相关论文: Statistical convergence of nets in Riesz spaces
Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…
We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic…
In this paper, we study the connextion between lattice and Riesz homomorphisms in Riesz spaces. We prove, under a certain condition, that any lattice homomorphism on Riesz space is a Riesz homomorphism. This fits in the type of results by…
Strong convergence and convergence in probability were generalized to the setting of a Riesz space with conditional expectation operator, $T$, in [{{\sc Y. Azouzi, W.-C. Kuo, K. Ramdane, B. A. Watson}, {Convergence in Riesz spaces with…
We construct convergent and divergent lattices in negative curvature and give a precise asymptotic description of the behavior of their counting function.
We explore some convergence notions for set-convergence coming from modern summability methods. Specifically we will see the connections between Wijsman $f$-statistical convergence and Wijsman $f$-strong Ces\`aro convergence, when $f$ is a…
The omega limit sets plays a fundamental role to construct global attractors for topological semi-dynamical systems with continuous time or discrete time. Therefore, it is important to know when omega limit sets become nonempty compact…
Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…
A mixed lattice vector space is a partially ordered vector space with two partial orderings and certain lattice-type properties. In this paper we first give some fundamental results in mixed lattice groups, and then we investigate the…
In this paper, we give an explicitdescription of a class of positive measures on symmetric conesdefined by their Laplace transforms in the framework of the Rieszintegrals. This work is motivated by the importance of thesemeasures in…
Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…
The sizes of subsets of the natural numbers are typically quantified in terms of asymptotic (linear) and logarithmic densities. These concepts have been generalized to weighted $w$-densities, where a specific weight function $w$ plays a key…
We study the statistical properties of the counting function of lattice points inside thin annuli. By a conjecture of Bleher and Lebowitz, if the width shrinks to zero, but the area converges to infinity, the distribution converges to the…
We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
The aim of this note is to prove a law of large numbers for local patterns in discrete point processes. We investigate two different situations: a class of point processes on the one dimensional lattice including certain Schur measures, and…
Properties of Riesz capacity are developed with respect to the kernel exponent $p \in (-\infty,n)$, namely that capacity is monotonic as a function of $p$, that its endpoint limits recover the diameter and volume of the set, and that…
We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…