Related papers: A covariant, discrete time-frequency representatio…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required…
We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…
In this paper, we study the discrete time filtering problems for linear systems driven by fractional noises. The main difficulty comes from the non-Markovian of the noises. We construct the difference equation of the covariance process…
In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 34,…
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and…
The detection of objects in the presence of significant background noise is a problem of fundamental interest in sensing. In this work, we theoretically analyze a prototype target detection protocol, the quantum temporal correlation (QTC)…
We present a direct measurement of the spatiotemporal coherence of parametric down-conversion in the range of negative group-velocity dispersion. In this case, the frequency-angular spectra are ring-shaped and temporal coherence is coupled…
The spatial distribution of the zeros of the spectrogram is significantly altered when a signal is added to white Gaussian noise. The zeros tend to delineate the support of the signal, and deterministic structures form in the presence of…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
In this paper we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the…
Gravitational wave detectors produce time series of the gravitational wave strain co-added with instrument noise. For evenly sampled data, such as from laser interferometers, it has been traditional to Fourier transform the data and perform…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…
We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…
In this work, we revisit the problem of estimating the mean and covariance of an unknown $d$-dimensional Gaussian distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. The pioneering work of [DKK+16] gave a…
A signal with discrete frequency components, has a zero bispectrum if no linear combination of the frequencies equals one of the frequency components. We introduce fractional bispectrum in which for such signals the fractional bispectrum is…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
Quantum key distribution (QKD) provides information-theoretic security and satellite-based quantum key distribution (SatQKD) has demonstrated the potential to extend this communication security to intercontinental scales. However,…