Related papers: First Steps towards Categorical Algebraic Artifici…

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…

There are many different models of concurrent processes. The goal of this work is to introduce a common formalized framework for current research in this area and to eliminate shortcomings of existing models of concurrency. Following up the…

We present a calculus that models a simple sort of process interaction. Our calculus consists of a collection of terms together with a rewrite relation, parameterised by an arbitrary multicategory whose morphisms we understand as…

In open systems, i.e. systems operating in an environment that they cannot control and with components that may join or leave, behaviors can arise as side effects of intensive components interaction. Finding ways to understand and design…

In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…

We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…

Nowadays, we are surrounded by a large number of complex phenomena ranging from rumor spreading, social norms formation to rise of new economic trends and disruption of traditional businesses. To deal with such phenomena,Complex Adaptive…

This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…

Human action is naturally compositional: humans can easily recognize and perform actions with objects that are different from those used in training demonstrations. In this paper, we study the compositionality of action by looking into the…

Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…

Results obtained in the past for free boson systems at zero and nonzero temperature are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to…

Rather than simply recognizing the action of a person individually, collective activity recognition aims to find out what a group of people is acting in a collective scene. Previ- ous state-of-the-art methods using hand-crafted potentials…

The goal of this paper is to advance an extensible theory of living systems using an approach to biomathematics and biocomputation that suitably addresses self-organized, self-referential and anticipatory systems with multi-temporal…

We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship…

We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and…

In this paper we consider a class of partial integro-differential equations of fractional order, motivated by an equation which arises as a result of modeling surface-volume reactions in optical biosensors. We solve these equations by…

The aim of section 1 is to define the homotopic functor to category of Abelian groups, connected with the special classes of bundles with fiber matrix algebra or projective space. The aim of section 2 is to define some generalization of the…

In this survey, we summarize some results in the literature involving the mesh category, which is a combinatorial representation of the category of modules over a finite-dimensional associative algebra. We discuss Riedtmann's well-behaved…

This essay provides a critical overview of the mathematical kinetic theory of active particles, which is used to model and study collective systems consisting of interacting living entities, such as those involved in behavior and evolution.…

Coalgebras for analytic functors uniformly model graph-like systems where the successors of a state may admit certain symmetries. Examples of successor structure include ordered tuples, cyclic lists and multisets. Motivated by goals in…