Related papers: Causal analysis, Correlation-Response and Dynamic …

Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…

We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous…

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…

The way a relativistic system approaches fluid dynamical behaviour can be understood physically through the signals that will contribute to its linear response to perturbations. What these signals are is captured in the analytic structure…

The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…

Uncovering causal relationships in data is a major objective of data analytics. Causal relationships are normally discovered with designed experiments, e.g. randomised controlled trials, which, however are expensive or infeasible to be…

Causality plays a central role in understanding interactions between variables in complex systems. These systems often exhibit state-dependent causal relationships, where both the strength and direction of causality vary with the value of…

This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…

We study the formation of coherent structures in a system with long-range interactions where particles moving on a circle interact through a repulsive cosine potential. Non equilibrium structures are shown to correspond to statistical…

Physical mechanisms of phase separation in living systems can play key physiological roles and have recently been the focus of intensive studies. The strongly heterogeneous and disordered nature of such phenomena in the biological domain…

Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…

Deep learning has revolutionized the field of artificial intelligence. Based on the statistical correlations uncovered by deep learning-based methods, computer vision has contributed to tremendous growth in areas like autonomous driving and…

Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure…

Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…

Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…

In modeling multivariate time series for either forecast or policy analysis, it would be beneficial to have figured out the cause-effect relations within the data. Regression analysis, however, is generally for correlation relation, and…

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative…

Concurrent systems identify systems, either software, hardware or even biological systems, that are characterized by sets of independent actions that can be executed in any order or simultaneously. Computer scientists resort to a causal…

Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable…