Related papers: Time series analysis with dynamic law exploration
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…
The evident contrast between the time symmetry of fundamental microscopic laws and the time asymmetry of macroscopic processes is a challenging physical problem. The observation of unitary evolution of a general physical system by an…
Considering the natural ventilation, the thermal behavior of buildings can be described by a linear time varying model. In this paper, we describe an implementation of model reduction of linear time varying systems. We show the consequences…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard quantum mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
Continuous-time series is essential for different modern application areas, e.g. healthcare, automobile, energy, finance, Internet of things (IoT) and other related areas. Different application needs to process as well as analyse a massive…
We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard Quantum Mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the…
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…
Temporal logic rules are often used in control and robotics to provide structured, human-interpretable descriptions of trajectory data. These rules have numerous applications including safety validation using formal methods, constraining…
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
An approach is suggested for analyzing time series by means of resummation techniques of theoretical physics. A particular form of such an analysis, based on the algebraic self-similar renormalization, is developed and illustrated by…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…