Related papers: On Stable embeddability of partitions
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian…
The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…
The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an…
We investigate the computational complexity of various decision problems related to conjugacy in finite inverse semigroups. We describe polynomial-time algorithms for checking if two elements in such a semigroup are ~p conjugate and whether…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number, let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let $\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is $\mathcal{F}$-finitely…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
We introduce a new class of "random" subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We establish necessary and sufficient conditions for solvability of…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such…
This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities:…
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra $A(\overline{\mathbb D})$. As a consequence, one obtains uniform closed subalgebras of $A(\overline{\mathbb D})$ which have arbitrarily…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
In this paper we study the partitioning approach for multiprocessor real-time scheduling. This approach seems to be the easiest since, once the partitioning of the task set has been done, the problem reduces to well understood uniprocessor…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…