Related papers: On the Groupoid Model of Computational Paths
The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…
We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
In this work, we use a labelled deduction system based on the concept of computational paths (sequence of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
By generalizing the notion of the path ideal of a graph, we study some algebraic properties of some path ideals associated to a line graph. We show that the quotient ring of these ideals are always sequentially Cohen-Macaulay and also…
In this work we realize Leavitt path algebras as partial skew groupoid rings. This yields a free path groupoid grading on Leavitt path algebras. Using this grading we characterize free path groupoid graded isomorphisms of Leavitt path…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
The use of a necessity modality in a typed $\lambda$-calculus can be used to separate it into two regions. These can be thought of as intensional vs. extensional data: data in the first region, the modal one, are available as code, and…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
One of the greatest research challenges of this century is to understand the neural basis for how behavior emerges in brain-body-environment systems. To this end, research has flourished along several directions but have predominantly…
The goal of this "Habilitation \`a diriger des recherches" is to present two different applications, namely computations of certain partition functions in probability and applications to integrable systems, of the topological recursion…
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…
Similarity networks are important abstractions in many information management applications such as recommender systems, corpora analysis, and medical informatics. For instance, by inducing similarity networks between movies rated similarly…
This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed…
Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…