As state-of-the-art quantum computers are capable of running increasingly complex algorithms, the need for automated methods to design and test potential applications rises. Equivalence checking circuits is an important, yet hardly automated, task in development software stack. Recently, new have been proposed that tackle this problem from widely different perspectives. One them based on ZX-cal...

In view of this representation, Crandall asked what integers are of the form of xy + yz + xz with x, y, z ≥ 1 and he made a conjecture that every odd integer greater than one can be written as xy + yz + xz. In this manuscript, we shall show that Crandall’s conjecture is indeed true. In fact, we are able to show Theorem 1.1. There are at most 19 integers which are not in the form of xy + yz + xz...

Stochastic gradient descent efficiently estimates maximum likelihood logistic regression coefficients from sparse input data. Regularization with respect to a prior coefficient distribution destroys the sparsity of the gradient evaluated at a single example. Sparsity is restored by lazily shrinking a coefficient along the cumulative gradient of the prior just before the coefficient is needed. 1...

Kuvainformaatiolle on tyypillistä, että kuvassa toisiaan lähellä olevat pisteet ovat usein tummuusasteeltaan samankaltaisia. Tutkitaan kuinka tätä dataa voidaan mallintaa stokastisella prosessilla, 2-ulotteisella fraktionaalisella Brownin liikkeellä (FBM). Mallin tarkoitus on mahdollistaa, esim. tiedonsiirron yhteydessä, kuvadatan kohtuullisen tarkka ennustaminen aiemmin välitetyn informaation ...

Let m 0; r 0; s 0; q 0 be xed integers. Suppose that R is an associative ring with unity 1 in which for each x; y 2 R there exist polynomials f(X) 2 X 2 Z ZX]; g(X); h(X) 2 XZ ZX] such that f1?g(yx m)gx; x r y ? x s f(yx m)x q ]f1?h(yx m)g = 0. Then R is commu-tative. Further, result is extended to the case when the integral exponents in the above property depend on the choice of x and y. Final...

Objective: The objective of this ex-vivo study is to compare the mean working length (in terms accurate length) with different intra-canal irrigant solutions in extracted teeth. Materials and Method: This experimental was conducted Operative dentistry department at Rehman College Dentistry Peshawar, from January 2019 June 2019. Sample size calculated using WHO sample calculator V.2.0 (1.1) 95 %...

Index 2 Preface This report provides a comprehensive survey about the field of perceptual fingerprinting. The purpose of fingerprinting is to extract a short perceptually invariant signature from a long message. This signature can be used for automatic identification in different systems. The report is a broad study, drawing on a wide range of published research. This report is devoted to be a ...