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We investigate \emph{magnitude} as a new unary and strictly Pareto-compliant quality indicator for finite approximation sets to the Pareto front in multiobjective optimization. Magnitude originates in enriched category theory and metric…
Given the first 20-100 coefficients of a typical generating function of the type that arises in many problems of statistical mechanics or enumerative combinatorics, we show that the method of differential approximants performs surprisingly…
We study approximation of embeddings between finite dimensional L_p spaces in the quantum model of computation. For the quantum query complexity of this problem matching (up to logarithmic factors) upper and lower bounds are obtained. The…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
We define and study a class of subshifts of finite type (SFTs) defined by a family of allowed patterns of the same shape where, for any contents of the shape minus a corner, the number of ways to fill in the corner is the same. The main…
We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0)…
We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories…
We describe some theoretical results on triangulations of surfaces and we develop a theory on roots, decompositions and genus-surfaces. We apply this theory to describe an algorithm to list all triangulations of closed surfaces with at most…
In this paper we explain certain systematic differences between algebraic and topological triangulated categories. A triangulated category is algebraic if it admits a differential graded model, and topological if it admits a model in the…
Capturing the similarities between human language units is crucial for explaining how humans associate different objects, and therefore its computation has received extensive attention, research, and applications. With the ever-increasing…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
This is the fourth (and last) prepublication version of a book on derived categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for the theory of derived categories, and to…
A finite directed category is a $k$-linear category with finitely many objects and an underlying poset structure, where $k$ is an algebraically closed field. This concept unifies structures such as $k$-linerizations of posets and finite EI…
One of the first remarkable results in the representation theory of artin algebras, due to Auslander and Ringel-Tachikawa, is the characterization of when an artin algebra is representation-finite. In this paper, we investigate aspects of…
We study truncated objects using elementary methods. Concretely, we use universes and the resulting natural number object to define internal truncation levels and prove they behave similar to standard truncated objects. Moreover, we take an…
In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…
We define the notion of right $n$-angulated category, which generalizes the notion of right triangulated category. Let $\mathcal{C}$ be an additive category or $n$-angulated category and $\mathcal{X}$ a covariantly finite subcategory, we…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is…
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely…