This paper is concerned with the numerical solution of high-dimensional FokkerPlanck equations related to multi-dimensional diffusion with polynomial coefficients or Pearson diffusions. Classification of multi-dimensional Pearson diffusion follows from the classification of one-dimensional Pearson diffusion. There are six important classes of Pearson diffusion three of them possess an infinite ...

We study capacitated network flow problems with demands defined on a countably infinite collection of nodes having finite degree. This class of network flow models includes, for example, all infinite horizon deterministic dynamic programs with finite action sets, because these are equivalent to the problem of finding a shortest path in an infinite directed network. We derive necessary and suffi...

The simplex solution algorithm for linear programs (LP) can be considered as a sub-gradient direction method therefore a full gradient solution algorithm might be more efficient. We have developed a full gradient method which consists of three phases. The initialization phase provides the initial tableau which may not have a full set of basis. The push phase uses a full gradient vector of the o...

A methodology is introduced for rapid reduced-order solution of stochastic partial differential equations. On the random domain, a generalized polynomial chaos expansion (GPCE) is used to generate a 9 reduced subspace. GPCE involves expansion of the random variable as a linear combination of basis functions defined using orthogonal polynomials from the Askey series. A proper orthogonal 11 decom...

We rst show how to represent sharp posterior probability distributions using real valued coe cients on broadly-tuned basis functions. Then we show how the precise times of spikes can be used to convey the real-valued coe cients on the basis functions quickly and accurately. Finally we describe a simple simulation in which spiking neurons learn to model an image sequence by tting a dynamic gener...

Strong feasibility of MPC problems is usually enforced by constraining the state at the final prediction step to a controlled invariant set. However, such terminal constraints fail to enforce strong feasibility in a rich class of MPC problems, for example when employing move-blocking. In this paper a generalized, least restrictive approach for enforcing strong feasibility of MPC problems is pro...

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if ...

An algorithm and its first implementation in C# are presented for assembling arbitrary quantum circuits on the base of Hadamard and Toffoli gates and for constructing multivariate polynomial systems over the finite field Z2 arising when applying the Feynman’s sum-over-paths approach to quantum circuits. The matrix elements determined by a circuit can be computed by counting the number of common...

Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.