inproceedings{Mckinney2010, - title={Data structures for statistical computing in python}, - author={McKinney, Wes and others}, - booktitle={Proceedings of the 9th Python in Science Conference}, - volume={445}, - pages={51--56}, - year={2010}, - organization={Austin, TX} -} - -@Article{Mejias2013, - Title = {Learning Contrast-Invariant Cancellation of Redundant Signals in Neural Systems.}, - Author = {Jorge F. Mejias and Gary Marsat and Kieran Bol and Leonard Maler and Andr\'e Longtin}, - Journal = {PLoS Computational Biology}, - Year = {2013}, - Number = {9}, - Pages = {e1003180}, - Volume = {9} -} - -@Article{Menzel2005, - Title = {Honey bees navigate according to a map-like spatial memory}, - Author = {Menzel, Randolf and Greggers, Uwe and Smith, Alan and Berger, Sandra and Brandt, Robert and Brunke, Sascha and Bundrock, Gesine and H{\"u}lse, Sandra and Pl{\"u}mpe, Tobias and Schaupp, Frank and Sch{\"u}ttler, Elke and Stach, Silke and Stindt, Jan and Stollhoff, Nicola and Watzl, Sebastian}, - Journal = {{Proceedings of the National Academy of Sciences}}, - Year = {2005}, - Number = {8}, - Pages = {3040--3045}, - Volume = {102}, - - Abstract = {By using harmonic radar, we report the complete flight paths of displaced bees. Test bees forage at a feeder or are recruited by a waggle dance indicating the feeder. The flights are recorded after the bees are captured when leaving the hive or the feeder and are released at an unexpected release site. A sequence of behavioral routines become apparent: (i) initial straight flights in which they fly the course that they were on when captured (foraging bees) or that they learned during dance communication (recruited bees); (ii) slow search flights with frequent changes of direction in which they attempt to {\textquotedblleft}get their bearings{\textquotedblright}; and (iii) straight and rapid flights directed either to the hive or first to the feeding station and then to the hive. These straight homing flights start at locations all around the hive and at distances far out of the visual catchment area around the hive or the feeding station. Two essential criteria of a map-like spatial memory are met by these results: bees can set course at any arbitrary location in their familiar area, and they can choose between at least two goals. This finding suggests a rich, map-like organization of spatial memory in navigating honey bees.}, - Doi = {10.1073/{Proceedings of the National Academy of Sciences}.0408550102}, - Owner = {raab}, - Publisher = {National Academy of Sciences}, - Timestamp = {2020.02.11}, - Url = {https://www.{Proceedings of the National Academy of Sciences}.org/content/102/8/3040} -} - -@Article{Meredith2002, - title={On the neuronal basis for multisensory convergence: a brief overview}, - author={Meredith, M Alex}, - journal={Cognitive brain research}, - volume={14}, - number={1}, - pages={31--40}, - year={2002}, - publisher={Elsevier} -} - -@Article{Merkel1965, - title={Magnetismus und {R}ichtungsfinden zugunruhiger {R}otkehlchen ({E}rithacus rubecula)}, - author={Merkel, FW and Wiltschko, W}, - journal={Vogelwarte}, - volume={23}, - number={1}, - pages={71--77}, - year={1965} -} - -@Article{Metcalfe1995, - Title = {Fish recognize and prefer to shoal with poor competitors}, - Author = {Metcalfe, Neil B. and Thomson, Bruce C.}, - Journal = ProcRSocLondBBiolSci, - Year = {1995}, - Number = {1355}, - Pages = {207-210}, - Volume = {259}, - - Doi = {10.1098/rspb.1995.0030}, - Owner = {raab}, - Timestamp = {2020.01.27} -} - -@Article{Metzen2016, - title={Burst firing in the electrosensory system of gymnotiform weakly electric fish: mechanisms and functional roles}, - author={Metzen, Michael G and Krahe, R{\"u}diger and Chacron, Maurice J}, - journal={Frontiers in Computational Neuroscience}, - volume={10}, - pages={81}, - year={2016}, - publisher={Frontiers Media SA} -} - -@ARTICLE{Metzen2017, - AUTHOR = {M. G. Metzen and Maurice J. Chacron}, - TITLE = {Stimulus background influences phase invariant coding by correlated neural activity.}, - YEAR = {2017}, - JOURNAL = {eLife}, - VOLUME = {6}, - PAGES = {e24482} } - -@article{Metzen2018descending, - title={Descending pathways generate perception of and neural responses to weak sensory input}, - author={Metzen, Michael G and Huang, Chengjie G and Chacron, Maurice J}, - journal={PLoS Biology}, - volume={16}, - number={6}, - pages={e2005239}, - year={2018}, - publisher={Public Library of Science San Francisco, CA USA} -} - -@Article{Meyer1982, - Title = {Androgens alter the tuning of electroreceptors.}, - Author = {Meyer, J H and Zakon, H H}, - Journal = {Science}, - Year = {1982}, - Pages = {635--637}, - Volume = {217} -} - -@ARTICLE{Meyer1982Impedances, - AUTHOR = {J. Harlan Meyer}, - TITLE = {Behavioral responses of weakly electric fish to complex impedances.}, - JOURNAL = {JCompPhysiol}, - YEAR = {1982}, - VOLUME = {145}, - PAGES = {459--470} -} - -@Article{Meyer1987, - Title = {Hormone-induced and maturational changes in electric organ discharges and electroreceptor tuning in the weakly electric fishApteronotus}, - Author = {Meyer, J. Harlan -and Leong, Margaret -and Keller, Clifford H.}, - Journal = {JCompPhysiolA}, - Year = {1987}, - Number = {3}, - Pages = {385--394}, - Volume = {160}, - - Abstract = {Plasticity in the frequency of the electric organ discharge (EOD) and electroreceptor tuning of weakly electric fish was studied in the genusApteronotus. Both hormone-induced and maturational changes in EOD frequency and electroreceptor tuning were examined.Apteronotus is different from all other steroid-responsive weakly electric fish in that estradiol-17$\beta$, rather than androgens, induces discharge frequency decreases. This result can account for the `reversed' discharge frequency dimorphism found inApteronotus in which, counter to all other known sexually dimorphic electric fish, females have lower discharge frequencies than males. Studies of electroreceptor tuning inApteronotus indicate that electroreceptors are closely tuned to the frequency of the EOD. This finding was noted not only in adult animals, but also in juvenile animals shortly after the onset of their EODs. Tuning plasticity inApteronotus, as in other species studied, is associated with altered EOD frequencies and was noted in both maturational EOD changes and in estrogen-induced changes. Thus, tuning plasticity appears to be a general phenomenon which occurs concurrent with a variety of EOD changes.}, - Day = {01}, - Doi = {10.1007/BF00613028}, - Owner = {raab}, - Timestamp = {2020.02.11}, - Url = {https://doi.org/10.1007/BF00613028} -} - -@article{Michalski2017, - title={Otoferlin acts as a {Ca$^{2+}$} sensor for vesicle fusion and vesicle pool replenishment at auditory hair cell ribbon synapses}, - author={Michalski, Nicolas and Goutman, Juan D and Auclair, Sarah Marie and de Monvel, Jacques Boutet and Tertrais, Margot and Emptoz, Alice and Parrin, Alexandre and Nouaille, Sylvie and Guillon, Marc and Sachse, Martin and Ciric, Danica and Bahloul, Amel and Hardelin, Jean-Pierre and Sutton, Rodger Bryan and Avan, Paul and Krishnakumar, Shyam S. and Rothman, James E. and Dulon, Didier andSafieddine, Saaid and Petit, Christine}, - journal={Elife}, - volume={6}, - pages={e31013}, - year={2017}, -} - -@ARTICLE{Middleton2006, - AUTHOR = {Jason W. Middleton and Andr\'e Longtin and Jan Benda and Leonard Maler}, - TITLE = {The cellular basis for parallel neural transmission of a high-frequency stimulus and its low-frequency envelope.}, - JOURNAL = {Proceedings of the National Academy of Sciences}, - YEAR = {2006}, - VOLUME = {103}, - PAGES = {14596--14601} -} - -@ARTICLE{Middleton2007, - AUTHOR = {Jason W. Middleton and E. Harvey-Girard and Leonard Maler and Andr\'e Longtin}, - TITLE = {Envelope gating and noise shaping in populations of noisy neurons.}, - JOURNAL = {Physical Review E}, - YEAR = {2007}, - VOLUME = {75}, - PAGES = {021918} -} - -@ARTICLE{Migliaro2005, - AUTHOR = {Adriana Migliaro and Angel A. Caputi and Ruben Budelli}, - TITLE = {Theoretical analysis of pre-receptor image conditioning in weakly electric fish.}, - JOURNAL = {PLoS Computational Biology}, - YEAR = {2005}, - VOLUME = {1}, - PAGES = {e16} -} - -@article{Millman2002, - title={Effect of duration on amplitude-modulation masking}, - author={Millman, Rebecca E and Lorenzi, Christian and Apoux, Fr{\'e}d{\'e}ric and F{\"u}llgrabe, Christian and Green, Gary GR and Bacon, Sid P}, - journal={The Journal of the Acoustical Society of America}, - volume={111}, - number={6}, - pages={2551--2554}, - year={2002}, - publisher={Acoustical Society of America} -} - -@Article{Miramontes1996, - Title = {The Nonlinear Dynamics of Survival and Social Facilitation in Termites}, - Author = {Octavio Miramontes and Og DeSouza}, - Journal = {J Theoret Biol}, - Year = {1996}, - Number = {4}, - Pages = {373 - 380}, - Volume = {181}, - - Abstract = {This paper describes a study on termites, investigating the relationship between increasing group size and individual worker longevity under resource-deprived conditions. It was found that survival was significantly lower for isolated individuals and higher for individuals in bigger group sizes, suggesting that social interactions play an important role in the mechanisms leading to longer survival. A computer model, incorporating individual interactions among mobile cellular automata is presented along with experiments.}, - Doi = {https://doi.org/10.1006/jtbi.1996.0138}, - Owner = {raab}, - Timestamp = {2020.01.21}, - Url = {http://www.sciencedirect.com/science/article/pii/S0022519396901381} -} - -@article{Moller1972, - title={Coding of amplitude and frequency modulated sounds in the cochlear nucleus of the rat}, - author={M{\o}ller, Aage R}, - journal={Acta Physiologica Scandinavica}, - volume={86}, - number={2}, - pages={223--238}, - year={1972}, - publisher={Wiley Online Library} -} - -@article{Moller1976, - title={Dynamic properties of primary auditory fibers compared with cells in the cochlear nucleus}, - author={M{\o}ller, Aage R}, - journal={Acta Physiologica Scandinavica}, - volume={98}, - number={2}, - pages={157--167}, - year={1976}, - publisher={Wiley Online Library} -} - -@Article{Montgomery1984, - Title = {Frequency Response Characteristics of primary and secondary Neurons in the electrosensory System of the Thornback Ray.}, - Author = {J.C. 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Even neurons of the same molecular type have notable intrinsic differences. Largely unknown, however, is the degree to which these differences impair or assist neural coding. We examined the outputs from a single type of neuron, the mitral cells of the mouse olfactory bulb, to identical stimuli and found that each cell's spiking response was dictated by its unique biophysical fingerprint. Using this intrinsic heterogeneity, diverse populations were able to code for twofold more information than their homogeneous counterparts. In addition, biophysical variability alone reduced pair-wise output spike correlations to low levels. 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Troy Smith}, - TITLE = {Co-adaptation of electric organ discharges and chirps in {South} {American} ghost knifefishes ({Apteronotidae}).}, - JOURNAL = {Journal of Physiology-Paris}, - YEAR = {2016}, - VOLUME = {110}, - PAGES = {200--215} -} - -@article{Phillips1990, - title={Neural representation of sound amplitude in the auditory cortex: effects of noise masking}, - author={Phillips, Dennis P}, - journal={Behavioural Brain Research}, - volume={37}, - number={3}, - pages={197--214}, - year={1990}, - publisher={Elsevier} -} - -@article{Plomp1967, - title={Beats of mistuned consonances}, - author={Plomp, Reinier}, - journal={The Journal of the Acoustical Society of America}, - volume={42}, - number={2}, - pages={462--474}, - year={1967} -} - -@Article{Poggio1985, - Title = {Ill-posed problems in early vision: from computational - theory to analogue networks.}, - Author = {T. Poggio and C. 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Far less is known about their behaviors in more natural-like settings, where fish are less constrained in space and time. We tracked individual fish in a population of fourteen brown ghost knifefish (Apteronotus leptorhynchus) housed in a large 2 m3 indoor tank based on their electric organ discharges (EOD). The tank contained four different natural-like microhabitats (gravel, plants, isolated stones, stacked stones). In particular during the day individual fish showed preferences for specific habitats which provided appropriate shelter. Male fish with higher EOD frequencies spent more time in their preferred habitat during the day, moved more often between habitats during the night, and less often during the day in comparison to low-frequency males. Our data thus revealed a link between dominance indicated by higher EOD frequency, territoriality, and a more explorative personality in male A. leptorhynchus. 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Jarrod and - Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and - Kern, Robert and Larson, Eric and Carey, C J and - Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and - {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and - Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and - Harris, Charles R. and Archibald, Anne M. and - Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and - {van Mulbregt}, Paul and {SciPy 1.0 Contributors}}, - title = {{{SciPy} 1.0: Fundamental Algorithms for Scientific - Computing in Python}}, - journal = {Nature Methods}, - year = {2020}, - volume = {17}, - pages = {261--272}, - adsurl = {https://rdcu.be/b08Wh}, - doi = {10.1038/s41592-019-0686-2}, -} - -@Article{Sen2006, - title={Functionality of cochlear micromechanics-as elucidated by upward spread of masking and two tone suppression}, - author={Sen, D and Allen, Jont B}, - journal={Acoustics Australia}, - volume={34}, - number={1}, - pages={37}, - year={2006} -} - -@Article{Serrano2003, - Title = {Gradual frequency rises in interacting black ghost knifefish, \textit{Apteronotus albifrons}}, - Author = {Serrano-Fern{\'a}ndez, P.}, - Journal = JCompPhysiolA, - Year = {2003}, - Number = {9}, - Pages = {685--692}, - Volume = {189}, - - Abstract = {The present paper highlights the relationship between social status and production of gradual frequency rises in interacting \textit{Apteronotus albifrons}. The gradual frequency rise production was mathematically inferred and a discrete classification deliberately avoided. The results showed little gradual frequency rise production before the hierarchy settlement. Afterwards, only the dominant fish kept this gradual frequency rise production at low levels, while the subdominant fish drastically increased it in all following interaction contexts. 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Fortune}, - TITLE = {Beyond the {Jamming Avoidance Response}: weakly electric fish respond to the envelope of social electrosensory signals.}, - JOURNAL = {Journal of Experimental Biology}, - YEAR = {2012}, - VOLUME = {215}, - PAGES = {4196--4207} -} - -@article{stamper2012JAR, - title={Beyond the {Jamming Avoidance Response}: weakly electric fish respond to the envelope of social electrosensory signals}, - author={Stamper, Sarah A and Madhav, Manu S and Cowan, Noah J and Fortune, Eric S}, - journal={Journal of Experimental Biology}, - volume={215}, - number={23}, - pages={4196--4207}, - year={2012}, - publisher={Company of Biologists} -} - -@Article{Stamper2012Shuttle, - Title = {Active sensing via movement shapes spatiotemporal patterns of sensory feedback.}, - Author = {Sarah A. Stamper and Eatai Roth and Noah J. Cowan and Eric S. Fortune}, - Journal = {Journal of Experimental Biology}, - Year = {2012}, - Pages = {1567-1574}, - Volume = {215} -} - -@Article{Stamper2013, - Title = {Perception and coding of envelopes in weakly electric fishes.}, - Author = {Sarah A. Stamper and Eric S. Fortune and Maurice J. Chacron}, - Journal = {Journal of Experimental Biology}, - Year = {2013}, - Pages = {2393-2402}, - Volume = {216} -} - -@ARTICLE{Steinbach1970, - AUTHOR = {A. B. Steinbach}, - TITLE = {Diurnal movements and discharge characteristics of electric gymnotid fishes in the {Rio Negro}, {Brazil}}, - JOURNAL = {The Biological Bulletin}, - YEAR = {1970}, - VOLUME = {138}, - PAGES = {200--210} -} - -@Article{Stephens2013, - Title = {Independent Evolution of Visual and Electrosensory Spezializations in Different Lineages of Mormyrid Electric Fishes.}, - Author = {Jennifer A. Stephens and Kimberley V. Sukhum and Bruce A. 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Evidence collected from schooling animals suggests that the process is somewhat democratic, with nearest neighbors and the majority shaping overall collective behavior. In animals with hierarchical social structures such as primates or wolves, however, such democracy may be complicated by dominance. Strandburg-Peshkin et al. monitored all the individuals within a baboon troop continuously over the course of their daily activities. Even within this highly socially structured species, movement decisions emerged via a shared process. Thus, democracy may be an inherent trait of collective behavior.Science, this issue p. 1358Conflicts of interest about where to go and what to do are a primary challenge of group living. However, it remains unclear how consensus is achieved in stable groups with stratified social relationships. Tracking wild baboons with a high-resolution global positioning system and analyzing their movements relative to one another reveals that a process of shared decision-making governs baboon movement. Rather than preferentially following dominant individuals, baboons are more likely to follow when multiple initiators agree. When conflicts arise over the direction of movement, baboons choose one direction over the other when the angle between them is large, but they compromise if it is not. 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Lewis and Andr\'e Longtin}, - TITLE = {Coding conspecific identity and motion in the electric sense.}, - JOURNAL = {PLoS Computational Biology}, - YEAR = {2005}, - VOLUME = {8}, - PAGES = {e1002564} -} - -@Article{Yuille2006, - Title = {Vision as Bayesian inference: analysis by synthesis?}, - Author = {Alan Yuille and Daniel Kersten}, - Journal = TICS, - Year = {2006}, - Number = {7}, - Pages = {301-308}, - Volume = {10} -} - - -@article{Zakon2002, - author = {H. H. Zakon and Oestreich, J. and Tallarovic, S. and Triefenbach, F.}, - journal = {Journal of Physiology-Paris}, - number = {5--6}, - pages = {451--458}, - title = {{EOD} modulations of brown ghost electric fish: {JAR}s, chirps, rises, and dips}, - volume = {96}, - year = {2002} -} - -@ARTICLE{Zakon2008, - AUTHOR = {Harold H. Zakon and Derrick J. Zwickl and Ying Lu and David M. 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-\newcommand{\abcsumshort}{\ensuremath{A(\bcsumshort{})}}%sum -\newcommand{\abconeshort}{\ensuremath{A(|\bconeshort{}|)}}%sum - -\newcommand{\abcsumb}{\ensuremath{A(\bcsum{})=\fbasesolid{}}}%sum -\newcommand{\bcdiff}{\ensuremath{||\bctwo{}| - |\bcone{}||}}%diff of both beat frequencies - -\newcommand{\bcsumb}{\ensuremath{\bcsum{} =\fbasesolid{}}}%su\right m -\newcommand{\bcsumbn}{\ensuremath{\bcsum{} \neq \fbasesolid{}}}%su\right m -\newcommand{\bctwob}{\ensuremath{\bctwo{} =\fbasesolid{}}}%sum -\newcommand{\bconeb}{\ensuremath{\bcone{} =\fbasesolid{}}}%sum -\newcommand{\bcsumbtwo}{\ensuremath{\bcsum{}=2 \fbasesolid{}}}%sum -\newcommand{\bcsumbc}{\ensuremath{\bcsum{}=\fbasecorr{}}}%sum -\newcommand{\bcsume}{\ensuremath{\bcsum{}=f_{\rm{EOD}}}}%sum -\newcommand{\bcsumehalf}{\ensuremath{\bcsum{}=f_{\rm{EOD}}/2}}%sum - -\newcommand{\bcdiffb}{\ensuremath{\bcdiff{}=\fbasesolid{}}}%diff of both beat frequencies -\newcommand{\bcdiffbc}{\ensuremath{\bcdiff{}=\fbasecorr{}}}%diff of both beat frequencies -\newcommand{\bcdiffe}{\ensuremath{\bcdif{}f=f_{\rm{EOD}}}}%diff of both -\newcommand{\bcdiffehalf}{\ensuremath{\bcdiff{}=f_{\rm{EOD}}/2}}%diff of both - -\newcommand{\burstcorr}{\ensuremath{{Corrected}}} -\newcommand{\cvbasecorr}{CV\ensuremath{_{BaseCorrected}}} -\newcommand{\cv}{CV\ensuremath{_{Base}}}%\cvbasecorr{} -\newcommand{\nli}{PNL\ensuremath{(\fbase{})}}%Fr$_{Burst}$ -\newcommand{\nlicorr}{PNL\ensuremath{(\fbasecorr{}})}%Fr$_{Burst}$ -\newcommand{\suscept}{$|\chi_{2}|$} -\newcommand{\susceptf}{$|\chi_{2}|(f_1, f_2)$} -\newcommand{\frcolor}{pink lines} - -\newcommand{\rec}{\ensuremath{\rm{R}}}%{\ensuremath{con_{R}}} -\newcommand{\rif}{\ensuremath{\rm{RIF}}} -\newcommand{\ri}{\ensuremath{\rm{RI}}}%sum -\newcommand{\rf}{\ensuremath{\rm{RF}}}%sum -\newcommand{\withfemale}{\rm{ROC}\ensuremath{\rm{_{Female}}}}%sum \textit{ -\newcommand{\wofemale}{\rm{ROC}\ensuremath{\rm{_{NoFemale}}}}%sum -\newcommand{\dwithfemale}{\rm{\ensuremath{\auc_{Female}}}}%sum CV\ensuremath{_{BaseCorrected}} -\newcommand{\dwofemale}{\rm{\ensuremath{\auc_{NoFemale}}}}%sum -\newcommand{\fp}{\ensuremath{\rm{FP}}}%sum -\newcommand{\cd}{\ensuremath{\rm{CD}}}%sum - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{document} - -\maketitle - -%\paragraph{Short title:} -%\paragraph{Corresponding author:}Jan Grewe, E-mail: jan.grewe@uni-tuebingen.de -%\paragraph{Conflict of interest:}The authors declare no conflict of interest. -%\paragraph{Author Contributions:} All authors designed the study and discussed the results. AB performed the data analyses and modeling, AB and JG drafted the paper, all authors discussed and revised the manuscript. - -\paragraph{Keywords:} population coding $|$ conduction delay $|$ heterogeneity $|$ electric fish $|$ mutual information - - -% Please keep the abstract below 300 words -\section{Abstract} -Neuronal processing is inherently nonlinear --- spiking thresholds or rectification in synapses are central to neuronal computations. Nevertheless, linear response theory has been instrumental in understanding, for example, the impact of noise or synchronous spikes on signal transmission, or the emergence of oscillatory activity. At higher signal-to-noise ratios, however, the third term in the Volterra series becomes relevant. This second-order susceptibility captures nonlinear interactions between pairs of stimulus frequencies. Theoretical results for leaky integrate-and-fire neurons suggest strong responses at the sum of two input frequencies only when these frequencies or their sum match the neuron's baseline firing rate. We here analyze second-order susceptibilities in two types of primary electroreceptor afferents, P-units of the active and ampullary cells of the passive electrosensory system of the wave-type electric fish \textit{Apteronotus leptorhynchus}. In our combined experimental and modeling approach we find the predicted weakly nonlinear responses in some P-units with very low baseline interspike-interval variability and much stronger in all ampullary cells, which are less noisy than P-units. Such nonlinear responses boost responses to weak sinusoidal stimuli and are therefore of immediate relevance for wave-type electric fish that are exposed to superpositions of many frequencies in social contexts. - -% Please keep the Author Summary between 150 and 200 words -% Use the first person. PLOS ONE authors please skip this step. -% Author Summary not valid for PLOS ONE submissions. -%\section{Author summary} -%Weakly electric fish use their self-generated electric field to detect a wide range of behaviorally relevant stimuli. Intriguingly, they show detection performances of stimuli that are (i) extremely weak and (ii) occur in the background of strong foreground signals, reminiscent of what is often described as the cocktail party problem. Such performances are achieved by boosting the signal detection through nonlinear mechanisms. We here analyze nonlinear encoding in two different populations of primary electrosensory afferents of the weakly electric fish. We derive the rules under which nonlinear effects can be observed in both electrosensory subsystems. In a combined experimental and modeling approach we generalize the approach of nonlinear susceptibility to systems that respond to amplitude modulations of a carrier signal. - - -\section{Introduction} - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{plot_chi2.pdf} - \caption{\label{fig:lifresponse} First- (linear) and second-order response functions of the leaky integrate-and-fire model. \figitem{A} Magnitude of the first-order response function $|\chi_1(f_1)|$, also known as ``gain'' quantifies the response amplitude relative to the stimulus amplitude, both measured at the stimulus frequency. \figitem{B} Magnitude of the second-order response function $|\chi_2(f_1, f_2)|$ quantifies the response at the sum of two stimulus frequencies. For linear systems, the second-order response function is zero, because linear systems do not create new frequencies and thus there is no response at the summed frequencies. The plots show the analytical solutions from \citep{Lindner2001} and \citep{Voronenko2017} with $\mu = 1.1$ and $D = 0.001$.} -\end{figure*} - -Nonlinear processes are key to neuronal information processing. Decision-making is a fundamentally nonlinear process on the systemic level. On the cellular level, spiking neurons are inherently nonlinear: whether an action potential is elicited depends on the membrane potential to exceed a threshold \citep{Hodgkin1952, Koch1995}. Because of such nonlinearities, understanding and predicting neuronal responses to sensory stimuli is in general a difficult task. - -At the heart of nonlinear system identification is the Volterra series \citep{Rieke1999}. Second-order kernels have been used to predict firing rate responses of catfish retinal ganglion cells \citep{Marmarelis1972}. -In the frequency domain, second-order kernels are known as second-order response functions or susceptibilities. They quantify the amplitude of the response at the sum and difference of two stimulus frequencies. Adding also third-order kernels, spike trains of spider mechanoreceptors have been predicted from sensory stimuli \citep{French2001}. The nonlinear nature of Y cells in contrast to the more linear responses of X cells in cat retinal ganglion cells has been demonstrated using second-order kernels \citep{Victor1977}. Interactions between different frequencies in the response of neurons in visual cortices of cats and monkeys have been studied using bispectra, the crucial constituent of the second-order susceptibility \citep{Schanze1997}. Locking of chinchilla auditory nerve fibers to pure tone stimuli is captured by second-order kernels \citep{Temchin2005}. In paddlefish ampullary afferents, bursting in response to strong, natural sensory stimuli boosts nonlinear responses in the bicoherence, the bispectrum normalized by stimulus and response spectra \citep{Neiman2011}. - -Noise linearizes nonlinear systems \citep{Yu1989, Chialvo1997} and therefore noisy neural systems can be well described by linear response theory in the limit of small stimulus amplitudes \citep{Roddey2000, Doiron2004, Rocha2007, Sharafi2013}. When increasing stimulus amplitude, at first the contribution of the second-order kernel of the Volterra series becomes relevant in addition to the linear one. For these weakly nonlinear responses of leaky-integrate-and-fire (LIF) neurons, an analytical expression for the second-order susceptibility has been derived \citep{Voronenko2017} in addition to its linear response function \citep{Lindner2001}. In the superthreshold regime, where the LIF generates a baseline firing rate in the absence of an external stimulus, the linear response function has a peak at the baseline firing rate and its harmonics (\subfigrefb{fig:lifresponse}{A}) and the second-order susceptibility shows very distinct ridges of elevated nonlinear responses, exactly where two stimulus frequencies equal or add up to the neuron's baseline firing rate (\subfigrefb{fig:lifresponse}{B}). In experimental data, such structures in the second-order susceptibility have not been reported yet. - -Here we study weakly nonlinear responses in two electrosensory systems in the wave-type electric fish \textit{Apteronotus leptorhynchus}. These fish generate a quasi-sinusoidal dipolar electric field (electric organ discharge, EOD). In communication contexts \citep{Walz2014, Henninger2018} the EODs of close-by fish superimpose and lead to amplitude modulations (AMs), called beats (two-fish interaction), and modulations of beats, called envelopes (multiple-fish interaction) \citep{Yu2005, Fotowat2013}. Therefore, stimuli with multiple distinct frequencies are part of the everyday life of wave-type electric fish \citep{Benda2020} and interactions of these frequencies in the electrosensory periphery are to be expected. P-type electroreceptor afferents of the tuberous electrosensory system, the P-units, use nonlinearities to extract and encode these AMs in their time-dependent firing rates \citep{Bastian1981a, Walz2014, Middleton2006, Stamper2012Envelope, Savard2011, Barayeu2023}. P-units are heterogeneous in their baseline firing rates as well as in their intrinsic noise levels, as quantified by the coefficient of variation (CV) of the interspike intervals (ISI) \citep{Grewe2017, Hladnik2023}. Low-CV P-units have a less noisy firing pattern that is closer to pacemaker firing, whereas high-CV P-units show a more irregular firing pattern that is closer to a Poisson process. On the other hand, ampullary cells of the passive electrosensory system are homogeneous in their response properties and have very low CVs \citep{Grewe2017}. - -Field observations have shown that courting males were able to react to distant intruder males despite the strong EOD of the nearby female \citep{Henninger2018}. Weakly nonlinear responses are of direct relevance in this setting since they could boost responses to the faint signal of the distant intruder and thus improve detection \citep{Schlungbaum2023}. - - - -%\notejb{in Voronenko they talk about second-order response functions and not of susceptibilities}\notesr{Ja das ist wahr, aber so wie ich das verstehe sind das synonyme, oder etwa nicht?} - - - -\section{Results} - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{motivation.pdf} - \caption{\label{fig:motivation} Nonlinearity in an electrophysiologically recorded P-unit of \lepto{} in a three-fish setting (cell identifier ``2021-08-03-ac"). Receiver with EOD frequency $\feod{} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both encountered fish lead to a beat contrast of 10\,\%. Top: Scheme of a nonlinear system. Second row: Interference of the receiver EOD with the EODs of other fish. Third row: Spike trains of the P-unit. Fourth row: Firing rate, retrieved as the convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem{A} Baseline condition: Only the receiver is present. The baseline firing rate \fbase{} dominates the power spectrum of the firing rate. \figitem{B} The receiver and the fish with EOD frequency $f_{1}=631$\,Hz are present. \figitem{C} The receiver and the fish with EOD frequency $f_{2}=797$\,Hz are present. \figitem{D} All three fish with the EOD frequencies \feod{}, $f_{1}$ and $f_{2}$ are present. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate. - } -\end{figure*} - -Theoretical work on leaky integrate-and-fire and conductance-based models suggests a distinct structure of the second-order response function for neurons with low levels of intrinsic noise driven in the super-threshold regime with low stimulus amplitudes (\figrefb{fig:lifresponse}, \citealp{Voronenko2017}). Here, we re-analyze a large set of recordings of P-units and ampullary cells of the active and passive electrosensory systems of the brown ghost knifefish \textit{Apteronotus leptorhynchus} together with simulations of LIF-based models of P-unit spiking to search for such weakly nonlinear responses in real neurons. We start with a few example P-units to demonstrate the basic concepts. - - -\subsection{Nonlinear responses in P-units stimulated with two beat frequencies} - - - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{nonlin_regime.pdf} - \caption{\label{fig:nonlin_regime} Nonlinear response of a model P-unit to increasing beat amplitudes in a three-fish or two-beat setting. The model used has the cell identifier 2013-01-08-aa (table~\ref{modelparams}). \figitem{A--D}. Top -- stimulus consisting of two beats, with different contrasts. The beat frequencies are 30\,Hz (\bone{}) and 130\,Hz (\btwo{}). \btwo{} is equal to the baseline firing rate \fbase{}. The contrasts of both beats are equal in a panel, and increase from \panel{A} to \panel{D}. Middle -- spike response of the model P-unit to the stimulus above. Bottom -- power spectrum of the firing rate of this P-unit model. Nonlinear effects at \bsum{} (orange marker) in the power spectrum of the P-unit firing rate increase for intermediate contrasts (\panel{B}), decrease for stronger contrasts (\panel{C}) and again increase for very strong contrasts (\panel{D}). \figitem{E} Amplitude of the linear (\bone{}, \btwo{}) and nonlinear (\bdiff{}, \bsum{}) responses of the model P-units plotted for increasing beat contrasts (contrasts increase equally for both beats). } -\end{figure*} - - -Without any external stimulation, a P-unit fires action potentials at a spontaneous baseline rate \fbase{} to the fish's own EOD of frequency \feod{}. Accordingly, a peak at \fbase{} is present in the power spectrum of this baseline activity (\subfigrefb{fig:motivation}{A}). Superposition of the receiver's EOD with an EOD of another fish with frequency $f_1$ results in a beat, a periodic amplitude modulation of the receiver's EOD. The frequency of the beat is given by the difference frequency $\Delta f_1 = f_1 - \feod$ between the two fish. P-units encode this beat in their firing rate \citep{Bastian1981a, Barayeu2023} and consequently, a peak at this beat frequency appears the the power spectrum of the response (\subfigrefb{fig:motivation}{B}). A second peak at the first harmonic indicates a nonlinear response that here is easily identified by the clipping of the P-unit's firing rate at zero. Pairing the fish with another fish with a higher beat frequency $\Delta f_2 = f_2 - \feod$ results in a weaker response with a single peak in the response power spectrum (\subfigrefb{fig:motivation}{C}). Note that $\Delta f_2$ has been chosen to match the P-unit's baseline firing rate. - - -When stimulating the fish with both frequencies, additional peaks appear in the response power spectrum at the sum \bsum{} and the difference frequency \bdiff{} (\subfigrefb{fig:motivation}{D}). Thus, the response is not equal to the sum of the responses to the two beats presented separately. These peaks at the sum and the difference of the two stimulus frequencies are a hallmark of nonlinear interactions that by definition are absent in linear systems. - - -The beat stimuli in the example were strong and partially revealed saturating nonlinearities of the P-units. For weakly nonlinear responses we need to use stimuli of much lower amplitudes. - - -The response of a P-unit to varying beat amplitudes can be modeled by a leaky-integrate-and-fire (LIF) model, fitted to the baseline firing properties an electrophysiologically measured P-unit. In the chosen P-unit model nonlinear peaks (orange marker) appear for intermediate beat contrasts (\subfigrefb{fig:motivation}{B}), decrease for stronger contrasts (\subfigrefb{fig:motivation}{C}) and again emerges for very strong beat contrasts (\subfigrefb{fig:motivation}{D}). Thus two regimes of nonlinearity can be observed for intermediate and strong beat amplitudes (\subfigrefb{fig:motivation}{E}). - -For this example, we have chosen two specific stimulus (beat) frequencies. For a full characterization of the nonlinear responses, we need to measure the response of the P-units to many different combinations of stimulus frequencies. - - - - - -\subsection{Nonlinear signal transmission in low-CV P-units} -Weakly nonlinear responses are expected in cells with sufficiently low intrinsic noise levels, i.e. low baseline CVs \citep{Voronenko2017}. P-units fire action potentials probabilistically phase-locked to the self-generated EOD \citep{Bastian1981a}. Skipping of EOD cycles leads to the characteristic multimodal ISI distribution with maxima at integer multiples of the EOD period (\subfigrefb{fig:cells_suscept}{A}). In this example, the baseline ISI distribution has a CV$_{\text{base}}$ of 0.2, which is at the lower end of the P-unit population \citep{Hladnik2023}. Spectral analysis of the baseline activity shows two major peaks: the first is located at the baseline firing rate \fbase, the second is located at the discharge frequency \feod{} of the electric organ and is flanked by two smaller peaks at $\feod \pm \fbase{}$ (\subfigref{fig:cells_suscept}{B}). - - -\begin{figure*}[t] -\includegraphics[width=\columnwidth]{cells_suscept.pdf} -\caption{\label{fig:cells_suscept} Linear and nonlinear stimulus encoding in a low-CV P-unit (cell identifier ``2010-06-21-ai"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) measures the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \Eqnref{linearencoding_methods}, computed from the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation of 10\,s duration. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.} -\end{figure*} - -Noise stimuli, here random amplitude modulations (RAM) of the EOD (\subfigref{fig:cells_suscept}{C}, top trace, red line), are commonly used to characterize stimulus-driven responses of sensory neurons using transfer functions (first-order susceptibility), spike-triggered averages, or stimulus-response coherences. Here, we additionally estimate the second-order susceptibility to quantify nonlinear encoding. P-unit spikes align more or less clearly with fluctuations in the RAM stimulus. A higher stimulus intensity, here a higher contrast of the RAM relative to the EOD amplitude (see methods), entrains the P-unit response more clearly (light and dark purple for low and high contrast stimuli, \subfigrefb{fig:cells_suscept}{C}). Linear encoding, quantified by the transfer function \Eqnref{linearencoding_methods}, is similar for the two RAM contrasts in this low-CV P-unit (\subfigrefb{fig:cells_suscept}{D}), as expected for a linear system. The first-order susceptibility is low for low frequencies, peaks in the range below 100\,Hz and then falls off again% \notejb{Cite Moe paper?}. - -The second-order susceptibility, \Eqnref{eq:susceptibility}, quantifies the amplitude and phase of the stimulus-evoked response at the sum \fsum{} for each combination of two stimulus frequencies \fone{} and \ftwo{}. Large values of the second-order susceptibility indicate stimulus-evoked peaks in the response spectrum at the summed frequency that cannot be explained by linear response theory. Similar to the first-order susceptibility, the second-order susceptibility can be estimated directly from the response evoked by a RAM stimulus that simulates the neuron with a whole range of frequencies simultaneously (\subfigsref{fig:cells_suscept}{E, F}). For a LIF driven in the super-threshold regime, theory predicts nonlinear interactions between the two stimulus frequencies, when the two frequencies \fone{} and \ftwo{} or their sum \fsum{} exactly match the neuron's baseline firing rate \fbase{} \citep{Voronenko2017}. Only then, additional stimulus-evoked peaks appear in the spectrum of the spiking response that would show up in the second-order susceptibility as a horizontal, a vertical, and an anti-diagonal line (\subfigrefb{fig:lifresponse}{B}, pink triangle in \subfigsref{fig:cells_suscept}{E, F}). - -For the low-CV P-unit, we observe a band of slightly elevated second-order susceptibility for the low RAM contrast at \fsumb{} (yellowish anti-diagonal between pink edges, \subfigrefb{fig:cells_suscept}{E}). This structure vanishes for the stronger stimulus (\subfigref{fig:cells_suscept}{F}). Further, the overall level of the second-order susceptibility is reduced with increasing stimulus strength. To quantify the structural changes in the susceptibility matrices we projected susceptibility values onto the diagonal by taking the mean over all anti-diagonals (\subfigrefb{fig:cells_suscept}{G}). For the low RAM contrast this projected second-order susceptibility indeed has a small peak at \fbase{} (\subfigrefb{fig:cells_suscept}{G}, dot on top line). For the higher RAM contrast, however, this peak vanishes and the overall level of the second-order susceptibility is reduced (\subfigrefb{fig:cells_suscept}{G}). The reason behind this reduction is that a RAM with a higher contrast is not only a stimulus with an increased amplitude, but also increases the total noise in the system. Increased noise is known to linearize signal transmission \citep{Longtin1993, Chialvo1997, Roddey2000, Voronenko2017} and thus the second-order susceptibility is expected to decrease. - -In contrast, a high-CV P-unit (CV$_{\text{base}}=0.4$) does not exhibit pronounced nonlinearities even at low stimulus contrasts (\figrefb{fig:cells_suscept_high_CV}). - - -\subsection{Ampullary afferents exhibit strong nonlinear interactions} - -\begin{figure*}[t] -\includegraphics[width=\columnwidth]{ampullary.pdf} - \caption{\label{fig:ampullary} Linear and nonlinear stimulus encoding in an ampullary afferent (cell identifier ``2012-04-26-ae"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, with a cutoff frequency of 150\,Hz) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \Eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green) of 10\,s duration. \figitem{E, F} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate the baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. } -\end{figure*} - -Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. Electric fish possess an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogenous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.06$--$0.22$) \citep{Grewe2017}. Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and its harmonics. Since the cells do not fire phase-locked to the EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is not an AM but a stimulus that is added to the self-generated EOD, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal loses its distinct peak at \fsum{} and its overall level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). - - -\subsection{Model-based estimation of the nonlinear structure} -In the example recordings shown above (\figsrefb{fig:cells_suscept} and \fref{fig:ampullary}), we only observe nonlinear responses on the anti-diagonal of the second-order susceptibility, where the sum of the two stimulus frequencies matches the neuron's baseline firing rate, which is in line with theoretical expectations \citep{Voronenko2017}. However, a pronounced nonlinear response at frequencies \foneb{} or \ftwob{}, although predicted by theory, cannot be observed. Here we investigate how these discrepancies can be understood. - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{model_and_data.pdf} - \caption{\label{model_and_data} Estimation of second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ 0.5\,s long trials of an electrophysiological recording of another low-CV P-unit (cell 2012-07-03-ak, $\fbase=120$\,Hz, CV=0.20) driven with a weak RAM stimulus with contrast 2.5\,\%. Pink edges mark the baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of trials as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ stimulus repetitions. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as a signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). In addition to one million trials, this reveals the full expected structure of the second-order susceptibility.} -\end{figure*} - -%\notejb{Since the model overestimated the sensitivity of the real P-unit, we adjusted the RAM contrast to 0.9\,\%, such that the resulting spike trains had the same CV as the electrophysiological recorded P-unit during the 2.5\,\% contrast stimulation (see table~\ref{modelparams} for model parameters).} \notejb{chi2 scale is higher than in real cell} - -One reason could be simply too little data for a good estimate of the second-order susceptibility. Electrophysiological recordings are limited in time, and therefore responses to only a limited number of trials, i.e. repetitions of the same RAM stimulus, are available. As a consequence, the cross-spectra, \Eqnref{eq:crosshigh}, are insufficiently averaged and the full structure of the second-order susceptibility might be hidden in finite-data noise. This experimental limitation can be overcome by using a computational model for the P-unit, a stochastic leaky integrate-and-fire model with adaptation current and dendritic preprocessing, and parameters fitted to the experimentally recorded P-unit (\figrefb{flowchart}) \citep{Barayeu2023}. The model faithfully reproduces the second-order susceptibility of a low-CV cell estimated from the same low number of trials as in the experiment ($\n{}=11$, compare \panel{A} and \panel[ii]{B} in \figrefb{model_and_data}). - -In simulations of the model, we can increase the number of trials beyond what would be experimentally possible, here to one million (\subfigrefb{model_and_data}\,\panel[iii]{B}). The estimate of the second-order susceptibility indeed improves. It gets less noisy and the diagonal at \fsum{} is emphasized. However, the expected vertical and horizontal lines at \foneb{} and \ftwob{} are still mainly missing. - -Using a broadband stimulus increases the effective input-noise level and this may linearize signal transmission and suppress potential nonlinear responses \citep{Longtin1993, Chialvo1997, Roddey2000, Voronenko2017}. Assuming that the intrinsic noise level in this P-unit is small enough, the full expected structure of the second-order susceptibility should appear in the limit of weak AMs. Again, this cannot be done experimentally, because the problem of insufficient averaging becomes even more severe for weak AMs (low contrast). In the model, however, we know the time course of the intrinsic noise and can use this knowledge to determine the susceptibilities by input-output correlations via the Furutsu-Novikov theorem \citep{Furutsu1963, Novikov1965}. This theorem, in its simplest form, states that the cross-spectrum $S_{x\eta}(\omega)$ of a Gaussian noise $\eta(t)$ driving a nonlinear system and the system's output $x(t)$ is proportional to the linear susceptibility according to $S_{x\eta}(\omega)=\chi(\omega)S_{\eta\eta}(\omega)$. Here $\chi(\omega)$ characterizes the linear response to an infinitely weak signal $s(t)$ in the presence of the background noise $\eta(t)$. Likewise, the nonlinear susceptibility can be determined in an analogous fashion from higher-order input-output cross-spectra (see methods, equations \eqref{eq:crosshigh} and \eqref{eq:susceptibility}) \citep{Egerland2020}. In line with an alternative derivation of the Furutsu-Novikov theorem \citep{Lindner2022}, we can split the total noise and consider a fraction of it as a stimulus. This allows us to calculate the susceptibility from the cross-spectrum between the output and this stimulus fraction of the noise. Adapting this approach to our P-unit model (see methods), we replace the intrinsic noise by an approximately equivalent RAM stimulus $s_\xi(t)$ and a weak remaining intrinsic noise $\sqrt{2D \, c_{\rm{noise}}} \cdot \xi(t)$ with $c_\text{noise} = 0.1$ (see methods, equations \eqref{eq:ram_split}, \eqref{eq:Noise_split_intrinsic}, \eqref{eq:Noise_split_intrinsic_dendrite}, \subfigrefb{model_and_data}\,\panel[i]{C}). We tune the amplitude of the RAM stimulus $s_\xi(t)$ such that the output firing rate and variability (CV) are the same as in the baseline activity (i.e. full intrinsic noise $\sqrt{2D}\xi(t)$ in the voltage equation but no RAM) and compute the cross-spectra between the RAM part of the noise $s_\xi(t)$ and the output spike train. This procedure has two consequences: (i) by means of the cross-spectrum between the output and \signalnoise, which is a large fraction of the noise, the signal-to-noise ratio of the measured susceptibilities is drastically improved; (ii) the total noise in the system has been reduced (by what was before the external RAM stimulus $s(t)$), which makes the system more nonlinear. For both reasons we now see the expected nonlinear features in the second-order susceptibility for a sufficient number of trials (\subfigrefb{model_and_data}\,\panel[iii]{C}), but not for a number of trials comparable to the experiment (\subfigrefb{model_and_data}\,\panel[ii]{C}). In addition to the strong response for \fsumb{}, we now also observe pronounced nonlinear responses at \foneb{} and \ftwob{} (vertical and horizontal lines, \subfigrefb{model_and_data}\,\panel[iii]{C}). - -Note, that the increased number of trials goes along with a substantial reduction of second-order susceptibility values (\subfigrefb{model_and_data}\,\panel[iii]{C}), that saturate in its peak values for $N>10^6$ (\figrefb{fig:trialnr}). This demonstrates the limited reliability of an estimate of the second-order susceptibility that is based on 11 trials only. However, we would like to point out that already the limited number of trials used in the experiments reveals key features of the nonlinear response. - -With high levels of intrinsic noise, we would not expect the nonlinear response features to survive. Indeed, we do not find these features in a high-CV P-unit and its corresponding model (not shown). - - -\subsection{Second-order susceptibility can explain nonlinear peaks in pure sinewave stimulation} -We estimated the second-order susceptibility of P-unit responses using RAM stimuli. In particular, we found pronounced nonlinear responses in the limit of weak stimulus amplitudes. How do these findings relate to the situation of two pure sinewave stimuli with finite amplitudes that approximate the interference of EODs of real animals? For the P-units, the relevant signals are the beat frequencies \bone{} and \btwo{} that arise from the interference of either of the two foreign EODs with the receiving fish's own EOD (\figref{fig:motivation}). In the introductory example, the response power spectrum showed peaks from nonlinear interactions at the sum of the two beat frequencies (orange marker, \subfigrefb{fig:motivation}{D}) and at the difference between the two beat frequencies (red marker, \subfigrefb{fig:motivation}{D}). In this example, $\Delta f_{2}$ was similar to \fbase{}, corresponding to the horizontal line of the second-order susceptibility estimated for a vanishing external RAM stimulus (\subfigrefb{model_and_data}\,\panel[iii]{C}). In the three-fish example, there was a second nonlinearity at the difference between the two beat frequencies (red dot, \subfigrefb{fig:motivation}{D}), that is not covered by the so-far shown part of the second-order susceptibility (\subfigrefb{model_and_data}\,\panel[iii]{C}), in which only the response at the sum of the two stimulus frequencies is addressed. % less prominent, - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{model_full.pdf} - \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility, \Eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ trials of model simulations in the noise-split condition (cell 2013-01-08-aa, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants. Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. The baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters corresponds to the beat frequencies used for the stimulation with pure sine waves in the subsequent panels and indicates the sum/difference of those beat frequencies. \figitem{B--E} Black line -- power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three-fish scenario). The contrast of beat beats is 0.02. Colored circles highlight the height of selected peaks in the power spectrum. Grey line -- power spectral density of model in the baseline condition. \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{E} None of the two beat frequencies matches \fbase{}.} -\end{figure*} - -However, the second-order susceptibility \Eqnref{eq:susceptibility} is a spectral measure that is based on Fourier transforms and thus is also defined for negative stimulus frequencies. The full \susceptf{} matrix is symmetric with respect to the origin. In the upper-right and lower-left quadrants of \susceptf{}, stimulus-evoked responses at \fsum{} are shown, whereas in the lower-right and upper-left quadrants nonlinear responses at the difference \fdiff{} are shown (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigrefb{fig:model_full}{A} for nonlinear responses at \fsum{} and extend into the upper-left quadrant (representing \fdiff) where they fade out towards more negative $f_1$ frequencies. The peak in the response power-spectrum at \fdiff{} evoked by pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) is predicted by the horizontal line in the upper-left quadrant (\subfigrefb{fig:model_full}{A}, \citealp{Schlungbaum2023}). -Is it possible based on the second-order susceptibility estimated by means of RAM stimuli (\subfigrefb{fig:model_full}{A}) to predict nonlinear responses in a three-fish setting? We can test this by stimulating the same model with two beats with weak amplitudes (\subfigrefb{fig:model_full}{B--E}). If we choose a frequency combination where the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{B}), as expected from \suscept. If instead we choose two beat frequencies that differ by \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{C}). If only one beat frequency is equal to \fbase{}, both a peak at the sum and at the difference frequency are present in the P-unit response (\subfigrefb{fig:model_full}{D}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{E}). - -\begin{figure*}[tp] - \includegraphics[width=\columnwidth]{data_overview_mod.pdf} - \caption{\label{fig:data_overview} Nonlinear responses in P-units and ampullary cells. The second-order susceptibility is condensed into the peakedness of the nonlinearity, \nli{} \Eqnref{eq:nli_equation}, that relates the amplitude of the projected susceptibility at a cell's baseline firing rate to its median (see \subfigrefb{fig:cells_suscept}{G}). Each of the recorded neurons contributes at maximum with two stimulus contrasts. Black squares and circles highlight recordings conducted in a single cell. Squares in \panel{A, C, E} correspond to the cell in \figrefb{fig:cells_suscept} and circles to the cell in \figrefb{fig:cells_suscept_high_CV}. Squares in \panel{B, D, F} correspond to the cell in \figrefb{fig:ampullary}. \figitem{A, B} There is a negative correlation between the CV during baseline and \nli. \figitem{C, D} There is a negative correlation between the CV during stimulation and \nli. \figitem{E, F} \nli{} is plotted against the response modulation, (see methods), an indicator of the subjective stimulus strength for a cell. There is a negative correlation between response modulation and \nli. Restricting the analysis to the weakest stimulus that was presented to each unique neuron, does not change the results. The number of unique neurons is 221 for P-units and 45 for ampullary cells. - % The two example P-units shown before are highlighted with dark markers in \subfigrefb{fig:data_overview}{A, C, E} (squares -- \figrefb{fig:cells_suscept}, circles -- \figrefb{fig:cells_suscept_high_CV}). - % Several of the recorded neurons contribute with two samples to the population analysis as their responses have been recorded to two different contrasts of the same RAM stimulus. Higher stimulus contrasts lead to a stronger drive and thus stronger response modulations (see color code bar in \subfigref{fig:data_overview}{A}, see methods). - % The example cell shown above (\figref{fig:ampullary}) was recorded at two different stimulus intensities and the \nli{} values are highlighted with black squares. - } -\end{figure*} - -%\Eqnref{response_modulation} -\subsection{Low CVs and weak stimuli are associated with strong nonlinearity} -All the statements about nonlinear encoding in p-type and ampullary electroreceptor afferents based on single-cell examples shown above are supported by the analysis of our pool of 221 P-units and 47 ampullary afferents recorded in 71 specimens. For comparison across cells we summarize the structure of the second-order susceptibilities in a single number, the peakedness of the nonlinearity \nli{} \Eqnref{eq:nli_equation}, that characterizes the size of the expected peak of the projections of a \suscept{} matrix onto its diagonal at the baseline firing rate (e.g. \subfigref{fig:cells_suscept}{G}). \nli{} assumes high values when the peak at \fbase{} is pronounced relative to the median of projections onto the diagonal and is small when there is no distinct peak. The \nli{} values of the P-unit population depend weakly on the CV of the baseline ISI distribution. Cells with lower baseline CVs tend to have more pronounced peaks in their projections than those that have high baseline CVs (\subfigrefb{fig:data_overview}{A}). This negative correlation is more pronounced against the CV measured during stimulation (\subfigrefb{fig:data_overview}{C}). - -The effective stimulus strength also plays an important role. We quantify the effect a stimulus has on a cell's response by the response modulation --- the standard deviation of a cell's firing rate in response to a RAM stimulus. P-units are heterogeneous in their sensitivity, their response modulations to the same stimulus contrast vary a lot \citep{Grewe2017}. Cells with weak responses to a stimulus, be it an insensitive cell or a weak stimulus, have higher \nli{} values and thus a more pronounced ridge in the second-order susceptibility at \fsumb{} in comparison to strongly responding cells that basically have flat second-order susceptibilities (\subfigrefb{fig:data_overview}{E}). How pronounced nonlinear response components are in P-units thus depends on the baseline CV (a proxy for the internal noise level), and both the CV and response strength during stimulation (effective output noise). -%(Pearson's $r=-0.35$, $p<0.001$)221 P-units and 47 (Pearson's $r=-0.16$, $p<0.01$) -%In a P-unit population where each cell is represented not by several contrasts but by the lowest recorded contrast, \nli{} significantly correlates with the CV during baseline ($r=-0.17$, $p=0.01$), the response modulation ($r=-0.35$, $p<0.001$) and \fbase{} ($r=-0.32$, $p<0.001$).%, $\n{}=221$*, $\n{}=221$******, $\n{}=221$ - -The population of ampullary cells is generally more homogeneous, with lower baseline CVs than P-units. Accordingly, \nli{} values of ampullary cells are indeed much higher than in P-units by about a factor of ten. Ampullary cells also show a negative correlation with baseline CV. Again, sensitive cells with strong response modulations are at the bottom of the distribution and have \nli{} values close to one (\subfigrefb{fig:data_overview}{B, D}). The weaker the response modulation, because of less sensitive cells or weaker stimulus amplitudes, the stronger the nonlinear component of a cell's response (\subfigrefb{fig:data_overview}{F}). -%(Pearson's $r=-0.35$, $p < 0.01$) (Pearson's $r=-0.59$, $p < 0.0001$) - -\section{Discussion} - - -%\notejb{Even though the extraction of the AM itself requires a \notejb{nonlinearity} \citep{Middleton2006, Stamper2012Envelope, Savard2011, Barayeu2023} encoding the time-course of the AM is linear over a wide range of AM amplitudes and frequencies \citep{Xu1996, Benda2005, Gussin2007, Grewe2017, Savard2011}. In the context of social signaling among three fish, we observe an AM of the AM, also referred to as second-order envelope or just social envelope \citep{Middleton2006, Savard2011, Stamper2012Envelope}. Encoding this again requires nonlinearities \citep{Middleton2006} and it was shown that a subpopulation of P-units is sensitive to envelopes \citep{Savard2011} and exhibit nonlinearities e.g. when driven by strong stimuli \citep{Nelson1997, Chacron2004}.} - -%\notejb{Leftovers from introduction} -%\notejb{Phase-locking to the own field also leads to a representation of \feod{} in the P-unit firing rate (see \figref{fig:cells_suscept}\panel{B}) \citep{Sinz2020}.} - - -%\notejb{The appearing difference peak is known as the social envelope \citep{Stamper2012Envelope, Savard2011}. The neuron shown here clearly encodes the envelope. Whether P-units in general encode envelopes has been the subject of controversy, some works do not consider P-units as envelope encoders \citep{Middleton2006}, while others identify some P-units as envelope encoders \citep{Savard2011}. } - - -%\notejb{Weakly nonlinear responses versus saturation regime} - - -%\notejb{Estimating the infinite Volterra series from limited experimental data is usually limited to the first two or three kernels, which might not be sufficient for a proper prediction of the neuronal response \citep{French2001}. Making assumptions about the nonlinearities in a system reduces the amount of data needed for parameter estimation. In particular, models combining linear filtering with static nonlinearities \citep{Chichilnisky2001}, have been successful in capturing functionally relevant neuronal computations in visual \citep{Gollisch2009} as well as auditory systems \citep{Clemens2013}. On the other hand, linear methods based on backward models for estimating the stimulus from neuronal responses, have been extensively used to quantify information transmission in neural systems \citep{Theunissen1996, Borst1999, Wessel1996, Chacron?}, because backward models do not need to generate action potentials \citep{Rieke1999}.} - - -%\notejb{Note in the discussion that \suscept{} predicts stimulus-evoked responses whereas in the power spectrum, we see peaks even if they are unrelated to the stimulus. Like the baseline firing rate.} - -% TO DISCUSSION: -%Even though the second-order susceptibilities here were estimated from data and models with a modulated (EOD) carrier (\figrefb{fig:model_full}) they are in good accordance with the second-order susceptibilities found in LIF models without a carrier \citep{Voronenko2017, Schlungbaum2023}. - - -%\,\panel[iii]{C} -\subsection{Theory applies to systems with and without carrier} -Theoretical work \citep{Voronenko2017} explained analytically the occurrence of nonlinear products when a LIF model neuron is stimulated with pure sine waves. To investigate whether the same mechanisms occur in electroreceptor afferents which are driven by AMs of a carrier and not by pure sine-waves, we followed the previous approach and quantified the second-order susceptibility from responses to white-noise stimuli \citep{Voronenko2017, Egerland2020, Neiman2011fish, Nikias1993}. We expected to see elevated second-order susceptibility where either of the foreign signals matches the baseline firing rate ($f_1=\fbase{}$ or $f_2=\fbase{}$) or when the sum equals the baseline firing rate of the neuron (\fsumb{}) creating a triangular pattern of elevated \suscept{} e.g.\,\subfigref{model_and_data}\,\panel[iii]{C}. Indeed, we find traces of the same nonlinearities in the neuronal responses of p-type electroreceptor afferents. The nonlinear pattern observed in the experimental data, however, matches the expectations only partially and only in a subset of neurons (\figsref{fig:cells_suscept} and \ref{fig:ampullary}). Nevertheless, the theory holds also for systems that are driven by AMs of a carrier and is thus more widely applicable. - -\subsection{Intrinsic noise limits nonlinear responses} -Only those P-units that exhibit low coefficients of variation (CV) of the interspike-interval distribution (\subfigref{fig:cells_suscept}{A}) in their unperturbed baseline response show the expected nonlinearities (\subfigref{fig:data_overview}{A}). Such low-CV cells are rare among the 221 P-units that we used in this study. The afferents of the passive electrosensory system, the ampullary cells, however, have generally lower CVs and show a much clearer nonlinearity pattern than the low-CV P-unit exemplified here (compare \figsref{fig:cells_suscept} and \ref{fig:ampullary}). The single ampullary cell featured in \figref{fig:ampullary} is representative of the majority of ampullary cells analyzed here. All ampullary cells have CVs below 0.4 with a median around 0.12 and the observed \nli{}s are 10-fold higher than in P-units. - -The CV serves as a proxy for the intrinsic noise in the cells. In both cell types, we observe a negative correlation between \nli{} and the CV, indicating that it is the level of intrinsic noise that plays a role here. These findings are in line with previous studies that propose that noise linearizes the system \citep{Roddey2000, Chialvo1997, Voronenko2017}. More intrinsic noise has been demonstrated to increase the CV and reduce nonlinear phase-locking in vestibular afferents \citep{Schneider2011}. Reduced noise, on the other hand, has been associated with stronger nonlinearity in pyramidal cells of the ELL \citep{Chacron2006}. Further support for the notion of noise limiting the nonlinearity comes from our P-unit LIF model that faithfully reproduces P-unit activity \citep{Barayeu2023}. We can use this model and apply a noise-split \citep{Lindner2022} based on the Furutsu-Novikov theorem \citep{Novikov1965, Furutsu1963}, to increase the signal-to-noise ratio in the cell while keeping the overall response variability constant (see methods). Treating 90\,\% of the total noise as a signal and simulating large numbers of trials uncovers the full nonlinear structure (\figref{model_and_data}) seen in LIF neurons and the analytical derivations when driven with sine-wave stimuli \citep{Voronenko2017}. - -% -\subsection{Noise stimulation approximates the real three-fish interaction} -Our analysis is based on the neuronal responses to white noise stimulus sequences. For the P-units, the stimulus was a random amplitude modulation (RAM) while it was a direct noise stimulus for the ampullary cells. These broad-band stimuli have the advantage that all behaviorally relevant frequencies can be measured with a single stimulus presentation and it is a widely used approach to characterize sensory coding \citep{French1973, Marmarelis1999, Borst1999, Chacron2005, Grewe2017}. However, these stimuli also increase the total level of noise in the system and may have a linearizing effect on signal transmission. In our P-unit models, we were able to make use of the Furutsu-Novikov theorem to estimate nonlinear signal transmission for zero-amplitude stimulation. Only with this procedure and many trials, we find for low-CV P-units all the pronounced ridges in the second-order susceptibility that we would expect according to theory \citep{Voronenko2017}. - -In the natural situation, the stimuli are periodic signals defined by the difference frequencies. How well can we extrapolate from the white noise analysis to the pure sinewave situation? %\notejg{Predictions from the X2 matrix and the equations in Voronekov} - -In contrast to the situation with individual frequencies (direct sine-waves or sinusoidal AMs) during noise stimulation, the total power of the stimulus is equally distributed on all frequencies leading to a weaker signal-to-noise ratio. This explains that the nonlinearity pattern in the electroreceptor recordings only partially matches the expectation (\figsref{fig:cells_suscept},\,\ref{fig:ampullary}) while the single-frequency stimulation shows nonlinear interference when the individual stimulus frequencies ($f_1, f_2, \Delta f_1, \Delta f_2$) match the baseline firing rate (\figref{fig:motivation}, \subfigref{fig:model_full}{B--E}). With the noise-splitting trick, we could show that in low-CV cells, that have a low-CV and are not subject to strong stimulation, the full nonlinearity pattern is present but covered by the intrinsic noise. We thus conclude that the presence of the anti-diagonal pattern in the \suscept{} matrix is sufficient to conclude that the same nonlinear interactions happen here. This also validates the application of the white noise approach to characterize the full \suscept{} matrix instead of using all combinations of individual frequencies. - - - -% The nonlinearity of ampullary cells in paddlefish \citep{Neiman2011fish} has been previously accessed with bandpass limited white noise. - -% Here it was demonstrated that the second-order susceptibility for the two RAM noise input frequencies \fone{} and \ftwo{} can approximate a three-fish setting, where the driving force for the P-unit are two beats with frequencies \bone{} and \btwo{}. This was confirmed by a low-CV P-unit, where nonlinearities in the P-unit response occurred at the sum and difference of the beat frequencies for pure sine-wave stimulation (\figrefb{fig:motivation}). In this P-unit the nonlinearity appeared in a three-wave setting with \bone{} being close to \fbase{}, corresponding to a frequency combination on the vertical line at \foneb{} in the second-order susceptibility (\subfigrefb{fig:model_full}{B}). This implies that even if only the diagonal structure can be accessed with noise stimulation in the second-order susceptibility in an experiment (\subfigrefb{fig:model_full}{A}), it can be taken as an indicator that the whole nonlinear structure should be present during pure sine-wave stimulation in the same cell. With this RAM stimulation was demonstrated to be an effective method to scan the three-fish or two-beat plane and estimate the whole theoretically predicted nonlinear structure in experimentally recorded cells. - -\subsection{Selective readout versus integration of heterogeneous populations}% Nonlinearity might be influenced once integrating from a P-unit population with heterogeneous baseline properties}%Heterogeneity of P-units might influence - -The observed nonlinear effects might facilitate the detectability of faint signals during a three-fish setting, the electrosensory cocktail party. These nonlinear effects are, however, very specific with respect to the relation of stimulus frequencies and the P-unit baseline frequency. The EOD frequencies of the interacting fish would be drawn from the distributions of EOD frequencies found in male and female fish \citep{Hopkins1974Eigen, Meyer1987, Henninger2018, Henninger2020}. To be behaviorally relevant the faint signal detection would require reliable neuronal signaling irrespective of the individual EOD frequencies. -P-units, however, are very heterogeneous in their baseline firing properties \citep{Grewe2017, Hladnik2023}. The baseline firing rates vary in wide ranges (50--450\,Hz). This range covers substantial parts of the beat frequencies that may occur during animal interactions which is limited to frequencies below the Nyquist frequency (0 -- \feod/2) \citep{Barayeu2023}. It is thus likely that there are P-units that match approximately the specificities of the different encounters. - -On the other hand, the nonlinearity was found only in low-CV P-units (with white noise stimulation). The CVs are also very heterogeneous (0.1--1.4, \figref{fig:data_overview}\panel{A}) in our sample. Only a small fraction of the P-units have a sufficiently low level of intrinsic noise and will exhibit nonlinear responses. The P-units project to the ELL \citep{Krahe2014} and the integrating pyramidal cells in the different segments receive inputs in the range of 10s to 1000s of neurons \citep{Maler2009a}. Since the receptive fields of the pyramidal neurons are patches of adjacent receptors on the fish's body surface \citep{Bastian2002, Maler2009a, Haggard2023} and the input heterogeneity does not depend on the location of the receptor on the fish body \citep{Hladnik2023} the pyramidal cell input population will be heterogeneous. Heterogeneity was shown to be generally advantageous for the encoding in this \citep{Hladnik2023} and other systems \citep{Padmanabhan2010, Beiran2018}. At the same time, it contradicts the apparent need for a selective readout of low-CV cells to maintain information arising through nonlinear interactions. -A possible readout mechanism should be the topic of future studies that need to take into account that the nonlinearities are stronger in pure sine-wave stimulation and the fraction of cells that show it under naturalistic stimulation might be larger than expected from the distribution of CVs. - -\subsection{Behavioral relevance of nonlinear interactions} -The behavioral relevance of the weak signal detection in P-units is evident from the courtship context observed in freely interacting animals \citep{Henninger2018}. Outside courtship behavior, the encoding of secondary or social envelopes is a common need \citep{Stamper2012Envelope}. In a previous study, it was demonstrated that information about low-frequency secondary envelopes would not be present in P-units' responses but would arise through nonlinear processing downstream in the ELL \citep{Middleton2006, Middleton2007}. Based on our work we would predict that only a small subset of cells, with low CVs, should encode the social envelopes under white noise stimulation. An absence of low-CV cells in the population analyzed in the previous studies could explain their conclusions. On the other hand, another study showed that P-units with strong nonlinearities, low firing rates and, high CVs could indeed encode social envelopes \citep{Savard2011}. These findings are in contrast to the previously mentioned work \citep{Middleton2007} and, at first glance, also to our results. The missing link, that has not been considered in this work, might be the bursting of P-units, the repeated firing of spikes after one EOD period interleaved with longer intervals of quietness \citep{Chacron2004}. Bursting was not explicitly addressed in the previous work, still, the reported high CVs of the envelope encoding P-units indicate a higher rate of bursting \citep{Savard2011}. How bursts influence the second-order susceptibility of P-units will be addressed in the following works \citep{Barayeu2024}. Note that in this work we operated in a regime of weak stimuli and that the envelope encoding addressed in \citep{Savard2011,Middleton2007} operates in a regime of strong stimuli, where the firing rate is saturated. The exact transition from the nonlinearities in a regime of weak stimuli to a regime of strong stimuli could be addressed in further P-unit studies. - -Sinusoidal AMs are relevant in interactions with a few fish. We can understand the noise as the presence of many animals with individual EOD frequencies at the same time. Under noise stimulation, nonlinearities were demonstrated to be strong for weak stimuli but were shown to decrease for stronger noise stimuli (\figrefb{fig:cells_suscept}). As long as the noise signal is weak, those fish are distant and the nonlinearity is maintained. An increasing stimulus amplitude would indicate that many fish are close to the receiver and a decrease of nonlinear effects can be observed. These findings imply that the nonlinear effects arising in the presence of three fish decline the more fish join. \lepto{} usually prefers small groups of fish \citep{Stamper2010}. Thus, the described second-order susceptibility might still be behaviorally relevant under natural conditions. The decline of nonlinear effects when several fish are present might be an adaptive process reducing the number of frequencies represented in its primary sensory afferents to a minimum. Such representation would still leave room to create nonlinear effects at later processing steps in higher-order neurons. - -The afferents of the passive electrosensory system, the ampullary cells, were found to exhibit much stronger nonlinearities than P-units (\figref{fig:data_overview}). The adequate stimulus for this system is a direct stimulation not an amplitude modulation. In this sense, the ampullary cells are closer to the LIF models used by Voroneko and colleagues \citep{Voronenko2017} and we can thus expect that the same nonlinear mechanisms are at work here. For the ampullary system, the sinewave stimulation is not as relevant as for the P-unit system. Ampullary cells encode low-frequency exogenous electric signals such as muscle potentials induced by prey movement \citep{Kalmijn1974, Engelmann2010, Neiman2011fish}. The simultaneous muscle activity of a swarm of prey (such as \textit{Daphnia}) resembles Gaussian white noise \citep{Neiman2011fish}, similar to the stimuli used here. Our results show some similarities with the analyses by Neiman and Russel \citep{Neiman2011fish} who study the encoding in ampullary afferents in the paddlefish. There, the power spectrum of the spontaneous activity also shows a peak at the baseline frequency (internal oscillator) but also at the oscillation frequency measured at the epithelium and interactions of both. Most of the latter disappear in the case of external stimulation, though. Here we find only peaks at the baseline frequency of the neuron and its harmonics. There are interesting similarities and dissimilarities; stimulus encoding in the paddlefish as well as in the brown ghost is very linear for low frequencies and there are nonlinearities in both systems. Linear encoding in the paddlefish shows a gap in the spectrum at the frequency of the epithelial oscillation, instead, the nonlinear response is very pronounced there. In \lepto{}, the dominating frequency under baseline conditions is the baseline firing rate, and we do see increased nonlinearity in this frequency range. The baseline frequency, however, is outside the linear coding range \citep{Grewe2017} while it is within the linear coding range in paddlefish \citep{Neiman2011fish}. Interestingly, the nonlinear response in the paddlefish ampullaries increases with stimulus intensity while it disappears in our case (\subfigrefb{fig:data_overview}{F}). The population of ampullary cells is much more homogeneous with respect to the baseline rate (131$\pm$29\,Hz) and stimulus encoding properties than the P-units \citep{Grewe2017}. This implies that, if the stimulus contains the appropriate frequency components that sum up to the baseline rate, there should be a nonlinear response at a frequency that is similar to the full population of ampullary cells (the baseline frequency) that is outside the linear coding range. Postsynaptic cells integrating ampullary input might be able to extract this nonlinear response from the input population. How such nonlinear effects in ampullary cells might influence prey detection should be addressed in further studies. - -\subsection{Conclusion} -We have demonstrated that there are pronounced nonlinear responses in the primary electrosensory afferents of the weakly electric fish \lepto{}, systems that are very often characterized using linear methods. The observed nonlinearities match the expectations from previous theoretical studies \citep{Voronenko2017}. We can confirm that the theory applies also to systems that are encoding amplitude modulations of a carrier signal. Comparisons of P-units and ampullary cells showed that it is the level of intrinsic noise that determines how strongly nonlinear the system acts. Using the second-order susceptibility estimated from the responses to white noise stimuli provides an easy way to determine the nonlinearity of the system under study. P-units share several features with mammalian -auditory nerve fibers and such nonlinear effects might also be expected in the auditory system during the encoding of amplitude modulations \citep{Joris2004}. - -\section{Methods} - -\subsection{Experimental subjects and procedures} - -Within this project, we re-evaluated datasets that were recorded between 2010 and 2023 at the Ludwig Maximilian University (LMU) M\"unchen and the Eberhard-Karls University T\"ubingen. All experimental protocols complied with national and European law and were approved by the respective Ethics Committees of the Ludwig-Maximilians Universität München (permit no. 55.2-1-54-2531-135-09) and the Eberhard-Karls Unversität Tübingen (permit no. ZP 1/13 and ZP 1/16). -The final sample consisted of 221 P-units and 47 ampullary electroreceptor afferents recorded in 71 weakly electric fish of the species \lepto{}. The original electrophysiological recordings were performed on male and female weakly electric fish of the species \lepto{} that were obtained from a commercial supplier for tropical fish (Aquarium Glaser GmbH, Rodgau, -Germany). The fish were kept in tanks with a water temperature of $25\pm1\,^\circ$C and a conductivity of around $270\,\micro\siemens\per\centi\meter$ under a 12\,h:12\,h light-dark cycle. - -Before surgery, the animals were deeply anesthetized via bath application with a solution of MS222 (120\,mg/l, PharmaQ, Fordingbridge, UK) buffered with Sodium Bicarbonate (120\,mg/l). The posterior anterior lateral line nerve (pALLN) was exposed by making a small cut into the skin covering the nerve. The cut was placed dorsal of the operculum just before the nerve descends towards the anterior lateral line ganglion (ALLNG). Those parts of the skin that were to be cut were locally anesthetized by cutaneous application of liquid lidocaine hydrochloride (20\,mg/ml, bela-pharm GmbH). During the surgery, water supply was ensured by a mouthpiece to maintain anesthesia with a solution of MS222 (100\,mg/l) buffered with Sodium Bicarbonate (100\,mg/l). After surgery, fish were immobilized by intramuscular injection of from 25\,$\micro$l to 50\,$\micro$l of tubocurarine (5\,mg/ml dissolved in fish saline; Sigma-Aldrich). -Respiration was then switched to normal tank water and the fish was transferred to the experimental tank. - -\subsection{Experimental setup} -For the recordings fish were positioned centrally in the experimental tank, with the major parts of their body submerged into the water. Those body parts that were above the water surface were covered with paper tissue to avoid drying of the skin. Local analgesia was refreshed in intervals of two hours by cutaneous reapplication of Lidocaine (2\,\%; bela-pharm, Vechta, Germany) around the surgical wounds. Electrodes (borosilicate; 1.5\,mm outer diameter; GB150F-8P; Science Products, Hofheim, Germany) were pulled to a resistance of 50--100\,\mega\ohm{} (model P-97; Sutter Instrument, Novato, CA) and filled with 1\,M KCl solution. Electrodes were fixed in a microdrive (Luigs-Neumann, Ratingen, Germany) and lowered into the nerve (\figrefb{fig:setup}, blue triangle). Recordings of electroreceptor afferents were amplified and lowpass filtered at 10\,kHz (SEC-05, npi-electronics, Tamm, Germany, operated in bridge mode). All signals, neuronal recordings, recorded EOD, and the generated stimulus, were digitized with sampling rates of 20 or 40\,kHz (PCI-6229, National Instruments, Austin, TX). RELACS (\url{www.relacs.net}) running on a Linux computer was used for online spike and EOD detection, stimulus generation, and calibration. Recorded data was then stored on the hard drive for offline analysis. - -\subsection{Identification of P-units and ampullary cells} -The neurons were classified into cell types during the recording by the experimenter. P-units were classified based on baseline firing rates of 50--450\,Hz and a clear phase-locking to the EOD and, their responses to amplitude modulations of their own EOD \citep{Grewe2017, Hladnik2023}. Ampullary cells were classified based on firing rates of 80--200\,Hz absent phase-locking to the EOD, and responses to low-frequency sinusoidal stimuli \citep{Grewe2017}. We here selected only those cells of which the neuron's baseline activity as well as the responses to frozen noise stimuli were recorded. - -\subsection{Electric field recordings} - The electric field of the fish was recorded in two ways: 1. we measured the so-called \textit{global EOD} with two vertical carbon rods ($11\,\centi\meter$ long, 8\,mm diameter) in a head-tail configuration (\figrefb{fig:setup}, green bars). The electrodes were placed isopotential to the stimulus. This signal was differentially amplified with a factor between 100 and 500 (depending on the recorded animal) and band-pass filtered (3 to 1500\,Hz pass-band, DPA2-FX; npi electronics, Tamm, Germany). 2. The so-called \textit{local EOD} was measured with 1\,cm-spaced silver wires located next to the left gill of the fish and orthogonal to the fish's longitudinal body axis (amplification 100 to 500 times, band-pass filtered with 3 to 1\,500\,Hz pass-band, DPA2-FX; npi-electronics, Tamm, Germany, \figrefb{fig:setup}, red markers). This local measurement recorded the combination of the fish's own field and the applied stimulus and thus serves as a proxy of the transdermal potential that drives the electroreceptors. - -\subsection{Stimulation} -The stimulus was isolated from the ground (ISO-02V, npi-electronics, Tamm, Germany) and delivered via two horizontal carbon rods (30 cm length, 8 mm diameter) located $15\,\centi\meter$ laterally to the fish (\figrefb{fig:setup}, gray bars). The stimulus was calibrated with respect to the local EOD. - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{Settup} - \caption{\label{fig:setup} Electrophysiolocical recording setup. The fish, depicted as a black scheme and surrounded by isopotential lines, was positioned in the center of the tank. Blue triangle -- electrophysiological recordings were conducted in the posterior anterior lateral line nerve (pALLN). Gray horizontal bars -- electrodes for the stimulation. Green vertical bars -- electrodes to measure the \textit{global EOD} placed isopotential to the stimulus, i.e. recording fish's unperturbed EOD. Red dots -- electrodes to measure the \textit{local EOD} picking up the combination of fish's EOD and the stimulus. The local EOD was measured with a distance of 1 \,cm between the electrodes. All measured signals were amplified, filtered, and stored for offline analysis.} -\end{figure*} - -\subsection{White noise stimulation}\label{rammethods} -The fish were stimulated with band-limited white noise stimuli with a cut-off frequency of 150, 300 or 400\,Hz. The stimulus intensity is given as the contrast, i.e. the standard deviation of the white noise stimulus in relation to the fish's EOD amplitude. The contrast varied between 1 and 20\,\%. Only cell recordings with at least 10\,s of white noise stimulation were included for the analysis. When ampullary cells were recorded, the white noise was directly applied as the stimulus. To create random amplitude modulations (RAM) for P-unit recordings, the EOD of the fish was multiplied with the desired random amplitude modulation profile (MXS-01M; npi electronics). - -% and between 2.5 and 40\,\% for \eigen - -\subsection{Data analysis} Data analysis was performed with Python 3 using the packages matplotlib \citep{Hunter2007}, numpy \citep{Walt2011}, scipy \citep{scipy2020}, pandas \citep{Mckinney2010}, nixio \citep{Stoewer2014}, and thunderfish (\url{https://github.com/bendalab/thunderfish}). - -%sklearn \citep{scikitlearn2011}, - -\paragraph{Baseline analysis}\label{baselinemethods} -The baseline firing rate \fbase{} was calculated as the number of spikes divided by the duration of the baseline recording (on average 18\,s). The coefficient of variation (CV) was calculated as the standard deviation of the interspike intervals (ISI) divided by the average ISI: $\rm{CV} = \sqrt{\langle (ISI- \langle ISI \rangle) ^2 \rangle} / \langle ISI \rangle$. If the baseline was recorded several times in a recording, the average \fbase{} and CV were calculated. - -\paragraph{White noise analysis} \label{response_modulation} -In the stimulus-driven case, the neuronal activity of the recorded cell is modulated around the average firing rate that is similar to \fbase{} and in that way encodes the time-course of the stimulus. -The time-dependent response of the neuron was estimated from the spiking activity -\begin{equation}\label{eq:spikes} -x_k(t) = \sum_i\delta(t-t_{k,i}) -\end{equation} -recorded for each stimulus presentation, $k$, by kernel convolution with a Gaussian kernel - -\begin{equation} -K(t) = \scriptstyle \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{t^2}{2\sigma^2}} -\end{equation} -with $\sigma$ the standard deviation of the Gaussian which was set to 2.5\,ms if not stated otherwise. For each trial $k$ the $x_k(t)$ is convolved with the kernel $K(t)$ - -\begin{equation} - r_k(t) = x_k(t) * K(t) = \int_{-\infty}^{+\infty} x_k(t') K(t-t') \, \mathrm{d}t' \;, -\end{equation} -where $*$ denotes the convolution. $r(t)$ is then calculated as the across-trial average -\begin{equation} - r(t) = \left\langle r_k(t) \right\rangle _k. -\end{equation} - -To quantify how strongly the neuron is driven by the stimulus we quantified the response modulation as the standard deviation $\sigma_{M} = \sqrt{\langle (r(t)-\langle r(t) \rangle_t)^2\rangle_t}$, where $\langle \cdot \rangle_t$ indicates averaging over time. - -\paragraph{Spectral analysis}\label{susceptibility_methods} -The neuron is driven by the stimulus and thus the spiking response $x(t)$, \Eqnref{eq:spikes}, depends on the stimulus $s(t)$. To investigate the relation between stimulus and response we calculated the first- and second-order susceptibility of the neuron to the stimulus in the frequency domain. The Fourier transforms of $s(t)$ and $x(t)$ are denoted as $\tilde s(\omega)$ and $\tilde x(\omega)$ and were calculated according to $\tilde x(\omega) = \int_{0}^{T} \, x(t) \cdot e^{- i \omega t}\,dt$, with $T$ being the signal duration. Stimuli had a duration of 10\,s and spectra of stimulus and response were calculated in separate segments of 0.5\,s with no overlap resulting in a spectral resolution of 2\,Hz. - -The power spectrum of the stimulus $s(t)$ was calculated as -\begin{equation} - \label{powereq} - \begin{split} - S_{ss}(\omega) = \frac{\langle \tilde s(\omega) \tilde s^* (\omega)\rangle}{T} - \end{split} -\end{equation} -with $\tilde s^* $ being the complex conjugate and $\langle ... \rangle$ denoting averaging over the segments. The power spectrum of the spike trains $S_{xx}(\omega)$ was calculated accordingly. The cross-spectrum $S_{xs}(\omega)$ between stimulus and evoked spike trains was calculated according to -\begin{equation} - \label{cross} - \begin{split} - S_{xs}(\omega) = \frac{\langle \tilde x(\omega) \tilde s^* (\omega)\rangle}{T} - \end{split} -\end{equation} -From $S_{xs}(\omega)$ and $ S_{ss}(\omega)$ we calculated the linear susceptibility (transfer function) as -\begin{equation} - \label{linearencoding_methods} - \begin{split} - \chi_{1}(\omega) = \frac{S_{xs}(\omega) }{S_{ss}(\omega) } - \end{split} -\end{equation} -The second-order cross-spectrum that depends on the two frequencies $\omega_1$ and $\omega_2$ was calculated according to -\begin{equation} - \label{eq:crosshigh} - S_{xss} (\omega_{1},\omega_{2}) = \frac{\langle \tilde x (\omega_{1}+\omega_{2}) \tilde s^* (\omega_{1})\tilde s^* (\omega_{2}) \rangle}{T} -\end{equation} -The second-order susceptibility was calculated by dividing the higher-order cross-spectrum by the spectral power at the respective frequencies. -\begin{equation} - \label{eq:susceptibility} - %\begin{split} - \chi_{2}(\omega_{1}, \omega_{2}) = \frac{S_{xss} (\omega_{1},\omega_{2})}{2S_{ss} (\omega_{1}) S_{ss} (\omega_{2})} - %\end{split} -\end{equation} -% Applying the Fourier transform this can be rewritten resulting in: -% \begin{equation} -% \label{susceptibility} -% \begin{split} -% \chi_{2}(\omega_{1}, \omega_{2}) = \frac{TN \sum_{n=1}^N \int_{0}^{T} dt\,r_{n}(t) e^{-i(\omega_{1}+\omega_{2})t} \int_{0}^{T}dt'\,s_{n}(t')e^{i \omega_{1}t'} \int_{0}^{T} dt''\,s_{n}(t'')e^{i \omega_{2}t''}}{2 \sum_{n=1}^N \int_{0}^{T} dt\, s_{n}(t)e^{-i \omega_{1}t} \int_{0}^{T} dt'\,s_{n}(t')e^{i \omega_{1}t'} \sum_{n=1}^N \int_{0}^{T} dt\,s_{n}(t)e^{-i \omega_{2}t} \int_{0}^{T} dt'\,s_{n}(t')e^{i \omega_{2}t'}} -% \end{split} -% \end{equation} -The absolute value of a second-order susceptibility matrix is visualized in \figrefb{fig:model_full}. There the upper right and the lower left quadrants characterize the nonlinearity in the response $x(t)$ at the sum frequency of the two input frequencies. The lower right and upper left quadrants characterize the nonlinearity in the response $x(t)$ at the difference of the input frequencies. - -\paragraph{Nonlinearity index}\label{projected_method} -We expect to see nonlinear susceptibility when $\omega_1 + \omega_2 = \fbase{}$. To characterize this we calculated the peakedness of the nonlinearity (PNL) as - \begin{equation} - \label{eq:nli_equation} - \nli{} = \frac{ \max D(\fbase{}-5\,\rm{Hz} \leq f \leq \fbase{}+5\,\rm{Hz})}{\mathrm{med}(D(f))} - \end{equation} -For this index, the second-order susceptibility matrix was projected onto the diagonal $D(f)$, by taking the mean of the anti-diagonals. The peakedness at the frequency $\fbase{}$ in $D(f)$ was quantified by finding the maximum of $D(f)$ in the range $\fbase{} \pm 5$\,Hz (\subfigrefb{fig:cells_suscept}{G}) and dividing it by the median of $D(f)$. - -If the same frozen noise was recorded several times in a cell, each noise repetition resulted in a separate second-order susceptibility matrix. The mean of the corresponding \nli{} values was used for the population statistics in \figref{fig:data_overview}. - -\subsection{Leaky integrate-and-fire models}\label{lifmethods} - -Leaky integrate-and-fire (LIF) models with a carrier were constructed to reproduce the specific firing properties of P-units \citep{Chacron2001, Sinz2020}. The sole driving input into the P-unit model during baseline, i.e. when no external stimulus was given, is the fish's own EOD modeled as a cosine wave -\begin{equation} - \label{eq:eod} - \carrierinput = y_{EOD}(t) = \cos(2\pi f_{EOD} t) - \end{equation} -with the EOD frequency $f_{EOD}$ and an amplitude normalized to one. - -In the model, the input \carrierinput{} was then first thresholded to model the synapse between the primary receptor cells and the afferent. -\begin{equation} - \label{eq:threshold2} - \lfloor \carrierinput \rfloor_0 = \left\{ \begin{array}{rcl} \carrierinput & ; & \carrierinput \ge 0 \\ 0 & ; & \carrierinput < 0 \end{array} \right. -\end{equation} -$\lfloor \carrierinput \rfloor_{0}$ denotes the threshold operation that sets negative values to zero (\subfigrefb{flowchart}{A}). - -The resulting receptor signal was then low-pass filtered to approximate passive signal conduction in the afferent's dendrite (\subfigrefb{flowchart}{B}) -\begin{equation} - \label{eq:dendrite} - \tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor \carrierinput \rfloor_{0} -\end{equation} -with $\tau_{d}$ as the dendritic time constant. Dendritic low-pass filtering was necessary to reproduce the loose coupling of P-unit spikes to the EOD while maintaining high sensitivity at small amplitude modulations. Because the input was dimensionless, the dendritic voltage was dimensionless, too. The combination of threshold and low-pass filtering extracts the amplitude modulation of the input \carrierinput. - -The dendritic voltage $V_d(t)$ was the input to a leaky integrate-and-fire (LIF) model -\begin{equation} - \label{eq:LIF} - \tau_{m} \frac{d V_{m}}{d t} = - V_{m} + \mu + \alpha V_{d} - A + \sqrt{2D}\xi(t) -\end{equation} -where $\tau_{m}$ is the membrane time-constant, $\mu$ is a fixed bias current, $\alpha$ is a scaling factor for $V_{d}$, $A$ is an inhibiting adaptation current, and $\sqrt{2D}\xi(t)$ is a white noise with strength $D$. All state variables except $\tau_m$ are dimensionless. - -The adaptation current $A$ followed -\begin{equation} - \label{eq:adaptation} - \tau_{A} \frac{d A}{d t} = - A -\end{equation} -with adaptation time constant $\tau_A$. - -Whenever the membrane voltage $V_m(t)$ crossed the spiking threshold $\theta=1$ a spike was generated, $V_{m}(t)$ was reset to $0$, the adaptation current was incremented by $\Delta A$, and integration of $V_m(t)$ was paused for the duration of a refractory period $t_{ref}$ (\subfigrefb{flowchart}{D}). -\begin{equation} - \label{spikethresh} - V_m(t) \ge \theta \; : \left\{ \begin{array}{rcl} V_m & \mapsto & 0 \\ A & \mapsto & A + \Delta A/\tau_A \end{array} \right. -\end{equation} - -% The static nonlinearity $f(V_m)$ was equal to zero for the LIF. In the case of an exponential integrate-and-fire model (EIF), this function was set to -% \begin{equation} -% \label{eifnl} -% f(V_m)= \Delta_V \text{e}^{\frac{V_m-1}{\Delta_V}} -% \end{equation} -% \citep{Fourcaud-Trocme2003}, where $\Delta_V$ was varied from 0.001 to 0.1. -%, \figrefb{eif} - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{flowchart.pdf} - \caption{\label{flowchart} - Components of the P-unit model. The main steps of the model are illustrated in the left column. The three other columns show the corresponding signals in three different settings: (i) the baseline situation, no external stimulus, only the fish's self-generated EOD (i.e. the carrier) is present. (ii) RAM stimulation, the carrier is amplitude modulated with a weak (2\,\% contrast) band-limited white-noise stimulus. (iii) Noise split condition in which 90\,\% of the internal noise is used as a driving RAM stimulus scaled with the correction factor $\rho$ (see text). Note that the mean firing rate and the CV of the ISI distribution is the same in this and the baseline condition. As an example, simulations of the model for cell ``2012-07-03-ak'' are shown (see table~\ref{modelparams} for model parameters). \figitem{A} Thresholding: a simple linear threshold was applied to the EOD carrier, \Eqnref{eq:eod}. \figitem{B} Subsequent dendritic low-pass filtering attenuates the carrier and carves out the AM signal. \figitem{C} Gaussian white-noise is added to the signal in \panel{B}. Note the reduced internal noise amplitude in the noise split (iii) condition. \figitem{D} Spiking output of the LIF model in response to the sum of B and C. \figitem{E} Power spectra of the LIF neuron's spiking activity. Under the baseline condition (\panel[i]{E}) there are several peaks, from left to right, at the baseline firing rate $\fbase{}$, $f_{EOD} - \fbase{}$, $f_{EOD}$, and $f_{EOD} + \fbase{}$. In the stimulus-driven regime (\panel[ii]{E}), there is only a peak at \feod, while under the noise split condition (\panel[iii]{E}) the same peaks as in the baseline condition are present.} -\end{figure*} - -\subsection{Numerical implementation} -The model's ODEs were integrated by the Euler forward method with a time-step of $\Delta t = 0.05$\,ms. The intrinsic noise $\xi(t)$ (\Eqnref{eq:LIF}, \subfigrefb{flowchart}{C}) was added by drawing a random number from a normal distribution $\mathcal{N}(0,\,1)$ with zero mean and standard deviation of one in each time step $i$. This number was multiplied with $\sqrt{2D}$ and divided by $\sqrt{\Delta t}$: -\begin{equation} - \label{eq:LIFintegration} - V_{m_{i+1}} = V_{m_i} + \left(-V_{m_i} + \mu + \alpha V_{d_i} - A_i + \sqrt{\frac{2D}{\Delta t}}\mathcal{N}(0,\,1)_i\right) \frac{\Delta t}{\tau_m} -\end{equation} - -\subsection{Model parameters}\label{paramtext} -The eight free parameters of the P-unit model $\beta$, $\tau_m$, $\mu$, $D$, $\tau_A$, $\Delta_A$, $\tau_d$, and $t_{ref}$, were fitted to both the baseline activity (baseline firing rate, CV of ISIs, serial correlation of ISIs at lag one, and vector strength of spike coupling to EOD) and the responses to step-like increases and decreases in EOD amplitude (onset-state and steady-state responses, effective adaptation time constant). For each simulation, the start parameters $A$, $V_{d}$ and $V_{m}$ were drawn from a random starting value distribution, estimated from a 100\,s baseline simulation after an initial 100\,s of simulation that was discarded as a transient. - -\subsection{Stimuli for the model} -The model neurons were driven with similar stimuli as the real neurons in the original experiments. To mimic the interaction with one or two foreign animals the receiving fish's EOD (\Eqnref{eq:eod}) was normalized to an amplitude of one and the respective EODs of a second or third fish were added.%\Eqnref{ eq.\,\ref{eq:eod} - -The random amplitude modulation (RAM) input to the model was created by drawing random amplitude and phases from Gaussian distributions for each frequency component in the range 0--300 Hz. An inverse Fourier transform was applied to get the final amplitude RAM time course. The input to the model was then -\begin{equation} - \label{eq:ram_equation} - y(t) = (1+ s(t)) \cdot \cos(2\pi f_{EOD} t) -\end{equation} -From each simulation run, the first second was discarded and the analysis was based on the last second of the data. The resulting spectra thus have a spectral resolution of 1\,Hz. -% \subsection{Second-order susceptibility analysis of the model} -% %\subsubsection{Model second-order nonlinearity} - -% The second-order susceptibility in the model was calculated with \Eqnref{eq:susceptibility}, resulting in matrices as in \figrefb{model_and_data} and \figrefb{fig:model_full}. For this, the model neuron was presented the input $x(t)$ for 2\,s, with the first second being dismissed as the transient. The second-order susceptibility calculation was performed on the last second, resulting in a frequency resolution of 1\,Hz. - -\subsection{Model noise split into a noise and a stimulus component}\label{intrinsicsplit_methods}% the Furutsu-Novikov Theorem with the same correlation function -According to previous works \citep{Lindner2022} the total noise of a LIF model ($\xi$) can be split up into several independent noise processes. Here we split the internal noise into two parts: (i) One part is treated as a driving input signal $s_\xi(t)$, a RAM stimulus where frequencies above 300\,Hz are discarded (\Eqnref{eq:ram_split}), and used to calculate the cross-spectra in \Eqnref{eq:crosshigh} and (ii) the remaining noise $\sqrt{2D \, c_{\rm{noise}}} \cdot \xi(t)$ that is treated as pure noise (\Eqnref{eq:Noise_split_intrinsic}). In this way, the effective signal-to-noise ratio can be increased while maintaining the total noise in the system. -%\sqrt{\rho \, 2D \,c_{\rm{signal}}} \cdot \xi(t) - -%(1-c_{\rm{signal}})\cdot\xi$c_{\rm{noise}} = 1-c_{\rm{signal}}$ -%c_{\rm{signal}} \cdot \xi -\begin{equation} - \label{eq:ram_split} - y(t) = (1+ s_\xi(t)) \cdot \cos(2\pi f_{EOD} t) -\end{equation} - -\begin{equation} - \label{eq:Noise_split_intrinsic_dendrite} - \tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor y(t) \rfloor_{0} -\end{equation} - - -\begin{equation} - \label{eq:Noise_split_intrinsic} - \tau_{m} \frac{d V_{m}}{d t} = - V_{m} + \mu + \alpha V_{d} - A + \sqrt{2D \, c_{\rm{noise}}} \cdot \xi(t) -\end{equation} -% das stimmt so, das c kommt unter die Wurzel! - -%\begin{equation} -% \label{Noise_split_intrinsic} -% V_{m_{i+1}} = V_{m_i} + \left(-V_{m_i} + \mu + \alpha V_{d_i} - A_i + \sqrt{\frac{2D c_{\rm{noise}}}{\Delta t}}\mathcal{N}(0,\,1)_i\right) \frac{\Delta t}{\tau_m} -%\end{equation} - - - -In the here used model a small portion of the original noise was assigned to the noise component ($c_{\rm{noise}} = 0.1$, \subfigrefb{flowchart}\,\panel[iii]{C}) and a big portion used as the signal component ($c_{\rm{signal}} = 0.9$, \subfigrefb{flowchart}\,\panel[iii]{A}). For the noise split to be valid \citep{Lindner2022} both components must add up to the initial 100\,\% of the total noise and the baseline properties as the firing rate and the CV of the model are maintained. This is easily achieved in a model without a carrier if the condition $c_{\rm{signal}}+c_{\rm{noise}}=1$ is satisfied. The situation here is more complicated. After the original noise was split into a signal component with $c_{\rm{signal}}$, the frequencies above 300\,Hz were discarded and the signal strength was reduced after the dendritic low pass filtering. To compensate for these transformations the initial signal component was multiplied with the factor $\rho$, keeping the baseline CV (only carrier) and the CV during the noise split comparable, and resulting in $s_\xi(t)$. $\rho$ was found by bisecting the plane of possible factors and minimizing the error between the CV during baseline and stimulation. - -%that was found by minimizing the error between the -%Furutsu-Novikov Theorem \citep{Novikov1965, Furutsu1963}\Eqnref{eq:ram_split}, (red in \subfigrefb{flowchart}\,\panel[iii]{A}) bisecting the space of possible $\rho$ scaling factors -%$\rho$ a scaling factor that compensates (see below) for the signal transformations the amplitude modulation stimulus undergoes in the model, i.e. the threshold and the dendritic lowpass. -%In our case the model has a carrier (the fish's self-generated EOD) and we thus want to drive the model with an amplitude modulation stimulus - - -% See section \ref{lifmethods} for model and parameter description. -\begin{table*}[hp!] - \caption{\label{modelparams} Model parameters of LIF models, fitted to 2 electrophysiologically recorded P-units \citep{Ott2020}.} - \begin{center} - \begin{tabular}{lrrrrrrrr} - \hline - \bfseries $cell$ & \bfseries $\beta$ & \bfseries $\tau_{m}$/ms & \bfseries $\mu$ & \bfseries $D$/$\mathbf{ms}$ & \bfseries $\tau_{A}$/ms & \bfseries $\Delta_A$ & \bfseries $\tau_{d}$/ms & \bfseries $t_{ref}$/ms \\\hline -2012-07-03-ak& $10.6$& $1.38$& $-1.32$& $0.001$& $96.05$& $0.01$& $1.18$& $0.12$ \\ -2013-01-08-aa& $4.5$& $1.20$& $0.59$& $0.001$& $37.52$& $0.01$& $1.18$& $0.38$ \\ -2018-05-08-ae& $139.6$& $1.49$& $-21.09$& $0.214$& $123.69$& $0.16$& $3.93$& $1.31$ \\ - \hline - \end{tabular} - \end{center} -\end{table*}% 2013-01-08-aa % 2012-07-03-ak - -%\notejb{to methods: ``Note that the signal component \signalnoise{} is added as an amplitude modulation and is thus limited with respect to its spectral content by the Nyquist frequency of the carrier, half the EOD frequency. It thus has a reduced high-frequency content as compared to the intrinsic noise. Adding these discarded high-frequency components to the intrinsic noise does not affect the results here (not shown).''} - - -% Either type in your references using -% \begin{thebibliography}{} -% \bibitem{} -% Text -% \end{thebibliography} -% -% or -% -% Compile your BiBTeX database using our plos2015.bst -% style file and paste the contents of your .bbl file -% here. See http://journals.plos.org/plosone/s/latex for -% step-by-step instructions. -% -%\bibliographystyle{apalike}%alpha}%}%alpha}%apalike} -\bibliography{journalsabbrv,references} -% \bibliographystyle{apalike} %or any other style you like -%\bibliography{references} -%\bibliography{journalsabbrv,references} -\newpage - -\section{Supporting information} - -\subsection{S1 Second-order susceptibility of high-CV P-unit} -CVs in P-units can range up to 1.5 \citep{Grewe2017, Hladnik2023}. We show the same analysis as in \figrefb{fig:cells_suscept} for an example higher-CV P-unit. Similar to the low-CV cell, high-CV P-units fire at multiples of the EOD period (\subfigrefb{fig:cells_suscept_high_CV}{A}). In contrast to low-CV P-units, however, the higher CV characterizes the noisier baseline firing pattern and the peak at \fbase{} is less pronounced in the power spectrum of the baseline activity (\subfigrefb{fig:cells_suscept_high_CV}{B}). High-CV P-units do not exhibit a clear nonlinear structure related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{fig:cells_suscept_high_CV}{E--F}), nor in the projected diagonals (\subfigrefb{fig:cells_suscept_high_CV}{G}). The overall level of nonlinearity, however, shows the same dependence on the stimulus contrast. It is much reduced for high-contrast stimuli that drive the neuron much stronger (\subfigrefb{fig:cells_suscept_high_CV}{F}). - -\label{S1:highcvpunit} -\begin{figure*}[!ht] -\includegraphics[width=\columnwidth]{cells_suscept_high_CV.pdf} - \caption{\label{fig:cells_suscept_high_CV} Response of experimentally measured noisy P-units (cell identifier ``2018-08-24-af") with a relatively high CV of 0.34 to RAM stimuli with two different contrasts. \figitem{A} Interspike intervals (ISI) distribution during baseline. \figitem{B} Baseline power spectrum. \figitem{C} Top: EOD carrier (gray) with RAM (red). Center: Spike trains in response to the 5\,\% RAM contrast. Bottom: Spike trains in response to the 10\,\% RAM contrast. \figitem{D} First-order susceptibility (\Eqnref{linearencoding_methods}). \figitem{E} Absolute value $|\chi_2(f_1, f_2)|$ of the second-order susceptibility, \Eqnref{eq:susceptibility}, for the 5\,\% RAM contrast. Pink lines -- edges of the structure when \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{F} $|\chi_2(f_1, f_2)|$ for the 10\,\% RAM contrast. \figitem{G} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel{E--F}. Gray dots: \fbase{}. Dashed lines: Medians of the projected diagonals.} -\end{figure*} - - -\begin{figure*}[t] - \includegraphics[width=\columnwidth]{trialnr.pdf} - \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of trials $\n$. While the estimate of the noise floor (10th and 90th percentile) of the $|\chi_2(f_1, f_2)|$ matrix does not saturate yet, the estimates of the high values in the matrix that make up the characteristic ridges saturate for $N>10^6$. The model used has the identifier 2013-01-08-aa (table~\ref{modelparams}). - } -\end{figure*} - -\end{document} - - - - -%\begin{itemize} -%\item \notejb{ \citep{French1973} Derivation of the Fourier transformed kernels measured with white noise.} -%\item \notejb{ \citep{French1976} Technical issues and tests of Fourier transformed kernels measured with white noise.} -%\item \notejb{ \citep{Victor1977} Cat retinal ganglion cells, gratings with sum of 6 or 8 sinusoids. X - versus Y cells. Peak at f1 == f2 in Y cells. X-cells rather linear. Discussion of mechanism, where a nonlinearity comes in along the pathway} -%\item \notejb{ \citep{Marmarelis1972} Temporal 2nd order kernels, how well do kernels predict responses, catfish retinal ganglion cells} -%\item \notejb{ \citep{Marmarelis1973} Temporal 2nd order kernels, how well do kernels predict responses} -%\item \notejb{ \citep{Victor1988} Cat retinal ganglion cells, the sum of sinusoids, very technical, one measurement similar to \citep{Victor1977}.} -%\item \notejb{\citep{Nikias1993} Third order spectra or bispectra. Very technical overview to higher order spectra} -%\item \notejb{ \citep{Mitsis2007} Spider mechanoreceptor. Linear filters, multivariate nonlinearity, and threshold. The second-order kernel is needed for this. Gaussian noise stimuli.} -%\item \notejb{ \citep{French2001} Time kernels up to 3rd order for predicting spider mechanoreceptor responses (spikes!)} -%\item \notejb{ \citep{French1999} Review on time domain nonlinear systems identification} -%\item \notejb{ \citep{Temchin2005, RecioSpinosa2005} 2nd order Wiener kernel for predicting chinchilla auditory nerve fiber firing rate responses. Strong 2nd order blob at characteristic frequency} -%\item \notejb{ \citep{Schanze1997} lots of bispectra, visual cortex MUA recordings} - -%\item \notejb{ \citep{Theunissen1996} Linear backward stimulus reconstruction in the context of information theory/signal-to-noise ratios} -%\item \notejb{ \citep{Wessel1996} Same as Theunissen1996 but for P-units} -%\item \notejb{ \citep{Neiman2011} cross bispectrum, bicoherence, mutual information, saturating nonlinearities, `` ampullary electroreceptors of paddlefish are perfectly suited to linearly encode weak low-frequency stimuli.''} - -%\item \notejb{ \citep{Chichilnisky2001} Linear Nonlinear Poisson model} -%\item \notejb{ \citep{Gollisch2009} Linear Nonlinear models in retina} -%\item \notejb{ \citep{Clemens2013} Grasshoppper model for female preferences} -%\end{itemize} diff --git a/trialnr.pdf b/trialnr.pdf index e728aa0..76f9757 100644 Binary files a/trialnr.pdf and b/trialnr.pdf differ diff --git a/trialnr.png b/trialnr.png deleted file mode 100644 index 029c8c8..0000000 Binary files a/trialnr.png and /dev/null differ diff --git a/trialnr.py b/trialnr.py index 552bde5..e286f37 100644 --- a/trialnr.py +++ b/trialnr.py @@ -50,7 +50,7 @@ def trialnr(): ax[0].set_xscale('log')#colors[s] ax[0].set_yscale('log') ax[0].set_xlabel('Trials [$N$]') - ax[0].set_ylabel('$|\chi_{2}|$\,[Hz]') + ax[0].set_ylabel(r'$|\chi_{2}|$\,[Hz]') ax[0].set_xlim(8, 10000000) ############################################ diff --git a/~WRL1966.tmp b/~WRL1966.tmp deleted file mode 100644 index d348194..0000000 Binary files a/~WRL1966.tmp and /dev/null differ