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Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Introduction. We investigate the generalization ability of models built on datasets containing a small number of subjects, recorded in single study protocols. Next, we propose and evaluate methods combining these datasets into a single,…
We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
We establish the asymptotic normality of the $G$-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator.…
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be…
We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Using non-smooth analysis and tools from geometric measure…
This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…
This paper extends the idea of a generalized estimator for a scalar parameter (Vos, 2022) to multi-dimensional parameters both with and without nuisance parameters. The title reflects the fact that generalized estimators provide more than…
Understanding the generalization behaviour of deep neural networks is a topic of recent interest that has driven the production of many studies, notably the development and evaluation of generalization "explainability" measures that…
A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian…
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…
The notion of a generalized scale emerged in recent joint work with Afsar-Brownlowe-Larsen on equilibrium states on C*-algebras of right LCM monoids, where it features as the key datum for the dynamics under investigation. This work…
We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras.