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models_big_fit_d_right.csv
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models_big_fit_d_right.csv
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,cell,EODf,a_zero,delta_a,dend_tau,input_scaling,mem_tau,noise_strength,ref_period,deltat,tau_a,threshold,v_base,v_offset,v_zero
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0,2011-10-25-ad-invivo-1,760.5,60.70561732896827,0.1575286757918413,0.0040752958611253,301.3786912934572,0.0029012439225658,0.0004404730695724,0.0007434544009651,5e-05,0.1160774474234297,1,0,-34.375,0
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1,2012-04-20-ak-invivo-1,826.07,142.73039605053253,0.3440867459292109,0.0042905816022802,373.7425313488243,0.0017358116367672,0.0001299460085402,0.0009347144390364,5e-05,0.2949535420035986,1,0,21.875,0
|
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2,2012-05-10-ad-invivo-1,891.62,54.35949425221348,0.2757269324823284,0.0022126296519269,267.1813908864623,0.0020271803274778,0.0010762626727976,0.0010968397753966,5e-05,0.1820036615143048,1,0,-31.25,0
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3,2012-06-27-ah-invivo-1,752.07,28.875515577269294,0.2052546848454184,0.0106126298694182,554.4436702347741,0.0017107204697516,0.0003684861730503,0.0012084459280246,5e-05,0.117841868494821,1,0,-148.4375,0
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4,2012-06-27-an-invivo-1,786.29,2.78603894862516,0.0293914484912648,0.0039856346028349,26.682508784285027,0.0013765267071105,6.497312050675181e-06,0.0008998947426172,5e-05,0.1303615925631519,1,0,-4.8828125,0
|
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5,2012-07-03-ak-invivo-1,928.45,1.1337603254658657,0.009636823781567,0.0011835211027475,10.551593612226275,0.0013790127193975,8.556460568825569e-07,0.0001160086835967,5e-05,0.0960461388826031,1,0,-1.318359375,0
|
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6,2012-07-12-ag-invivo-1,744.95,3.695738241953972,0.0362361913251436,0.0018084515871059,14.377436485984251,0.0011056964083457,8.456481114651883e-06,0.0011502269812458,5e-05,0.1115673798324191,1,0,-0.09765625,0
|
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7,2012-07-12-ap-invivo-1,772.92,14.804318060119332,0.0842150819139986,0.0013221092024793,44.13667585034951,0.0014555506316246,0.0001305641603721,0.0009740315668442,5e-05,0.0714312935754097,1,0,1.171875,0
|
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8,2012-12-13-af-invivo-1,673.56,23.49580814191164,0.1324559007885552,0.0100319507469257,427.7951451118343,0.00390366095004,0.0001647812583911,0.0009569332571649,5e-05,0.137553360369833,1,0,-111.71875,0
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9,2012-12-13-ag-invivo-1,667.87,6.068162568399253,0.0445796676973808,0.0015238677109309,95.4247123304821,0.0088281032115323,0.0017011294956245,0.0005315865912276,5e-05,0.2705776489276024,1,0,-22.65625,0
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10,2012-12-13-ah-invivo-1,664.7,28.779813371047524,0.1604926523355509,0.0131422563231108,365.45335373877225,0.0011890432540278,9.862742281751976e-05,0.0014219606674122,5e-05,0.1350142793970573,1,0,-87.5,0
|
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11,2012-12-13-an-invivo-1,657.91,5.882031759118175,0.0403947375117116,0.0010943455482541,34.97293775924098,0.0084065325207767,7.117154703489144e-05,0.0009063094776245,5e-05,0.1582718987844557,1,0,-3.515625,0
|
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12,2012-12-13-ao-invivo-1,657.82,3.281355058730276,0.021994247695007,0.0013722348516982,16.707319333864564,0.0022121021747954,2.699000827997524e-05,0.0008575662334429,5e-05,0.0567186777585402,1,0,-1.26953125,0
|
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13,2012-12-20-aa-invivo-1,668.32,5.156967843782446,0.0418928047894062,0.0022289499682628,75.29252126936278,0.0046106912756426,0.0001168819438512,6.124940707783572e-05,5e-05,0.0693451908879711,1,0,-17.96875,0
|
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14,2012-12-20-ab-invivo-1,738.71,9.280347979087807,0.0239941118906323,0.0012066470927458,46.57993094588944,0.001345591696621,2.898541169815908e-05,0.0011385589203656,5e-05,0.0480050250939148,1,0,-4.78515625,0
|
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15,2012-12-20-ac-invivo-1,744.95,7.430387927489267,0.0345947908745731,0.0025268601414655,43.13386881776496,0.0015547575080636,2.5201073241309866e-05,0.0008625278566343,5e-05,0.0697455808204499,1,0,-5.6640625,0
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16,2012-12-20-ad-invivo-1,759.82,23.049443800356883,0.0750537749678186,0.0045390033895884,124.17804604983468,0.001064631925566,5.637609476304271e-05,0.0010943556029644,5e-05,0.0931679653142917,1,0,-16.2109375,0
|
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17,2012-12-20-ae-invivo-1,763.79,28.80721245217218,0.0698601314329484,0.0053715638461618,190.0928565977152,0.0016453158616621,7.131900555392491e-05,0.0009171798026672,5e-05,0.0611504542659933,1,0,-31.8359375,0
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18,2012-12-21-ai-invivo-1,787.12,36.7842414315693,0.1276318469527911,0.003148853518619,291.18540792514136,0.0020959669717419,0.0005516021341412,0.0012049087410326,5e-05,0.1274364412424319,1,0,-54.6875,0
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19,2012-12-21-ak-invivo-1,796.83,1.7017134980024364,0.0107676608954073,0.0014891509741628,17.982140250050847,0.0015468480651836,7.212072105475155e-05,0.0011152141595196,5e-05,0.0872019091417939,1,0,-3.22265625,0
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20,2012-12-21-am-invivo-1,806.15,4.716159805342061,0.0366776497932095,0.0049998563824837,85.64267738935817,0.0024101257355043,6.079363931198496e-05,0.0011255575558147,5e-05,0.0544681581478567,1,0,-21.484375,0
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21,2012-12-21-an-invivo-1,812.7,5.582036062660869,0.0274227877592669,0.0021553825904866,47.67902220120489,0.0013301530347246,7.299532589864554e-05,0.0012649531095061,5e-05,0.0844907244000913,1,0,-8.984375,0
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22,2013-01-08-aa-invivo-1,800.63,1.1104651443148157,0.0086025843138997,0.0011824418111601,4.462416862986384,0.0011980061424283,1.3402510884404094e-06,0.0003831341515515,5e-05,0.0375245582825626,1,0,0.5859375,0
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23,2014-06-06-ac-invivo-1,800.02,55.08594100237285,0.1519649495271567,0.0023988269653892,382.9362788343988,0.0049762867320738,0.0040047212224557,0.00061712749485,5e-05,0.1119510050767536,1,0,-70.703125,0
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24,2014-06-06-ag-invivo-1,800.12,31.66707022561787,0.2557302246794765,0.006208253008106,350.33971367925733,0.0027828062970542,0.0054194309581835,0.0011980490757128,5e-05,0.1125024266724631,1,0,-81.25,0
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25,2014-12-03-ai-invivo-1,858.5,31.486601023741528,0.2910677134182297,0.0213624955015925,537.3333472412701,0.0034013650498773,0.0007413675790491,0.0008191902158733,5e-05,0.1937871715568695,1,0,-139.0625,0
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26,2014-12-11-aa-invivo-1,651.29,110.31713694365598,1.522266574846523,0.0227436979863408,499.4468540444777,0.0010908984221126,0.0008265394573652,0.0010262164681389,5e-05,0.8644462875159566,1,0,-50.0,0
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27,2014-12-11-ad-invivo-1,650.07,8.858446542191944,0.1769308951576087,0.0034407397494916,81.4459768691674,0.0056094441582848,0.0003040524647618,0.0009215234011342,5e-05,0.3609179195014541,1,0,-16.40625,0
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28,2015-01-15-ab-invivo-1,708.7,29.079679157252954,0.2337139842832452,0.0027630060027207,144.15528554521688,0.0039045887899447,0.004264028976842,0.0005758880667202,5e-05,0.0840743542566496,1,0,-18.75,0
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29,2015-01-20-ac-invivo-1,749.16,8.001503570988135,0.0931857528999433,0.0071105073351134,57.637181305666346,0.003112217193646,9.441371117738886e-05,0.0005985361977974,5e-05,0.3642277333930833,1,0,-9.5703125,0
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30,2015-01-20-ae-invivo-1,775.45,20.985342649544325,0.2413286124255497,0.0129190289618216,944.1126644859896,0.0021193505389306,0.0015655925442817,0.0012881064318266,5e-05,0.2283240154087572,1,0,-280.46875,0
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31,2015-01-20-af-invivo-1,778.15,9.088845198675005,0.1221611050309276,0.0030393173302233,122.26700325769885,0.0025711422027881,0.0025657999527073,0.0012176143643482,5e-05,0.0348591022930843,1,0,-31.25,0
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32,2018-01-10-al,822.43,26.852490056000995,0.1993953919884298,0.0017458564371883,66.70148566718731,0.0014616352764523,0.0008768697373108,0.0012151254594324,5e-05,0.1340861591329578,1,0,5.46875,0
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33,2018-05-08-aa-invivo-1,643.65,23.90042739559335,0.1798294135622658,0.0014978457325112,196.79744698301027,0.0089985815116623,0.0186574994727682,0.0012206757789855,5e-05,0.0834244388001465,1,0,-38.28125,0
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34,2018-05-08-ab-invivo-1,646.62,21.14334023928029,0.1791831401134067,0.0021110702241677,74.44012660456099,0.0021041118380944,0.0004955183093439,0.0008417932875559,5e-05,0.1649339650514045,1,0,-3.125,0
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35,2018-05-08-ac-invivo-1,655.16,5.7344822372910205,0.0536487866361306,0.0012215288834369,23.53137733496618,0.0019583210219127,0.0001738567947328,0.0009188584913498,5e-05,0.1416692216230782,1,0,-1.5625,0
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36,2018-05-08-ad-invivo-1,655.66,10.56270995846859,0.0450137669359761,0.0013544139474406,32.871669695970056,0.0011290166943145,9.029073720834468e-05,0.0007800007176441,5e-05,0.083006053467486,1,0,-0.09765625,0
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37,2018-05-08-ae-invivo-1,649.48,23.23600244127288,0.1649467891961967,0.0039292156627142,139.62843570490134,0.0014895499625897,0.0002143670567366,0.0013078805846238,5e-05,0.1236854639152384,1,0,-21.09375,0
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38,2018-05-08-af-invivo-1,649.93,50.67440031212505,0.1594254584697739,0.0088708778370809,266.86501353697287,0.0011885343507996,0.0001676848771398,0.0011045939825865,5e-05,0.0619649028437271,1,0,-35.15625,0
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39,2018-05-08-ai-invivo-1,653.62,17.97588058957365,0.122233686236529,0.0022403560787985,58.600496136896105,0.0011393995473654,0.0002070984219592,0.0014268613608903,5e-05,0.0723557500363594,1,0,-1.5625,0
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40,2018-06-25-ad-invivo-1,840.79,62.49268603283534,0.2394747446372235,0.0018839278762954,286.0953844311519,0.0023896710179589,0.0024372601380732,0.0010856424997856,5e-05,0.09634714314913,1,0,-29.6875,0
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41,2018-06-26-ah-invivo-1,778.22,9.308930279015678,0.0509027516704495,0.0014501642110434,32.28227188413107,0.0013032229469945,0.0001834593236253,0.0007002061078699,5e-05,0.0899122501049571,1,0,-0.1953125,0
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models_big_fit_starting_vals_transient_100_len_100small.csv
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models_big_fit_starting_vals_transient_100_len_100small.csv
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susceptibility1.pdf
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susceptibility1.pdf
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@ -472,12 +472,12 @@ In this work, the second-order susceptibility in the spiking responses of P-unit
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P-units are heterogeneous in their baseline firing properties \citealp{Grewe2017, Hladnik2023} and differ in their noisiness, which is represented by the coefficient of variation (CV) of the interspike intervals (ISI). Low-CV P-units have a regular firing pattern and are less noisy, whereas high-CV P-units have a less regular firing pattern.
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Second-order susceptibility is expected to be especially pronounced for low-CV cells \citealp{Voronenko2017}. In the following first low-CV P-units will be addressed in \subfigrefb{cells_suscept}{A}.
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P-units probabilistically phase-lock to the EOD of the fish, firing at the same phase but not in every EOD cycle, resulting in a multimodal ISI histogram with maxima at integer multiples of the EOD period (\subfigrefb{cells_suscept}\,\panel[i]{A}, left). The strongest peak in the baseline power spectrum of the firing rate of a P-unit is the \feod{} peak, and the second strongest peak is the mean baseline firing rate \fbase{} peak (\subfigrefb{cells_suscept}\,\panel[i]{A}, right). The power spectrum of P-units is symmetric around half \feod, with baseline peaks appearing at $\feod \pm \fbase{}$.
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P-units probabilistically phase-lock to the EOD of the fish, firing at the same phase but not in every EOD cycle, resulting in a multimodal ISI histogram with maxima at integer multiples of the EOD period (\subfigrefb{cells_suscept}{A}). The strongest peak in the baseline power spectrum of the firing rate of a P-unit is the \feod{} peak, and the second strongest peak is the mean baseline firing rate \fbase{} peak (\subfigrefb{cells_suscept}{B}). The power spectrum of P-units is symmetric around half \feod, with baseline peaks appearing at $\feod \pm \fbase{}$.
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Noise stimuli, as random amplitude modulations (RAM) of the EOD, are common stimuli during P-unit recordings. In the following, the amplitude of the noise stimulus will be quantified as the standard deviation and will be expressed as a contrast (unit \%) in relation to the receiver EOD. The spikes of P-units slightly align with the RAM stimulus with a low contrast (light purple) and are stronger driven in response to a higher RAM contrast (dark purple, \subfigrefb{cells_suscept}\,\panel[ii]{A}). The linear encoding (see \eqnref{linearencoding_methods}) is comparable between the two RAM contrasts in this low-CV P-unit (\subfigrefb{cells_suscept}\,\panel[iii]{A}).%visualized by the gain of the transfer function,\suscept{}
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Noise stimuli, as random amplitude modulations (RAM) of the EOD, are common stimuli during P-unit recordings. In the following, the amplitude of the noise stimulus will be quantified as the standard deviation and will be expressed as a contrast (unit \%) in relation to the receiver EOD. The spikes of P-units slightly align with the RAM stimulus with a low contrast (light purple) and are stronger driven in response to a higher RAM contrast (dark purple, \subfigrefb{cells_suscept}{C}). The linear encoding (see \eqnref{linearencoding_methods}) is comparable between the two RAM contrasts in this low-CV P-unit (\subfigrefb{cells_suscept}{D}).%visualized by the gain of the transfer function,\suscept{}
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To quantify the second-order susceptibility in a three-fish setting the noise stimulus was set in relation to the corresponding P-unit response in the Fourier domain, resulting in a matrix where the nonlinearity at the sum frequency \fsum{} in the firing rate is depicted for two noise frequencies \fone{} and \ftwo{} (\eqnref{susceptibility}, \subfigrefb{cells_suscept}\,\panel[iv]{A}--\panel[v]{A}). Note that the RAM stimulus can be decomposed in frequencies $f$, that approximate the beat frequencies $\Delta f$, occurring in case of pure sine-wave stimulation (\subfigrefb{motivation}{D}). Thus the nonlinearity accessed with the RAM stimulation at \fsum{} (\subfigrefb{cells_suscept}\,\panel[iv]{A}) is comparable to the nonlinearity appearing during pure sine-wave stimulation at \bsum{} (orange peak, \subfigrefb{motivation}{D}). Based on the theory \citealp{Voronenko2017} nonlinearities should arise when \fone{}, \ftwo{} or \fsum{} are equal to \fbase{} (upper right quadrant in \figrefb{plt_RAM_didactic2}), which would imply a triangular nonlinearity shape highlighted by the pink triangle corners in \subfigrefb{cells_suscept}\,\panel[iv]{A}--\panel[v]{A}. A slight diagonal nonlinearity band appears for the low RAM contrast when \fsumb{} is satisfied (yellow diagonal between pink edges, \subfigrefb{cells_suscept}\,\panel[iv]{A}). Since the matrix contains only anti-diagonal elements, the structural changes were quantified by the mean of the anti-diagonals, resulting in the projected diagonal (\subfigrefb{cells_suscept}\,\panel[vi]{A}). For a low RAM contrast the \fbase{} peak in the projected diagonal is slightly enhanced (\subfigrefb{cells_suscept}\,\panel[vi]{A}, gray dot on light purple line). For the higher RAM contrast, the overall second-order susceptibility is reduced (\subfigrefb{cells_suscept}\,\panel[v]{A}), with no pronounced \fbase{} peak in the projected diagonal (\subfigrefb{cells_suscept}\,\panel[vi]{A}, dark purple line). In addition, there is an offset between the projected diagonals, demonstrating that the second-order susceptibility is reduced for RAM stimuli with a higher contrast (\subfigrefb{cells_suscept}\,\panel[vi]{A}).
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To quantify the second-order susceptibility in a three-fish setting the noise stimulus was set in relation to the corresponding P-unit response in the Fourier domain, resulting in a matrix where the nonlinearity at the sum frequency \fsum{} in the firing rate is depicted for two noise frequencies \fone{} and \ftwo{} (\eqnref{susceptibility}, \subfigrefb{cells_suscept}{E--F}). Note that the RAM stimulus can be decomposed in frequencies $f$, that approximate the beat frequencies $\Delta f$, occurring in case of pure sine-wave stimulation (\subfigrefb{motivation}{D}). Thus the nonlinearity accessed with the RAM stimulation at \fsum{} (\subfigrefb{cells_suscept}{E}) is comparable to the nonlinearity appearing during pure sine-wave stimulation at \bsum{} (orange peak, \subfigrefb{motivation}{D}). Based on the theory \citealp{Voronenko2017} nonlinearities should arise when \fone{}, \ftwo{} or \fsum{} are equal to \fbase{} (upper right quadrant in \figrefb{plt_RAM_didactic2}), which would imply a triangular nonlinearity shape highlighted by the pink triangle corners in \subfigrefb{cells_suscept}{E--F}. A slight diagonal nonlinearity band appears for the low RAM contrast when \fsumb{} is satisfied (yellow diagonal between pink edges, \subfigrefb{cells_suscept}{E}). Since the matrix contains only anti-diagonal elements, the structural changes were quantified by the mean of the anti-diagonals, resulting in the projected diagonal (\subfigrefb{cells_suscept}{G}). For a low RAM contrast the \fbase{} peak in the projected diagonal is slightly enhanced (\subfigrefb{cells_suscept}{G}, gray dot on light purple line). For the higher RAM contrast, the overall second-order susceptibility is reduced (\subfigrefb{cells_suscept}{F}), with no pronounced \fbase{} peak in the projected diagonal (\subfigrefb{cells_suscept}{G}, dark purple line). In addition, there is an offset between the projected diagonals, demonstrating that the second-order susceptibility is reduced for RAM stimuli with a higher contrast (\subfigrefb{cells_suscept}{G}).
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%There a triangle is plotted not only if the frequency combinations are equal to the \fbase{} fundamental but also to the \fbase{} harmonics (two triangles further away from the origin).
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%In this figure a part of \fsumehalf{} is marked with the orange diagonal line.
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@ -490,7 +490,7 @@ To quantify the second-order susceptibility in a three-fish setting the noise st
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\end{figure*}
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\subsection{High-CV P-units do not exhibit any nonlinear interactions}%frequency combinations
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Based on the theory strong nonlinearities in spiking responses are not predicted for cells with irregular firing properties and high CVs \citealp{Voronenko2017}. CVs in P-units can range up to 1.5 \citealp{Grewe2017, Hladnik2023} and as a next step the second-order susceptibility of high-CV P-units will be presented. As low-CV P-units, high-CV P-units fire at multiples of the EOD period (\subfigrefb{cells_suscept_high_CV}\,\panel[i]{A}, left). In contrast to low-CV P-units high-CV P-units are noisier in their firing pattern and have a less pronounced mean baseline firing rate peak \fbase{} in the power spectrum of their firing rate during baseline (\subfigrefb{cells_suscept_high_CV}\,\panel[i]{A}, right). High-CV P-units do not exhibit any nonlinear structures related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{cells_suscept_high_CV}\,\panel[iv]{A}--\panel[v]{A}), nor in the projected diagonals (\subfigrefb{cells_suscept_high_CV}\,\panel[vi]{A}). As in low-CV P-units (\subfigrefb{cells_suscept}\,\panel[v]{A}), the mean second-order susceptibility decreases with higher RAM contrasts in high-CV P-units (\subfigrefb{cells_suscept_high_CV}\,\panel[v]{A}).
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Based on the theory strong nonlinearities in spiking responses are not predicted for cells with irregular firing properties and high CVs \citealp{Voronenko2017}. CVs in P-units can range up to 1.5 \citealp{Grewe2017, Hladnik2023} and as a next step the second-order susceptibility of high-CV P-units will be presented. As low-CV P-units, high-CV P-units fire at multiples of the EOD period (\subfigrefb{cells_suscept_high_CV}{A}). In contrast to low-CV P-units high-CV P-units are noisier in their firing pattern and have a less pronounced mean baseline firing rate peak \fbase{} in the power spectrum of their firing rate during baseline (\subfigrefb{cells_suscept_high_CV}{B}). High-CV P-units do not exhibit any nonlinear structures related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{cells_suscept_high_CV}{E--F}), nor in the projected diagonals (\subfigrefb{cells_suscept_high_CV}{G}). As in low-CV P-units (\subfigrefb{cells_suscept}{F}), the mean second-order susceptibility decreases with higher RAM contrasts in high-CV P-units (\subfigrefb{cells_suscept_high_CV}{F}).
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\begin{figure*}[ht]%hp!
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\includegraphics{ampullary}
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@ -500,7 +500,7 @@ Based on the theory strong nonlinearities in spiking responses are not predicted
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\end{figure*}
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\subsection{Ampullary cells exhibit strong nonlinear interactions}%with lower CVs as P-units
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\lepto{} posses another primary sensory afferent population, the ampullary cells, with overall low \fbase{} (80--200\,Hz) and low CV values (0.08--0.22, \citealp{Grewe2017}). Ampullary cells do not phase-lock to the EOD, with no maxima at multiples of the EOD period and smoothly unimodal distributed ISIs (\subfigrefb{ampullary}\,\panel[i]{A}, left). Ampullary cells do not have a peak at \feod{} in the baseline power spectrum of the firing rate with no symmetry around it (\subfigrefb{ampullary}\,\panel[i]{A}, right). Instead, the \fbase{} peak is very pronounced with clear harmonics. When being exposed to a noise stimulus with a low contrast, ampullary cells exhibit very pronounced bands when \fsum{} is equal to \fbase{} or its harmonic in the second-order susceptibility matrix, implying that this cell is especially nonlinear at these frequency combinations (yellow diagonals, \subfigrefb{ampullary}\,\panel[iv]{A}). With higher noise stimuli contrasts these bands disappear (\subfigrefb{ampullary}\,\panel[v]{A}) and the projected diagonal is lowered (\subfigrefb{ampullary}\,\panel[vi]{A}, dark green).
|
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\lepto{} posses another primary sensory afferent population, the ampullary cells, with overall low \fbase{} (80--200\,Hz) and low CV values (0.08--0.22, \citealp{Grewe2017}). Ampullary cells do not phase-lock to the EOD, with no maxima at multiples of the EOD period and smoothly unimodal distributed ISIs (\subfigrefb{ampullary}{A}). Ampullary cells do not have a peak at \feod{} in the baseline power spectrum of the firing rate with no symmetry around it (\subfigrefb{ampullary}{B}). Instead, the \fbase{} peak is very pronounced with clear harmonics. When being exposed to a noise stimulus with a low contrast, ampullary cells exhibit very pronounced bands when \fsum{} is equal to \fbase{} or its harmonic in the second-order susceptibility matrix, implying that this cell is especially nonlinear at these frequency combinations (yellow diagonals, \subfigrefb{ampullary}{E}). With higher noise stimuli contrasts these bands disappear (\subfigrefb{ampullary}{F}) and the projected diagonal is lowered (\subfigrefb{ampullary}{G}, dark green).
|
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|
||||
These nonlinearity bands are more pronounced in ampullary cells than they were in P-units (compare \figrefb{ampullary} and \figrefb{cells_suscept}). Ampullary cells with their unimodal ISI distribution are closer than P-units to the LIF models without EOD carrier, where the predictions about the second-order susceptibility structure have mainly been elaborated on \citealp{Voronenko2017}. All here analyzed ampullary cells had CVs lower than 0.3 and exhibited strong nonlinear effects in accordance with the theoretical predictions \citealp{Voronenko2017}.
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%and here this could be confirmed experimentally.
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@ -558,7 +558,7 @@ The small \fdiff{} peak in the power spectrum of the firing rate appearing durin
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%Second-order susceptibility for all frequencies
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\subsection{Low CVs are associated with strong nonlinearity on a population level}%when considering
|
||||
So far second-order susceptibility was illustrated only with single-cell examples (\figrefb{cells_suscept}, \figrefb{ampullary}). For a P-unit comparison on a population level, the second-order susceptibility of P-units was expressed in a nonlinearity index \nli{}, see \eqnref{nli_equation}, that characterized the peakedness of the \fbase{} peak in the projected diagonal (\subfigrefb{cells_suscept}\,\panel[vi]{A}). \nli{} has high values when the \fbase{} peak in the projected diagonal is especially pronounced, as in the low-CV ampullary cell (\subfigrefb{ampullary}\,\panel[vi]{A}, light green). The two noise stimulus contrasts of this ampullary cell are highlighted in the population statics of ampullary cells with dark circles (\subfigrefb{data_overview_mod}{A}). The higher noise stimulus contrast is associated with a less pronounced peak in the projected diagonal (\subfigrefb{ampullary}\,\panel[vi]{A}, dark green) and is represented with a lower \nli{} value (\subfigrefb{data_overview_mod}{A}, dark circle close to the origin). In an ampullary cell population, there is a negative correlation between the CV during baseline and \nli{}, meaning that the diagonals are pronounced for low-CV cells and disappear towards high-CV cells (\subfigrefb{data_overview_mod}{A}). Since the same stimulus can be strong for some cells and faint for others, the noise stimulus contrast is not directly comparable between cells. A better estimation of the subjective stimulus strength is the response modulation of the cell (see methods section \ref{response_modulation}). Ampullary cells with stronger response modulations have lower \nli{} scores (red in \subfigrefb{data_overview_mod}{A}, \subfigrefb{data_overview_mod}{C}). The so far shown population statistics comprised several RAM contrasts per cell and if instead each ampullary cell is represented with the lowest recorded contrast, then \nli{} significantly correlates with the CV during baseline ($r=-0.46$, $p<0.001$), the response modulation ($r=-0.6$, $p<0.001$) but not with \fbase{} ($r=0.2$, $p=0.16$).%, $\n{}=51$, $\n{}=51$, $\n{}=51${*}{*}{*}^*^*^*each cell can contribute several RAM contrasts in
|
||||
So far second-order susceptibility was illustrated only with single-cell examples (\figrefb{cells_suscept}, \figrefb{ampullary}). For a P-unit comparison on a population level, the second-order susceptibility of P-units was expressed in a nonlinearity index \nli{}, see \eqnref{nli_equation}, that characterized the peakedness of the \fbase{} peak in the projected diagonal (\subfigrefb{cells_suscept}{G}). \nli{} has high values when the \fbase{} peak in the projected diagonal is especially pronounced, as in the low-CV ampullary cell (\subfigrefb{ampullary}{G}, light green). The two noise stimulus contrasts of this ampullary cell are highlighted in the population statics of ampullary cells with dark circles (\subfigrefb{data_overview_mod}{A}). The higher noise stimulus contrast is associated with a less pronounced peak in the projected diagonal (\subfigrefb{ampullary}{G}, dark green) and is represented with a lower \nli{} value (\subfigrefb{data_overview_mod}{A}, dark circle close to the origin). In an ampullary cell population, there is a negative correlation between the CV during baseline and \nli{}, meaning that the diagonals are pronounced for low-CV cells and disappear towards high-CV cells (\subfigrefb{data_overview_mod}{A}). Since the same stimulus can be strong for some cells and faint for others, the noise stimulus contrast is not directly comparable between cells. A better estimation of the subjective stimulus strength is the response modulation of the cell (see methods section \ref{response_modulation}). Ampullary cells with stronger response modulations have lower \nli{} scores (red in \subfigrefb{data_overview_mod}{A}, \subfigrefb{data_overview_mod}{C}). The so far shown population statistics comprised several RAM contrasts per cell and if instead each ampullary cell is represented with the lowest recorded contrast, then \nli{} significantly correlates with the CV during baseline ($r=-0.46$, $p<0.001$), the response modulation ($r=-0.6$, $p<0.001$) but not with \fbase{} ($r=0.2$, $p=0.16$).%, $\n{}=51$, $\n{}=51$, $\n{}=51${*}{*}{*}^*^*^*each cell can contribute several RAM contrasts in
|
||||
|
||||
|
||||
The P-unit population has higher baseline CVs and lower \nli{} values (\subfigrefb{data_overview_mod}{B}) that are weaker correlated than in the population of ampullary cells. The negative correlation (\subfigrefb{data_overview_mod}{B}) is increased when \nli{} is plotted against the response modulation of P-units (\subfigrefb{data_overview_mod}{D}). The two example P-units shown before (\figrefb{cells_suscept}) are highlighted with dark circles in \subfigrefb{data_overview_mod}{B, D}. High-CV P-units and strongly driven P-units have lower \nli{} values (\subfigrefb{data_overview_mod}{B, D}). 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{} ($r=-0.32$, $p<0.001$).%, $\n{}=221$*, $\n{}=221$******, $\n{}=221$
|
||||
@ -750,7 +750,7 @@ We expect to see non-linear susceptibility when $\omega_1 + \omega_2 = f_{Base}$
|
||||
NLI(f_{Base}) = \frac{\max_{f_{Base}-5\,\rm{Hz} \leq f \leq f_{Base}+5\,\rm{Hz}} D(f)}{\mathrm{med}(D(f))}
|
||||
\end{equation}
|
||||
\notejg{sollte es $D(\omega)$ sein?}
|
||||
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 $f_{Base}$ in $D(f)$ was quantified by finding the maximum of $D(f)$ in the range $f_{Base} \pm 5$\,Hz (\subfigrefb{cells_suscept}\,\panel[vi]{A}, gray area) and dividing it by the median of $D(f)$.
|
||||
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 $f_{Base}$ in $D(f)$ was quantified by finding the maximum of $D(f)$ in the range $f_{Base} \pm 5$\,Hz (\subfigrefb{cells_suscept}{G}, gray area) 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{data_overview_mod}.
|
||||
\notejg{should go to the legend: calculated based on the first frozen noise repeat.}
|
||||
|
||||
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Reference in New Issue
Block a user