Studies have shown the presence of considerable amounts of redundancy in Internet traffic content. Recent works are exploring possibilities for exploiting network traffic redundancy, but these works invariably focus on fixed wireline networks. Unlike wireline networks, wireless and mobile environments exhibit unique challenges and opportunities in the context of redundancy elimination. In this ...

Background Routine screening for distress is internationally recommended as a necessary standard for good cancer care given its high prevalence and negative consequences on quality of life. This study attempts to support validation of Distress Thermometer (DT) in Shiraz, Iran and in the second step to investigate privilege/priority of DT over other referent criterion measures. Material and m...

The Large Deviation Principle is derived for several unbounded additive functionals of centered stationary Gaussian processes. For example, the rate function corresponding to 1 T ∫ T 0 X t dt is the Fenchel-Legendre transform of L(y) = − 1 4π ∫∞ −∞ log(1−4πyf(s))ds, where Xt is a continuous time process with the bounded spectral density f(s). Similar results in the discrete-time version are obt...

It is proved that, for T ε 6 G = G(T ) 6 2 √ T , ∫︁ 2T T (︁ I1(t+G,G)− I1(t, G) )︁2 dt = TG 3 ∑︁ j=0 aj log (︁√ T G )︁ +Oε(T 1+εG1/2 + T 1/2+εG2) with some explicitly computable constants aj (a3 > 0) where, for fixed k ∈ N, Ik(t, G) = 1 √ π ∫︁ ∞ −∞ |ζ( 1 2 + it+ iu)| 2ke−(u/G) 2 du. The generalizations to the mean square of I1(t+U,G)−I1(t, G) over [T, T+H] and the estimation of the mean square ...

Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain the asymptotic formula ∫ T 0 (E(t)) dt = T P3(logT ) +Oε(T ), where P3 is a polynomial of degree three in log T with positive leading coefficient. The expone...

0 |ζ( 1 2 + it)| 4 dt ∼ T 2π2 log T (T → ∞), this means that |ζ( 1 2 + it)| is small “most of the time”. The problem, then, is to evaluate asymptotically the measure of the subset of [0, T ] where |ζ( 1 2 + it)| is “small”. There are several ways in which one can proceed, and a natural way is the following one. Let c > 0 be a given constant, let μ(·) denote measure, and let Ac(T ) := {0 < t ≤ T...

Liouville proved that certain integrals, most famously ∫ e−x 2 dx, cannot be expressed in elementary terms. We explain how to give precise meaning to the notion of integration “in elementary terms”, and we formulate Liouville’s theorem that characterizes the possible form of elementary antiderivatives. Using this theorem, we deduce a practical criterion for proving such impossibility results in...

We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube {0, 1}. Our main result is the following structural theorem: any submodular function is -close in `2 to a real-valued decision tree (DT) of depth O(1/ ). This immediately implies that any submodular function is -close to a function of at most 2 ) vari...