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In wave propagation theories, many problems of multi-sensor systems utilize time delay in their solution in signal processing. This technique finds great utility in seismic exploration and static correction (low-velocity weathering), which…
In this paper a new distributed asynchronous algorithm is proposed for time synchronization in networks with random communication delays, measurement noise and communication dropouts. Three different types of the drift correction algorithm…
In the field of numerical integration, methods specially tuned on oscillating functions, are of great practical importance. Such methods are needed in various branches of natural sciences, particularly in physics, since a lot of physical…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…
We present a high-precision temporal-spatial phase-demodulation algorithm for phase-shifting interferometry (PSI) affected by random/systematic phase-stepping errors. Laser interferometers in standard optical-shops suffer from several error…
Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
This paper develops a channel estimation technique for millimeter wave (mmWave) communication systems. Our method exploits the sparse structure in mmWave channels for low training overhead and accounts for the phase errors in the channel…
The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery…
Adaptive homodyne estimation of a continuously evolving optical phase using time-symmetric quantum smoothing has been demonstrated experimentally to provide superior accuracy in the phase estimate compared to adaptive or nonadaptive…
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in…
We present new tight bounds for averaging differential inclusions, which we apply to multi-frequency inclusions consisting of a sum of time periodic set-valued mappings. For this family of inclusions we establish an a tight estimate of…
Bayesian methods are becoming more widely used in asteroseismic analysis. In particular, they are being used to determine oscillation frequencies, which are also commonly found by Fourier analysis. It is important to establish whether the…
Smoothing is essential to many oceanographic, meteorological and hydrological applications. The interval smoothing problem updates all desired states within a time interval using all available observations. The fixed-lag smoothing problem…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
We propose and analyze a heterogenous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic averaging method (SAM) suggested here may provide…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
This paper describes a new method for reducing the error in a classifier. It uses an error correction update that includes the very simple rule of either adding or subtracting the error adjustment, based on whether the variable value is…