Related papers: Tricky Arithmetic
We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field Fp2 of prime square order, obtained by combining estimates on gaps between prime numbers together with an optimal…
In this paper we show some multiplicity estimates theorems for a connected algebraic group (not necessarily commutative) $G$ over an algebraically closed subfield of $\mathbb{C}$. More specifically, under particular assumptions on the…
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…
We give a simple proof of a sharp bound of Ahlfors--Beurling operator on complex-valued radial functions. In the language of the Calculus of Variation we prove a certain estimates for stretch and twist functions. Our estimate go slightly…
This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.
This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of…
This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the…
These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than…
This is an expository survey on recent sum-product results in finite fields. We present a number of sum-product or "expander" results that say that if $|A| > p^{2/3}$ then some set determined by sums and product of elements of $A$ is nearly…
This paper is based on a talk given to motivated high school (and younger) students at a BAMA (Bay Area Math Adventure) event. Some of the methods used to study primes and twin primes are introduced.
Rejoinder to "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]
We show that the auxiliary variable method (M{\o}ller et al., 2006; Murray et al., 2006) for inference of Markov random fields can be viewed as an approximate Bayesian computation method for likelihood estimation.
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
In this article we will give a affirmative answer to Gilbert's conjecture on Hardy spaces of Clifford analytic functions in upper half-space of $\mathbb{R}^8$. It depends on a explicit construction of Spinor space $\mathcal{R}_8$ and…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
This is, with minor modifications, a text read at the 114th Statistical Mechanics meeting, in honor of D.Ruelle and Y.Sinai, at Rutgers, Dec.13-15, 2015. It does not attempt to analyze, or not even just quote, all works of David Ruelle; I…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
This rejoinder responds to discussions by of Caimo, Niezink, and Schweinberger and Fritz of ''A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks'' by Krivitsky, Coletti, and Hens, all…