Related papers: Diagonals and Block-Ordered Relations
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal equivalence is the natural extension of the well-known…
Learning physics requires understanding the applicability of fundamental principles in a variety of contexts that share deep features. One way to help students learn physics is via analogical reasoning. Students can be taught to make an…
This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic…
Duality is most often defined as a relationship between convex functions. If those functions are nonconvex, classical duality breaks down. Notwithstanding, we show that another kind of duality still exists, not between the functions…
A sibling of a relational structure $R$ is any structure $S$ which can be embedded into $R$ and, vice versa, in which $R$ can be embedded. Let $sib(R)$ be the number of siblings of $R$, these siblings being counted up to isomorphism.…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We study the geometrical features of the order parameter's fluctuations near the critical point of mixed-order phase transitions in randomly interdependent spatial networks. In contrast to continuous transitions, where the structure of the…
We investigate permutations in terms of their cycle structure and descent set. To do this, we generalize the classical bijection of Gessel and Reutenauer to deal with permutations that have some ascending and some descending blocks. We then…
For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…
Visual paradoxes like the Penrose staircase present a fundamental tension: locally coherent geometric relationships that cannot be realized globally. Inspired by Penrose's observations connecting such paradoxes to cohomology, we develop a…
A chain of coupled chaotic elements with different time scales is studied. In contrast with the adiabatic approximation, we find correlations between faster and slower elements when the differences in the time scales of the elements lie…
This article suggests that thinking about the role of reference frames can provide new insight into Extended Wigner's Friend scenarios. This involves appealing to symmetries to make a principled distinction between properties of a system…
Document-level relation extraction (DocRE) involves identifying relations between entities distributed in multiple sentences within a document. Existing methods focus on building a heterogeneous document graph to model the internal…
We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
A relation extends another relation consistently if its symmetric, respectively its asymmetric, part contains the corresponding part of the smaller relation. It is shown that there exists no finite circular chain made from two transitive…