Universal resonant ultracold molecular scattering

The elastic scattering amplitudes of indistinguishable, bosonic, strongly-polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semi-classical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these univeral characteristics are predicted. PACS numbers: 34.50.Cx, 31.15.ap, 33.15.-e, 34.20.-bComment: 4 pages, 5 figure

Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples

B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches

Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

B-splines, Pólya curves, and duality

AbstractLocal duality between B-splines and Pólya curves is examined, mostly from the viewpoint of computer-aided geometric design. Certain known results for the two curve types are shown to be related. A few new results for Pólya curves and a curve scheme related to B-splines also follow from these investigations

Coordinate Space HFB Calculations for the Zirconium Isotope Chain up to the Two-Neutron Dripline

We solve the Hartree-Fock-Bogoliubov (HFB) equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice utilizing the Basis-Spline expansion method. Results are presented for the neutron-rich zirconium isotopes up to the two-neutron dripline. In particular, we calculate binding energies, two-neutron separation energies, normal densities and pairing densities, mean square radii, quadrupole moments, and pairing gaps. Very large prolate quadrupole deformations (beta2=0.42,0.43,0.47) are found for the (102,104,112)Zr isotopes, in agreement with recent experimental data. We compare 2-D Basis-Spline lattice results with the results from a 2-D HFB code which uses a transformed harmonic oscillator basis.Comment: 9 pages, 9 figure

Kernel Approximation on Manifolds II: The L∞L_{\infty}-norm of the L2L_2-projector

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Ana

Single Image Super-Resolution Using Multi-Scale Convolutional Neural Network

Methods based on convolutional neural network (CNN) have demonstrated tremendous improvements on single image super-resolution. However, the previous methods mainly restore images from one single area in the low resolution (LR) input, which limits the flexibility of models to infer various scales of details for high resolution (HR) output. Moreover, most of them train a specific model for each up-scale factor. In this paper, we propose a multi-scale super resolution (MSSR) network. Our network consists of multi-scale paths to make the HR inference, which can learn to synthesize features from different scales. This property helps reconstruct various kinds of regions in HR images. In addition, only one single model is needed for multiple up-scale factors, which is more efficient without loss of restoration quality. Experiments on four public datasets demonstrate that the proposed method achieved state-of-the-art performance with fast speed

Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

A PCR Assay for Specific Detection of the Pandemic \u3cem\u3eVibrio parahaemolyticus\u3c/em\u3e O3:K6 Clone from Shellfish

The current standard method for identifying Vibrio parahaemolyticus serotype O3:K6, an emerging pathogen with apparent enhanced virulence characteristics, typically takes 4 to 6 d to complete and requires serotyping. To provide a more rapid strategy, we optimized a polymerase chain reaction (PCR)-based assay for specific detection of V. parahaemolyticus O3:K6. Of 78 V. parahaemolyticus isolates and other related species; only strains classified into the V. parahaemolyticus O3:K6 clonal group (n = 39) showed positive results in the PCR assay. The assay detected 2.3 cells/PCR reaction and 310 cells/g using bacterial cultures and inoculated oyster samples, respectively. Sensitive and specific detection of V. parahaemolyticus O3:K6 was possible following a 6-h enrichment