SEAPODYM is a model developed initially for investigating spatial tuna population dynamics under the influence of both fishing and environmental effects. The model is based on advection-diffusion-reaction equations. The main features of this model are i) forcing by environmental data (either observed or modeled), ii) prediction of both temporal and spatial distribution of age-structured populat...

An edge-ordering of a graph G = (V,E) is a bijection φ : E → {1, 2, . . . , |E|}. Given an edge-ordering, a sequence of edges P = e1, e2, . . . , ek is an increasing path if it is a path in G which satisfies φ(ei) < φ(ej) for all i < j. For a graph G, let f(G) be the largest integer ` such that every edge-ordering of G contains an increasing path of length `. The parameter f(G) was first studie...

We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave function—even for an, inevitably inadequate, orthodox derivation. Dedicated to Joel Lebowitz, with love and admiration, for his 70...

The (1, 0) supersymmetry in six dimensions admits a tensor multiplet which contains a secondrank antisymmetric tensor field with a self-dual field strength and a dilaton. We describe the fully supersymmetric coupling of this multiplet to Yang-Mills multiplet, in the absence of supergravity. The self-duality equation for the tensor field involves a Chern-Simons modified field strength, the gauge...

This paper provides an exposition of some recent research regarding system-theoretic aspects of continuous-time recurrent (dynamic) neural networks with sigmoidal activation functions. The class of systems is introduced and discussed, and a result is cited regarding their universal approximation properties. Known characterizations of controllability, observability, and parameter identifiability...

Experimental design for cellular networks based on sensitivity analysis is studied in this work. Both optimal and robust experimental design strategies are developed for the IκBNF-κB signal transduction model. Based on local sensitivity analysis, the initial IKK intensity is calculated using an optimal experimental design process, and several scalarization measures of the Fisher information mat...

We derive a new set of equations which describe a continuous one parameter family of expanding wave solutions of the Einstein equations such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology, is embedded as a single point in this family. All of the spacetime metrics associated with this family satisfy the equation of state p = ρc/3, correct ...

We study the mixing time of random walks on small-world networks modelled as follows: starting with the 2-dimensional periodic grid, each pair of vertices {u, v} with distance d > 1 is added as a “long-range” edge with probability proportional to d−r, where r ≥ 0 is a parameter of the model. Kleinberg studied a close variant of this network model and proved that the (decentralised) routing time...

*The research for this paper was funded by an Australian Research Council Discovery Grant (DP 0773489). The authors are grateful to the Australian Bureau of Statistics for their permission to use the HES unit record data sets and to Dr. Paul Blacklow for permitting the use of demand parameter estimates obtained by him. Helpful comments from seminar participants at the University of Melbourne ar...

We prove a new projection formula for the four-parameter family of orthogonal polynomials outside of the Askey-Wilson class. By carefully analyzing the recurrence relations we manage to overcome the lack of explicit expression for the orthogonality measure. Research partially supported by NSF grants #INT-03-32062, #DMS-05-04198, and by the C.P. Taft Memorial Fund. Permanent address: Faculty of ...