670 research outputs found
A Recurrent Cooperative/Competitive Field for Segmentation of Magnetic Resonance Brain Imagery
The Grey-White Decision Network is introduced as an application of an on-center, off-surround recurrent cooperative/competitive network for segmentation of magnetic resonance imaging (MRI) brain images. The three layer dynamical system relaxes into a solution where each pixel is labeled as either grey matter, white matter, or "other" matter by considering raw input intensity, edge information, and neighbor interactions. This network is presented as an example of applying a recurrent cooperative/competitive field (RCCF) to a problem with multiple conflicting constraints. Simulations of the network and its phase plane analysis are presented
Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier LtdThis Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov–Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China (05KJB110154), the NSF of Jiangsu Province of China (BK2006064), and the National Natural Science Foundation of China (10471119)
Why are probabilistic laws governing quantum mechanics and neurobiology?
We address the question: Why are dynamical laws governing in quantum
mechanics and in neuroscience of probabilistic nature instead of being
deterministic? We discuss some ideas showing that the probabilistic option
offers advantages over the deterministic one.Comment: 40 pages, 8 fig
Statistical physics of neural systems with non-additive dendritic coupling
How neurons process their inputs crucially determines the dynamics of
biological and artificial neural networks. In such neural and neural-like
systems, synaptic input is typically considered to be merely transmitted
linearly or sublinearly by the dendritic compartments. Yet, single-neuron
experiments report pronounced supralinear dendritic summation of sufficiently
synchronous and spatially close-by inputs. Here, we provide a statistical
physics approach to study the impact of such non-additive dendritic processing
on single neuron responses and the performance of associative memory tasks in
artificial neural networks. First, we compute the effect of random input to a
neuron incorporating nonlinear dendrites. This approach is independent of the
details of the neuronal dynamics. Second, we use those results to study the
impact of dendritic nonlinearities on the network dynamics in a paradigmatic
model for associative memory, both numerically and analytically. We find that
dendritic nonlinearities maintain network convergence and increase the
robustness of memory performance against noise. Interestingly, an intermediate
number of dendritic branches is optimal for memory functionality
A "Cellular Neuronal" Approach to Optimization Problems
The Hopfield-Tank (1985) recurrent neural network architecture for the
Traveling Salesman Problem is generalized to a fully interconnected "cellular"
neural network of regular oscillators. Tours are defined by synchronization
patterns, allowing the simultaneous representation of all cyclic permutations
of a given tour. The network converges to local optima some of which correspond
to shortest-distance tours, as can be shown analytically in a stationary phase
approximation. Simulated annealing is required for global optimization, but the
stochastic element might be replaced by chaotic intermittency in a further
generalization of the architecture to a network of chaotic oscillators.Comment: -2nd revised version submitted to Chaos (original version submitted
6/07
Multiplicative versus additive noise in multi-state neural networks
The effects of a variable amount of random dilution of the synaptic couplings
in Q-Ising multi-state neural networks with Hebbian learning are examined. A
fraction of the couplings is explicitly allowed to be anti-Hebbian. Random
dilution represents the dying or pruning of synapses and, hence, a static
disruption of the learning process which can be considered as a form of
multiplicative noise in the learning rule. Both parallel and sequential
updating of the neurons can be treated. Symmetric dilution in the statics of
the network is studied using the mean-field theory approach of statistical
mechanics. General dilution, including asymmetric pruning of the couplings, is
examined using the generating functional (path integral) approach of disordered
systems. It is shown that random dilution acts as additive gaussian noise in
the Hebbian learning rule with a mean zero and a variance depending on the
connectivity of the network and on the symmetry. Furthermore, a scaling factor
appears that essentially measures the average amount of anti-Hebbian couplings.Comment: 15 pages, 5 figures, to appear in the proceedings of the Conference
on Noise in Complex Systems and Stochastic Dynamics II (SPIE International
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