Related papers: Short-time dynamics in active systems: the Vicsek …
Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…
We study numerically the critical behavior of a modified, active Asakura-Oosawa model for colloid-polymer mixtures. The colloids are modeled as self-propelled particles with Vicsek-like interactions. This system undergoes phase separation…
Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as…
Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and…
Short time Monte Carlo methods are used to study the nonequilibrium ferromagnetic phase transition in a majority vote model in two dimensions. The existance of an initial critical slip regime is verified. The measured values of dyamic…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
Latent variable models have been widely applied for the analysis of time series resulting from experimental neuroscience techniques. In these datasets, observations are relatively smooth and possibly nonlinear. We present Variational…
Motivated by neuroscience applications, we introduce the concept of qualitative detection, that is, the problem of determining on-line the current qualitative dynamical behavior (e.g., resting, oscillating, bursting, spiking etc.) of a…
We numerically study a discretized Vicsek model (DVM) with particles orienting in $q$ possible orientations in two dimensions. The study probes the significance of anisotropic orientation and microscopic interaction on the macroscopic…
Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day…
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…
Markov State Modeling has recently emerged as a key technique for analyzing rare events in thermal equilibrium molecular simulations and finding metastable states. Here we export this technique to the study of friction, where strongly…
We study the crossover between equilibrium and off-equilibrium dynamical universality classes in the Vicsek model near its ordering transition. Starting from the incompressible hydrodynamic theory of Chen et al \cite{chen2015critical}, we…
While equilibrium phase transitions are well described by a free-energy landscape, there are few tools to describe general features of their non-equilibrium counterparts. On the other hand, near-equilibrium free-energies are easily…
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice…