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Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification,…

We consider random polytopes in the $d$-dimensional Euclidean space that are the convex hulls i.i.d. random points selected according to beta-prime distributions. These distributions are rotationally symmetric, heavy-tailed, and their…

Several consistency notions are available for a lower prevision P assessed on a set D of gambles (bounded random variables), ranging from the well known coherence to convexity and to the recently introduced 2-coherence and 2-convexity. In…

Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology,…

One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called…

We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses.…

Let $\cal P$ be a finite classical polar space of rank $d$. An $m$-regular system with respect to $(k - 1)$-dimensional projective spaces of $\cal P$, $1 \le k \le d - 1$, is a set $\cal R$ of generators of $\cal P$ with the property that…

The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex…

Proximity catch digraphs (PCDs) are based on proximity maps which yield proximity regions and are special types of proximity graphs. PCDs are based on the relative allocation of points from two or more classes in a region of interest and…

We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic L\"owner Evolution methods. These quantities are shown to…

A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As…

The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…

It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a…

We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…

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…

Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which…

This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of…

In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of $n$-coherent and $n$-convex conditional previsions, at the varying of $n$. We investigate which such previsions are the…