469 research outputs found
Competing synapses with two timescales: a basis for learning and forgetting
Competitive dynamics are thought to occur in many processes of learning
involving synaptic plasticity. Here we show, in a game theory-inspired model of
synaptic interactions, that the competition between synapses in their weak and
strong states gives rise to a natural framework of learning, with the
prediction of memory inherent in a timescale for `forgetting' a learned signal.
Among our main results is the prediction that memory is optimized if the weak
synapses are really weak, and the strong synapses are really strong. Our work
admits of many extensions and possible experiments to test its validity, and in
particular might complement an existing model of reaching, which has strong
experimental support.Comment: 7 pages, 3 figures, to appear in Europhysics Letter
Eigenvalue Distributions for a Class of Covariance Matrices with Applications to Bienenstock-Cooper-Munro Neurons Under Noisy Conditions
We analyze the effects of noise correlations in the input to, or among, BCM
neurons using the Wigner semicircular law to construct random,
positive-definite symmetric correlation matrices and compute their eigenvalue
distributions. In the finite dimensional case, we compare our analytic results
with numerical simulations and show the effects of correlations on the
lifetimes of synaptic strengths in various visual environments. These
correlations can be due either to correlations in the noise from the input LGN
neurons, or correlations in the variability of lateral connections in a network
of neurons. In particular, we find that for fixed dimensionality, a large noise
variance can give rise to long lifetimes of synaptic strengths. This may be of
physiological significance.Comment: 7 pages, 7 figure
Toward Fulfilling the Promise of Molecular Medicine in Fragile X
Fragile X syndrome (FXS) is the most common inherited form of mental retardation and a leading known cause of autism. It is caused by loss of expression of the fragile X mental retardation protein (FMRP), an RNA-binding protein that negatively regulates protein synthesis. In neurons, multiple lines of evidence suggest that protein synthesis at synapses is triggered by activation of group 1 metabotropic glutamate receptors (Gp1 mGluRs) and that many functional consequences of activating these receptors are altered in the absence of FMRP. These observations have led to the theory that exaggerated protein synthesis downstream of Gp1 mGluRs is a core pathogenic mechanism in FXS. This excess can be corrected by reducing signaling by Gp1 mGluRs, and numerous studies have shown that inhibition of mGluR5, in particular, can ameliorate multiple mutant phenotypes in animal models of FXS. Clinical trials based on this therapeutic strategy are currently under way. FXS is therefore poised to be the first neurobehavioral disorder in which corrective treatments have been developed from the bottom up: from gene identification to pathophysiology in animals to novel therapeutics in humans. The insights gained from FXS and other autism-related single-gene disorders may also assist in identifying molecular mechanisms and potential treatment approaches for idiopathic autism.Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.)National Institute of Mental Health (U.S.)FRAXA Research Foundatio
Random Walks for Spike-Timing Dependent Plasticity
Random walk methods are used to calculate the moments of negative image
equilibrium distributions in synaptic weight dynamics governed by spike-timing
dependent plasticity (STDP). The neural architecture of the model is based on
the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which
forms a negative image of the reafferent signal from the fish's own electric
discharge to optimize detection of sensory electric fields. Of particular
behavioral importance to the fish is the variance of the equilibrium
postsynaptic potential in the presence of noise, which is determined by the
variance of the equilibrium weight distribution. Recurrence relations are
derived for the moments of the equilibrium weight distribution, for arbitrary
postsynaptic potential functions and arbitrary learning rules. For the case of
homogeneous network parameters, explicit closed form solutions are developed
for the covariances of the synaptic weight and postsynaptic potential
distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat
Fourier-Space Crystallography as Group Cohomology
We reformulate Fourier-space crystallography in the language of cohomology of
groups. Once the problem is understood as a classification of linear functions
on the lattice, restricted by a particular group relation, and identified by
gauge transformation, the cohomological description becomes natural. We review
Fourier-space crystallography and group cohomology, quote the fact that
cohomology is dual to homology, and exhibit several results, previously
established for special cases or by intricate calculation, that fall
immediately out of the formalism. In particular, we prove that {\it two phase
functions are gauge equivalent if and only if they agree on all their
gauge-invariant integral linear combinations} and show how to find all these
linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint
number for reference 22
An associative network with spatially organized connectivity
We investigate the properties of an autoassociative network of
threshold-linear units whose synaptic connectivity is spatially structured and
asymmetric. Since the methods of equilibrium statistical mechanics cannot be
applied to such a network due to the lack of a Hamiltonian, we approach the
problem through a signal-to-noise analysis, that we adapt to spatially
organized networks. The conditions are analyzed for the appearance of stable,
spatially non-uniform profiles of activity with large overlaps with one of the
stored patterns. It is also shown, with simulations and analytic results, that
the storage capacity does not decrease much when the connectivity of the
network becomes short range. In addition, the method used here enables us to
calculate exactly the storage capacity of a randomly connected network with
arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA
How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation
This paper addresses two questions in the context of neuronal networks
dynamics, using methods from dynamical systems theory and statistical physics:
(i) How to characterize the statistical properties of sequences of action
potentials ("spike trains") produced by neuronal networks ? and; (ii) what are
the effects of synaptic plasticity on these statistics ? We introduce a
framework in which spike trains are associated to a coding of membrane
potential trajectories, and actually, constitute a symbolic coding in important
explicit examples (the so-called gIF models). On this basis, we use the
thermodynamic formalism from ergodic theory to show how Gibbs distributions are
natural probability measures to describe the statistics of spike trains, given
the empirical averages of prescribed quantities. As a second result, we show
that Gibbs distributions naturally arise when considering "slow" synaptic
plasticity rules where the characteristic time for synapse adaptation is quite
longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure
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