Related papers: Compositional Exploration of Combinatorial Scienti…
We construct a combinatorial moduli space closely related to the KSV-compactification of the moduli space of bordered marked Riemann surfaces. The open part arises from symmetric metric ribbon graphs. The compactification is obtained by…
Computational models of music, while providing good descriptions of melodic development, still cannot fully grasp the general structure comprised of repetitions, transpositions, and reuse of melodic material. We present a corpus of strongly…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
Cartesian differential categories come equipped with a differential combinator that formalizes the derivative from multi-variable differential calculus, and also provide the categorical semantics of the differential $\lambda$-calculus. An…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics.…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Starting from a N=1 scalar supermultiplet in 2+1 dimensions, we demonstrate explicitly the appearance of induced N=1 vector and scalar supermultiplets of composite operators made out of the fundamental supersymmetric constituents. We…
Aligning machine representations with human understanding is key to improving interpretability of machine learning (ML) models. When classifying a new image, humans often explain their decisions by decomposing the image into concepts and…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
We revisit Kapranov and Voevodsky's idea of spaces modelled on combinatorial pasting diagrams, now as a framework for higher-dimensional rewriting and the basis of a model of weak omega-categories. In the first part, we elaborate on…
We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that…
A folded type model is developed for analyzing compositional data. The proposed model involves an extension of the $\alpha$-transformation for compositional data and provides a new and flexible class of distributions for modeling data…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…