Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Maximization of a Linear Utility Function over the Set of the Housing Market Short-Term Equilibria

AMS subject classification: 90C05, 90A14.

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

New Upper Bounds for Some Spherical Codes

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

Derivation of Context-free Stochastic L-Grammar Rules for Promoter Sequence Modeling Using Support Vector Machine

Formal grammars can used for describing complex repeatable structures such as DNA sequences. In this paper, we describe the structural composition of DNA sequences using a context-free stochastic L-grammar. L-grammars are a special class of parallel grammars that can model the growth of living organisms, e.g. plant development, and model the morphology of a variety of organisms. We believe that parallel grammars also can be used for modeling genetic mechanisms and sequences such as promoters. Promoters are short regulatory DNA sequences located upstream of a gene. Detection of promoters in DNA sequences is important for successful gene prediction. Promoters can be recognized by certain patterns that are conserved within a species, but there are many exceptions which makes the promoter recognition a complex problem. We replace the problem of promoter recognition by induction of context-free stochastic L-grammar rules, which are later used for the structural analysis of promoter sequences. L-grammar rules are derived automatically from the drosophila and vertebrate promoter datasets using a genetic programming technique and their fitness is evaluated using a Support Vector Machine (SVM) classifier. The artificial promoter sequences generated using the derived L- grammar rules are analyzed and compared with natural promoter sequences.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

On a Stochastic Partial Differential Equation with a Noisy Term

2000 Mathematics Subject Classification: 60H15, 60H40