Sparse Recovery Analysis of Preconditioned Frames via Convex Optimization

Orthogonal Matching Pursuit and Basis Pursuit are popular reconstruction algorithms for recovery of sparse signals. The exact recovery property of both the methods has a relation with the coherence of the underlying redundant dictionary, i.e. a frame. A frame with low coherence provides better guarantees for exact recovery. An equivalent formulation of the associated linear system is obtained via premultiplication by a non-singular matrix. In view of bounds that guarantee sparse recovery, it is very useful to generate the preconditioner in such way that the preconditioned frame has low coherence as compared to the original. In this paper, we discuss the impact of preconditioning on sparse recovery. Further, we formulate a convex optimization problem for designing the preconditioner that yields a frame with improved coherence. In addition to reducing coherence, we focus on designing well conditioned frames and numerically study the relationship between the condition number of the preconditioner and the coherence of the new frame. Alongside theoretical justifications, we demonstrate through simulations the efficacy of the preconditioner in reducing coherence as well as recovering sparse signals.Comment: 9 pages, 5 Figure

Quantum Error Correction via Convex Optimization

We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.Comment: 16 page

Carbon Monoxide Oxidation Promoted by Surface Polarization Charges in a CuO/Ag Hybrid Catalyst.

Composite structures have been widely utilized to improve material performance. Here we report a semiconductor-metal hybrid structure (CuO/Ag) for CO oxidation that possesses very promising activity. Our first-principles calculations demonstrate that the significant improvement in this system's catalytic performance mainly comes from the polarized charge injection that results from the Schottky barrier formed at the CuO/Ag interface due to the work function differential there. Moreover, we propose a synergistic mechanism underlying the recovery process of this catalyst, which could significantly promote the recovery of oxygen vacancy created via the M-vK mechanism. These findings provide a new strategy for designing high performance heterogeneous catalysts

Inlet technology for powered-lift aircraft

The concepts, analytical tools, and experimental data available for designing inlets for powered lift aircraft are discussed. It is shown that inlets can be designed to meet noise, distortion, and cruise drag requirements at the flight and engine operating conditions of a powered lift aircraft. The penalty in pressure recovery for achieving the required noise suppression was 0.3 percent

New understanding of the shape-memory response in thiol-epoxy click systems: towards controlling the recovery process

Our research group has recently found excellent shape-memory response in “thiol-epoxy” thermosets obtained with click-chemistry. In this study, we use their well-designed, homogeneous and tailorable network structures to investigate parameters for better control of the shape-recovery process. We present a new methodology to analyse the shape-recovery process, enabling easy and efficient comparison of shape-memory experiments on the programming conditions. Shape-memory experiments at different programming conditions have been carried out to that end. Additionally, the programming process has been extensively analysed in uniaxial tensile experiments at different shape-memory testing temperatures. The results showed that the shape-memory response for a specific operational design can be optimized by choosing the correct programming conditions and accurately designing the network structure. When programming at a high temperature (T » Tg), under high network mobility conditions, high shape-recovery ratios and homogeneous shape-recovery processes are obtained for the network structure and the programmed strain level (eD). However, considerably lower stress and strain levels can be achieved. Meanwhile, when programming at temperatures lower than Tg, considerably higher stress and strain levels are attained but under low network mobility conditions. The shape-recovery process heavily depends on both the network structure and eD. Network relaxation occurs during the loading stage, resulting in a noticeable decrease in the shape-recovery rate as eD increases. Moreover, at a certain level of strain, permanent and non-recoverable deformations may occur, impeding the completion and modifying the whole path of the shape-recovery process.Postprint (author's final draft

Erasure coding for distributed matrix multiplication for matrices with bounded entries

Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has demonstrated that straggler mitigation can be viewed as a problem of designing erasure codes. For matrices $\mathbf A$ and $\mathbf B$, the technique essentially maps the computation of $\mathbf A^T \mathbf B$ into the multiplication of smaller (coded) submatrices. The stragglers are treated as erasures in this process. The computation can be completed as long as a certain number of workers (called the recovery threshold) complete their assigned tasks. We present a novel coding strategy for this problem when the absolute values of the matrix entries are sufficiently small. We demonstrate a tradeoff between the assumed absolute value bounds on the matrix entries and the recovery threshold. At one extreme, we are optimal with respect to the recovery threshold and on the other extreme, we match the threshold of prior work. Experimental results on cloud-based clusters validate the benefits of our method

The application of the ventilation equations to cleanrooms - Part 2: Decay of contamination

This article is the second of a three-part series that investigates the application of the ventilation equations to designing and testing cleanrooms. This part is concerned with the decay equation. The recovery test, described in ISO 14644-3 (2005) is discussed, and improvements recommended. The application of the decay equation to the ‘clean up’ requirement given in the EU GGMP (2008) is also discussed. Finally, a method is considered that calculates the time needed for airborne contamination in cleanroom areas to decay to acceptable concentrations

Low-Cost Compressive Sensing for Color Video and Depth

A simple and inexpensive (low-power and low-bandwidth) modification is made to a conventional off-the-shelf color video camera, from which we recover {multiple} color frames for each of the original measured frames, and each of the recovered frames can be focused at a different depth. The recovery of multiple frames for each measured frame is made possible via high-speed coding, manifested via translation of a single coded aperture; the inexpensive translation is constituted by mounting the binary code on a piezoelectric device. To simultaneously recover depth information, a {liquid} lens is modulated at high speed, via a variable voltage. Consequently, during the aforementioned coding process, the liquid lens allows the camera to sweep the focus through multiple depths. In addition to designing and implementing the camera, fast recovery is achieved by an anytime algorithm exploiting the group-sparsity of wavelet/DCT coefficients.Comment: 8 pages, CVPR 201

Area targeting and storage temperature selection for heat recovery loops

Inter-plant heat integration across a large site can be achieved using a Heat Recovery Loop (HRL). In this paper the relationship between HRL storage temperatures, heating and cooling utility savings (heat recovery) and total HRL exchanger area is investigated. A methodology for designing a HRL based on a ΔTmin approach is compared to three global optimisation approaches where heat exchangers are constrained to have either the same Number of Heat Transfer Units (NTU), Log-Mean Temperature Difference (LMTD) or no constraints (actual global optimum). Analysis is performed using time averaged flow rate and temperature data. Attention is given to understanding the actual temperature driving force of the HRL heat exchangers compared to the apparent driving force as indicated by the composite curves. The cold storage temperature is also varied to minimise the total heat exchanger area. Results for the same heat recovery level show that the ΔTmin approach is effective at minimising total area to within 5 % of the unconstrained global optimisation approach. The study also demonstrates the efficiency of the ΔT min approach to HRL design compared to the other methods which require considerable computational resources