The study of BCK-algebras was initiated by K. Iséki in 1966 as a generalization of the concept of set-theoretic difference and propositional calculus. The hyperstructure theory (called also multialgebras) is introduced in 1934 by Marty [6] at the 8th congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, bu...

MOTIVATION PSORTb has remained the most precise bacterial protein subcellular localization (SCL) predictor since it was first made available in 2003. However, the recall needs to be improved and no accurate SCL predictors yet make predictions for archaea, nor differentiate important localization subcategories, such as proteins targeted to a host cell or bacterial hyperstructures/organelles. Suc...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Nowadays multiagent systems (MAS for short) [1] are used as a tool to understand the structure, the behaviour and the functions of biological processes. Indeed, MAS enable living organisms to be simulated in order to perceive what characterizes these selforganizing systems. They are used in order to discern how these organisms can produce achievements that exceed the sum of all the performances...

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

BACKGROUND HIV is primarily transmitted by sexual intercourse and predominantly infects people in Third World countries. Here an important medical need is self-protection for women, particularly in societies where condoms are not widely accepted. Therefore, availability of antiviral microbicides may significantly reduce sexual HIV transmission in such environments. METHODS Here, we investigat...

The problem of not only how but also why cells divide can be tackled using recent ideas. One idea from the origins of life - Life as independent of its constituents - is that a living entity like a cell is a particular pattern of connectivity between its constituents. This means that if the growing cell were just to get bigger the average connectivity between its constituents per unit mass - it...

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

In this thesis, we introduce new models of quantum computation to study the potential and limitations of quantum computer algorithms. Our models are based on algebraic extensions of the qubit Clifford gates (CNOT, Hadamard and π/4-phase gates) and Gottesman’s stabilizer formalism of quantum codes. We give two main kinds of technical contributions with applications in quantum algorithm design, c...

In this paper, we study hypergroups determined by lattices introduced by Varlet and Comer, especially we enumerate Varlet and Comer hypergroups of orders less than 50 and 13, respectively. 1 Basic definitions and results An algebraic hyperstructure is a natural generalization of a classical algebraic structure. More precisely, an algebraic hyperstructure is a non-empty set H endowed with one or...