Related papers: On Nyquist-Shannon Theorem with one-sided half of …
In this paper we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov's theorem for the empirical measure associated to finite sequences of…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…
Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally,…
Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse…
We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive…
We give an analogy between non-reversible Markov chains and electric networks much in the flavour of the classical reversible results originating from Kakutani, and later Kem\'eny-Snell-Knapp and Kelly. Non-reversibility is made possible by…
This paper considers lossy source coding of $n$-dimensional memoryless sources and shows an explicit approximation to the minimum source coding rate required to sustain the probability of exceeding distortion $d$ no greater than $\epsilon$,…
We study sampling of Fourier Integral Operators $A$ at rates $sh$ with $s$ fixed and $h$ a small parameter. We show that the Nyquist sampling limit of $Af$ and $f$ are related by the canonical relation of $A$ using semiclassical analysis.…
We discuss the problems of uniqueness, sampling and reconstruction with derivatives in the space of bandlimited functions. We prove that if X is sequence of real numbers such that the maximum gap between two consecutive samples is less than…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown…
The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
Boson Sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be…
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical…
The time slice axiom states that the observables which can be measured within an arbitrarily small time interval suffice to predict all other observables. While well known for free field theories where the validity of the time slice axiom…
Both sampling a time-varying signal, and its spectral analysis are activities subjected to theoretically compelling, such as Shannon's theorem and the objectively limiting of the frequency's resolution. Usually, the signals' spectra are…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…