1 Linearity of expectation Now let us see some extensions of the basic method. Theorem 1 (Linearity of expectation). Let X1, · · · , Xn be random variables and X = c1X1+ · · ·+ cnXn, where ci’s are constants. Then EX = c1 EX1 + · · ·+ cn EXn. Proof. We prove it by induction. The base case of n = 1 is trivial. For the inductive step, it is sufficient to show that E[X + Y ] = E[X] + E[Y ] for two...

the rational expectations permanent income hypothesis implies that consumption follows a martingale. however, most empirical tests have rejected the hypothesis. those empirical tests are based on linear models. if the data generating process is non-linear, conventional tests may not assess some of the randomness properly. as a result, inference based on conventional tests of linear models can b...

Flow analysis is a ubiquitous and much-studied component of compiler technology—and its variations abound. Amongst the most well known is Shivers’ 0CFA; however, the best known algorithm for 0CFA requires time cubic in the size of the analyzed program and is unlikely to be improved. Consequently, several analyses have been designed to approximate 0CFA by trading precision for faster computation...

Let S = K[x1, . . . , xn] be a polynomial ring over a field K, and E = ∧ 〈y1, . . . , yn〉 an exterior algebra. The linearity defect ldE(N) of a finitely generated graded E-module N measures how far N departs from “componentwise linear”. It is known that ldE(N) < ∞ for all N . But the value can be arbitrary large, while the similar invariant ldS(M) for an S-module M is always at most n. We will ...

We study the notion of solvability in the resource calculus, an extension of the λ-calculus modelling resource consumption. Since this calculus is non-deterministic, two different notions of solvability arise, one optimistic (angelical, may) and one pessimistic (demoniac, must). We give a syntactical, operational and logical characterization for the may-solvability and only a partial characteri...

Let Dist(f; g) = Pru [ f(u)6=g(u) ] denote the relative distance between functions f; g mapping from a group G to a group H , and let Dist(f) denote the minimum, over all linear functions (homomorphisms) g, of Dist(f; g). Given a function f : G ! H we let Err(f) = Pru;v [ f(u)+f(v)6=f(u+v) ] denote the rejection probability of the BLR (Blum-Luby-Rubinfeld) linearity test. Linearity testing is t...

The paper presents an analysis of the statistical efficiency of the sinewave histogram test used for estimating the unknown transition levels of an analog-to-digital converter. Accordingly, at first a closed–form determination of the Cramér–Rao bound is derived under the assumption of a noiseless stimulus signal. Both unbiased and biased versions of the bound are described in order to account f...

The assumption of linearity is tested using five statistical tests for the US and the Canadian unemployment rates. An AR(p) model was used to remove any linear structure from the series. Strong evidence in favour of non−linearity was found in the case of Canada. The result for the US is not so clear cut. The author would like to thank Chung−Ming Kuan, David Chappell, Chris Martin and Costas Mil...

Background: Cone-beam computed tomography (CBCT) scanners for image-guided radiotherapy are in clinical use today, but there has been no consensus on uniform acceptance to verify the CBCT image quality yet. The present work proposed new methods to fully evaluate the performance of CBCT in its three-dimensional (3D) reconstruction space. Materials and Methods: Compared to the traditional methods...

Linearity tests are randomized algorithms which have oracle access to the truth table of some function f , which are supposed to distinguish between linear functions and functions which are far from linear. Linearity tests were first introduced by Blum, Luby and Rubenfeld in [BLR93], and were later used in the PCP theorem among other applications. The quality of a linearity test is described by...