Related papers: The Nyquist-Shannon sampling theorem and the atomi…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…
A "meta-analysis" is a method for comparison and combination of nonperturbative parton distribution functions (PDFs) in a nucleon obtained with heterogeneous procedures and assumptions. Each input parton distribution set is converted into a…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
In the framework of the Statistical Multifragmentation Model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the…
Parton distributions functions (PDFs), which are essential to the interpretation of data from high energy colliders, are measured by representing them as functional forms containing many parameters. Those parameters are determined by…
In recent years, an increasing amount of data is collected in different and often, not cooperative, databases. The problem of privacy-preserving, distributed calculations over separated databases and, a relative to it, issue of private data…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
Let $ X_1, \ldots, X_n $ be independent random variables taking values in the alphabet $ \{0, 1, \ldots, r\} $, and $ S_n = \sum_{i = 1}^n X_i $. The Shepp--Olkin theorem states that, in the binary case ($ r = 1 $), the Shannon entropy of $…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
For the four-state protocol of quantum key distribution, optimum sets of probe parameters are calculated for the most general unitary probe in which each individual transmitted photon is made to interact with the probe so that the signal…
Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion.…
Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…
The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…
We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
This study proposes a computationally efficient semiparametric distribution estimator, which is a slight modification of the naive mixture proposed by Schuster and Yakowitz (1985) and Olkin and Spiegelman (1987). The proposed method is…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for…