数据分析、统计与概率

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the…

Anomalous diffusion, process in which the mean-squared displacement of system states is a non-linear function of time, is usually identified in real stochastic processes by comparing experimental and theoretical displacements at relatively…

Consider a network of M >> 1 nodes connected by N >> 1 links, in which the distribution of the number of links per node follows a power law with exponent 0<\alpha <1. The power law is naturally truncated due to the fact that N is finite. A…

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems (L-BFGS-B) is used…

The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes,…

The concept of a digital cavity is presented. The functionality of a tunable radio-frequency/microwave cavity with unrestricted Q-factor is implemented. The theoretical aspects of the cavity and its potential applications in high resolution…

We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…

Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…

We address the question of distance record-setting by a random walker in the presence of measurement error, $\delta$, and additive noise, $\gamma$ and show that the mean number of (upper) records up to $n$ steps still grows universally as…

Voting online with explicit ratings could largely reflect people's preferences and objects' qualities, but ratings are always irrational, because they may be affected by many unpredictable factors like mood, weather, as well as other…

Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…

Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…

In this paper a general second order semi-Markov reward model is presented. Equations for the higher order moments of the reward process are presented for the first time and applied to wind energy production. The application is executed by…

We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural…

A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…

We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length (MDL) principle which seeks to minimize the total amount of information required to…

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical…

A new approach, which is proposed in this paper allows one to construct the Bellman function V(t,x) and optimal control u(t) directly,i.e.,without any reference to the Bellman equation, by way of using strong large deviations principle for…