Related papers: Can averaged orbits be used to extract scaling fun…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
Human motor activities are known to exhibit scale-free long-term correlated fluctuations over a wide range of timescales, from few to thousands of seconds. The fundamental processes originating such fractal-like behavior are not yet…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
In a recent Letter, Hunt and Ott argued that SHORT-period unstable periodic orbits (UPOs) would be the invariant sets associated with a chaotic attractor that are most likely to optimize the time average of some smooth scalar performance…
We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…
Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion…
In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…
We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
The measurement of data over time and/or space is of utmost importance in a wide range of domains from engineering to physics. Devices that perform these measurements therefore need to be extremely precise to obtain correct system…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…
We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
Outlying curves often occur in functional or longitudinal datasets, and can be very influential on parameter estimators and very hard to detect visually. In this article we introduce estimators of the mean and the principal components that…