Related papers: Generalized Tukey reducibility between $\sigma$-di…

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of…

We answer one of the main questions in generalized descriptive set theory, the Friedman-Hyttinen-Kulikov conjecture on the Borel reducibility of the Main Gap. We show a correlation between Shelah's Main Gap and generalized Borel…

For superpartner masses not much heavier than the weak scale $M=M_{\rm W}$, large logarithmic corrections of the Sudakov type arise at TeV energies. In this paper we discuss the general structure of electroweak supersymmetric (susy) Sudakov…

The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…

We prove that for any prime $\ell$, any finite group has as many irreducible complex characters of degree prime to $\ell$ as the normalizers of its Sylow $\ell$-subgroups. This equality was conjectured by John McKay. The conjecture was…

The concept of weighted $\beta\gamma$ - summability of order $\theta$ in case of fuzzy functions is introduced and classified into ordinary and absolute sense. Several inclusion relations among the sets are investigated. Also we have found…

A $\Sigma$-construction of Solovay is partially extended to the case of intermediate sets which are not necessarily subsets of the ground model. As an application, we prove that, for a given name $t$, the set of all sets $t[G]$, $G$ being…

We introduce two kinds of generalized $s$-convex functions on real linear fractal sets $\mathbb{R}^{\alpha}(0<\alpha<1)$. And similar to the class situation, we also study the properties of these two kinds of generalized $s$-convex…

Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey's halfspace median ($\frac{1} {3}$) has been obtained in literature. In this paper, we establish the result under…

A $\Sigma$-construction of Solovay is extended to the case of intermediate sets which are not necessarily subsets of the ground model, with a more transparent description of the resulting forcing notion than in the classical paper of…

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

One partially ordered set, $Q$, is a Tukey quotient of another, $P$, if there is a map $\phi : P \to Q$ carrying cofinal sets of $P$ to cofinal sets of $Q$. Two partial orders which are mutual Tukey quotients are said to be Tukey…

The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex…

With the desire to apply the Dempster-Shafer theory to complex real world problems where the evidential strength is often imprecise and vague, several attempts have been made to generalize the theory. However, the important concept in the…

Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie…

We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological groups admitting an $\omega^\omega$-base, we introduce the…

We discuss some consequences of the fact that symmetry groups appearing in compactified (super-)gravity may be non-simply connected. The possibility to add fermions to a theory results in a simple criterion to decide whether a 3-dimensional…

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…

The Tukey-$\lambda$ distribution has interesting properties including (i) for some parameters values it has finite support, and for others infinite support, and (ii) it can mimic several other distributions such that parameter estimation…