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By extending the response function approach developed in nonlinear optics, we analytically derive an expression for the non-Markovianity [Laine, et al, Phys. Rev. A 81, 062115 (2010)] in the time evolution of a system in contact with a…
Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the…
Causality analysis is a powerful tool for determining cause-and-effect relationships between variables in a system by quantifying the influence of one variable on another. Despite significant advancements in the field, many existing studies…
The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…
This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the…
We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
The fluctuation-dissipation theory is grounded on the Langevin condition expressing the local independence between the thermal force and the particle velocity history. Upon hydrodynamic grounds, it is reasonable to relax this condition in…
In this paper we prove new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of…
Padmanabhan (1996) has suggested a model to relate the nonlinear two - point correlation function to the linear two - point correlation function. In this paper, we extend this model in two directions: (1) By averaging over the initial…
One of the basic aims in science is to unravel the chain of cause and effect of particular systems. Especially for large systems this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to…
The exponential correlation function is theoretically incorrect in the entire frequency range of interest for processes described in terms of linear response theory. The Lorentzian lineshape results from an inconsistent assumption of…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex…
In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. Theory and experiment have shown that in small electrical conductors the non-linear I-V-characteristic…
Causal inference and model interpretability research are gaining increasing attention, especially in the domains of healthcare and bioinformatics. Despite recent successes in this field, decorrelating features under nonlinear environments…