Related papers: Modelling Concurrency with Comtraces and Generaliz…

Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula…

Hoare and He's theory of reactive processes provides a unifying foundation for the formal semantics of concurrent and reactive languages. Though highly applicable, their theory is limited to models that can express event histories as…

Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…

Traces form a coarse notion of semantic equivalence between states of a process, and have been studied coalgebraically for various types of system. We instantiate the finitary coalgebraic trace semantics framework of Hasuo et al. for…

Generalized splines are an algebraic combinatorial framework that generalizes and unifies various established concepts across different fields, most notably the classical notion of splines and the topological notion of GKM theory. The…

In this paper we focus on concurrent processes built on synchronization by means of futures. This concept is an abstraction for processes based on a main execution thread but allowing to delay some computations. The structure of a general…

Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

Generalized synchronization is plausibly the most complex form of synchronization. Previous studies have revealed the existence of weak or strong forms of generalized synchronization depending on the multi- or mono-valued nature of the…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…

Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…

We show how one can twist the definition of Hochschild homology of an algebra or a DG algebra by inserting a possibly non-additive trace functor. We then prove that many of the usual properties of Hochschild homology survive such a…

Concurrent data structures serve as fundamental building blocks for concurrent computing. Many concurrent counterparts have been designed for basic sequential mechanisms; however, one notable omission is a concurrent tree that supports…

That shared features between train and test data are required for generalisation in artificial neural networks has been a common assumption of both proponents and critics of these models. Here, we show that convolutional architectures avoid…

In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…

We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard…