Related papers: Extractors for small zero-fixing sources
Principal points were first introduced by Flury: for a positive integer $n$, $n$ principal points of a random variable are the $n$ points that minimize the mean squared distance between the random variable and the nearest of the $n$ points.…
Quantum random number generators (QRNGs) based on quadrature measurements of the vacuum have so far used balanced homodyne detection to obtain a source of high entropy. Here we propose a simple direct detection measurement scheme using only…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees…
We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…
We consider random sampling in finitely generated shift-invariant spaces $V(\Phi) \subset {\rm L}^2(\mathbb{R}^n)$ generated by a vector $\Phi = (\varphi_1,\ldots,\varphi_r) \in {\rm L}^2(\mathbb{R}^n)^r$. Following the approach introduced…
In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect…
Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result…
The recent paper [27] provides a statistical analysis for efficient detection of signal components when missing data samples are present. Here we focus our attention to some complex-valued discrete random variables $X_l(m,N)$ ($0\le l\le…
As a fundamental phenomenon in nature, randomness has a wide range of applications in the fields of science and engineering. Among different types of random number generators (RNG), quantum random number generator (QRNG) is a kind of…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
Locating the sources of forced low-frequency oscillations in power systems is an important problem. A number of proposed methods demonstrate their practical usefulness, but many of them rely on strong modeling assumptions and provide poor…
The fractal dimension is a central quantity in nonlinear dynamics and can be estimated via several different numerical techniques. In this review paper we present a self-contained and comprehensive introduction to the fractal dimension. We…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…
We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…
We study the possibility of deterministic protocols for extracting work from quantum systems. Focusing on the two-point measurement work extraction scenario, we prove that, with enough copies of the system, such zero-fluctuation protocols…
Post-processing of the raw bits produced by a true random number generator (TRNG) is always necessary when the entropy per bit is insufficient for security applications. In this paper, we derive a tight bound on the output min-entropy of…
Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two…
We present the first feasible method for sampling a dynamic data stream with deletions, where the sample consists of pairs $(k,C_k)$ of a value $k$ and its exact total count $C_k$. Our algorithms are for both Strict Turnstile data streams…