In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network (SVN). The development of the algorithms is based on the logarithmic cost and l0-norm constraint. Simulations for Gaussian and impulsive scenarios are conducted to demonstrate the superior performance of the proposed algorithms as compared with the existing a...

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.

The problem of computing the lower tail of a Gaussian norm is considered in this paper. Based on large deviations arguments, a bound on these tails is derived which is tighter than those obtained by other methods. Conditional exponential moment bounds are also derived and as an application, L 2 type Onsager-Machlup functionals for diiusions are computed.

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

We consider the mean uniform (mixed) norms for a sequence of Gaussian random functions. For a wide class of Gaussian processes and fields the (2 log n)1/2-asymptotic for mixed norms is found whenever the volume of the index set is of order n and tends to infinity, for example, n-length time interval for random processes. Some numerical examples demonstrate the rate of convergence for the obtain...

Abstract. Let Ω ⊆ R have minimal Gaussian surface area among all sets satisfying Ω = −Ω with fixed Gaussian volume. Let A = Ax be the second fundamental form of ∂Ω at x, i.e. A is the matrix of first order partial derivatives of the unit normal vector at x ∈ ∂Ω. For any x = (x1, . . . , xn+1) ∈ R, let γn(x) = (2π)−n/2e 2 1+···+x 2 n+1. Let ‖A‖2 be the sum of the squares of the entries of A, and...

In this seminar report, we present in detail the proof of a recent result due to J. Briët and T. Vidick, improving an estimate in a 2008 paper by D. Pérez-Garćıa, M. Wolf, C. Palazuelos, I. Villanueva, and M. Junge, estimating the growth of the deviation in the tripartite Bell inequality. The proof requires a delicate estimate of the norms of certain trilinear (or d-linear) forms on Hilbert spa...

The Cauchyand periodic boundary value problem for the nonlinear Schrödinger equations in n space dimensions ut − i∆u = (∇u) β , |β| = m ≥ 2, u(0) = u0 ∈ H s+1 x is shown to be locally well posed for s > sc := n 2 − 1 m−1 , s ≥ 0. In the special case of space dimension n = 1 a global L-result is obtained for NLS with the nonlinearity N(u) = ∂x(u ). The proof uses the Fourier restriction norm met...

Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the unquenched SU(3) configurations produced by the MILC collaboration and compared with quenched gauge configurations of SU(2) first copy of the overrelaxation gauge fixing, the parallel tempering (PT) gauge fixing and quenched SU(3) 564 configurations. We measure the color symmetric and th...