Machine learning has enjoyed astounding practical success in a wide range of applications in recent years—practical success that often hurries ahead of our theoretical understanding. The standard framework for machine learning theory assumes full supervision, that is, training data consists of correctly labeled i.i.d. examples from the same task that the learned classifier is supposed to be app...

Let A be a finite subset of N including 0 and let fA(n) be the number of ways to write n = ∑∞i=0 ǫi2 , where ǫi ∈ A. We consider asymptotics of the summatory function sA(r,m) of fA(n) from m2 r to m2 − 1, and show that sA(r,m) ∼ c(A,m) ∣A∣ r for some nonzero c(A,m) ∈ Q.

A recent paper demonstrated that two lenslet arrays with focal lengths f1 and f2, separated by f1 + f2, change the direction of transmitted light rays approximately like the interface between isotropic media with refractive indices n1 and n2, where n1/n2 = −f1/f2 [J. Courtial, New J. Phys. 10, 083033 (2008)]. This is true if light passes through corresponding lenslets, that is lenslets that sha...

On the basis of Braaten and Segel’s representation of the electromagnetic dispersion relations in a QED plasma we check the numerical accuracy of several published analytic approximations to the plasma neutrino emission rates. As we find none of them satisfactory we derive a new analytic approximation which is accurate to within 4% where the plasma process dominates. The correct emission rates ...

We analyze the impact of recent solar and atmospheric data in the determination of the neutrino oscillation parameters, taking into account that both the solar νe and the atmospheric νμ may convert to a mixture of active and sterile neutrinos. Furthermore, in the context of the atmospheric neutrino problem we discuss an extended mechanism of neutrino propagation which combines both oscillations...

In this study, an integrated structure of the air separation unit, natural gas liquids recovery equipped with nitrogen removal unit is developed. In this regard, advanced exergy and exergoeconomic analyses are used to examine the irreversibility, possible improvements and the cost of the inefficiencies of the process. The exergy analysis presents information on the origin of the irreversibility...