相关论文: Grid method for divergence of averages

We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…

Simulating potential cascading failures can be useful for avoiding or mitigating such events. Currently, existing steady-state analysis tools are ill-suited for simulating cascading outages as they do not model frequency dependencies, they…

In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and…

We present a general approach to the problem of determining the asymptotic order of the variance of the optimal score between two independent random sequences defined over an arbitrary finite alphabet. Our general approach is based on…

This paper considers a class of nonautonomous slow-fast stochastic partial differential equations driven by $\alpha$-stable processes for $\alpha\in (1,2)$. By introducing the evolution system of measures, we establish an averaging…

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a.\ random transpositions) on the complete graph. In the case…

In this paper we introduce a new notion of convergence of sparse graphs which we call Large Deviations or LD-convergence and which is based on the theory of large deviations. The notion is introduced by "decorating" the nodes of the graph…

In this paper we develop and use the two-timing method for a systematic study of a scalar advection caused by a general oscillating velocity field. Mathematically, we study and classify the multiplicity of distinguished limits and…

The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…

Large-scale graph machine learning is challenging as the complexity of learning models scales with the graph size. Subsampling the graph is a viable alternative, but sampling on graphs is nontrivial as graphs are non-Euclidean. Existing…

Determining the universality class of a system exhibiting critical phenomena is one of the central problems in physics. There are several methods to determine this universality class from data. As methods performing collapse plots onto…

In this paper, we propose a unified convergence analysis for a class of generic shuffling-type gradient methods for solving finite-sum optimization problems. Our analysis works with any sampling without replacement strategy and covers many…

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…

We explore oscillatory behaviour in a family of periodically driven spin chains which are subject to a weak measurement followed by post-selection. We discover a transition to an oscillatory phase as the strength of the measurement is…

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…

We prove that for every $\epsilon>0$ there exists $\delta>0$ such that the following holds. Let $\mathcal{C}$ be a collection of $n$ curves in the plane such that there are at most $(\frac{1}{4}-\epsilon)\frac{n^{2}}{2}$ pairs of curves…

We present a method for graph clustering that is analogous to gradient ascent methods previously proposed for clustering points in space. The algorithm, which can be viewed as a max-degree hill-climbing procedure on the graph, iteratively…

The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit…

In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$.…