Proximity for Sums of Composite Functions

We propose an algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigate its asymptotic behavior. Applications to best approximation and image recovery are described

A forward-backward view of some primal-dual optimization methods in image recovery

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide efficient solutions to large-scale optimization problems. The objective of this paper is to show that a number of existing algorithms can be derived from a general form of the forward-backward algorithm applied in a suitable product space. Our approach also allows us to develop useful extensions of existing algorithms by introducing a variable metric. An illustration to image restoration is provided

An optical heterodyne densitometer

Researchers are developing an optical heterodyne densitometer with the potential to measure optical density over an unprecedented dynamic range with high accuracy and sensitivity. This device uses a Mach-Zender interferometer configuration with heterodyne detection to make direct comparisons between optical and RF attenuators. Researchers expect to attain measurements of filter transmittance down to 10 to the minus 12th power with better than 1 percent uncertainty. In addition, they intend to extend the technique to the problem of measuring low levels of light scattering from reflective and transmissive optics

Analytical solutions to the spin-1 Bose-Einstein condensates

We analytically solve the one-dimensional coupled Gross-Pitaevskii equations which govern the motion of F=1 spinor Bose-Einstein condensates. The nonlinear density-density interactions are decoupled by making use of the unique properties of the Jacobian elliptical functions. Several types of complex stationary solutions are deduced. Furthermore, exact non-stationary solutions to the time-dependent Gross-Pitaevskii equations are constructed by making use of the spin-rotational symmetry of the Hamiltonian. The spin-polarizations exhibit kinked configurations. Our method is applicable to other coupled nonlinear systems.Comment: 12 figure

Evidence for Two Gaps and Breakdown of the Uemura Plot in Ba0.6_{0.6}K0.4_{0.4}Fe2_2As2_2 Single Crystals

We report a detailed investigation on the lower critical field $H_{c1}$ of the superconducting Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ (FeAs-122) single crystals. A pronounced kink is observed on the $H_{c1}(T)$ curve, which is attributed to the existence of two superconducting gaps. By fitting the data $H_{c1}(T)$ to the two-gap BCS model in full temperature region, a small gap of $\Delta_a(0)=2.0\pm 0.3$ meV and a large gap of $\Delta_b(0)=8.9\pm 0.4$ meV are obtained. The in-plane penetration depth $\lambda_{ab}(0)$ is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in FeAs-122 superconductors.Comment: 5 pages, 4 figure

Optimal competitiveness for the Rectilinear Steiner Arborescence problem

We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the {\em Rectilinear Steiner Arborescence} ($RSA$). We improve the lower bound and the upper bound on the competitive ratio for $RSA$ from $O(\log N)$ and $\Omega(\sqrt{\log N})$ to $\Theta(\frac{\log N}{\log \log N})$, where $N$ is the number of Steiner points. This separates the competitive ratios of $RSA$ and the Symetric-$RSA$, two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of $RSA$. For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for $RSA$)

Shennan Road and the Modernization of Shenzhen Architecture

Shenzhensetsanexampleforrapiddevelopmentofurbanplanningandconstruction.It was the starting point of the most massive city-construction movement in contemporary China. In less than 40 years, many representative urban space and buildings on the mainmast-west highway—-ShennanRoad,have witnessed the for mation of the banded multi-center structural layout and the miraculous expansion of the city. Many of those iconic buildings are designed by Hong Kong or foreign architects. With the continuous development of the length and width of Shennan road, its broad and prosperous image is not only a symbol of the fruits of reform and opening up in Shenzhen or even China, but also contains the growth history of Shenzhen’s architectural modernization. This paper reviews and summarizes the changes of the urban fabric and the design trend of representative buildings along with the Shennan Road in different periods by the historical research methods. Combined with the transfer path of the city center, this study analyzes what kind of unique role the street and buildings act as in the developmentofurbanstructureinShenzhen,and expound what other urban functions and symbolic meaning they have. In the context of globalization, this article discusses how do the buildings designed by foreign architects change our city,thedrivenfactors behind the phenomenon of the design trend change. This research can make a supplement to the history and theory of the modernization of contemporary Chinese architecture