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We study the complexity of learning and approximation of self-bounding functions over the uniform distribution on the Boolean hypercube ${0,1}^n$. Informally, a function $f:{0,1}^n \rightarrow \mathbb{R}$ is self-bounding if for every $x…

Machine Learning · Computer Science 2019-06-04 Vitaly Feldman , Pravesh Kothari , Jan Vondrák

We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than…

Probability · Mathematics 2013-04-10 Andrew Mastin , Patrick Jaillet

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…

Quantum Physics · Physics 2012-07-11 Vittorio Giovannetti , Seth Lloyd , Lorenzo Maccone

In this paper we study the inefficiency ratio of stable equilibria in load balancing games introduced by Asadpour and Saberi [3]. We prove tighter lower and upper bounds of 7/6 and 4/3, respectively. This improves over the best known bounds…

Computer Science and Game Theory · Computer Science 2015-12-14 Akaki Mamageishvili , Paolo Penna

Quantum measurements have intrinsic properties which seem incompatible with our everyday-life macroscopic measurements. Macroscopic Quantum Measurement (MQM) is a concept that aims at bridging the gap between well understood microscopic…

Quantum Physics · Physics 2018-01-17 Marc-Olivier Renou , Nicolas Gisin , Florian Fröwis

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…

Numerical Analysis · Mathematics 2021-12-28 Larry Allen , Robert C. Kirby

In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or $q$-gamma…

Classical Analysis and ODEs · Mathematics 2014-11-04 Feng Qi

In this paper, we investigate the Mill's ratio estimation problem and get two new inequalities. Compared to the well known results obtained by Gordon, they becomes tighter. Furthermore, we also discuss the inverse Q-function approximation…

Information Theory · Computer Science 2021-06-22 Pingyi Fan

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

Classical Analysis and ODEs · Mathematics 2012-07-25 Imdat Iscan

In this paper, we extend the definition of qx-asymptotic function, for extended real-valued function that define on an infinite dimensional topological normed space without lower semicontinuity or quasi-convexity condition. As the main…

Functional Analysis · Mathematics 2023-02-01 Fatemeh Fakhar , Hamid Reza Hajishari , Zeinab Soltani

A fundamental question in Dynamical Systems is to identify regions of phase/parameter space satisfying a given property (stability, linearization, etc). Given a family of analytic circle diffeomorphisms depending on a parameter, we obtain…

Dynamical Systems · Mathematics 2018-06-15 Jordi-Lluís Figueras , Alex Haro , Alejandro Luque

We give a necessary condition that a separable measurement can be implemented by local quantum operations and classical communication (LOCC) in any finite number of rounds of communication, generalizing and strengthening a result obtained…

Quantum Physics · Physics 2015-07-01 Scott M. Cohen

A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…

Numerical Analysis · Mathematics 2018-04-20 V. L. Makarov , D. V. Dragunov

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

Statistics Theory · Mathematics 2019-09-11 Johannes O. Royset , Roger J-B Wets

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

Information Theory · Computer Science 2019-07-24 Lucien Bacharach , Carsten Fritsche , Umut Orguner , Eric Chaumette

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

In this paper, we investigated the boundedness of multilinear fractional strong maximal operator $\mathcal{M}_{\mathcal{R},\alpha}$ associated with rectangles or related to more general basis with multiple weights…

Classical Analysis and ODEs · Mathematics 2015-12-31 Mingming Cao , Qingying Xue , Kozo Yabuta

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…

Optimization and Control · Mathematics 2024-03-06 Erik Berglund , Jiaojiao Zhang , Mikael Johansson

We show that under a number of rather plausible assumptions QCD spectrum may contain a number of mesons which have not been predicted or observed. Such states will have the quantum numbers of two existing mesons and masses very close to the…

High Energy Physics - Phenomenology · Physics 2008-11-26 Thomas D. Cohen , Boris A. Gelman , Shmuel Nussinov

This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on bounded convex sets, a complete characterization of this…

Optimization and Control · Mathematics 2026-05-26 V. S. T. Long , N. M. Nam