相关论文: Everything you wish to know about correlations but…

The problem of calculating real-time correlation functions is formulated in terms of an imaginary-time partial differential equation. The latter is solved analytically for the perturbed harmonic oscillator and compared with the known exact…

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…

We emphasize the importance of choosing an appropriate correlation function to reduce numerical errors in calculating the linear-response function as a Fourier transformation of a time-dependent correlation function. As an example we take…

The estimation of the correlation between time series is often hampered by the asynchronicity of the signals. Cumulating data within a time window suppresses this source of noise but weakens the statistics. We present a method to estimate…

The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…

Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in…

It is commonly assumed that a specific testing occasion (task, design, procedure, etc.) provides insights that generalise beyond that occasion. This assumption is infrequently carefully tested in data. We develop a statistically principled…

We derive a relation similar to the fluctuation theorem for work done on a system obeying Langevin dynamics with thermal and colored noises. Then, we propose a method of calculating the correlation function of the colored noise by using…

The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…

Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…

The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…

In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a…

A modelling language is described which is suitable for the correlation of information when the underlying functional model of the system is incomplete or uncertain and the temporal dependencies are imprecise. An efficient and incremental…

We consider gapless models of statistical mechanics. At zero temperatures correlation functions decay asymptotically as powers of distance in these models. Temperature correlations decay exponentially. We used an example of solvable model…

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…

In order to investigate the reliability of the classical approximation for non-perturbative real time correlation functions at finite temperature we study the two-point correlator for the anharmonic oscillator. For moderately large times…