Related papers: On Stable embeddability of partitions
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…
We study two partial orders on $[x_1,...,x_n]$, the free abelian monoid on ${x_1,...,x_n}$. These partial orders, which we call the ``strongly stable'' and the ``stable'' partial order, are defined by the property that their filters are…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
Recent advancements in photon induced near-field electron microscopy (PINEM) enable the preparation, coherent manipulation and characterization of free-electron quantum states. The available measurement consists of electron energy…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some favourable properties, the n-optimal matrices of partitions. We use this to improve a decomposition result…
Natural frequencies and normal modes are basic properties of a structure which play important roles in analyses of its vibrational characteristics. As their computation reduces to solving eigenvalue problems, it is a natural arena for…
Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…
The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
In this paper we compute the rank and exhibit a presentation for the monoids of all $P$-stable and $P$-order preserving partial permutations on a finite set $\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)…
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to…
We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…
We investigate four partial orderings on the space of quantum measurements (i.e on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1)…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…
Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie…
For partially ordered sets $X$ we consider the square matrices $M^{X}$ with rows and columns indexed by linear extensions of the partial order on $X$. Each entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of the…
The stability of word embedding algorithms, i.e., the consistency of the word representations they reveal when trained repeatedly on the same data set, has recently raised concerns. We here compare word embedding algorithms on three corpora…