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Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

We study properties of functions with bounded variation in Carnot-Ca\-ra\-th\'eo\-do\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group: We establish a semidirect product…

Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the…

The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of experiments in applied statistics. In this paper we study some…

We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…

We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every totally disconnected set with finite Hausdorff measure of…

Let $d(G)$ be the smallest cardinality of a generating set of a finite group $G.$ We give a complete classification of the finite groups with the property that, whenever $ \langle x_1, \dots, x_{d(G)} \rangle = \langle y_1, \dots, y_{d(G)}…

Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…

Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology is a productively countably tight space, which yields some…

We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…

Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a nondecreasing sequence of pseudometrics $\{\nu_n\}$ on $M^T$ (the set of all functions from $T$ into $M$), called the \emph{joint modulus of variation}. We prove that if two…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

Inspired by very ampleness of Zariski Geometries, we introduce and study the notion of a very ample family of plane curves in any strongly minimal set, and the corresponding notion of a very ample strongly minimal set (characterized by the…

We exhibit a class of "relatively curved" $\vec{\gamma}(t) := (\gamma_1(t),\dots,\gamma_n(t))$, so that the pertaining multi-linear maximal function satisfies the sharp range of H\"{o}lder exponents, \[ \left\| \sup_{r > 0} \ \frac{1}{r}…