Duality between Multidimensional Convolutional Codes and Systems

Multidimensional convolutional codes generalize (one dimensional) convolutional codes and they correspond under a natural duality to multidimensional systems widely studied in the systems literature.Comment: 16 pages LaTe

A Geometry for Multidimensional Integrable Systems

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one obtains a geometric description of the operators. A dual theory is also possible, based on a deformation of differential forms. This calculus is applied to a number of multidimensional integrable systems, such as the KP hierarchy, thus obtaining a geometrical description of these systems. The limit in which the deformation disappears corresponds to taking the dispersionless limit in these hierarchies.Comment: LaTeX, 29 pages. To be published in J.Geom.Phy

Executive Information Systems' Multidimensional Models

Executive Information Systems are design to improve the quality of strategic level of management in organization through a new type of technology and several techniques for extracting, transforming, processing, integrating and presenting data in such a way that the organizational knowledge filters can easily associate with this data and turn it into information for the organization. These technologies are known as Business Intelligence Tools. But in order to build analytic reports for Executive Information Systems (EIS) in an organization we need to design a multidimensional model based on the business model from the organization. This paper presents some multidimensional models that can be used in EIS development and propose a new model that is suitable for strategic business requests.Executive Information Systems (EIS), Decision Support Systems (DSS), multidimensional models, Business Intelligence tools, On-Line Analytical Processing (OLAP)

Multidimensional Epistasis and the Advantage of Sex

Kondrashov and Kondrashov (2001) suggest that there is usually a disadvantage for sex in systems with multidimensional epistasis. They define systems of 'unidimensional epistasis' to be those where the fitness of a genotype is a function of the number of mutations it carries, and in contrast describe a system where the fitness of a genotype is a function of the numbers of mutations in two (or more) disjoint subsets of loci creating 'multidimensional epistasis'. In an example landscape an asexual population evolves fit genotypes about twice as fast as a sexual one. Here we examine other landscapes with multidimensional epistasis and find cases where an asexual population evolves fit genotypes 20 and 180 times slower than a sexual population

Moment instabilities in multidimensional systems with noise

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a simple, dominant eigenvalue and stationary, white noise. When the noise is small, we obtain general expressions for the approximate asymptotic distribution and moment Lyapunov exponents. In the case of larger noise, the second moment is calculated using a different approach, which gives an exact result for some types of noise. We analyze the dependence of the moments on the system's dimension, relevant system properties, the form of the noise, and the magnitude of the noise. We determine a critical value for noise strength, as a function of the unperturbed system's convergence rate, above which the second moment diverges and large fluctuations are likely. Analytical results are validated by numerical simulations. We show that our results cannot be extended to the continuous time limit except in certain special cases.Comment: 21 pages, 15 figure

Multidimensional Dynamical Systems Accepting the Normal Shift

The dynamical systems of the form \ddot\bold r=\bold F (\bold r,\dot\bold r) in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force field \bold F(\bold r,\dot\bold r) of the dynamical systems with weak and complete normality are derived.Comment: AMS-TeX, ver. 2.1, IBM AT-386, size 16K (ASCII), short versio

The Symbolic Dynamics Of Multidimensional Tiling Systems

We prove a multidimensional version of the theorem that every shift of finite type has a power that can be realized as the same power of a tiling system. We also show that the set of entropies of tiling systems equals the set of entropies of shifts of finite type