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In [1], Sinopoli et al. analyze the problem of optimal estimation for linear Gaussian systems where packets containing observations are dropped according to an i.i.d. Bernoulli process, modeling a memoryless erasure channel. In this case…

Optimization and Control · Mathematics 2010-05-17 Yilin Mo , Bruno Sinopoli

We provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected…

Data Analysis, Statistics and Probability · Physics 2017-10-18 Xiaofeng Luo

In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations.…

Numerical Analysis · Mathematics 2013-07-10 Giacomo Dimarco

The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-07-30 Andrea Borghesi , Giuseppe Tagliavini , Michele Lombardi , Luca Benini , Michela Milano

By intentionally underestimating the rate of convergence of exact-diagonalization values for the mass or energy gaps of finite systems, we form families of sequences of gap estimates. The gap estimates cross zero with generically nonzero…

Statistical Mechanics · Physics 2009-10-30 Howard L. Richards , Naomichi Hatano , M. A. Novotny

We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…

Data Analysis, Statistics and Probability · Physics 2010-11-16 O. Gunnarsson , M. W. Haverkort , G. Sangiovanni

An arbitrary $m\times n$ Boolean matrix $M$ can be decomposed {\em exactly} as $M =U\circ V$, where $U$ (resp. $V$) is an $m\times k$ (resp. $k\times n$) Boolean matrix and $\circ$ denotes the Boolean matrix multiplication operator. We…

Discrete Mathematics · Computer Science 2015-12-29 Yuan Sun , Shiwei Ye , Yi Sun , Tsunehiko Kameda

Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9…

Risk Management · Quantitative Finance 2017-10-17 Greig Smith , Goncalo dos Reis

We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing…

Statistics Theory · Mathematics 2023-06-28 Zeyu Jia , Yury Polyanskiy , Yihong Wu

A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…

Astrophysics · Physics 2007-05-23 István Szapudi , Alexander S. Szalay

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…

Number Theory · Mathematics 2017-05-25 Florian Luca , Igor E. Shparlinski

We compute the critical exponents $\nu$, $\eta$ and $\omega$ of $O(N)$ models for various values of $N$ by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually…

Statistical Mechanics · Physics 2020-04-30 Gonzalo De Polsi , Ivan Balog , Matthieu Tissier , Nicolás Wschebor

A variational formulation is introduced for the Oseen equations written in terms of vor\-ti\-city and Bernoulli pressure. The velocity is fully decoupled using the momentum balance equation, and it is later recovered by a post-process. A…

Numerical Analysis · Mathematics 2021-11-04 Veronica Anaya , David Mora , Amiya K. Pani , Ricardo Ruiz-Baier

We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…

High Energy Physics - Lattice · Physics 2009-09-29 Ulli Wolff

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…

Quantum Physics · Physics 2023-03-06 Joseph G. Smith , Crispin H. W. Barnes , David R. M. Arvidsson-Shukur

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

Numerical Analysis · Mathematics 2020-08-05 Ken'ichiro Tanaka , Alexis Akira Toda

The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…

Data Structures and Algorithms · Computer Science 2018-04-26 Allan Grønlund , Kasper Green Larsen , Alexander Mathiasen , Jesper Sindahl Nielsen , Stefan Schneider , Mingzhou Song

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

Statistics Theory · Mathematics 2023-11-22 Trung Dang , Jasper C. H. Lee , Maoyuan Song , Paul Valiant

We discuss the main stages of development of the error calculation since the beginning of XIX-th century by insisting on what prefigures the use of Dirichlet forms and emphasizing the mathematical properties that make the use of Dirichlet…

History and Overview · Mathematics 2014-01-14 Nicolas Bouleau

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and…

Optimization and Control · Mathematics 2018-01-26 Giacomo Baggio