Related papers: A concept of antifragility for dynamical systems
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
We introduce a new measure of the structure of a liquid which is the softness of the mean-field potential developed by us earlier. We find that this softness is sensitive to small changes in the structure. We then study its correlation with…
In this paper, we present a method of estimating the volatility of a signal that displays stochastic noise (such as a risky asset traded on an open market) utilizing Linear Predictive Coding. The main purpose is to associate volatility with…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
This paper discusses some links properties of operators with the well- known physical concepts of hyperstability, passivity, energy dissipativeness and conservativeness with positive realness properties of the transfer functions in linear…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
We introduce a metric for evaluating the robustness of a classifier, with particular attention to adversarial perturbations, in terms of expected functionality with respect to possible adversarial perturbations. A classifier is assumed to…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…
We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
To the reduct problems of decision system, the paper proposes the notion of dynamic core according to the dynamic reduct model. It describes various formal definitions of dynamic core, and discusses some properties about dynamic core. All…
We review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions.
Uncertainty is an important feature of dynamic systems, and entropy has been widely used to measure this attribute. In this Letter, we prove that state aggregation and decomposition can decrease and increase the entropy, respectively, of…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…