Bio-PEPA: An Extension of the Process Algebra PEPA for Biochemical Networks

In this work we introduce Bio-PEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA to deal with some features of biological models, such as stoichiometry and the use of generic kinetic laws. Bio-PEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. Finally, we show a representation of a model, concerning a simple genetic network, in the new language.     

An equivalence principle for electromagnetics through Clifford's geometric algebras

As already pointed out by several authors, a given electromagnetic medium creates an effective geometry and a given geometry creates an effective medium—what we call the equivalence principle for electromagnetics. This bears some resemblance to the kinematic aspects of the interaction between masses and the spacetime metric of general relativity. In this article, using Clifford's geometric algebras defined over the tangent and cotangent bundles of spacetime, we generalize the topological interpretation of this equivalence principle: introducing a transformation that we call the vacuum form reduction, we are led to a fictitious spacetime corresponding to a special class of bianisotropic media (in the materials interpretation) and which reduces to spacetime vacuum as a particular case (in the topological interpretation). We illustrate our theoretical approach with two examples: transformation and moving media.     

A GENERAL SYSTEM LOGICAL THEORY

The General System Logical Theory (GSLT) is obtained by combining Resconi's logical theory of systems with Jessel's theory of secondary sources. In the present paper we give a first account of GSLT, of its foundation, its main features, and most obvious applications. GSLT is defined by its aims and concretized by a new specific concept, that of an Elementary Logical System (ELS). ELS may be connected with Lie algebras. The systems formerly dealt with by Resconi's and Jessel's separate theories are identified as particular ELS. Subsequently are built up various networks of ELS, leading thus to natural and powerful extensions of the classical feedback theory. Finally GSLT is applied to three very different topics: wave propagations (or any physical nature), Riemann geometries and chemical controls, showing thus its versatility and usefulness.     

Formalization of interrelations between operators and data within the framework of an extended algebra of algorithms

A system of algorithmic algebras is considered whose basic concepts are newly interpreted to formalize the interrelation between operators and data of such a system. A modified formal instrument is constructed that extends the possibilities of design and transformation of regular schemes of algorithms. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 170–182, November–December 2008.     

Propositional compositions of partial predicates

Compositions of partial predicates of the highest abstraction level that form the basis of infinitary propositional logics are defined and investigated. The compositions are completely described in terms of special algebras called Klee ne algebras, and a complete system of identities is constructed for such compositions. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 3–19, March–April, 2000.     

A Qualitative Model for Time Granularity

This paper addresses the problem of granularity in temporal representation in the context of text analysis. In contrast with other fields where granularity levels are essentially quantitative, in natural language the different levels are not always precisely defined and granularity is of a more subtle and qualitative nature. A model is proposed for representing such phenomena, based on time units and time units intervals. Time units represent chunks of time which are considered indivisible at a given granularity level, but which may be refined and contain other time units or intervals at a higher granularity level. The structure of the set of time units and intervals is studied and a relation algebra is defined which extends the traditional Allen's Point or Interval Algebra. Weak and strong representations of this algebra are proposed. We claim that such representations, called grained temporal structures, are adequate for coping with dynamic qualitative changes of granularity. A logic with restricted quantifiers is proposed for formalizing temporal knowledge and examples are discussed which show the relevance of the model for natural language analysis.     

Ring-like structures corresponding to pseudo MV-algebras

The natural bijective correspondence between MV-algebras and pseudorings is generalized to the case of pseudo MV-algebras. We first introduce the concepts of non-commutative pseudorings and strong pseudo De Morgan algebras. Then, we show that they both correspond to pseudo MV-algebras via symmetric difference in a natural bijective way. This work was supported by NSFC Major Research Program 60496324; NSFC Key Research Program 60736011; NSFC 60603002; Pre-973 Project 2001CCA03000; 863 High-Tech Project 2001AA113130; 973 Project 2001CB312004; CAS Brain and Mind Science Project.     

Programs with restoration of computations

In this article, the notion of a program with restoration of computations is introduced, i.e., such a program that makes it possible to renew interrupted computations from any intermediate value obtained before an interruption of its operation. As is shown, any operator specified by a regular scheme of algorithmic algebra can be computed by a program with this property. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 173–181, January–February, 2000.     

Structure theorem for five-dimensional estimation algebras

The problem of classification of finite-dimensional estimation algebras was formally proposed by Brockett in his lecture at International Congress of Mathematicians in 1983. Due to the difficulty of the problem, in the early 1990s Brockett suggested that one should understand the low-dimensional estimation algebras first. In this paper we give classification of estimation algebras of dimension at most five. Although the classification of finite-dimensional estimation algebra of maximal rank was completed by Yau and his coworkers Chen, Chiou, Hu, Wong and Wu; the problem of classification of non-maximal rank finite-dimensional estimation algebra is still wide open except for the case of state space dimension 2. Hopefully, the result of this paper will shed some light on the non-maximal rank estimation algebras.     

Function algebraic characterizations of the polytime functions

We give function algebraic characterizations of the polynomial time computable functions using unbounded recursion schemes without introducing extra notions such as safe and normal in variables and tiering in word algebras. Received: December 9 1998.