Related papers: Compositional Exploration of Combinatorial Scienti…
We consider the problem of enumeration of planar maps and revisit its one-matrix model solution in the light of recent combinatorial techniques involving conjugated trees. We adapt and generalize these techniques so as to give an…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of…
The aim of these notes is to introduce the intuition motivating the notion of a "complicial set", a simplicial set with certain marked "thin" simplices that witness a composition relation between the simplices on their boundary. By varying…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…
In software system design, one of the purposes of diagrammatic modeling is to explain something (e.g., data tables) to others. Very often, syntax of diagrams is specified while the intended meaning of diagrammatic constructs remains…
We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We…
K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…
Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Scholars often explore literature outside of their home community of study. This exploration process is frequently hampered by field-specific jargon. Past computational work often focuses on supporting translation work by removing jargon…
Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
Assembly-based tools provide a powerful modeling paradigm for non-expert shape designers. However, choosing a component from a large shape repository and aligning it to a partial assembly can become a daunting task. In this paper we…
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial…