Given a domain G, a reflection vector field d(·) on ∂G, the boundary of G, and drift and dispersion coefficients b(·) and σ(·), let L be the usual second-order elliptic operator associated with b(·) and σ(·). Under mild assumptions on the coefficients and reflection vector field, it is shown that when the associated submartingale problem is well posed, a probability measure π on Ḡ with π(∂G) = ...

This research is being conducted under the Ocean Acoustics Graduate Traineeship / Special Research Award program. The first year of this award was FY10. The goal of this research is the study of new geoacoustic inverse methods using the information in the acoustic vector field. The fundamental question addressed by this effort is whether knowledge of the vector field can improve estimates for s...

A direct method based on oblique projections is adapted to compute the stationary distribution vector of a finite Markov chain. The algorithm can also be used to compute the group inverse of the corresponding generator matrix. It is shown how to update the stationary vector and other quantities of interest when one row of the transition probability matrix is modified. A GTH-like variant that ap...

In this paper a new electromagnetic nondestructive system for inspection of train hollow axle is presented. The system allows to observe changes of vector AC fields in order to enhance the probability of proper classification. The performance of the system is verified using hollow axle sample with artificial notches of different depths. The experimental results are presented and discussed. Keyw...

In this note we show that the message authentication code 128-EIA3 considered for adoption as a third integrity algorithm in the emerging mobile standard LTE is vulnerable to a simple existential forgery attack. This attack allows, given any message and the associated MAC value under an unknown integrity key and an initial vector, to predict the MAC value of a related message under the same key...

We consider random multivariate quadtries obtained from n points independently and uniformly distributed on the unit cube of Rd. Let Nn(y) be the complexity of the standard partial match algorithm for fixed vector y, where y is a vector in Rs, 0 < s < d. We study Nn = supy Nn(y), the worst-case time for partial match. Among other things, we show that partial match is very stable, in the sense t...

The Barankin bound is generalized to the vector case in the mean square error sense. Necessary and sufficient conditions are obtained to achieve the lower bound. To obtain the result, a simple finite dimensional real vector valued generalization of the Riesz representation theorem for Hilbert spaces is given. The bound has the form of a linear matrix inequality where the covariances of any unbi...

This note analyzes the distribution of fixed-weight vectors obtained by the following procedure: generate a sequence of uniform random integers with a moderate number of bits; force the bottom bits of the sequence to be a standard fixed-weight vector; sort the sequence; and extract the bottom bits. This note shows, for example, that this procedure with 32-bit integers produces any particular we...

We apply the cross-entropy (CE) method to problems in clustering and vector quantization. The CE algorithm involves the following iterative steps: (a) the generation of clusters according to a certain parametric probability distribution, (b) updating the parameters of this distribution according to the Kullback-Leibler cross-entropy. Through various numerical experiments we demonstrate the high...

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require t...