Related papers: An Adaptive Algorithm for Synchronization in Diffu…
A new model of neural networks described by the memristive and diffusive Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown with absorbing sets in the state spaces. Through sharp and uniform grouping estimates and…
This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…
We consider synchronization of coupled chaotic systems and propose an adaptive strategy that aims at evolving the strength of the coupling to achieve stability of the synchronized evolution. We test this idea in a simple configuration in…
Synchronization phenomena are pervasive in coupled nonlinear systems across the natural world and engineering domains. Understanding how to dynamically identify the parameter space (or network structure) of coupled nonlinear systems in a…
Recent theoretical models of diffusion processes, conceptualized as coupled Ornstein-Uhlenbeck systems, predict a hierarchy of interaction timescales, and consequently, the existence of a synchronization gap between modes that commit at…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…
Top-tier parallel computing clusters continue to accumulate more and more computational power with more and better CPUs and Networks. This allows, especially for environmental simulations, computations with larger domain sizes and better…
Supercomputers have revolutionized how industries and scientific fields process large amounts of data. These machines group hundreds or thousands of computing nodes working together to execute time-consuming programs that require a large…
We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
Systems such as sensor networks and teams of autonomous robots consist of multiple autonomous entities that interact with each other in a distributed, asynchronous manner. These entities need to keep track of the state of the system as it…
We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each…
Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
This paper considers the distributed optimization of a sum of locally observable, non-convex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…