Related papers: A mixed multifractal analysis for quasi Ahlfors ve…
This paper studies weakly mixing (singular) and mixing masas in type $\rm{II}_{1}$ factors from a bimodule point of view. Several necessary and sufficient conditions to characterize the normalizing algebra of a masa are presented. We also…
A two-parameter extension of the density-scaled double hybrid approach of Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)] is presented. It is based on the explicit treatment of a fraction of multideterminantal exact exchange. The…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
In the present update work we consider properly defined two-parameter quasi-probability densities that, e.g., can be used as witness for quantum behaviour for a class of pure states as expressed in terms of a self-adjoint observable angular…
We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…
Multifractal analysis is a powerful approach for characterizing ergodic or localized nature of eigenstates in complex quantum systems. In this context, the eigenvectors of random matrices belonging to invariant ensembles naturally serve as…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
We extend to the context of metric measured spaces, with a measure that satisfies upper Ahlfors growth conditions the validity of (generalized) H\"{o}lder continuity results for the solution of a Fredholm integral equation of the second…
We explore the consequences of a set of axioms which extend Scarsini's axioms for bivariate measures of concordance to the multivariate case and exhibit the following results: (1) A method of extending measures of concordance from the…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical…
Consider a sequence of linear contractions $S_{j}(x)=\varrho x+d_{j}$ and probabilities $p_{j}>0$ with $\sum p_{j}=1$. We are interested in the self-similar measure $\mu =\sum p_{j}\mu \circ S_{j}^{-1}$, of finite type. In this paper we…
A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
We extend classical basis constructions from Fourier analysis to attractors for affine iterated function systems (IFSs). This is of interest since these attractors have fractal features, e.g., measures with fractal scaling dimension.…
Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit -- quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analysed.…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…