Related papers: Noisy time series generation by feed-forward netwo…

We consider first-passage percolation on a ladder, i.e. the graph {0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an…

Diffusion models have been used for probabilistic time series forecasting and show strong potential. However, fixed noise schedules often produce intermediate states that are hard to invert and a terminal state that deviates from the near…

The generation of high-quality, long-sequenced time-series data is essential due to its wide range of applications. In the past, standalone Recurrent and Convolutional Neural Network-based Generative Adversarial Networks (GAN) were used to…

Recurrent Neural Networks (RNNs) have been widely applied to deal with temporal problems, such as flood forecasting and financial data processing. On the one hand, traditional RNNs models amplify the gradient issue due to the strict time…

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial…

It is well-known that gene activation/deactivation dynamics may be a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we investigate the effect of realistic…

This article explains phase noise, jitter, and some slower phenomena in digital integrated circuits, focusing on high-demanding, noise-critical applications. We introduce the concept of phase type and time type phase noise. The rules for…

The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a…

The scaling of transient times to zero-lag synchronization in networks composed of excitable units is shown to be governed by three features of the graph representing the network: the longest path between pairs of neurons (diameter), the…

Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…

Recently, diffusion models have gained popularity due to their impressive generative abilities. These models learn the implicit distribution given by the training dataset, and sample new data by transforming random noise through the reverse…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

The cascade model generates a food web at random. In it the species are labeled from 0 to $m$, and arcs are given at random between pairs of the species. For an arc with endpoints $i$ and $j$ ($i<j$), the species $i$ is eaten by the species…

We propose a feed-forward perturbation-based method that uses the noisy received signal to compensate for nonlinear distortion, which outperforms the conventional decision-based method and avoids decision feedback. Additionally, combining…

In this article, a general information-plus-noise transmission model is assumed, the receiver end of which is composed of a large number of sensors and is unaware of the noise pattern. For this model, and under reasonable assumptions, a set…

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…

A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e, patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z.…