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		\begin{center}
		{\Huge TITEL \par}
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		{\Large Masterthesis \par}
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		{der Mathematisch-Naturwissenschaftlichen Fakultät \par} {der Eberhard Karls Universität Tübingen \par}
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		{Erstkorrektor: \\
		Zweitkorrektor: Prof.~Dr.~Jan Benda \par}
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		{Lehrbereich für Neuroethologie}
		
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		\large vorgelegt von \par
		\large Alexander Mathias Ott \par
		Abgabedatum: 30.11.2017
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\section*{Eigenständigkeitserklärung}

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Hiermit erkläre ich, dass ich die vorgelegte Arbeit selbstständig verfasst habe und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe. 

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Außerdem erkläre ich, dass die eingereichte Arbeit weder vollständig noch in wesentlichen Teilen Gegenstand eines anderen Prüfungsverfahrens gewesen ist.






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	$\overline{\text{Unterschrift}\hspace{6cm}}$ & $\overline{\text{Ort, Datum}\hspace{4cm}}$ \\
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\section{Abstract}
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\section{Introduction}

\begin{enumerate}
	\item electric fish
	\begin{enumerate}
		\item general: habitat, 
		\item as model animal for ethology
		\item electric organ + eod
		\item sensory neurons p- and t(?)-type
	\end{enumerate}
	\item sensory perception
	\begin{enumerate}
		\item receptor -> heterogenic population
		\item further analysis limited by what receptors code for - P-Units encoding 
		\item p-type neurons code AMs
	\end{enumerate}
	
	\item goal be able to simulate heterogenic population to analyse full coding properties -> many cells at the same time needed -> only possible in vitro/ with model simulations
	
	\item Possible to draw representative values for model parameters to generate a population ?
	

\end{enumerate}

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\section{Materials and Methods}

\subsection{Notes:}

\begin{enumerate}
	
	\item Construction of model
	\begin{enumerate}
		\item Explain general LIF
		\item parameters explanation, dif. equations
		\item Explain addition of adaption current
		\item note addition of noise
		\item check between alpha in fire-rate model adaption and a-delta in LIFAC
		\item check for noise independence from step-size (?)
	\end{enumerate}
	
	\item Data generation
	\begin{enumerate}
		\item How data was measured / which data used
		\item How data was chosen -> at least 30s baseline, 7 contrasts with 7 trials
		\item experimental protocells were allowed by XYZ (before 2012: All experimental protocols were approved and complied with national and regional laws (file no. 55.2-1-54-2531-135-09). between 2013-2016 ZP 1/13 Regierungspräsidium Tübingen and after 2016 ZP 1/16 Regierungspräsidium Tübingen)
	\end{enumerate}
	
	\item behavior parameters:
	\begin{enumerate}
		\item which behaviors were looked at / calculated and why (bf, vs, sc, cv, fi-curve...)
		\item how exactly were they calculated in the cell and model
	\end{enumerate}		
	
	\item Fitting of model to data
	\begin{enumerate}
		\item which variables where determined beforehand (None, just for start parameters)
		\item which variables where fit 
		\item What method was used (Nelder-Mead) and why/(how it works?)
		\item fit routine ? (currently just all at the same time)
	\end{enumerate}
\end{enumerate}


\section{Results}

\begin{enumerate}

\item how well does the fitting work? 

\item distribution of behavior parameters (cells and models)

\item distributions of parameters

\item correlations: between parameters between parameters and behavior

\item correlation between final error and behavior parameters of the cell -> hard to fit cell types

\item (response to SAM stimuli)
\end{enumerate}


\section{Discussion}



\section{Possible Sources}

\subsection{Henriette Walz - Thesis}
\subsubsection{Nervous system - Signal encoding}
\begin{enumerate}
\item single neurons are the building blocks of the nervous system (Cajal 1899)
\item encoding of information in spike frequency - rate code(first description(?) Adrian 1928) also find examples! (light flash intensity Barlow et al. 1971, )
\item encoding info in inter spike intervals (Singer and Gary 1995)
\item encoding time window (Theunissen and Miller 1995) "This time window is the time scale in which the encoding is assumed to take placewithin the nervous system
\item encoding is noisy (Mainen and Sejnowski 1995, Tolhurst et al 1983, Tomko and Crapper 1974 -> review Faisal et al 2008) in part because of stimulus properties but also cell properties (Ion channel stochasticity (van Rossum et al.,2003))
\item noise can be beneficial to encoding -> “stochastic
resonance” (weak stimuli on thresholding devices like neurons, noice allows coding of sub threshold stimuli) (Benzi et al., 1981)
\item single neurons are anatomically and computationally independant units, the
representation and processing of information in vertebrate nervous systems is distributed
over groups or networks of cells (for a review, see Pouget et al., 2000)
\item It has
been shown that the synchrony among cells carries information on a very fine temporal
scale in different modalities, from olfaction (Laurent, 1996) to vision (Dan et al., 1998)
\item In the electrosensory system it was shown before that communica-
tion signals change the synchrony of the receptor population (Benda et al., 2005, 2006)
and that this is read out by cells in the successive stages of the electrosensory pathway
(Marsat and Maler, 2010, 2012; Marsat et al., 2009).
\item An advantage of rate coding in populations is that it is fast. The rate in
single neurons has to be averaged over a time window, that is at least as long as the
minimum interspike interval. In contrast, the population rate can follow the stimulus
instantaneous, as it does not have to be averaged over time but can be averaged over
cells (Knight, 1972a).
\item In a population of neurons subject to neuronal noise, stochastic resonance occurs
even if the stimulus is strong enough to trigger action potentials itself (supra-threshold
stochastic resonance described by Stocks, 2000; see Fig. 1.1 B
\item Cells of the same type and from the same population often vary in their stimulus sen-
sitivity (Ringach et al., 2002) as well as in their baseline activity properties (Gussin et al., 2007; Hospedales et al., 2008)
\item Heterogeneity has been shown to improve infor-
mation coding in both situations, in the presence of noise correlations, for example in
the visual system cells (Chelaru and Dragoi, 2008) or when correlations mainly originate
from shared input as in the olfactory system (Padmanabhan and Urban, 2010)
\item A prerequisite to a neural code thus is that it can be read out by other neurons (Perkel
and Bullock, 1968).
\item Developement and evolution shape the func-
tioning of many physiological systems and there is evidence that they also shape the
encoding mechanisms of nervous systems. For example, the development of frequency
selectivity in the auditory cortex has been shown to be delayed in animals stimulated
with white noise only (Chang and Merzenich, 2003). Also, several encoding mecha-
nisms can be related to the selective pressure that the energetic consumption of the ner-
vous system has exerted on its evolution (Laughlin, 2001; Niven and Laughlin, 2008).
These finding conformed earlier theoretical predictions that had proposed that coding
should be optimised to encode natural stimuli in an energy-efficient way (Barlow, 1972). -> importance of using natrual stimuli as the coding and nervous system could be optimised for unknown stimuli features not contained in the artificial stimuli like white noise.
\end{enumerate}
\subsubsection{electrosensory system - electric fish}

\begin{enumerate}
\item For decades, studies examining the neurophysiological systems of weakly electric
fish have provided insights into how natural behaviours are generated using relatively
simple sensorimotor circuits (for recent reviews see: Chacron et al., 2011; Fortune, 2006;
Marsat and Maler, 2012). Further, electrocommunication signals are relatively easy to
describe, classify and simulate, facilitating quantification and experimental manipula-
tion. Weakly electric fish are therefore an ideal system for examining how communica-
tion signals influence sensory scenes, drive sensory system responses, and consequently
exert effects on conspecific behaviour.
\item The weakly electric fish use active electroreception to navigate and communicate under
low light conditions (Zupanc et al., 2001).
\item In active electroreception, animals produce
an electric field using and electric organ (and this electric field is therefore called the
electric organ discharge, EOD) and infer, from changes of the EOD, information about
the location and identification of objects and conspecifics in their vicinity (e.g. Kelly
et al., 2008; MacIver et al., 2001). However, perturbations result not only from objects
and other fish, but also from self-motion and other factors. All of these together make
up the electrosensory scene. The perturbed version of the fish’s own field on its skin
is called the electric image (Caputi and Budelli, 2006), which is sensed via specialised
receptors distributed over the body surface (Carr et al., 1982).
\item In A. leptorhynchus, the
dipole-like electric field (electric organ discharge, EOD) oscillates in a quasi-sinusoidal
fashion at frequencies from 700 to 1100 Hz (Zakon et al., 2002) with males emitting at
higher frequencies than females (Meyer et al., 1987).
\item The EOD of each individual fish
has a specific frequency (the EOD frequency, EODf) that remains stable in time (exhibit-
ing a coefficient of variation of the interspikes intervals as low as $2 ∗ 10^{−4} $; Moortgat et al., 1998).
\item During social encounters, wave-type fish often modulate the frequency as
well as the amplitude of their field to communicate (Hagedorn and Heiligenberg, 1985).
\item Communication signals in A. leptorhynchus have been clas-
sified into two classes: (i) chirps are transient and stereotyped EODf excursions over
tens of milliseconds (Zupanc et al., 2006), while (ii) rises are longer duration and more
variable modulations of EODf, typically lasting for hundreds of milliseconds to sec-
onds (Hagedorn and Heiligenberg, 1985; Tallarovic and Zakon, 2002). (OLD INFO ? RISES NOW OVER MINUTES/HOURS)
\end{enumerate}

\subsubsection{P-Units encoding}

\begin{enumerate}
\item In baseline conditions (stimulus only own EOD), they fire irregularly at a certain baseline rate. Action potentials occur approximately at a certain phase of the EOD cycle, they are phase-locked to the EOD, but only with a certain probability to each cycle. The baseline rate differs from cell to cell (compare the two example cells in Fig. 2.2 A and B, Gussin et al., 2007)
\item Since tuberous receptors are distributed over the whole body and the EOD spans the
whole surrounding, all P-units of a given animal are stimulated with a similar stimulus
(see Kelly et al. (2008) for an exact model of the EOD). Their noise sources are, however,
uncorrelated (Chacron et al., 2005b).
\item In response to a step increase in EOD amplitude, P-units exhibit pronounced spike frequency
adaptation (Benda et al., 2005; Chacron et al., 2001b; Nelson et al., 1997; Xu et al., 1996).
\end{enumerate}

\subsubsection{Chapter 4 - other models}
\begin{enumerate}
\itemKashimori et al.
(1996) built a conductance-based model of the whole electroreceptor unit and were able to qualitatively reproduce the behaviour of different types of tuberous units.
\item Nelson
et al. (1997) constrained a stochastically spiking model by linear filters of the previously determined P-unit frequency tuning.
\item Kreiman et al. (2000) used the same frequency
filters to stimulate a noisy perfect integrate-and-fire neuron with which they investi-
gated the variability of cell responses to random amplitude modulations (RAMs).
\item To reproduce the probabilistic phase-locked firing and the correlations of the ISIs, Chacron
et al. (2000) used a noisy leaky integrate-and-fire model with refractoriness as well as a
dynamical threshold.
\item Benda et al. (2005) used a firing rate model with a negative adap-
tation current to reproduce the high-pass behaviour of P-units.
\end{enumerate}

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