数据分析、统计与概率

We analyze the famous Wolf's sunspot numbers. We discovered that the distribution of the sunspot number fluctuations is a mixture of the BHP distribution with the Gaussian distribution.

We study the trajectories of a single colloidal particle as it hops between two energy wells A and B, which are sculpted using adjacent optical traps by controlling their respective power levels and separation. Whereas the dynamical…

We consider a simple random walk on the T-fractal and we calculate the exact mean time $\tau^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting…

Competitive exclusion, a key principle of ecology, can be generalized to understand many other complex systems. Individuals under surviving pressure tend to be different from others, and correlations among them change correspondingly to the…

We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…

We investigate the predictability of extreme events in time series. The focus of this work is to understand under which circumstances large events are better predictable than smaller events. Therefore we use a simple prediction algorithm…

In this paper we show how to go beyond the study of the topological properties of the Internet, by measuring its dynamical state using special active probing techniques and the methods of network tomography. We demonstrate this approach by…

Current community detection algorithms operate by optimizing a statistic called modularity, which analyzes the distribution of positively weighted edges in a network. Modularity does not account for negatively weighted edges. This paper…

Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional ``principal object'': a principal cubic complex. This complex is a…

Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data…

This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…

We use Lagrange multipliers to extend the traditional definition of Transverse Mass used in experimental high energy physics. We demonstrate the method by implementing it to derive a new Transverse Mass that can be used as a discriminator…

In this paper, a minimalist, completely distributed freeway traffic information system is introduced. It involves an autonomous, vehicle-based jam front detection, the information transmission via inter-vehicle communication, and the…

A system of differential equations is proposed designed as to identify communities in weighted networks. The input is a symmetric connectivity matrix $A_{ij}$. A priori information on the number of communities is not needed. To verify the…

Experimental program review in our field may benefit from a more quantitative framework within which to quantitatively discuss the scientific merit of a proposed program of research, and to assess the scientific merit of a particular…

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors…

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity.…