Related papers: Retracing some paths in Process Algebra

A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.

The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…

We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

This is a brief description of the classical part of the Standard Model of particles and interactions, using the language of vector bundles over the spacetime and operations on them.

Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with…

We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…

An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…

This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…

We introduce "geometric" partial comodules over coalgebras in monoidal categories, as an alternative notion to the notion of partial action and coaction of a Hopf algebra introduced by Caenepeel and Janssen. The name is motivated by the…

The familiar trace of a square matrix generalizes to a trace of an endomorphism of a dualizable object in a symmetric monoidal category. To extend these ideas to other settings, such as modules over non-commutative rings, the trace can be…

A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a…

This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…

Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…

Threads as considered in basic thread algebra are primarily looked upon as behaviours exhibited by sequential programs on execution. It is a fact of life that sequential programs are often fragmented. Consequently, fragmented program…

Comprehensive understanding of particle motion in microfluidic devices is essential to unlock novel technologies for shape-based separation and sorting of microparticles like microplastics, cells and crystal polymorphs. Such particles…

We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this…

A categorical approach to linear control systems is introduced. Feedback actions on linear systems arises as a symmetric monoidal category. Stable feedback isomorphisms generalize enlargement of pairs of matrices. Subcategory of locally…

The theory of path algebras is usually circunscripted to the study of representations, usually linked to finite graphs. In our work, we focus on studying the structure of path algebras over a field associated to arbitrary graphs. We…

In this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category $\mathcal{C}$ endowed with a symmetric $2$-trace, one can attach a cyclic (resp. cocyclic)…