Related papers: Size of exceptional sets in weakly mixing systems
Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…
A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
Document sketching using Jaccard similarity has been a workable effective technique in reducing near-duplicates in Web page and image search results, and has also proven useful in file system synchronization, compression and learning…
We establish a dichotomy for the rate of the decay of the Ces\`aro averages of correlations of sufficiently regular functions for typical interval exchange transformations (IET) which are not rigid rotations (for which weak mixing had been…
We prove that a finite set of natural numbers $J$ satisfies that $J\cup\{0\}$ is not Sidon if and only if for any operator $T$, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that $T$ is weakly mixing. As an application we show the…
Let $A$ and $B$ be sets in a finite vector space. In this paper, we study the magnitude of the set $A\cap f(B)$, where $f$ runs through a set of transformations. More precisely, we will focus on the cases that the set of transformations is…
This study delves into equilibrium problems, focusing on the identification of finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium…
In this article, for generalized projective spaces with any weights, we prove four main theorems in three different contexts where the Unital Set Condition USC (Definition $2.8$) on ideals is further examined. In the first context we prove,…
We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event $\mathcal A$ such that if…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding…
We investigate mixing properties of piecewise affine non-Markovian maps acting on $[0,1]^2$ or $[0,1]^3$ and preserving the Lebesgue measure, which are natural generalizations of the {\it heterochaos baker maps} introduced in [Y. Saiki, H.…
Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing…
This work is concerned with the fundamental scaling laws of quasi-complementary sequence sets (QCSSs) by understanding how large the set size (denoted by $M$) can grow with the flock size ($K$) and the sequence length ($N$). We first…
Effective versions of strong measure zero sets are developed for various levels of complexity and computability. It is shown that the sets can be equivalently defined using a generalization of supermartingales called odds supermartingales,…
Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no…
We investigate the connection between measure and capacity for the space of nonempty closed subsets of {0,1}*. For any computable measure, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed sets…