Biomedical subjects

J P L Hatchett

Publications and source records attributed to J P L Hatchett.

5 recordsLinked to original sources

PubMed2006

Criticality on networks with topology-dependent interactions.

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping gamma'=(gamma-mu)(1-mu) describes how a shift of the standard exponent gamma of the degree distribution can absorb the effect of degree-dependent pair interactions J(ij) proportional to (k(i)k(j))(-mu), where k(i) stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

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PubMed2006

Analytic solution of neural network with disordered lateral inhibition.

The replica method has played a key role in analyzing systems with disorder, e.g., the Sherrington-Kirkpatrick (SK) model, and associative neural networks. Here we study the influence of disorder in the lateral inhibition type interactions on the cooperative and uncooperative behavior of recurrent neural networks by using the replica method. Although the interaction between neurons has a dependency on distance, our model can be solved analytically. Bifurcation analysis identifies the boundaries between paramagnetic, ferromagnetic, spin-glass, and localized phases. In the localized phase, the network shows a bump like activity, which is often used as a model of spatial working memory or columnar activity in the visual cortex. Simulation results show that disordered interactions can stabilize the drift the of bump position, which is commonly observed in conventional lateral inhibition type neural networks.

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PubMed2005

Dynamic rewiring in small world networks.

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine the order parameters of our system at total equilibrium, probing both spin and graph statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.

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PubMed2005

Dynamical replica analysis of disordered Ising spin systems on finitely connected random graphs.

We study the dynamics of macroscopic observables such as the magnetization and the energy per degree of freedom in Ising spin models on random graphs of finite connectivity, with random bonds and/or heterogeneous degree distributions. To do so, we generalize existing versions of dynamical replica theory and cavity field techniques to systems with strongly disordered and locally treelike interactions. We illustrate our results via application to, e.g., +/-J spin glasses on random graphs and of the overlap in finite connectivity Sourlas codes. All results are tested against Monte Carlo simulations.

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PubMed2005

Trading interactions for topology in scale-free networks.

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, gamma'=(gamma-mu)/(1-mu), describes how a shift of the standard exponent gamma of the degree distribution P(q) can absorb the effect of degree-dependent pair interactions J(ij)proportional to(q(i)q(j))(-mu). The replica technique, cavity method, and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and nonequilibrium systems, and is illustrated with interdisciplinary applications.

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