Related papers: The M\"obius transform on symmetric ordered struct…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching…
A conformal structure on a manifold $M^n$ induces natural second order conformally invariant operators, called M\"obius and Laplace structures, acting on specific weight bundles of $M$, provided that $n\ge 3$. By extending the notions of…
Moebius number systems represent points using sequences of Moebius transformations. Thorough the paper, we are mainly interested in representing the unit circle (which is equivalent to representing R\cup\{\infty\}). The main aim of the…
We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders, which include SPT…
In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their…
Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, raise in the quantum computation, bin-packing and matrix analysis. We find the…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…
The paper is devoted to developing subdifferential theory for set-valued mappings taking values in ordered infinite-dimensional spaces. This study is motivated by applications to problems of vector and set optimization with various…
We study several aspects of the M\"{o}bius function, $\mu[\sigma,\pi]$, on the poset of permutations under the pattern containment order. First, we consider cases where the lower bound of the poset is indecomposable. We show that…
In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…