We study tolerant linearity testing under general distributions. Given groups G and H, a distribution μ on G, and oracle access to a function f : G→ H, we consider the task of approximating the smallest μ-distance of f to a homomorphism h : G→ H, where the μ-distance between f and h is the probability that f(x) 6= h(x) when x is drawn according to the distribution μ. This question is intimately...

Econometric modelling using automatic algorithms such as PcGets (Hendry and Krolzig, 2001) and Autometrics (Doornik, 2007) has recently become popular. This paper considers automatic model selection when there is non-linearity inherent in the process. The strategy uses a new test for nonlinearity, specifies the general model using polynomials if linearity is rejected, and undertakes a general-t...

Phased arrays in CMOS for consumer communication bands aim to enhance receiver performance by exploiting beamforming with antenna arrays. Sensitivity increases with the number of antenna elements through array gain and interferers can be cancelled through the spatial filtering of the beam pattern [1]. For the latter, the linearity of the receiver before the beamforming summing point becomes a b...

The function f : F2 → F2 is k-linear if it returns the sum (over F2) of exactly k coordinates of its input. We introduce strong lower bounds on the query complexity for testing whether a function is k-linear. We show that for any k ≤ n 2 , at least k−o(k) queries are required to test k-linearity, and we show that when k ≈ n 2 , this lower bound is nearly tight since 4 3 k+o(k) queries are suffi...

2 The Linearity of Expectation and small tweakings 11 2.1 Revisiting the Ramsey Number R(n, n) . . . . . . . . . . . . . . . . . . . 11 2.2 List Chromatic Number and minimum degree . . . . . . . . . . . . . . . 11 2.3 The Daykin-Erdős conjecture . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 An Example from Combinatorial Geometry . . . . . . . . . . . . . . . . . 14 2.5 Graphs with High...

The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a path-based model of processes which is also a model of affine-linear logic. This connection yields an affine-linear language for processes, automatically respecting open-map bisimulation, in which a range of process operations can be expressed. An operational semantics is provi...

Scintillator is a critical component to detect high-energy particles or rays, which widely used in deep space exploration, security inspection, and nondestructive testing medical diagnosis, such as X-ray imaging computed tomography (CT). However, the wider application of traditional inorganic organic scintillators limited by complex operation process poor adaptability changeable environment, th...

 Background: The aim of this study was to investigate the ability of Iranian medical and dental students in thinking critically and to assess their ability in using definite components of critical thinking (CT). Methods: Multistage cluster sampling was utilized to recruit 125 preclinical (1st, 2nd and 3rd year of study) students in Yazd Shaheed Sadoughi University of Medical Sciences in Yazd, I...

We consider the issue of coding for non-multicast networks. For multicast networks, it is known that linear operations over a field no larger than the number of receivers are sufficient to achieve all feasible connections. In the case of nonmulticast networks, necessary and sufficient conditions are known, if we restrict ourselves to linear codes over a finite field [1]. However, no linearity s...

The tests were carried out on a carbonfibre reinforced structure with a number of wires with different kind of installation. The peak value of the current impulses ranges from 20 kA up to 200 kA and the comparison shows, that a reasonable linearity exists for carbonfibre reinforced material and that the deviations are always on the save side. The verification of the linearity has been checked t...