In many practical applications, the data is organized along a manifold of lower dimension than the dimension of the embedding space. This additional information can be used when learning the model parameters of Gaussian mixtures. Based on a mismatch measure between the Euclidian and the geodesic distance, manifold constrained responsibilities are introduced. Experiments in density estimation sh...

In this paper two new fading distributions, the α−η−μ Distribution and α−κ−μ Distribution, are presented. The α − η − μ distribution includes the α − μ, Nakagami-m, Nakagami-q, Weibull, Hoyt, Rayleigh, Exponential, and the OneSided Gaussian distributions as special cases. The α − κ − μ distribution includes the α − μ, Nakagami-m, Weibull, Rice, Rayleigh, Exponential, and the One-Sided Gaussian ...

We consider the sequential Bayesian op-timization problem with bandit feedback,adopting a formulation that allows for the re-ward function to vary with time. We modelthe reward function using a Gaussian pro-cess whose evolution obeys a simple Markovmodel. We introduce two natural extensionsof the classical Gaussian process upper confi-dence bound (GP-UCB) algorit...

Derivatives are essential ingredients of a wide range of numerical algorithms. We focus on the accumulation of Jacobian matrices by Gaussian elimination on a sparse implementation of the extended Jacobian. A symbolic algorithm is proposed to determine the fill-in. The first version of the new algorithm results in a speedup of five compared to the elimination algorithm that does not exploit spar...

A generalization of Finsler structures on surfaces is proposed and the differential invariants of such structures are developed. The information obtained is then used to construct examples of Finsler structures and generalized Finsler structures which satisfy various interesting curvature conditions. In particular, examples are constructed of non-Riemannian Finsler structures on the 2-sphere wh...

in this paper, we present a numerical algorithm for solving matrix equations $(a otimes b)x = f$  by extending the well-known gaussian elimination for $ax = b$. the proposed algorithm has a high computational efficiency. two numerical examples are provided to show the effectiveness of the proposed algorithm.

In this paper we show that the knowledge of noise statistics contaminating a signal can be effectively used to choose an optimal Gaussian filter to eliminate noise. Very specifically, we show that the additive white Gaussian noise (AWGN) contaminating a signal can be filtered best by using a Gaussian filter of specific characteristics. The design of the Gaussian filter bears relationship with t...

1.1. Stirling’s formula. Laplace’s approach to Stirling’s formula is noteworthy first, because it makes a direct connection with the Gaussian (normal) distribution (whereas in other approaches the Gaussian distribution enters indirectly, or not at all), and second, because it provides a general strategy for the asymptotic approximation of a large class of integrals with a large parameter. Stirl...

Let C(n; N) = R H N tr Z 2n (dZ) denote a matrix integral by a U(N)-invariant gaussian measure on the space H N of hermitian N N matrices. The integral is known to be always a positive integer. We derive a simple combinatorial interpretation of this integral in terms of rook conngurations on Ferrers boards. The formula C(n; N) = (2n ? 1)!! n X k=0 N k + 1 n k 2 k found by J. Harer and D. Zagier...

We show that the Sudakov factor from the resummation of double logarithms ln(s/k T ) contained in the distribution functions is responsible for the kT smearing mechanism employed in the next-to-leading-order QCD (αα 2 s) calculations of direct photon production. s is the center-of-mass energy, and kT the transverse momentum carried by a parton in a colliding hadron. This factor exhibits the app...