Related papers: Data-scientific study of Kronecker coefficients
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
These notes are an expanded version of a talk given by the second author. Our main interest is focused on the challenging problem of computing Kronecker coefficients. We decided, at the beginning, to take a very general approach to the…
Quantum simulators offer powerful means to investigate strongly correlated quantum matter. However, interpreting measurement outcomes in such systems poses significant challenges. Here, we present a theoretical framework for information…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
To describe certain facets of non-classicality, it is necessary to quantify properties of operations instead of states. This is the case if one wants to quantify how well an operation detects non-classicality, which is a necessary…
We explore the information geometry and asymptotic behaviour of estimators for Kronecker-structured covariances, in both growing-$n$ and growing-$p$ scenarios, with a focus towards examining the quadratic form or partial trace estimator…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
We determine the asymptotic behavior of the coefficients of Hecke polynomials. In particular, this allows us to determine signs of these coefficients when the level or the weight is sufficiently large. In all but finitely many cases, this…
Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]. This article considers the basic properties that a…
The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups; namely, given three partitions $\lambda, \mu, \tau$ of $n$, the multiplicity of $\lambda$ in $\mu \otimes \tau$ is…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
We prove explicit versions of the Kronecker-Weyl theorems, both in a discrete and a continuous settings, without any linear independence hypothesis. As an application, we propose an alternative approach to problems concerning asymptotic…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of…
The nonclassicality of quantum states is a fundamental resource for quantum technologies and quantum information tasks in general. In particular, a pivotal aspect of quantum states lies in their coherence properties, encoded in the…
Consider a case-control study in which we have a random sample, constructed in such a way that the proportion of cases in our sample is different from that in the general population---for instance, the sample is constructed to achieve a…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
The model implied by factor score predictors does not reproduce the non-diagonal elements of the observed covariance matrix as well as the factor loadings. It is therefore investigated whether it is possible to estimate factor loadings for…
We study analogues of Kronecker coefficients for symmetric inverse semigroups, for dual symmetric inverse semigroups and for the inverse semigroups of bijections between subquotients of finite sets. In all cases we reduce the problem of…
In this paper we apply a method of Robinson and Taulbee for computing Kronecker coefficients together with other ingredients and show that the multiplicity of each component in a Kronecker square can be obtained from an evaluation of a…