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The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…
Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements,…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We analyze different data of the variation of the fine structure constant obtained with different methods to check their consistency.We test consistency using the modified Student test and confidence intervals. We split the data sets in…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr,…
The Rayleigh criterion is a widely known limit in the resolution of incoherent sources with classical measurements in the spatial domain. Unsurprisingly the estimation of the time delay between two weak incoherent signals is afflicted by an…
We present a new method for complex frequency estimation in several variables, extending the classical (1d) ESPRIT-algorithm. We also consider how to work with data sampled on non-standard domains (i.e going beyond multi-rectangles).
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal…
In this paper we consider the problem of the limits concerning the physical information that can be extracted from the analysis of one or more time series (light curves) typical of astrophysical objects. On the basis of theoretical…
This paper considers the recovery of continuous time signals from the magnitude of its samples. It uses a combination of structured modulation and oversampling and provides sufficient conditions on the signal and the sampling system such…
The problem of estimating the frequencies of an exponential sum has been studied extensively over the last years. It can be understood as a sparse estimation problem, as it strives to identify the sparse representation of a signal using…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…
Broadband femtosecond-laser frequency combs are filtered to spectrographically resolvable frequency-mode spacing, and the limitations of using cavities for spectral filtering are considered. Data and theory are used to show implications to…
The paper investigates recoverability of sequences from their periodic subsequences and offers some modification of the approach suggested in papers arXiv:1605.00414 and arXiv:1803.02233. It is shown that there exists a class of sequences…