19 research outputs found
Tables, Memorized Semirings and Applications
We define and construct a new data structure, the tables, this structure
generalizes the (finite) -sets sets of Eilenberg \cite{Ei}, it is versatile
(one can vary the letters, the words and the coefficients). We derive from this
structure a new semiring (with several semiring structures) which can be
applied to the needs of automatic processing multi-agents behaviour problems.
The purpose of this account/paper is to present also the basic elements of this
new structures from a combinatorial point of view. These structures present a
bunch of properties. They will be endowed with several laws namely : Sum,
Hadamard product, Cauchy product, Fuzzy operations (min, max, complemented
product) Two groups of applications are presented. The first group is linked to
the process of "forgetting" information in the tables. The second, linked to
multi-agent systems, is announced by showing a methodology to manage emergent
organization from individual behaviour models
Some Open Problems in Combinatorial Physics
We point out four problems which have arisen during the recent research in
the domain of Combinatorial Physics
Rational Hadamard products via Quantum Diagonal Operators
We use the remark that, through Bargmann-Fock representation, diagonal
operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product
to give some properties (like the stability of periodic fonctions) of the
Hadamard product by a rational fraction. In particular, we provide through this
way explicit formulas for the multiplication table of the Hadamard product in
the algebra of rational functions in \C[[z]]
Automata-based Adaptive Behavior for Economical Modelling Using Game Theory
In this chapter, we deal with some specific domains of applications to game
theory. This is one of the major class of models in the new approaches of
modelling in the economic domain. For that, we use genetic automata which allow
to build adaptive strategies for the players. We explain how the automata-based
formalism proposed - matrix representation of automata with multiplicities -
allows to define semi-distance between the strategy behaviors. With that tools,
we are able to generate an automatic processus to compute emergent systems of
entities whose behaviors are represented by these genetic automata
Transitive Hall sets
We give the definition of Lazard and Hall sets in the context of transitive
factorizations of free monoids. The equivalence of the two properties is
proved. This allows to build new effective bases of free partially commutative
Lie algebras. The commutation graphs for which such sets exist are completely
characterized and we explicit, in this context, the classical PBW rewriting
process
Automata-based adaptive behavior for economic modeling using game theory
In this paper, we deal with some specific domains of applications to game
theory. This is one of the major class of models in the new approaches of
modelling in the economic domain. For that, we use genetic automata which allow
to buid adaptive strategies for the players. We explain how the automata-based
formalism proposed - matrix representation of automata with multiplicities -
allows to define a semi-distance between the strategy behaviors. With that
tools, we are able to generate an automatic processus to compute emergent
systems of entities whose behaviors are represented by these genetic automata
Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization
In this work, an effective construction, via Sch\"utzenberger's monoidal
factorization, of dual bases for the non commutative symmetric and
quasi-symmetric functions is proposed
Independence of hyperlogarithms over function fields via algebraic combinatorics
We obtain a necessary and sufficient condition for the linear independence of
solutions of differential equations for hyperlogarithms. The key fact is that
the multiplier (i.e. the factor in the differential equation ) has
only singularities of first order (Fuchsian-type equations) and this implies
that they freely span a space which contains no primitive. We give direct
applications where we extend the property of linear independence to the largest
known ring of coefficients