Efficient Parallel Simulations of Asynchronous Cellular Arrays

A definition for a class of asynchronous cellular arrays is proposed. An example of such asynchrony would be independent Poisson arrivals of cell iterations. The Ising model in the continuous time formulation of Glauber falls into this class. Also proposed are efficient parallel algorithms for simulating these asynchronous cellular arrays. In the algorithms, one or several cells are assigned to a processing element (PE), local times for different PEs can be different. Although the standard serial algorithm by Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller can simulate such arrays, it is usually believed to be without an efficient parallel counterpart. However, the proposed parallel algorithms contradict this belief proving to be both efficient and able to perform the same task as the standard algorithm. The results of experiments with the new algorithms are encouraging: the speed-up is greater than 16 using 25 PEs on a shared memory MIMD bus computer, and greater than 1900 using 2**14 PEs on a SIMD computer. The algorithm by Bortz, Kalos, and Lebowitz can be incorporated in the proposed parallel algorithms, further contributing to speed-up. [In this paper I invented the update-cites-of-local-time-minima parallel simulation scheme. Now the scheme is becoming popular. Many misprints of the original 1987 Complex Systems publication are corrected here.-B.L.]Comment: 26 pages, 10 figure

The Structure of The Group of Polynomial Matrices Unitary in The Indefinite Metric of Index 1

We consider the group M of all polynomial matrices U(z) = U0 + U1*z + U2*z*z +...+Uk*z*...*z, k=0,1,... that satisfy equation U(z)*D*U(z)" = D with the diagonal n*n matrix D=diag{-1,1,1,...1}. Here n > 1, U(z)" = U0" + U1"*z + U2"*z*z + ..., and symbol A" for a constant matrix A denotes the Hermitiean conjugate of A. We show that the subgroup M0 of those U(z) in M, that are normalized by the condition U(0)=I, is the free product of certain groups. The matrices in each group-multiples are explicitly and uniquely parametrized so that every U=U(z) in M0 can be represented in the form U = G1 * G2 * ... * Gs with n*n polynomial matrix multiples G1, G2, ..., each of which belong to its group-multiple, and so that any two consecutive Gi and G(i+1) belong to two different group-multiples. The uniqueness of such parametrization for a given U includes the number of multiples s, their particular sequence G1,G2,... and the multiples themselves with their respective parametrization; all these items can be defined in only one way once the U is given

Fast Simulation of Multicomponent Dynamic Systems

A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations. Concrete examples of simulations that range from econometric modeling to communications to material science are used to illustrate these techniques and concepts. The algorithmic and modeling methods discussed include event-driven processing, ``anticipating'' data structures, and ``lazy'' evaluation, Poisson dispenser, parallel processing by cautious advancements and by synchronous relaxations. The paper gives examples of how these techniques and models are employed in assessing efficiency of capacity management methods in wireless and wired networks, in studies of magnetization, crystalline structure, and sediment formation in material science, in studies of competition in economics.Comment: 38 pages, 9 figure

Theory of sexes by Geodakian as it is advanced by Iskrin

In 1960s V.Geodakian proposed a theory that explains sexes as a mechanism for evolutionary adaptation of the species to changing environmental conditions. In 2001 V.Iskrin refined and augmented the concepts of Geodakian and gave a new and interesting explanation to several phenomena which involve sex, and sex ratio, including the war-years phenomena. He also introduced a new concept of the "catastrophic sex ratio." This note is an attempt to digest technical aspects of the new ideas by Iskrin.Comment: 9 page

Why The Results of Parallel and Serial Monte Carlo Simulations May Differ

Parallel Monte Carlo simulations often expose faults in random number generatorsComment: 2 page

Study of Electron-Vibrational Interaction in Molecular Aggregates Using Mean-Field Theory: From Exciton Absorption and Luminescence to Exciton-Polariton Dispersion in Nanofibers

We have developed a model in order to account for electron-vibrational effects on absorption, luminescence of molecular aggregates and exciton-polaritons in nanofibers. The model generalizes the mean-field electron-vibrational theory developed by us earlier to the systems with spatial symmetry, exciton luminescence and the exciton-polaritons with spatial dispersion. The correspondence between manifestation of electron-vibrational interaction in monomers, molecular aggregates and exciton-polariton dispersion in nanofibers is obtained by introducing the aggregate line-shape functions in terms of the monomer line-shape functions. With the same description of material parameters we have calculated both the absorption and luminescence of molecular aggregates and the exciton-polariton dispersion in nanofibers. We apply the theory to experiment on fraction of a millimeter propagation of Frenkel exciton polaritons in photoexcited organic nanofibers made of thiacyanine dye.Comment: 18 pages, 6 figure

The Structure of the Inverse to the Sylvester Resultant Matrix

Given polynomials a(z) of degree m and b(z) of degree n, we represent the inverse to the Sylvester resultant matrix of a(z) and b(z), if this inverse exists, as a canonical sum of m+n dyadic matrices each of which is a rational function of zeros of a(z) and b(z). As a result, we obtain the polynomial solutions X(z) of degree n-1 and Y(z) of degree m-1 to the equation a(z)X(z)+b(z)Y(z)=c(z), where c(z) is a given polynomial of degree m+n-1, as follows: X(z) is a Lagrange interpolation polynomial for the function c(z)/a(z) over the set of zeros of b(z) and Y(z) is the one for the function c(z)/b(z) over the set of zeros of a(z).Comment: 11 page

Flaglets: Exact Wavelets on the Ball

We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the spherical harmonic transform with damped Laguerre polynomials on the radial half-line. The resulting wavelets, called flaglets, extract scale-dependent, spatially localised features in three-dimensions while treating the tangential and radial structures separately. Both the Fourier-Laguerre and the flaglet transforms are theoretically exact thanks to a novel sampling theorem on the ball. Our implementation of these methods is publicly available and achieves floating-point accuracy when applied to band-limited signals.Comment: 1 page, 1 figure, Proceedings of International BASP Frontiers Workshop 2013. Codes are publicly available at http://www.s2let.org and http://www.flaglets.or

Extended Euler-Lagrange and Hamiltonian Conditions in Optimal Control of Sweeping Processes with Controlled Moving Sets

This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by applications to hysteresis, we consider a general setting where moving sets are given as inverse images of closed subsets of finite-dimensional spaces under nonlinear differentiable mappings dependent on both state and control variables. Developing the method of discrete approximations and employing generalized differential tools of first-order and second-order variational analysis allow us to derive nondegenerated necessary optimality conditions for such problems in extended Euler-Lagrange and Hamiltonian forms involving the Hamiltonian maximization. The latter conditions of the Pontryagin Maximum Principle type are the first in the literature for optimal control of sweeping processes with control-dependent moving sets

Determination of Functional Network Structure from Local Parameter Dependence Data

In many applications, such as those arising from the field of cellular networks, it is often desired to determine the interaction (graph) structure of a set of differential equations, using as data measured sensitivities. This note proposes an approach to this problem