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We find an explicit combinatorial gradient vector field on the well known complex S (Salvetti complex) which models the complement to an arrangement of complexified hyperplanes. The argument uses a total ordering on the facets of the…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
In the recent years, we have witnessed the development of multi-label classification methods which utilize the structure of the label space in a divide and conquer approach to improve classification performance and allow large data sets to…
We introduce labelled sequent calculi for quantified modal logics with definite descriptions. We prove that these calculi have the good structural properties of G3-style calculi. In particular, all rules are height-preserving invertible,…
The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz\'alez, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it…
In this work, we study semi-supervised multi-label node classification problem in attributed graphs. Classic solutions to multi-label node classification follow two steps, first learn node embedding and then build a node classifier on the…
Finite matroids are combinatorial structures that express the concept of linear independence. In 1964, G.-C. Rota conjectured that the coefficients of the "characteristic polynomial" of a matroid $M$, polynomial whose coefficients enumerate…
This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees.…
In 1985, Golumbic and Scheinerman established an equivalence between comparability graphs and containment graphs, graphs whose vertices represent sets, with edges indicating set containment. A few years earlier, McMorris and Zaslavsky…
Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne's category admits a unique nontrivial family of modified trace functions. Such modified trace…
Lettericity is a graph parameter introduced by Petkov\v{s}ek in 2002 in order to study well-quasi-orderability under the induced subgraph relation. In the world of permutations, geometric griddability was independently introduced in 2013 by…
In this paper, we provide a unified definition of mediated graph, a combinatorial structure with multiple applications in mathematical optimization. We study some geometric and algebraic properties of this family of graphs and analyze…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
Collective classification has been intensively studied due to its impact in many important applications, such as web mining, bioinformatics and citation analysis. Collective classification approaches exploit the dependencies of a group of…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels.…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…