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New technologies for recording the activity of large neural populations during complex behavior provide exciting opportunities for investigating the neural computations that underlie perception, cognition, and decision-making. Nonlinear…

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…

We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…

We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…

The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…

This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power…

Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…

A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features…

Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of…

Detecting and quantifying non-equilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a non-invasive approach of measuring…

Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organising system can convert consumed energy into macroscopic order. We study an…

We show that active transport processes in biological systems can be understood through a local equilibrium description formulated at the mesoscale, the scale to describe stochastic processes. This new approach uses the method established…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…