A Characterization of Locally Testable Affine-Invariant Properties via Decomposition Theorems

Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$ satisfies $\mathcal{P}$ and rejects when $f$ is "far" from satisfying $\mathcal{P}$. In this paper, we give a characterization of affine-invariant properties that are (two-sided error) testable with a constant number of queries. The characterization is stated in terms of decomposition theorems, which roughly claim that any function can be decomposed into a structured part that is a function of a constant number of polynomials, and a pseudo-random part whose Gowers norm is small. We first give an algorithm that tests whether the structured part of the input function has a specific form. Then we show that an affine-invariant property is testable with a constant number of queries if and only if it can be reduced to the problem of testing whether the structured part of the input function is close to one of a constant number of candidates.Comment: 27 pages, appearing in STOC 2014. arXiv admin note: text overlap with arXiv:1306.0649, arXiv:1212.3849 by other author

Rapidity and Pseudorapidity distributions of the Various Hadron-Species Produced in High Energy Nuclear Collisions : A Systematic Approach

With the help of a phenomenological approach outlined in the text in some detail, we have dealt here with the description of the plots on rapidity and pseudorapidity spectra of some hadron-secondaries produced in various nucleus-nucleus interactions at high energies. The agreement between the measured data and the attempted fits are, on the whole, modestly satisfactory excepting a very narrow central region in the vicinity of y=$\eta$=0. At last, hints to how the steps suggested in the main body of the text to proceed with the description of the measured data given in the plots could lead finally to a somewhat systematic methodology have also been made.Comment: 21 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1011.209

Quantum Renormalization Group for 1 Dimensional Fermion Systems

Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary Conditions(BC), may be regarded as a simple way for obtaining first estimates of many properties of quantum lattice systems. By applying this method to the 1-dimensional free and interacting fermion system, we obtain the ground state energy with much higher accuracy than the standard RG. We also calculate the density-density correlation function in the free-fermion case which shows good agreement with the exact result.Comment: LaTex file, 1 PS figur

Why people choose negative expected return assets - an empirical examination of a utility theoretic explanation

Using a theoretical extension of the Friedman and Savage (1948) utility function developed in Bhattacharyya (2003), we predict that for financial assets with negative expected returns, expected return will be a declining and convex function of skewness. Using a sample of U.S. state lottery games, we find that our theoretical conclusions are supported by the data. Our results have external validity as they also hold for an alternative and more aggregated sample of lottery game data.