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A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
Many textual software languages share common concepts such as defining and referencing elements, hierarchical structures constraining the visibility of names, and allowing for identical names for different element kinds. Symbol tables are…
Self-rationalizing models that also generate a free-text explanation for their predicted labels are an important tool to build trustworthy AI applications. Since generating explanations for annotated labels is a laborious and costly pro…
We study abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of new dynamical variables; however, we avoid the use of the dual lattice…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We introduce a family of multitask variational methods for semi-supervised sequence labeling. Our model family consists of a latent-variable generative model and a discriminative labeler. The generative models use latent variables to define…
We embed the category of complex manifolds into the simplicial category of prestacks on the simplicial site of Stein manifolds, a prestack being a contravariant simplicial functor from the site to the category of simplicial sets. The…
The polytopic definition introduced recently describing the topology of manifolds is used to formulate a generating function pertinent to its topological properties. In particular, a polynomial in terms of one variable and a tori underlying…
There have recently been several developments in synthetic mathematics using extensions of dependent type theory with univalence and higher inductive types: simplicial homotopy type theory, synthetic algebraic geometry and synthetic Stone…
In modern multilabel classification problems, each data instance belongs to a small number of classes from a large set of classes. In other words, these problems involve learning very sparse binary label vectors. Moreover, in large-scale…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…
In the setting of homotopy type theory, each type can be interpreted as a space. Moreover, given an element of a type, i.e. a point in the corresponding space, one can define another type which encodes the space of loops based at this…
Slattery (2007) described computational methods to enumerate, construct, and identify finite groups of squarefree order. We generalise Slattery's result to the class of finite groups that have cyclic Sylow subgroups and provide an…
A Standard Operating Procedure (SOP) defines a low-level, step-by-step written guide for a business software workflow. SOP generation is a crucial step towards automating end-to-end software workflows. Manually creating SOPs can be…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…
Metaphor generation is a challenging task which can impact many downstream tasks such as improving user satisfaction with dialogue systems and story generation. This paper tackles the problem of Chinese nominal metaphor generation by…
The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit…
Language models can produce convincing scientific analyses, but repeated generations on the same data do not guarantee the same result. A researcher may regenerate an identical query and receive a different fit, a different peak position or…
This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the computational results in the paper "Hamiltonian…