A compositional approach to synchronize two dimensional networks of processors
The problem of synchronizing a network of identical processors that work synchronously at discrete steps is studied. Processors are arranged as an array of m rows and n columns and can exchange each other only one bit of information. We give algorithms which synchronize square arrays of (n × n) processors and give some general constructions to synchronize arrays of (m × n) processors. Algorithms are given to synchronize in time n2, , and 2n a square array of (n × n) processors. Our approach...
A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is ℤ-congruent to its transpose is also discussed. An affirmative answer is given for the incidence matrices and the Tits matrices of positive one-peak posets I.
A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006A MATHEMATICA package for finding Lie symmetries of partial differential equations is presented. The package is designed to create and solve the associated determining system of equations, the full set of solutions of which generates the widest permissible local Lie group of point symmetry transformations. Examples illustrating the functionality of the package's tools...
In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal’cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case. Another...
In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal'cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case....
We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones proposed that are suitable to perform this representation task for a lattice L different from the unit interval....
Designing classifiers may follow different goals. Which goal to prefer among others depends on the given cost situation and the class distribution. For example, a classifier designed for best accuracy in terms of misclassifications may fail when the cost of misclassification of one class is much higher than that of the other. This paper presents a decision-theoretic extension to make fuzzy rule generation cost-sensitive. Furthermore, it will be shown how interpretability aspects and the costs of...