Related papers: Small object arguments, plus-construction, and lef…
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
We consider the challenge of preference elicitation in systems that help users discover the most desirable item(s) within a given database. Past work on preference elicitation focused on structured models that provide a factored…
Feature construction can contribute to comprehensibility and performance of machine learning models. Unfortunately, it usually requires exhaustive search in the attribute space or time-consuming human involvement to generate meaningful…
We prove that, assuming Vop\venka's principle, every small projectivity class in a locally presentable category is accessible.
In this article the notions of (quasi weakly hereditary) general closure operator $\mb{C}$ on a category $\cx$ with respect to a class $\cm$ of morphisms, and quasi factorization structures in a category $\cx$ are introduced. It is shown…
Since its introduction in 2012, the factorization theory for rational motions quickly evolved and found applications in theoretical and applied mechanism science. We provide an accessible introduction to motion factorization with many…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously…
One of the fundamental results in the theory of localization for discrete Schr\"odinger operators with random potentials is the exponential decay of Green's function and the absence of continuous spectrum. In this paper we provide a new…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…
Let F(X,n):= X^n-\Delta be the complementary of the union \Delta of the diagonals of X^n and let U be a quotient of F(X,n) (possibly trivial) by a subgroup of the symmetric group S_n. We construct compactifications of U in products of…
The only known constructive factorization algorithm for linear partial differential operators (LPDOs) is Beals-Kartashova (BK) factorization \cite{bk2005}. One of the most interesting features of BK-factorization: at the beginning all the…
Small, finite entities are easier and simpler to manipulate than gigantic, infinite ones. Consequently huge chunks of mathematics are devoted to methods reducing the study of big, cumbersome objects to an analysis of their finite building…
We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as…
We explore the connection between the factorisation of virtual corrections to multi-particle massless gauge theory amplitudes and the problem of subtraction at NNLO and beyond. Taking inspiration from virtual factorisation, we provide a set…
Automatic few-shot font generation is a practical and widely studied problem because manual designs are expensive and sensitive to the expertise of designers. Existing few-shot font generation methods aim to learn to disentangle the style…
The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems (AWFSs) to cover some important examples that are not locally presentable categories. Secondly, to prove that…
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently…
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process…