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ShawEmpiricalSHCPaper.tex
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ShawEmpiricalSHCPaper.tex
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%\documentclass[11pt, oneside]{article} % use "amsart" instead of "article" for AMSLaTeX format
\documentclass[twocolumn]{svjour3} % Spring article format
\journalname{Journal of Computational Neuroscience}
\usepackage[utf8]{inputenc}
\usepackage{microtype}
\usepackage{geometry} % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper} % ... or a4paper or a5paper or ...
%\geometry{landscape} % Activate for for rotated page geometry
%\usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx} % Use pdf, png, jpg, or eps with pdflatex; use eps in DVI mode
% TeX will automatically convert eps --> pdf in pdflatex
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{mathptmx} % times font, as per journal
\usepackage{subfig} % subfigure labeling (e.g., 1a)
\usepackage{float} % adds the "H" placement option to force the figure to be inline
\usepackage{natbib}
\usepackage{multirow}
\usepackage{rotating}
\usepackage{array}
\usepackage{fixltx2e} % fix two column figure order
%\usepackage[textsize=tiny]{todonotes}
\usepackage[disable]{todonotes}
\usepackage{draftwatermark} % mark this as a draft
% centered overlap used to allow the expression for the summation range (under
% the sigma to extend under other parts of the equation.
% from Perlis, TUGboat Vol 0, no 0, 2001
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
\def\mathclap{\mathpalette\mathclapinternal}
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\renewcommand{\topfraction}{0.9} % allow more floats to fill most of the page
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% typing shortcuts
% short author and title for top of page (Springer specific)
\titlerunning{Dynamical Architecture for Adaptive Responses to Mechanical Loads}
\authorrunning{Shaw KM, Cullins MJ, McManus JM, Lu H, Thomas PJ, Chiel HJ}
\title{The Significance of Dynamical Architecture for Adaptive Responses to Mechanical Loads During Rhythmic Behavior}
\author{
Kendrick M.~Shaw \and Miranda J.~Cullins \and Jeffrey M.~McManus \and Hui Lu \and Peter J.~Thomas \and Hillel J.~Chiel}
%\date{} % Activate to display a given date or no date
\newlength{\figwidth}
\figwidth=\linewidth
\let\ifthesis=\iffalse
\institute{
Kendrick M.~Shaw \at
Department of Biology and Medical Scientist Training Program, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106, USA \\
\email{[email protected]} % \\
\and
Miranda J.~Cullins $\cdot$ Jeffrey M.~McManus $\cdot$ Hui Lu \at
Department of Biology, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106, USA
\and
Peter J.~Thomas \at
Departments of Mathematics, Biology and Cognitive Science, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106, USA \\
\email{[email protected]} % \\
\and
Hillel J.~Chiel \at
Departments of Biology, Neurosciences and Biomedical Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106, USA \\
\email{[email protected]} % \\
}
\date{Received: date / Accepted: date}
% The correct dates will be entered by the editor
\begin{document}
\listoftodos
\maketitle
\begin{abstract}
Many behaviors require reliably generating sequences of motor activity while
adapting the activity to incoming sensory information. This process has often
been conceptually explained as either fully dependent on sensory input (a
chain reflex) or fully independent of sensory input (an idealized central
pattern generator, or CPG), although the consensus of the field is that most neural
pattern generators lie somewhere between these two extremes. Many mathematical
models of neural pattern generators use limit cycles to generate the sequence
of behavior, but other models, such as a heteroclinic channel (an attracting
chain of saddle points), have been
suggested. To explore the continuum between CPGs and chain reflexes, in this
paper we describe a nominal model of feeding in
\textit{Aplysia californica} that can be smoothly shifted between a
generic limit cycle (where the velocity changes by less than an order of
magnitude throughout the cycle) and a heteroclinic channel (where the velocity
becomes small when the trajectory passes near saddle points). We then study
the behavior of the system in these two parameter regimes and compare the
behavior of the models with behavior recorded in the animal \textit{in vivo}
and \textit{in vitro}. We show that while both pattern generators can generate
similar behavior, the stable heteroclinic channel can better respond to
small changes in sensory input induced by load, and that the response matches
the changes seen when a load is added \textit{in vivo}. We then show that
the stable heteroclinic channel shows much more dramatic slowing of activity
than the generic limit cycle when sensory input is reduced, and show that
similar slowing with removal of proprioception is seen \textit{in vitro}.
Finally, we show that the distributions of burst lengths seen \textit{in
vivo} are better matched by the distribution expected from a stable
heteroclinic channel than that expected from a generic limit cycle.
These observations suggest that feeding behavior in \textit{Aplysia} may be
better described by a model using a heteroclinic channel than a more generic
limit cycle.
\keywords{Aplysia \and heteroclinic channel \and Central Pattern Generator \and Chain reflex \and Limit cycle}
% \PACS{PACS code1 \and PACS code2 \and more}
% \subclass{MSC code1 \and MSC code2 \and more}
\end{abstract}
\input{ShawEmpiricalSHCPaper_body}
\todo{move items in shc.bib into existing .bib files}
%\section*{Citations to consider}
%\begin{itemize}
% \item \citet{rabinovich_generation_2006}
% \item \citet{kirst_bifurcation_2007}
% \item \citet{ross_detecting_2010}
% \item \citet{rabinovich_robust_2011}
% \item \citet{woodman_building_2011}
% \item \citet{nowotny_pacemaker_2011}
% \item \citet{friston_perception_2012}
%\end{itemize}
\bibliographystyle{springer/spbasic}
\bibliography{shc.bib,math.bib,neuroscience.bib,reliability.bib}
\end{document}