10,183 research outputs found
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
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