We study the problem of classification of d-dimensional vectors into two classes (one of which is 'pure noise') based on a training sample of size m. The main specific feature is that the dimension d can be very large. We suppose that the difference between the distribution of the population and that of the noise is only in a shift, which is a sparse vector. For Gaussian noise, fixed sample siz...

We apply a spin-coherent states formalism to study the simplest version of a central-spin model, the so-called Mermin model, in which a given (central) spin 1/2 interacts symmetrically with a "bath" composed of N spins 1/2, characterized by a common frequency. The symmetric interaction allows one to restrict the problem to the fully symmetric sector of the Hilbert space associated with these N ...

In this paper, we study the limiting behavior of the BrownYork mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat 3-manifold can be approximated by some geometric invariants of a family of nearly round surfaces which approach to in...

The effect of an active reference in EEG recording is one of the oldest technical problems in EEG practice. In this paper, a method is proposed to approximately standardize the reference of scalp EEG recordings to a point at infinity. This method is based on the fact that the use of scalp potentials to determine the neural electrical activities or their equivalent sources does not depend on the...

If u(x, y) is an infinity harmonic function, i.e., a viscosity solution to the equation −∆∞u = 0 in Ω ⊂ Rm+1 then the function v(x, z) = u(x, ‖z‖) is infinity harmonic in the set {(x, z) : (x, ‖z‖) ∈ Ω} (provided u(x,−y) = u(x, y)).

We analyze the conditions under which the Synthetic Control (SC) estimator is unbiased. We show that the SC estimator is generally biased if treatment assignment is correlated with time-varying unobserved confounders, even when the number of pre-treatment periods goes to infinity and in settings where one should expect to have an almost perfect pre-treatment fit. While we also show that a modif...

A well-established model for the genealogy of a large population in equilibrium is Kingman’s coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the pop...

Received 19 May 2010; received in revised 30 October 2011; accepted 18 January 2012 ABSTRACT This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modificat...

Complete structural theorems for quasiasymptotics of distributions are presented in this article. For this, asymptotically homogeneous functions and associate asymptotically homogeneous functions at infinity with respect to a slowly varying function are employed. The proposed analysis, based on the concept of asymptotically and associate asymptotically homogeneous functions, allows to obtain ea...

We first describe the simulation procedure. Then we give theorems that are used in the main text. We also include many of the practical details that are used to implement the estimation procedure. WE SIMULATE the functions H 1 (X θ) and H 2 (X θ) for a given X and θ as follows. Set H 1 (X θ) = H 2 (X θ) = 0. Moreover, for every market, generate and store R draws from the distribution F with ide...