Related papers: On the maximal extension in the mixed ultradiffere…

We examine clusters in the cluster tube of rank $n+1$ using exceptional sequences in the abelian tube of rank $n+1$. Although the abelian tube has more exceptional sequences than the module categories of type $B_{n}/C_{n}$, we obtain a…

We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters.…

We investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…

We examine the supervised learning problem in its continuous setting and give a general optimality condition through techniques of functional analysis and the calculus of variations. This enables us to solve the optimality condition for the…

We prove that, the diffusivity and conductivity on $\mathbb{Z}^d$-Bernoulli percolation ($d \geq 2$) are infinitely differentiable in supercritical regime. This extends a result by Kozlov [Uspekhi Mat. Nauk 44 (1989), no. 2(266), pp 79 -…

We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney's classical extension theorem, with special emphasis on the existence of continuous linear extension operators. The focus is on Denjoy-Carleman classes…

A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…

Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of…

We show that, consistently, there is a Borel set which has uncountably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.

We demonstrate that the set $L^\infty(X, [-1,1])$ of all measurable functions over a Borel measure space $(X, \mathcal B, \mu )$ with values in the unit interval is typically non-polyhedric when interpreted as a subset of a dual space. Our…

We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…

Let $\mathcal R$ be a $\Sigma^1_1$ binary relation, and recall that a set $A$ is $\mathcal R$-discrete if no two elements of $A$ are related by $\mathcal R$. We show that in the Sacks and Miller forcing extensions of $L$ there is a…

We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum…

In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…

We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver of the endomorphism algebra of a basic cluster-tilting object in the cluster…

We study substitutions on countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik models for a class of such substitutions, known as left…

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…

We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…

Given a sequence $(M^n)^{\infty}_{n=1}$ of nonnegative martingales starting at $M^n_0=1$, we find a sequence of convex combinations $(\widetilde{M}^n)^{\infty}_{n=1}$ and a limiting process $X$ such that…