Related papers: Detecting Determinism in High Dimensional Chaotic …
Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
Identifying and suppressing unknown disturbances to dynamical systems is a problem with applications in many different fields. Here we present a model-free method to identify and suppress an unknown disturbance to an unknown system based…
Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
Determining causal relationship between high dimensional observations are among the most important tasks in scientific discoveries. In this paper, we revisited the \emph{linear trace method}, a technique proposed…
Our goal is to develop a partial ordering method for comparing stochastic choice functions on the basis of their individual rationality. To this end, we assign to any stochastic choice function a one-parameter class of deterministic choice…
Scale selection methods based on local extrema over scale of scale-normalized derivatives have been primarily developed to be applied sparsely --- at image points where the magnitude of a scale-normalized differential expression…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
Model-Based Diagnosis deals with the identification of the real cause of a system's malfunction based on a formal system model and observations of the system behavior. When a malfunction is detected, there is usually not enough information…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…