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Articles 1 - 8 of 8
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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 …
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, Mu-Wan Huang
Department of Mathematics: Dissertations, Theses, and Student Research
Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant K-theory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant K-groups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant K-groups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K …
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Fan Cohomology And Its Application To Equivariant K-Theory Of Toric Varieties, Suanne Au
Department of Mathematics: Dissertations, Theses, and Student Research
Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas …
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Department of Mathematics: Dissertations, Theses, and Student Research
In Feynman's Operational Calculi, a function of indeterminates in a commutative space is mapped to an operator expression in a space of (generally) noncommuting operators; the image of the map is determined by a choice of measures associated with the operators, by which the operators are 'disentangled.' Results in this area of research include formulas for disentangling in particular cases of operators and measures. We consider two ways in which this process might be facilitated. First, we develop a set of notations and operations for handling the combinatorial arguments that tend to arise. Second, we develop an intermediate space for …
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.