Related papers: Information algebra system of soft sets
We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components. We apply our work to obtain similar…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
We describe a technique to construct a set of check positions (and hence an information set) for every abelian code solely in terms of its defining set. This generalizes that given by Imai in \cite{Imai} in the case of binary TDC codes.
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding…
We analyze the effect of replacing several natural uses of definability in set theory by the weaker model-theoretic notion of algebraicity. We find, for example, that the class of hereditarily ordinal algebraic sets is the same as the class…
By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a logical framework in which this boundary is incorporated into…
Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in…
The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…
We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
Multivariate information decompositions hold promise to yield insight into complex systems, and stand out for their ability to identify synergistic phenomena. However, the adoption of these approaches has been hindered by there being…
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
In this paper we consider systems which consist of binary components with known reliabilities. We discuss their algebraic properties and define the corresponding algebraic structure, which we call the reliability algebra. We prove that the…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
In this paper, we suppose that the universe has an information processing layer, which coveys the informational contents accompanying the physical events. In this manner, universe is considered to be composed of several associative layers…
We consider biological individuality in terms of information theoretic and graphical principles. Our purpose is to extract through an algorithmic decomposition system-environment boundaries supporting individuality. We infer or detect…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…