Related papers: Unitary Correlation Sets
We formulate a conjecture on the behavior of the minimal free resolutions of sets of general points on arbitrary varieties embedded by complete linear series, in analogy with the well-known Minimal Resolution Conjecture for points in…
We search a simplest and minimal way to determine whether a given quantum system is entangled or separable. For this end, we propose binary correlation measurements in which restricted knowledge of only zero or non-zero correlations is…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
Following the earlier studies on embedded unitary ensembles generated by random two-body interactions [EGUE(2)] with spin SU(2) and spin-isospin SU(4) symmetries, developed is a general formulation, for deriving lower order moments of the…
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to direct sums of matrices of smaller…
We say that a sequence $\{x_n\}_{n \geq 1}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \rightarrow \infty} \frac{1}{N} \# \left\{ 1 \leq l \neq m \leq N \, : \, \left\lVert x_l-x_m \right\rVert < \frac{s}{N}…
Sentence encoders map sentences to real valued vectors for use in downstream applications. To peek into these representations - e.g., to increase interpretability of their results - probing tasks have been designed which query them for…
The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known…
We define a general product of two $n$-dimensional tensors $\mathbb {A}$ and $\mathbb {B}$ with orders $m\ge 2$ and $k\ge 1$, respectively. This product is a generalization of the usual matrix product, and satisfies the associative law.…
Extensions of nuclear supersymmetry are discussed, together with a proposal for new, more stringent and precise tests that probe the susy classification and specific two-particle correlations among supersymmetric partners. The combination…
In this paper we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the…
Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
New partial results are obtained related to the following old problem of Erd\"os: for any infinite set $X$ of real numbers to show that there is always a measurable (or, equivalently, closed) subset of reals of positive Lebesgue measure…
In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance…
We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be…
This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…