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Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris
Population Coding Of Tone Stimuli In Auditory Cortex: Dynamic Rate Vector Analysis, Peter Bartho, Carina Curto, Artur Luczak, Stephan L. Marguet, Kenneth D. Harris
Department of Mathematics: Faculty Publications
Neural representations of even temporally unstructured stimuli can show complex temporal dynamics. In many systems, neuronal population codes show “progressive differentiation,” whereby population responses to different stimuli grow further apart during a stimulus presentation. Here we analyzed the response of auditory cortical populations in rats to extended tones. At onset (up to 300 ms), tone responses involved strong excitation of a large number of neurons; during sustained responses (after 500 ms) overall firing rate decreased, but most cells still showed a statistically significant difference in firing rate. Population vector trajectories evoked by different tone frequencies expanded rapidly along an initially …
A Simple Model Of Cortical Dynamics Explains Variability And State Dependence Of Sensory Responses In Urethane-Anesthetized Auditory Cortex, Carina Curto, Shuzo Sakata, Stephan Marguet, Vladimir Itskov, Kenneth D. Harris
A Simple Model Of Cortical Dynamics Explains Variability And State Dependence Of Sensory Responses In Urethane-Anesthetized Auditory Cortex, Carina Curto, Shuzo Sakata, Stephan Marguet, Vladimir Itskov, Kenneth D. Harris
Department of Mathematics: Faculty Publications
The responses of neocortical cells to sensory stimuli are variable and state dependent. It has been hypothesized that intrinsic cortical dynamics play an important role in trial-to-trial variability; the precise nature of this dependence, however, is poorly understood. We show here that in auditory cortex of urethane-anesthetized rats, population responses to click stimuli can be quantitatively predicted on a trial-by-trial basis by a simple dynamical system model estimated from spontaneous activity immediately preceding stimulus presentation. Changes in cortical state correspond consistently to changes in model dynamics, reflecting a nonlinear, self-exciting system in synchronized states and an approximately linear system in …
Parameterizing The Growth-Decline Boundary For Uncertain Population Projection Models, Joan Lubben, Derek Boeckner, Richard Rebarber, Stuart Townley, Brigitte Tenhumberg
Parameterizing The Growth-Decline Boundary For Uncertain Population Projection Models, Joan Lubben, Derek Boeckner, Richard Rebarber, Stuart Townley, Brigitte Tenhumberg
Department of Mathematics: Faculty Publications
We consider discrete time linear population models of the form n(t + 1) = An(t) where A is a population projection matrix or integral projection operator, and represents a structured population at time t. It is well known that the asymptotic growth or decay rate of n(t) is determined by the leading eigenvalue of A. In practice, population models have substantial parameter uncertainty, and it might be difficult to quantify the effect of this uncertainty on the leading eigenvalue. For a large class of matrices and integral operators A, we …
Analysis Of Connections Between Pseudocodewords, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Analysis Of Connections Between Pseudocodewords, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Department of Mathematics: Faculty Publications
The role of pseudocodewords in causing noncodeword outputs in linear programming (LP) decoding, graph cover decoding, and iterative message-passing decoding is investigated. The three main types of pseudocodewords in the literature — linear programming pseudocodewords, graph cover pseudocodewords, and computation tree pseudocodewords — are reviewed and connections between them are explored. Some discrepancies in the literature on minimal and irreducible pseudocodewords are highlighted and clarified, and a value for the minimal degree cover necessary to realize an LP pseudocodeword is found. Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given. This allows for further …
Connections Between Computation Trees And Graph Covers, Deanna Dreher, Judy L. Walker
Connections Between Computation Trees And Graph Covers, Deanna Dreher, Judy L. Walker
Department of Mathematics: Faculty Publications
Connections between graph cover pseudocodewords and computation tree pseudocodewords are investigated with the aim of bridging the gap between the theoretically attractive analysis of graph covers and the more intractable analysis of iterative message-passing algorithms that are intuitively linked to graph covers. Both theoretical results and numerous examples are presented.