Related papers: Metastable states for an aggregation model with no…
Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
We study the performance of discrete-time consensus protocols in the presence of additive noise. When the consensus dynamic corresponds to a reversible Markov chain, we give an exact expression for a weighted version of steady-state…
Spectrum analysis systems in online water quality testing are designed to detect types and concentrations of pollutants and enable regulatory agencies to respond promptly to pollution incidents. However, spectral data-based testing devices…
Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
As machine-learning models grow in size, their implementation requirements cannot be met by a single computer system. This observation motivates distributed settings, in which intermediate computations are performed across a network of…
Persistent current is a hallmark of quantum phase coherence. We study the fate of the persistent current in a non-equilibrium setting, where a tight-binding ring is subjected to stochastic disorder as well as a fermionic reservoir attached…
This paper presents an adaptive ensemble control for stochastic systems subject to asymmetric noises and outliers. Asymmetric noises skew system observations, and outliers with large amplitude deteriorate the observations even further. Such…
We present a study of disorder origination and growth inside an ordered phase processes induced by the presence of multiplicative noise within mean-field approximation. Our research is based on the study of solutions of the nonlinear…
Diffusion models generate samples by iteratively denoising a Gaussian prior, traversing a sequence of noise levels that, in every published sampler, decreases monotonically. Six years of intensive work has refined nearly every aspect of…
Consistency training regularizes a model by enforcing predictions of original and perturbed inputs to be similar. Previous studies have proposed various augmentation methods for the perturbation but are limited in that they are agnostic to…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation…
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work…
General nonlinear continuous-time systems are considered for which its state is estimated via a packet-based communication network. We assume that the system has multiple sensor nodes, affected by measurement noise, which can transmit at…
The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be $\delta$-correlated in time, so that the evolution in question is…
From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world…
We introduce a class of exactly solvable models which exhibit an ordering noise-induced phase transition driven by an entropic mechanism. In contrast with previous studies, order does not appear in this case as a result of an instability of…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
Noise can induce time order in the dynamics of nonlinear dynamical systems. For example, coherence resonance occurs in various neuron models driven by a noise. In studies of coherence resonance, ensemble-averaged measures of the coherence…