Biomedical subjects

David Saad

Publications and source records attributed to David Saad.

5 recordsLinked to original sources

PubMed2006

Equilibration through local information exchange in networks.

We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.

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PubMed2006

Finite-connectivity spin-glass phase diagrams and low-density parity check codes.

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate , an RS critical transition point at while the critical RSB transition point is located at , to be compared with the corresponding Shannon bound . For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed.

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PubMed2003

Statistical mechanics of broadcast channels using low-density parity-check codes.

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

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PubMed1997

Efficient Training of Recurrent Neural Network with Time Delays.

Training recurrent neural networks to perform certain tasks is known to be difficult. The possibility of adding synaptic delays to the network properties makes the training task more difficult. However, the disadvantage of tough training procedure is diminished by the improved network performance. During our research of training neural networks with time delays we encountered a robust method for accomplishing the training task. The method is based on adaptive simulated annealing algorithm (ASA) which was found to be superior to other training algorithms. It requires no tuning and is fast enough to enable training to be held on low end platforms such as personal computers. The implementation of the algorithm is presented over a set of typical benchmark tests of training recurrent neural networks with time delays. Copyright 1996 Elsevier Science Ltd.

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PubMed1996

Radial Basis Function Networks: Generalization in Over-realizable and Unrealizable Scenarios.

Learning and generalization in a two-layer radial basis function network, with fixed centres of the basis functions, is examined within a stochastic training paradigm. Employing a Bayesian approach, expressions for generalization error are derived under the assumption that the generating mechanism (teacher) for the training data is also a radial basis function network, but one for which the basis function centres and widths need not correspond to those of the student network. The effects of regularization, via a weight decay term, are examined. The cases in which the student has greater representational power than the teacher (over-realizable), and in which the teacher has greater power than the student (unrealizable) are studied. Dependence on knowing the centres of the teacher is eliminated by introducing a single degree-of-confidence parameter. Finally, simulations are performed which validate the analytic results. Copyright 1996 Elsevier Science Ltd.

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