6,990 research outputs found
The Physics of Living Neural Networks
Improvements in technique in conjunction with an evolution of the theoretical
and conceptual approach to neuronal networks provide a new perspective on
living neurons in culture. Organization and connectivity are being measured
quantitatively along with other physical quantities such as information, and
are being related to function. In this review we first discuss some of these
advances, which enable elucidation of structural aspects. We then discuss two
recent experimental models that yield some conceptual simplicity. A
one-dimensional network enables precise quantitative comparison to analytic
models, for example of propagation and information transport. A two-dimensional
percolating network gives quantitative information on connectivity of cultured
neurons. The physical quantities that emerge as essential characteristics of
the network in vitro are propagation speeds, synaptic transmission, information
creation and capacity. Potential application to neuronal devices is discussed.Comment: PACS: 87.18.Sn, 87.19.La, 87.80.-y, 87.80.Xa, 64.60.Ak Keywords:
complex systems, neuroscience, neural networks, transport of information,
neural connectivity, percolation
http://www.weizmann.ac.il/complex/tlusty/papers/PhysRep2007.pdf
http://www.weizmann.ac.il/complex/EMoses/pdf/PhysRep-448-56.pd
Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity
We study the storage and retrieval of phase-coded patterns as stable
dynamical attractors in recurrent neural networks, for both an analog and a
integrate-and-fire spiking model. The synaptic strength is determined by a
learning rule based on spike-time-dependent plasticity, with an asymmetric time
window depending on the relative timing between pre- and post-synaptic
activity. We store multiple patterns and study the network capacity.
For the analog model, we find that the network capacity scales linearly with
the network size, and that both capacity and the oscillation frequency of the
retrieval state depend on the asymmetry of the learning time window. In
addition to fully-connected networks, we study sparse networks, where each
neuron is connected only to a small number z << N of other neurons. Connections
can be short range, between neighboring neurons placed on a regular lattice, or
long range, between randomly chosen pairs of neurons. We find that a small
fraction of long range connections is able to amplify the capacity of the
network. This imply that a small-world-network topology is optimal, as a
compromise between the cost of long range connections and the capacity
increase.
Also in the spiking integrate and fire model the crucial result of storing
and retrieval of multiple phase-coded patterns is observed. The capacity of the
fully-connected spiking network is investigated, together with the relation
between oscillation frequency of retrieval state and window asymmetry
Platonic model of mind as an approximation to neurodynamics
Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
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