Related papers: New Steiner systems from old ones by paramodificat…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
The Transformer architecture is widely used in natural language processing. Despite its success, the design principle of the Transformer remains elusive. In this paper, we provide a novel perspective towards understanding the architecture:…
Given a diagram of schemes, we can ask if a geometric object over one of them can be built from descent data (usually objects of the same type over the various other schemes in the diagram, together with compatibility isomorphisms). Using…
In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…
We theoretically find that the second-order topological insulator, i.e., corner states, can be engineered by coupling two copies of two-dimensional $\mathbb{Z}_2$ topological insulators with opposite spin-helicities. As concrete examples,…
We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.
We study petal diagrams of knots, which provide a method of describing knots in terms of permutations in a symmetric group $S_{2n+1}$. We define two classes of moves on such permutations, called trivial petal additions and crossing…
Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally-responsive materials therefore open up the possibility of creating a…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on lines in PG($n,p$) or codes in the Grassmannian, to form automorphisms groups in the Grassmanian and in its codes. These automorphisms are…
As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v,k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently…
Association schemes on triples (ASTs) are ternary analogues of classical association schemes, whose relations and adjacency algebras are ternary instead of binary. We provide a survey of the current progress in the study of ASTs,…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
We present a methodology for training foundational transformer models capable of processing collider data with diverse kinematic signatures. Our universal foundation model is designed for simultaneous analysis of all processes involving…
Despite their nearly universal adoption for large language models, the internal workings of transformers are not well understood. We aim to better understand the impact of removing or reorganizing information throughout the layers of a…
We present a rational approach to the design of half-metallic heterostructures which allows the design of an infinite number of half-metallic heterostructures. The wide range of materials that can be made half-metallic using our approach…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a…
A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm,…