Related papers: Sufficient Conditions for the Shrinking Wellness L…
Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…
Let $(X,d)$ be a compact metric space and $(X,\mathcal{A},\mu,T)$ a measure preserving dynamical system. Furthermore, given a real, positive function $\psi$, let $W(T, \psi)$ and $ R(T,\psi) $ respectively denote the shrinking target set…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
In the celebrated work of Friesecke, James and M\"uller '06 the authors derive a hierarchy of models for plates by carefully analyzing the $\Gamma$-convergence of the rescaled nonlinear elastic energy. The key ingredient of their proofs is…
Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy,…
We prove ballistic behaviour as well as an annealed functional central limit theorem for random walks in mixing random environments (RWRE). The ballistic hypothesis will be an effective polynomial condition as the one introduced by Berger,…
Meta-analysis combines results from multiple studies aiming to increase power in finding their common effect. It would typically reject the null hypothesis of no effect if any one of the studies shows strong significance. The partial…
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing…
We give a new criterion for ballistic behavior of random walks in random environments which are low disorder perturbations of the simple symmetric random walk on $\mathbb{Z}^d$, for $d\geq 2$. This extends the results established by…
Motivated by set estimation problems, we consider three closely related shape conditions for compact sets: positive reach, r-convexity and rolling condition. First, the relations between these shape conditions are analyzed. Second, we…
A sunflower with $r$ petals is a collection of $r$ sets so that the intersection of each pair is equal to the intersection of all of them. Erd\H{o}s and Rado proved the sunflower lemma: for any fixed $r$, any family of sets of size $w$,…
Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This…
For many types of graphs, criteria have been discovered that give necessary and sufficient conditions for an integer sequence to be the degree sequence of such a graph. These criteria tend to take the form of a set of inequalities, and in…
This paper defines the notion of a local equilibrium of quality $(r , s)$, $0 \leq r , s$, in a discrete exchange economy: a partial allocation and item prices that guarantee certain stability properties parametrized by the numbers $r$ and…
We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich inequalities to hold, and propose a new way to use the notion of Bessel pair to establish the optimal Hardy-Rellich type inequalities. Our results…
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…
We obtain sufficient criteria for simplicity of systems, that is, rings $R$ that are equipped with a family of additive subgroups $R_s$, for $s \in S$, where $S$ is a semigroup, satisfying $R = \sum_{s \in S} R_s$ and $R_s R_t \subseteq…
In this paper, we study the well extension of strict(irreflective) partial well orderings. We first prove that any partially well-ordered structure <A, R> can be extended to a well-ordered one. Then we prove that every linear extension of…
Much attention has been devoted recently to the development of machine learning algorithms with the goal of improving treatment policies in healthcare. Reinforcement learning (RL) is a sub-field within machine learning that is concerned…
A mathematical model of measurement of the perception of well-being for groups with increasing incomes, but proportionally unequal is proposed. Assuming that welfare grows with own income and decreases with relative inequality (income of…