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In this paper some combinatorial and homological tools are used to describe and give an explicit formula for the number of exceptional pairs (exceptional sequences of length two) for some classes of Nakayama Algebras and for the Auslander…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
We give a new perspective on the homological characterisations of amenability given by Johnson in the context of bounded cohomology and by Block and Weinberger in the context of uniformly finite homology. We examine the interaction between…
We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.
I review the proposal of Berenstein-Douglas for a completely general definition of Seiberg duality. To give evidence for their conjecture I present the first example of a physical dual pair and explicitly check that it satisfies the…
On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected n-orbifolds are manifolds. The latter improves the best previously known bound of Lytchak by…
Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod $2$ cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by two,…
This article explores the connections between graph-theoretical and topological approaches in the study of the Jordan curve theorem for grids. Building on the foundational work of Rosenfeld, who developed adjacency-based concepts on…
In this paper we prove results relating to two homotopy relations and four homology theories developed in the topology of digital images. We introduce a new type of homotopy relation for digitally continuous functions which we call "strong…
We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big…
A cohomology theory for "odd polygon" relations -- algebraic imitations of Pachner moves in dimensions 3, 5, ... -- is constructed. Manifold invariants based on polygon relations and nontrivial polygon cocycles are proposed. Example…
Let $T_P$ be the theory of beautiful pairs of algebraically closed fields of fixed characteristic. It is known that for real tuples in models of $T_P$, SU-rank coincides with Morley rank and can be computed effectively. Building on Pillay's…
This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…
A wide variety of problems in computational biology, most notably the assessment of orthology, are solved with the help of reciprocal best matches. Using an evolutionary definition of best matches that captures the intuition behind the…
Using the Cartan-Kahler theory, and results on real algebraic structures, we prove two embedding theorems. First, the interior of a smooth, compact 3-manifold may be isometrically embedded into a G_2-manifold as an associative submanifold.…
The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [24] which was tackled in 1996 [10]. In this paper, we first discuss unmatchable subsets in abelian groups. Then we formulate…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…