Related papers: Compositional Exploration of Combinatorial Scienti…

Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…

One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…

Co-clustering is a data mining technique used to extract the underlying block structure between the rows and columns of a data matrix. Many approaches have been studied and have shown their capacity to extract such structures in continuous,…

This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…

The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing "holes" or "incomplete parts", sometimes known as comb diagrams. We…

We present some results on (co)limits of diagrams in $\infty$-categories, as well as those in $(n, 1)$-categories. In particular, we deduce a way to reshape colimit diagrams into simplicial ones, and a characterisations of $n$-cofinality…

A model category is called combinatorial if it is cofibrantly generated and its underlying category is locally presentable. As shown in recent years, homotopy categories of combinatorial model categories share useful properties, such as…

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base…

As the use and diversity of diagrams across many disciplines grows, there is an increasing interest in the diagrams research community concerning how such diversity might be documented and explained. In this article, we argue that one way…

Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…

In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain…

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference…

We define a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an \'etale classifying space), and we study basic properties of this construction. As a case study, we construct the motivic analogs of…

Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…

We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…

Discovering pattern sets or global patterns is an attractive issue from the pattern mining community in order to provide useful information. By combining local patterns satisfying a joint meaning, this approach produces patterns of higher…

Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that…

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…