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Traditional statements of the celebrated Kalman filter algorithm focus on the estimation of state, but not the output. For any outputs, measured or auxiliary, it is usually assumed that the posterior state estimates and known inputs are…

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

With the increasing use of nonlinear devices in both generation and consumption of power, it is essential that we develop accurate and quick control for active filters to suppress harmonics. Time delays between input and output are…

Deep neural networks are highly susceptible to overfitting noisy labels, which leads to degraded performance. Existing methods address this issue by employing manually defined criteria, aiming to achieve optimal partitioning in each…

Typical experimental measurement is set up as a study of the system's response to a stationary external excitation. This approach considers any random fluctuation of the signal as spurious contribution which is to be eliminated via…

The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…

We proposed a real time Total-Variation denosing method with an automatic choice of hyper-parameter $\lambda$, and the good performance of this method provides a large application field. In this article, we adapt the developed method to the…

Noise correlation analysis is a detection tool for spatial structures and spatial correlations in the in-trap density distribution of ultracold atoms. In this book chapter, we discuss the implementation, properties and limitations of the…

We study the diversity of complex spatio-temporal patterns of random synchronous asymmetric neural networks (RSANNs). Specifically, we investigate the impact of noisy thresholds on network performance and find that there is a narrow and…

Estimating the proportion of signals hidden in a large amount of noise variables is of interest in many scientific inquires. In this paper, we consider realistic but theoretically challenging settings with arbitrary covariance dependence…

Verification of a quantum advantage in the presence of noise is a key open problem in the study of near-term quantum devices. In this work, we show how to assess the quality of photonic interference in a linear optical quantum device (boson…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Substantial improvement in accuracy of identified linear time-invariant single-input multi-output (SIMO) dynamical models is possible when the disturbances affecting the output measurements are spatially correlated. Using an orthogonal…

We develop a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light…

We consider the problem of estimating a signal subspace in the presence of interference that contaminates some proportion of the received observations. Our emphasis is on detecting the contaminated observations so that the signal subspace…

Randomized smoothing is a defensive technique to achieve enhanced robustness against adversarial examples which are small input perturbations that degrade the performance of neural network models. Conventional randomized smoothing adds…

The metrological ability of carefully designed probes can be spoilt by the presence of noisy processes occurring during their evolution. The noise is responsible for altering the evolution of the probes in such a way that bear little or no…

A method based on optical interferences for measuring optical nonlinearities is presented. In a proof-of-principle experiment, the technique is applied to the experimental determination of the intensity dependence of the photoionization…

The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…