updated diskussion

susceptibility1.tex

@@ -617,11 +617,18 @@ In this chapter strong nonlinear interactions were found in a subpopulation of l
 %associated with nonlinear effects as \fdiffb{} and \fsumb{} were  with the same firing rate  low-CV P-units
 %and \figrefb{ROC_with_nonlin} 
 
-The nonlinearity in this work are based on a low-CV P-unit model and might require a selective readout from a homogeneous population of low-CV cells to sustain. Since a receptive field is defined as a patch of adjacent receptors on the fish surface \citealp{Maler2009a} and P-units have heterogeneous baseline properties (CV and \fbasesolid{}) that do not depend on the location of the receptor on the fish body \citealp{Hladnik2023} as a result each pyramidal cell in the ELL will integrate over a heterogeneous and not homogeneous P-unit population. The center-surround receptive field organization of superficial and intermediate layer pyramidal cells in addition increases this heterogeneity of the integrated population. Heterogeneous populations with different baseline properties can be more advantageous for the encoding compared to homogeneous populations, as has been shown in P-units and models \citealp{Beiran2018, Hladnik2023}. 
+P-units are very heterogeneous in their baseline firing properties considering their baseline firing rates (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}), their CV and also their bursting. How this heterogeneity influences nonlinear effects when an population of P-units is integrated by the next connected pyramidal cells in the electrosensory lateral line lobe (ELL) should be addressed in further studies. 
+
+The nonlinearity in this work were found in low-CV P-units. For this nonlinear effects to sustain on a population level a selective readout from a homogeneous population of low-CV cells might be required. Since a receptive field is defined as a patch of adjacent receptors on the fish surface \citealp{Maler2009a} and P-units have heterogeneous baseline properties that do not depend on the location of the receptor on the fish body \citealp{Hladnik2023} as a result each pyramidal cell in the ELL will integrate over a heterogeneous and not homogeneous P-unit population. The center-surround receptive field organization of superficial and intermediate layer pyramidal cells in addition increases this heterogeneity of the integrated population. Heterogeneous populations with different baseline properties can be more advantageous for the encoding compared to homogeneous populations, as has been shown in P-units and models \citealp{Beiran2018, Hladnik2023}. 
 
 
 %\subsubsection{A heterogeneous readout is required to cover all female-intruder combinations} 
-A heterogeneous readout might be not only physiologically plausible but also required to address the electrosensory cocktail party for all female-intruder combinations. In this chapter, the improved intruder detection was present only for specific beat frequencies (\figrefb{ROC_with_nonlin}), corresponding to findings from previous literature \citealp{Schlungbaum2023}. If pyramidal cells would integrate only from P-units with the same mean baseline firing rate \fbasesolid{} not all female-male encounters, relevant for the context of the electrosensory cocktail party, could be covered (black square, \subfigrefb{ROC_with_nonlin}{C}). Only a heterogeneous population with different \fbasesolid{} (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}) could lead to a vertical displacement of the improved intruder detection (red diagonals in \subfigrefb{ROC_with_nonlin}{C}). Weather integrating from such a heterogeneous population with different \fbasesolid{} would cover this behaviorally relevant range in the electrosensory cocktail party should be addressed in further studies. 
+A heterogeneous readout might be not only physiologically plausible but also required since nonlinear effects depending on cell property \fbase{} and not on stimulus properties might be not behaviorally relevant. Nonlinear effects might facilitate the encoding of faint signals during a three fish setting, the electrosensory cocktail party. The EOD frequencies of the encoutered three fish would be drawn from the EOD frequency distribution of these fish and a stable faint signal detection would require a response irrespective of the individual EOD frequencies. Weather integrating from a heterogeneous population with different \fbasesolid{} (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}) would cover the behaviorally relevant range in the electrosensory cocktail party should be addressed in further studies. 
+
+%In this work, nonlinear effects were always found only for specific frequencies in relation to \fbase{}, corresponding to findings from previous literature \citealp{Voronenko2017}.
+%Only a heterogeneous population  could cover the whole stimulus space required during the electrosensory cocktail party.
+%If pyramidal cells would integrate only from P-units with the same mean baseline firing rate \fbasesolid{} not all fish encounters, relevant for the context of the electrosensory cocktail party, could be covered. 
+
 
 %
 %Second-order susceptibility was strongest the lower the CV of the use LIF model \citealp{Voronenko2017}.  
@@ -636,8 +643,13 @@ A heterogeneous readout might be not only physiologically plausible but also req
 
 %These low-frequency modulations of the amplitude modulation are
 \subsection{Encoding of secondary envelopes}%($\n{}=49$)	Whether this population of envelope encoders was in addition bursty was not addressed in the corresponding study
-The RAM stimulus used in this chapter is an approximation of the three-fish scenario, where the two generated beats are often slowly modulated at the difference between the two beat frequencies \bdiff{}, known as secondary or social envelope \citealp{Stamper2012Envelope}. In previous works it was shown that low-frequency secondary envelopes are extracted not in P-units but downstream of them in the ELL \citealp{Middleton2006} utilizing threshold nonlinear response curves of the involved neuron \citealp{Middleton2007}. This work addressed that only a small class of cells, with very low CVs would encode the social envolope. This small percentage of the low-CV cells would be in line with no P-units found in the work \citealp{Middleton2007}. On the other hand in previous literature the encoding of social envelopes was attributed to a large subpopulationof P-units with stronger nonlinearities, lower firing rates and higher CVs \citealp{Savard2011}. The explanation for these findings might be in another baseline properties of P-units, bursting, firing repeated burst packages of spikes interleaved with quiescence (unpublished work).
+The RAM stimulus used in this work is an approximation of the three-fish scenario, where the two generated beats are often slowly modulated at the difference between the two beat frequencies \bdiff{}, known as secondary or social envelope \citealp{Stamper2012Envelope}. 
+
+In previous works it was demonstrated that low-frequency secondary envelopes are extracted not in P-units but downstream of them in the ELL \citealp{Middleton2006} utilizing threshold nonlinear response curves of the involved neuron \citealp{Middleton2007}. Based on our work we would predict that only a small class of cells, with very low CVs, should encode the social envelope at the difference frequency. If the sample in that previous work  \citealp{Middleton2007} did not contain low CVs cells, This could explain the conclusion that P-units were identified not as envelope encoders. 
+
+On the other hand in previous literature the encoding of social envelopes was attributed to a subpopulation of P-units with strong nonlinearities, low firing rates and high CVs \citealp{Savard2011}. These findings are in contrast to the findings in the previously mentioned work \citealp{Middleton2007} and on first glance also to our findings. The missing link, that has not been considered in this work, might be bursting of P-units, the repeated firing of spikes after one EOD period interleaved with quiescence (unpublished work). Bursting was not explicitly addressed in the work \citealp{Savard2011}, still the high CVs of the envelope encoding P-units indicate a higher rate of bursting. How bursts influence the second-order susceptibility of P-units will be addressed in following works (in preparation). 
 
+%This small percentage of the low-CV cells would be in line with no P-units found in the work. 
 
 \subsection{More fish would decrease second-order susceptibility}%
 When using noise stimulation strong nonlinearity was demonstrated to appear for small noise stimuli but to decrease for stronger noise stimuli (\figrefb{cells_suscept}). A white noise stimulus is a proxy of many fish being present simultaneously. When the noise amplitude is small, those fish are distant and the nonlinearity is maintained. When the stimulus amplitude increases, many fish close to the receiver are mimicked 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. \eigen{} can usually be found in groups of three to four fish \citealp{Tan2005} and \lepto{} in groups of two \citealp{Stamper2010}. Thus the here described second-order susceptibility might still be behaviorally relevant for both species. The decline of nonlinear effects when several fish are present might be adaptive for the receiver, 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. How nonlinear effects might influence the three-fish setting known as the electrosensory cocktail party (see section \ref{cocktail party}, \citealp{Henninger2018}) will be addressed in the next chapter.

susceptibility1.tex.bak

@@ -617,11 +617,17 @@ In this chapter strong nonlinear interactions were found in a subpopulation of l
 %associated with nonlinear effects as \fdiffb{} and \fsumb{} were  with the same firing rate  low-CV P-units
 %and \figrefb{ROC_with_nonlin} 
 
-The nonlinearity in this work are based on a low-CV P-units. To sustain on a population level a selective readout from a homogeneous population of low-CV cells might be required. Since a receptive field is defined as a patch of adjacent receptors on the fish surface \citealp{Maler2009a} and P-units have heterogeneous baseline properties (CV and \fbasesolid{}) that do not depend on the location of the receptor on the fish body \citealp{Hladnik2023} as a result each pyramidal cell in the ELL will integrate over a heterogeneous and not homogeneous P-unit population. The center-surround receptive field organization of superficial and intermediate layer pyramidal cells in addition increases this heterogeneity of the integrated population. Heterogeneous populations with different baseline properties can be more advantageous for the encoding compared to homogeneous populations, as has been shown in P-units and models \citealp{Beiran2018, Hladnik2023}. 
+P-units are very heterogeneous in their baseline firing properties considering their baseline firing rates (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}), their CV and also their bursting. How this heterogeneity influences nonlinear effects when an population of P-units is integrated by the next connected pyramidal cells in the electrosensory lateral line lobe (ELL) should be addressed in further studies. 
+
+The nonlinearity in this work were found in low-CV P-units. For this nonlinear effects to sustain on a population level a selective readout from a homogeneous population of low-CV cells might be required. Since a receptive field is defined as a patch of adjacent receptors on the fish surface \citealp{Maler2009a} and P-units have heterogeneous baseline properties that do not depend on the location of the receptor on the fish body \citealp{Hladnik2023} as a result each pyramidal cell in the ELL will integrate over a heterogeneous and not homogeneous P-unit population. The center-surround receptive field organization of superficial and intermediate layer pyramidal cells in addition increases this heterogeneity of the integrated population. Heterogeneous populations with different baseline properties can be more advantageous for the encoding compared to homogeneous populations, as has been shown in P-units and models \citealp{Beiran2018, Hladnik2023}. 
 
 
 %\subsubsection{A heterogeneous readout is required to cover all female-intruder combinations} 
-A heterogeneous readout might be not only physiologically plausible but also required if nonlinear effects would be required independent of \fbase{}. If e.g. nonlinear effects would be considered to address the electrosensory cocktail party, a three fish setting where a detection of a faint signal is addressed for different fish situations. In this chapter, the improved intruder detection was present only for specific beat frequencies (\figrefb{ROC_with_nonlin}), corresponding to findings from previous literature \citealp{Schlungbaum2023}. If pyramidal cells would integrate only from P-units with the same mean baseline firing rate \fbasesolid{} not all female-male encounters, relevant for the context of the electrosensory cocktail party, could be covered (black square, \subfigrefb{ROC_with_nonlin}{C}). Only a heterogeneous population with different \fbasesolid{} (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}) could lead to a vertical displacement of the improved intruder detection (red diagonals in \subfigrefb{ROC_with_nonlin}{C}). Weather integrating from such a heterogeneous population with different \fbasesolid{} would cover this behaviorally relevant range in the electrosensory cocktail party should be addressed in further studies. 
+A heterogeneous readout might be not only physiologically plausible but also required since nonlinear effects depending on cell property \fbase{} and not on stimulus properties might be not behaviorally relevant. Nonlinear effects might facilitate the encoding of faint signals during a three fish setting, the electrosensory cocktail party. The EOD frequencies of the encoutered three fish would be drawn from the EOD frequency distribution of these fish and a stable faint signal detection would require a response irrespective of the individual EOD frequencies. In this work, nonlinear effects were always found only for specific frequencies in relation to \fbase{}, corresponding to findings from previous literature \citealp{Voronenko2017}. Weather integrating from a heterogeneous population with different \fbasesolid{} (50--450\,Hz, \citealp{Grewe2017, Hladnik2023}) would cover the behaviorally relevant range in the electrosensory cocktail party should be addressed in further studies. 
+
+%Only a heterogeneous population  could cover the whole stimulus space required during the electrosensory cocktail party.
+%If pyramidal cells would integrate only from P-units with the same mean baseline firing rate \fbasesolid{} not all fish encounters, relevant for the context of the electrosensory cocktail party, could be covered. 
+
 
 %
 %Second-order susceptibility was strongest the lower the CV of the use LIF model \citealp{Voronenko2017}.  
@@ -636,8 +642,11 @@ A heterogeneous readout might be not only physiologically plausible but also req
 
 %These low-frequency modulations of the amplitude modulation are
 \subsection{Encoding of secondary envelopes}%($\n{}=49$)	Whether this population of envelope encoders was in addition bursty was not addressed in the corresponding study
-The RAM stimulus used in this chapter is an approximation of the three-fish scenario, where the two generated beats are often slowly modulated at the difference between the two beat frequencies \bdiff{}, known as secondary or social envelope \citealp{Stamper2012Envelope}. In previous works it was shown that low-frequency secondary envelopes are extracted not in P-units but downstream of them in the ELL \citealp{Middleton2006} utilizing threshold nonlinear response curves of the involved neuron \citealp{Middleton2007}. This work addressed that only a small class of cells, with very low CVs would encode the social envolope. This small percentage of the low-CV cells would be in line with no P-units found in the work \citealp{Middleton2007}. On the other hand in previous literature the encoding of social envelopes was attributed to a large subpopulationof P-units with stronger nonlinearities, lower firing rates and higher CVs \citealp{Savard2011}. The explanation for these findings might be in another baseline properties of P-units, bursting, firing repeated burst packages of spikes interleaved with quiescence (unpublished work).
+The RAM stimulus used in this work is an approximation of the three-fish scenario, where the two generated beats are often slowly modulated at the difference between the two beat frequencies \bdiff{}, known as secondary or social envelope \citealp{Stamper2012Envelope}. In previous works it was demonstrated that low-frequency secondary envelopes are extracted not in P-units but downstream of them in the ELL \citealp{Middleton2006} utilizing threshold nonlinear response curves of the involved neuron \citealp{Middleton2007}. Based on our work we would predict that only a small class of cells, with very low CVs, should encode the social envolope at the difference frequency. The sample in that previous work  \citealp{Middleton2007} was limited, and if it did not contain cells as low CVs as mentioned here, this might be in line with the findings that P-units were determined as no envelope encoders. 
+
+On the other hand in previous literature the encoding of social envelopes was attributed to a subpopulation of P-units with strong nonlinearities, low firing rates and high CVs \citealp{Savard2011}. These findings are in contrast to the findings in the previously mentioned work \citealp{Middleton2007} and on first glance also to our findings. The missing link, that has not been considered in this work, might be bursting of P-units, the repeated firing of spikes after one EOD period interleaved with quiescence (unpublished work). Bursting was not explicitly addressed in the work \citealp{Savard2011}, still the high CVs of the envelope encoding P-units indicate a higher rate of bursting. How bursts influence the second-order susceptibility of P-units will be addressed in following works (in preparation). 
 
+%This small percentage of the low-CV cells would be in line with no P-units found in the work. 
 
 \subsection{More fish would decrease second-order susceptibility}%
 When using noise stimulation strong nonlinearity was demonstrated to appear for small noise stimuli but to decrease for stronger noise stimuli (\figrefb{cells_suscept}). A white noise stimulus is a proxy of many fish being present simultaneously. When the noise amplitude is small, those fish are distant and the nonlinearity is maintained. When the stimulus amplitude increases, many fish close to the receiver are mimicked 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. \eigen{} can usually be found in groups of three to four fish \citealp{Tan2005} and \lepto{} in groups of two \citealp{Stamper2010}. Thus the here described second-order susceptibility might still be behaviorally relevant for both species. The decline of nonlinear effects when several fish are present might be adaptive for the receiver, 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. How nonlinear effects might influence the three-fish setting known as the electrosensory cocktail party (see section \ref{cocktail party}, \citealp{Henninger2018}) will be addressed in the next chapter.