Related papers: Linear repetitivity and subadditive ergodic theore…
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
We extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number…
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using…
When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this…
We study set systems formed by neighborhoods in graphs of bounded twin-width. We start by proving that such graphs have linear neighborhood complexity, in analogy to previous results concerning graphs from classes with bounded expansion and…
Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. Proofs based on ultrafilters tend to be shorter and more…
We present an algebraic investigation of generalized and equiaffine curvature tensors in a given pseudo-Euclidean vector space and study different orthogonal, irreducible decompositions in analogy to the known decomposition of algebraic…
A way to add an extra dimension is briefly discussed.
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
In this paper, we investigate ergodic and fractal properties of the sets $$\Lambda_y:=\Big\{n\in\mathbb{N}:\ \{u_ny\}\in I_n\Big\},$$ where $\{\cdot\}$ denotes the fractional part function, $(u_n)_{n\in\mathbb{N}}$ is an increasing sequence…
The use of Lagrangian cuts proves effective in enhancing the lower bound of the master problem within the execution of benders-type algorithms, particularly in the context of two-stage stochastic programs. However, even the process of…
We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated…
Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we…
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…