Related papers: Two representation theorems of three-valued struct…
Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific…
Actors are embedded in networks of communication: the relations of the actors can be represented as the rows of a matrix, while the column vectors represent their communications. The two systems are structurally coupled in the co-variation:…
Modeling agent behavior is central to understanding the emergence of complex phenomena in multiagent systems. Prior work in agent modeling has largely been task-specific and driven by hand-engineering domain-specific prior knowledge. We…
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…
A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Given two sets of basis vectors in n-dimensional space, there exists a relation between their lengths and mutual angles, expressed as relations between the two metric matrices and the mixed matrix. In this paper these relations are given,…
Economies and societal structures in general are complex stochastic systems which may not lend themselves well to algebraic analysis. An addition of subjective value criteria to the mechanics of interacting agents will further complicate…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
This paper focuses linear and algebraic relations among multiple zeta values which were obtained in knot theory. It is shown that they can be derived from the associator relations, i.e. the pentagon equation and the shuffle relation.
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out.…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
This study extends Blackwell's (1953) comparison of information to a sequential social learning model, where agents make decisions sequentially based on both private signals and the observed actions of others. In this context, we introduce…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…