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Search Results: 1 - 10 of 599824 matches for " A. C. C. Coolen "
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Statistical Mechanics of Recurrent Neural Networks I. Statics
A. C. C. Coolen
Quantitative Biology , 2000,
Abstract: A lecture notes style review of the equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, coupled-oscillators). To be published in the Handbook of Biological Physics (North-Holland). Accompanied by a similar review (part II) dealing with the dynamics.
Statistical Mechanics of Recurrent Neural Networks II. Dynamics
A. C. C. Coolen
Quantitative Biology , 2000,
Abstract: A lecture notes style review of the non-equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, graded-response, coupled-oscillators). To be published in the Handbook of Biological Physics (North-Holland). Accompanied by a similar review (part I) dealing with the statics.
Non-equilibrium statistical mechanics of Minority Games
A. C. C. Coolen
Quantitative Finance , 2002,
Abstract: In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disordered stochastic processes without detailed balance, the canonical technique for finding exact solutions is found to be generating functional analysis a la De Dominicis, as originally developed in the spin-glass community.
Reply to cond-mat/0503325: Comment on `Generating functional analysis of Minority Games with real merket histories' by KH Ho, WC Man, FK Chow and HF Chau
A. C. C. Coolen
Quantitative Finance , 2005,
Abstract: The Comment cond-mat/0503325 is built around two core statements, both of which are plainly incorrect.
Generating functional analysis of Minority Games with real market histories
A. C. C. Coolen
Quantitative Finance , 2004, DOI: 10.1088/0305-4470/38/11/002
Abstract: It is shown how the generating functional method of De Dominicis can be used to solve the dynamics of the original version of the minority game (MG), in which agents observe real as opposed to fake market histories. Here one again finds exact closed equations for correlation and response functions, but now these are defined in terms of two connected effective non-Markovian stochastic processes: a single effective agent equation similar to that of the `fake' history models, and a second effective equation for the overall market bid itself (the latter is absent in `fake' history models). The result is an exact theory, from which one can calculate from first principles both the persistent observables in the MG and the distribution of history frequencies.
Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
A. Mozeika,A. C. C. Coolen
Physics , 2007, DOI: 10.1088/1751-8113/41/11/115003
Abstract: We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field probability distribution, and solve these within the replica symmetry ansatz. Although the theory is developed in a general setting, with a view to future applications in various other fields, in this paper we apply it mainly to the dynamics of the Glauber algorithm (extended with cooling schedules) when running on the so-called vertex cover optimization problem. Our theoretical predictions are tested against both Monte Carlo simulations and known results from equilibrium studies. In contrast to previous dynamical analyses based on deriving closed equations for only a small numbers of scalar order parameters, the agreement between theory and experiment in the present study is nearly perfect.
Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet
A. Mozeika,A. C. C. Coolen
Physics , 2009, DOI: 10.1088/1751-8113/42/19/195006
Abstract: We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations.
What you see is not what you get: how sampling affects macroscopic features of biological networks
A. Annibale,A. C. C. Coolen
Quantitative Biology , 2011,
Abstract: We use mathematical methods from the theory of tailored random graphs to study systematically the effects of sampling on topological features of large biological signalling networks. Our aim in doing so is to increase our quantitative understanding of the relation between true biological networks and the imperfect and often biased samples of these networks that are reported in public data repositories and used by biomedical scientists. We derive exact explicit formulae for degree distributions and degree correlation kernels of sampled networks, in terms of the degree distributions and degree correlation kernels of the underlying true network, for a broad family of sampling protocols that include (un-)biased node and/or link undersampling as well as (un-)biased link oversampling. Our predictions are in excellent agreement with numerical simulations.
Feed-Forward Chains of Recurrent Attractor Neural Networks Near Saturation
A. C. C. Coolen,L. Viana
Physics , 1996, DOI: 10.1088/0305-4470/29/24/011
Abstract: We perform a stationary state replica analysis for a layered network of Ising spin neurons, with recurrent Hebbian interactions within each layer, in combination with strictly feed-forward Hebbian interactions between successive layers. This model interpolates between the fully recurrent and symmetric attractor network studied by Amit el al, and the strictly feed-forward attractor network studied by Domany et al. Due to the absence of detailed balance, it is as yet solvable only in the zero temperature limit. The built-in competition between two qualitatively different modes of operation, feed-forward (ergodic within layers) versus recurrent (non- ergodic within layers), is found to induce interesting phase transitions.
Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions
Kazushi Mimura,A. C. C. Coolen
Physics , 2009, DOI: 10.1088/1751-8113/42/41/415001
Abstract: We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the system can be completely solved, due to the asymptotic absence of loops. For arbitrary graph symmetry, we solve the dynamics exactly for the first few time steps, and we construct approximate stationary solutions.
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