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What Matters in Neuronal Locking?
"... Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessa ..."
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Cited by 46 (10 self)
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Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 19 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.
Groupware and Authoring
, 1996
"... This book is a sign of its times. Each one of the chapters – papers written by European authors of various backgrounds – illustrates a departure from the style of theorizing that has been prominent in the social sciences for most of the century. Until very recently, models for behavioral phenomena w ..."
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Cited by 4 (0 self)
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This book is a sign of its times. Each one of the chapters – papers written by European authors of various backgrounds – illustrates a departure from the style of theorizing that has been prominent in the social sciences for most of the century. Until very recently, models for behavioral phenomena were chiefly based on numerical representations of the objects of concern, e.g. the subjects and the stimuli under study. This was due in large part to the influence of nineteenth century physics, which played the role of the successful older sister, the one that had to be imitated if one wished to be taken seriously in scientific circles. The mystical belief that there could be science only when the objects of concern were susceptible of measurement in the sense of physics was a credo that could not be violated without risks. Another, more honorable justification was that the numerical models were the only ones capable of feasible calculations. (In fact, these models were typically linear.) An early example of such theorizing in psychology is factor analysis, which attempted to represent the results of mental tests in a real vector space of small dimensionality, each subject
Random Linear Cellular Automata: Fractals associated with random multiplication of polynomials
"... Abstract Random multiplication of a given set of s polynomials with coe cients in a nite eld following a random sequence generated by Bernoulli trial with s possible outcomes is a (timedependent) linear cellular automaton (LCA). As in the case of LCA with states in a nite eld we associate with this ..."
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Cited by 1 (0 self)
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Abstract Random multiplication of a given set of s polynomials with coe cients in a nite eld following a random sequence generated by Bernoulli trial with s possible outcomes is a (timedependent) linear cellular automaton (LCA). As in the case of LCA with states in a nite eld we associate with this sequence a compact set the rescaled evolution set. The law of the iterated logarithm implies that this fractal set almost surely does not depend on the random sequence.
Seminar für Mathematik und
"... This book is a sign of its times. Each one of the chapters – papers written by European authors of various backgrounds – illustrates a departure from the style of theorizing that has been prominent in the social sciences for most of the century. Until very recently, models for behavioral phenomena w ..."
Abstract
 Add to MetaCart
This book is a sign of its times. Each one of the chapters – papers written by European authors of various backgrounds – illustrates a departure from the style of theorizing that has been prominent in the social sciences for most of the century. Until very recently, models for behavioral phenomena were chiefly based on numerical representations of the objects of concern, e.g. the subjects and the stimuli under study. This was due in large part to the influence of nineteenth century physics, which played the role of the successful older sister, the one that had to be imitated if one wished to be taken seriously in scientific circles. The mystical belief that there could be science only when the objects of concern were susceptible of measurement in the sense of physics was a credo that could not be violated without risks. Another, more honorable justification was that the numerical models were the only ones capable of feasible calculations. (In fact, these models were typically linear.) An early example of such theorizing in psychology is factor analysis, which attempted to represent the results of mental tests in a real vector space of small dimensionality, each subject