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The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and…

Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals and potentially result in severe consequences. Although…

Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points…

The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause…

In real dialogue scenarios, as there are unknown input noises in the utterances, existing supervised slot filling models often perform poorly in practical applications. Even though there are some studies on noise-robust models, these works…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery…

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…

Noise is both ubiquitous and generally deleterious in settings where precision is required. This is especially true in the quantum technology sector where system utility typically decays rapidly under its influence. Understanding the noise…

Roboticists usually test new control software in simulation environments before evaluating its functionality on real-world robots. Simulations reduce the risk of damaging the hardware and can significantly increase the development process's…

This paper deals with developing tests for checking whether an unknown system has certain structural properties. The tests that we are aiming at are in terms of noisy input-state-output data obtained from the unknown system. Since, in…

Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…

Boson sampling is one of the main quantum computation models to demonstrate the quantum computational advantage. However, this aim may be hard to realize considering two main kinds of noises, which are photon distinguishability and photon…

For random quantum circuits on $n$ qubits of depth $\Theta(\log n)$ with depolarizing noise, the task of sampling from the output state can be efficiently performed classically using a Pauli path method [Aharonov et al. Proceedings of the…

Power spectral densities are a common, convenient, and powerful way to analyze signals. So much so that they are now broadly deployed across the sciences and engineering---from quantum physics to cosmology, and from crystallography to…

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good…

The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…