Conserved Quantities of harmonic asymptotic initial data sets

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is rather difficult in general. We found a large family of initial data sets on which such a calculation can be carried out effectively. These are initial data sets of harmonic asymptotics, first proposed by Corvino and Schoen to solve the full vacuum constraint equation. In the second half of this article, the new total angular momentum and center of mass for these initial data sets are computed explicitly.Comment: 20 pages. Invited article for the volume "Surveys in Differential Geometry", a Jubilee Volume on General Relativity and Mathematics celebrating 100 Years of General Relativity, edited by L. Bieri and S.T. Ya

Floating-disk parylene micro check valve

A novel micro check valve which has nearly ideal fluidic shunting behaviors is presented. Featuring a parylene-based floating disk, this surface-micromachined check valve ultimately realizes both zero forward cracking pressure and zero reverse leakage in fluidic operations. Two different floating disk designs have been implemented to demonstrate functionality of the microvalve. Experimental data of underwater testing successfully show that in-channel floating-disk valves in both designs have great fluidic performance close to an ideal check valve, except the additional fluidic resistance in the order of 10^(13) N-s/m^5 based on dimensions of the fabricated devices. Their pressure loading limit have been confirmed to be higher than 300 kPa without water leakage. This type of micro check valve is believed to have great use of flow control in integrated microfluidics and lab-on-a-chip applications

A Micromechanical Parylene Spiral-Tube Sensor and Its Applications of Unpowered Environmental Pressure/Temperature Sensing

A multi-function micromechanical pressure/temperature sensor incorporating a microfabricated parylene spiral tube is presented. Its visible responses in expression of in situ rotational tube deformation enable unpowered sensing directly from optical device observation without electrical or any powered signal transduction. Sensor characterizations show promising pressure (14.46°/kPa sensitivity, 0.11 kPa resolution) and temperature (6.28°/°C sensitivity, 0.24 °C resolution) responses. Depending on different application requests, this sensor can be individually utilized to measure pressure/temperature of systems having one property varying while the other stabilized, such as intraocular or other in vivo pressure sensing of certain apparatus inside human bodies or other biological targets. A straightforward sensor-pair configuration has also been implemented to retrieve the decoupled pressure and temperature readouts, hence ultimately realizes a convenient environmental pressure and temperature sensing in various systems

Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies

From a perspective of designing or engineering for opinion formation games in social networks, the "opinion maximization (or minimization)" problem has been studied mainly for designing subset selecting algorithms. We furthermore define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the first-mover minimize the sum of expressed opinions by doing so-called "internal opinion design", knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We propose for the min player to play the "follow-the-perturbed-leader" algorithm in such Stackelberg game, obtaining losses depending on the other adversarial player's play. Since our strategy of subset selection is combinatorial in nature, the probabilities in a distribution over all the strategies would be too many to be enumerated one by one. Thus, we design a randomized algorithm to produce a (randomized) pure strategy. We show that the strategy output by the randomized algorithm for the min player is essentially an approximate equilibrium strategy against the other adversarial player

Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed 'overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.Comment: 14 pages, 11 figure