Related papers: Cut Vertices and Semi-Inclusive Deep Inelastic Pro…
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…
Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…
We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…
We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e.\ possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
We provide a general method to construct local infrared subtraction counterterms for unresolved radiative contributions to differential cross sections, to any order in perturbation theory. We start from the factorised structure of virtual…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
The integration of optimization problems within neural network architectures represents a fundamental shift from traditional approaches to handling constraints in deep learning. While it is long known that neural networks can incorporate…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Characterizing simultaneously diagonalizable (SD) matrices has been receiving considerable attention in the recent decades due to its wide applications and its role in matrix analysis. However, the notion of SD matrices is arguably still…
This paper presents a novel simplification method for removing vertices from an intrinsic triangulation corresponding to extrinsic vertices lying on near-developable (i.e., with limited Gaussian curvature) and general surfaces. We greedily…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
The main aim of this paper is to provide a description of neighbourhood operators in finitely complete categories with finite coproducts and a proper factorisation system such that the semilattice of admissible subobjects make a…
We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse…
The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
Some facts about von Neumann algebras and finite index inclusions of factors are viewed in the context of local quantum field theory. The possibility of local fields intertwining superselection sectors with braid group statistics is…