Added MA literature selection and grasshopper sketch SVGs.

main.tex

@@ -43,7 +43,7 @@ style=authoryear,
 \newcommand{\pc}{p(c_i,\,T)} % Probability density (general interval)
 \newcommand{\pclp}{p(c_i,\,\tlp)} % Probability density (lowpass interval)
 
-\section{The sensory world of a grasshopper}
+\section{Exploring a grashopper's sensory world}
 
 Strong dependence on acoustic signals for ranged communication\\
 - Diverse species-specific sound repertoires and production mechanisms\\
@@ -87,6 +87,19 @@ How can a human observer conceive a grasshopper's auditory percepts?\\
 - How to integrate the available knowledge on anatomy, physiology, ethology?\\
 $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model framework
 
+\textbf{Precursor work for model construction (special thanks to authors):}
+
+Linear-nonlinear modelling of behavioral responses to artificial songs\\
+- Feature expansion as implemented in our model: Major contribution!\\
+- Bank of linear filters, nonlinearity, temporal integration, feature weighting\\
+$\rightarrow$ \cite{clemens2013computational} (crickets)\\
+$\rightarrow$ \cite{clemens2013feature} (grasshoppers)\\
+$\rightarrow$ \cite{ronacher2015computational}\\
+\textbf{Own advancements/key differences}:\\
+1) Used boxcar functions as artificial "songs" (focus on few key parameters)\\
+$\rightarrow$ Now actual, variable songs (as naturalistic as possible)\\
+2) Fitted filters to behavioral data\\
+$\rightarrow$ More general, simpler, unfitted formalized Gabor filter bank
 
 \section{Developing a functional model of\\the grasshopper auditory pathway}
 
@@ -96,7 +109,7 @@ $\rightarrow$ Abstract, simplify, formalize $\rightarrow$ Functional model frame
 "Pre-split portion" of the auditory pathway:\\
 Tympanal membrane $\rightarrow$ Receptor neurons $\rightarrow$ Local interneurons
 
-Similar response/filter properties within receptor/interneuron populations (\cite{clemens2011})\\
+Similar response/filter properties within receptor/interneuron populations (\cite{clemens2011efficient})\\
 $\rightarrow$ One population-wide response trace per stage (no "single-cell resolution")
 
 \textbf{Stage-specific processing steps and functional approximations:}
@@ -140,7 +153,7 @@ $\rightarrow$ Highpass filter 10 Hz
 "Post-split portion" of the auditory pathway:\\
 Ascending neurons (AN) $\rightarrow$ Central brain neurons
 
-Diverse response/filter properties within AN population (\cite{clemens2011})\\
+Diverse response/filter properties within AN population (\cite{clemens2011efficient})\\
 - Pathway splitting into several parallel branches\\
 - Expansion into a decorrelated higher-dimensional sound representation\\
 $\rightarrow$ Individual neuron-specific response traces from this stage onwards
@@ -327,18 +340,29 @@ duty cycle-encoding quantity, mediated by threshold function $\nl$
 on the magnitude of the derivative of $c_i(t)$ in temporal proximity to time
 points at which $c_i(t)$ crosses threshold value $\thr$\\
 $\rightarrow$ The steeper the slope of $c_i(t)$, the less $T_1$ changes with scale variations\\
-$\rightarrow$ Extreme amplitudes of $c_i(t)$ (peaks/troughs)
+$\rightarrow$ If $T_1$ is invariant to scale variation in $c_i(t)$, then so is $\feat(t)$
 
-$\rightarrow$ Only amplitudes of \\
-$\rightarrow$ Absolute amplitudes of peaks/troughs of $c_i(t)$ \\
-$\rightarrow$ Acuity of peaks/troughs in $c_i(t)$ matters, not their absolute amplitude
-
-- From graded stimulus to categorical behavioral decision:\\
+- Suggests a relatively simple rule for optimal choice of threshold value $\thr$:\\
+$\rightarrow$ Find amplitude $c_i$ that maximizes absolute derivative of $c_i(t)$ over time\\
+$\rightarrow$ Optimal with respect to intensity invariance of $\feat(t)$, not necessarily for
+other criteria such as song-noise separation or diversity between features
 
+- Nonlinear operations can be used to detach representations from graded physical
+stimulus (to fasciliate categorical behavioral decision-making?):\\
+1) Capture sufficiently precise amplitude information: $\env(t)$, $\adapt(t)$\\
+$\rightarrow$ Closely following the AM of the acoustic stimulus\\
+2) Quantify relevant stimulus properties on a graded scale: $c_i(t)$\\
+$\rightarrow$ More decorrelated representation, compared to prior stages\\
+3) Nonlinearity: Distinguish between "relevant vs irrelevant" values: $\bi(t)$\\
+$\rightarrow$ Trading a graded scale for two or more categorical states\\
+4) Represent stimulus properties under relevance constraint: $\feat(t)$\\
+$\rightarrow$ Graded again but highly decorrelated from the acoustic stimulus\\
+5) Categorical behavioral decision-making requires further nonlinearities\\
+$\rightarrow$ Parameters of a behavioral response may be graded (e.g. approach speed),
+initiation of one behavior over another is categorical (e.g. approach/stay)
 
 \section{Discriminating species-specific song\\patterns in feature space}
 
-
 \section{Conclusions \& outlook}
 
 \end{document}