Related papers: Transient dynamics for sequence processing neural …

A variant of the optimal control problem is considered which is nonstandard in that the performance index contains "stochastic" integrals, that is, integrals against very irregular functions. The motivation for considering such performance…

We propose sequential transport (ST), a distributional framework for mediation analysis that combines optimal transport (OT) with a mediator directed acyclic graph (DAG). Instead of relying on cross-world counterfactual assumptions, ST…

We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…

Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…

Building on the phase reduction theory formulated for reaction-diffusion systems with spatial translational symmetry, we develop a data-driven method that reconstructs the spatiotemporal phase dynamics of traveling and oscillating patterns.…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a…

Microbial motion is typically analyzed by simplified models in which trajectories exhibit straight runs (perhaps with added Gaussian noise) followed by random, discrete tumbling events. We present the results of a statistical analysis of…

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific…

Detecting dynamic patterns of task-specific responses shared across heterogeneous datasets is an essential and challenging problem in many scientific applications in medical science and neuroscience. In our motivating example of rodent…

Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…

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…

To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where time-translational invariance is broken. We introduce a model of the dynamics that is…

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show…

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open…

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…

A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…

In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle…