数据分析、统计与概率
In a number of natural and social systems, the response to an exogenous shock relaxes back to the average level according to a long-memory kernel $\sim 1/t^{1+\theta}$ with $0 \leq \theta <1$. In the presence of an epidemic-like process of…
The evolution of open source software projects in Linux distributions offers a remarkable example of a growing complex self-organizing adaptive system, exhibiting Zipf's law over four full decades. We present three tests of the usually…
For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with…
With a small number of measurements, the three most well known estimators of a single parameter give very different results when estimating a scale parameter. A transformation of this scale parameter to a location parameter by using…
In this paper two connected Szilard single molecule engines (with different temperature) model of Maxwell's demon are used to demonstrate and analysis the logical compare operation. The logical and physical complexity of compare operations…
Recently, as an aid for musical analysis, in computational musicology mathematical and informatics tools have been developed to quantitatively characterize some aspects of musical compositions. To a musical composition can be attributed by…
We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk.…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
Signals from heart transplant recipients can be considered to be a natural source of information for a better understanding of the impact of the autonomic nervous system on the complexity of heart rate variability. Beat-to-beat heart rate…
We present an original and novel method based on random matrix approach that enables to distinguish the respective role of temporal autocorrelations inside given time series and cross correlations between various time series. The proposed…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
We present a new Monte-Carlo methodology to forecast the crude oil production of Norway and the U.K. based on a two-step process, (i) the nonlinear extrapolation of the current/past performances of individual oil fields and (ii) a…
For security, environmental, and regulatory purposes it is useful to continuously monitor wide areas for unexpected changes in radioactivity. We report on a temporal anomaly detection algorithm which uses mobile detectors to build a spatial…
In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $\mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals,…
Benford's Law is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
The k-sat problem is a prototypical constraint satisfaction problem. There are many algorithms to study k-sat problem, BP algorithm is famous one of them. But BP algorithm does not converge when $\alpha$(constraint density)is bigger than…
The unknown amplitude law q(x) defining an observed effect may be found using the principle of Extreme Physical Information. EPI is derived as follows. The observations follow an information flow J --> I, with J the information intrinsic to…
Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…
A method is proposed to reconstruct a cyclic time-inhomogeneous Markov pro- cess from measured data. First, a time-inhomogeneous Markov model is fit to the data, taken here from measurements on a wind turbine. From the time-dependent…