相关论文: On the dependence structure and quality of scrambl…

In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence structure of sampling schemes. The main goal of the…

Higher order scrambled digital nets are randomized quasi-Monte Carlo rules which have recently been introduced in [J. Dick, Ann. Statist., 39 (2011), 1372--1398] and shown to achieve the optimal rate of convergence of the root mean square…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

This paper investigates the sample dependence of critical points for neural networks. We introduce a sample-independent critical lifting operator that associates a parameter of one network with a set of parameters of another, thus defining…

Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…

We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…

We study the notion of $\gamma$-negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to $1$-negative dependence), but nevertheless it still ensures…

A general relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks.…

We study the probabilistic existence of point configurations satisfying the $(0, m, d)$-net property in base $b$ within a randomly generated point set of size $N$ in the $d$-dimensional unit cube. We first derive an upper bound on the…

The rapid advancement of technology underscores the critical importance of robustness in complex network systems. This paper presents a framework for investigating the structural robustness of interconnected network models. This paper…

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…

We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the…

We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…

The observation, design and analysis of mesh-like networks in bionics, polymer physics and biological systems has brought forward an extensive catalog of fascinating structures of which a subgroup share a particular, yet critically under…

We present two algorithms for learning the structure of a Markov network from data: GSMN* and GSIMN. Both algorithms use statistical independence tests to infer the structure by successively constraining the set of structures consistent…

In the random case setting, scrambled polynomial lattice rules as discussed in \cite{BD10} enjoy more favourable strong tractablility properties than scrambled digital nets. This short note discusses the application of scrambled polynomial…

We systematically study and compare damage spreading for random Boolean and threshold networks under small external perturbations (damage), a problem which is relevant to many biological networks. We identify a new characteristic…

We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…

This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…