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We study a simple, solvable model that allows us to investigate effects of credit contagion on the default probability of individual firms, in both portfolios of firms and on an economy wide scale.â€¦ (More)

We calculate equilibrium solutions for Ising spin models on â€˜small worldâ€™ lattices, which are constructed by superimposing random and sparse Poissonian graphs with finite average connectivity c ontoâ€¦ (More)

- Kosuke Hamaguchi, Jonathan Paul Lewis Hatchett, Masato Okada
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2006

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 inâ€¦ (More)

- Anthony C. C. Coolen, N. S. Skantzos, +4 authors T Nikoletopoulos
- 2005

1 Department of Mathematics, Kingâ€™s College London, The Strand, London WC2R 2LS, UK 2 Institute for Theoretical Physics, Celestijnenlaan 200D, Katholieke Universiteit Leuven, B-3001, Belgium 3 Rudolfâ€¦ (More)

- Isaac PÃ©rez Castillo, B. Wemmenhove, +4 authors T Nikoletopoulos
- 2004

We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitraryâ€¦ (More)

- Claudiu V. Giuraniuc, Jonathan Paul Lewis Hatchett, +4 authors Carlo Vanderzande
- Physical review letters
- 2005

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 beâ€¦ (More)

Abstract We study a credit-risk model which captures effects of economic interactions on a firmâ€™s default probability. Economic interactions are represented as a functionally defined graph, and theâ€¦ (More)

We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics. We solve our model in the thermodynamic limit using generating functionalâ€¦ (More)

- Jonathan Paul Lewis Hatchett, N. S. Skantzos, T Nikoletopoulos
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetricâ€¦ (More)

- N. S. Skantzos, Isaac PÃ©rez Castillo, Jonathan Paul Lewis Hatchett
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2005

We study XY spin systems on small-world lattices for a variety of graph structures, e.g., Poisson and scale-free, superimposed upon a one-dimensional chain. In order to solve this model we extend theâ€¦ (More)