Related papers: Noisy time series generation by feed-forward netwo…
Within the Landau-Ginzburg picture of phase transitions, scalar field theories develop phase separation because of a spontaneous symmetry-breaking mechanism. This picture works in thermodynamics but also in the dynamics of phase separation.…
The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which…
As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function…
Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an…
The widespread use of GPS devices has driven advances in spatiotemporal data mining, enabling machine learning models to simulate human decision making and generate realistic trajectories, addressing both data collection costs and privacy…
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
Attractors in asymmetric neural networks with deterministic parallel dynamics were shown to present a "chaotic" regime at symmetry eta < 0.5, where the average length of the cycles increases exponentially with system size, and an…
For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population,…
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel,…
We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a…
Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The…
We develop a method to investigate the effect of noise timescales on the first-passage time of nonlinear oscillators. Using Fredholm theory, we derive an exact integral equation for the mean event rate of a leaky-integrate-and-fire…
Diffusion posterior sampling solves inverse problems by combining a pretrained diffusion prior with measurement-consistency guidance, but it often fails to recover fine details because measurement terms are applied in a manner that is…
Alternators have recently been introduced as a framework for modeling time-dependent data. They often outperform other popular frameworks, such as state-space models and diffusion models, on challenging time-series tasks. This paper…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
In this work, the problem of communicating decisions of a classifier over a noisy channel is considered. With machine learning based models being used in variety of time-sensitive applications, transmission of these decisions in a reliable…
A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…