Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

语音通信降噪研究

语音通信系统中，语音通过信道传输将不可避免地引入码间串扰和信号畸变，同时受到噪声污染。本文在分析自适应盲均衡算法CMA(constant modulus algorithm）和改进盲均衡算法的基础上，考虑到自适应盲均衡技术在语音噪声控制方面能力有限，将自适应盲均衡技术与小波包掩蔽阈值降噪算法联合使用，形成一种基带语音增强新方法。仿真试验结果显示自适应盲均衡技术可以使星座图变得清晰而紧凑，有效减小误码率。研究证实该方法在语音信号ISI和畸变严重情况下，在白噪及有色噪声不同的噪声环境中都具有稳定的降噪能力，消噪同时可获得汉语普通话良好的听觉效果。     

A Biosilification Fusion Protein for a ‘Self‐immobilising’ Sarcosine Oxidase Amperometric Enzyme Biosensor

Monomeric sarcosine oxidase (mSOx) fusion with the silaffin peptide, R5, designed previously for easy protein production in low resource areas, was used in a biosilification process to form an enzyme layer electrode biosensor. mSOx is a low activity enzyme (10–20 U/mg) requiring high amounts of enzyme to obtain an amperometric biosensor signal, in the clinically useful range <1 mM sarcosine, especially since the K_m is >10 mM. An amperometric biosensor model was fitted to experimental data to investigate dynamic range. mSOx constructs were designed with 6H (6×histidine) and R5 (silaffin) peptide tags and compared with native mSOx. Glutaraldehyde (GA) cross‐linked proteins retained ～5 % activity for mSOx and mSOx‐6H and only 0.5 % for mSOx‐R5. In contrast R5 catalysed biosilification on (3‐mercaptopropyl) trimethoxysilane (MPTMS) and tetramethyl orthosilicate (TMOS) particles created a ‘self‐immobilisation’ matrix retaining 40 % and 76 % activity respectively. The TMOS matrix produced a thick layer (>500 μm) on a glassy carbon electrode with a mediated current due to sarcosine in the clinical range for sarcosinemia (0–1 mM). The mSOx‐R5 fusion protein was also used to catalyse biosilification in the presence of creatinase and creatininase, entrapping all three enzymes. A mediated GC enzyme linked current was obtained with dynamic range available for creatinine determination of 0.1–2 mM for an enzyme layer ～800 nm.     

Comparative study on transport properties of N-, P-, and As-doped SiC nanowires: Calculated based on first principles

According to the one-dimensional quantum state distribution, carrier scattering, and fixed range hopping model, the structural stability and electron transport properties of N-, P-, and As-doped SiC nanowires(N-SiCNWs, P-SiCNWs, and As-SiCNWs) are simulated by using the first principles calculations. The results show that the lattice structure of NSiCNWs is the most stable in the lattice structures of the above three kinds of doped SiCNWs. At room temperature,for unpassivated SiCNWs, the doping effect of P and As are better than that of N. After passivation, the conductivities of all doped SiCNWs increase by approximately two orders of magnitude. The N-SiCNW has the lowest conductivity. In addition, the N-, P-, As-doped SiCNWs before and after passivation have the same conductivity–temperature characteristics,that is, above room temperature, the conductivity values of the doped SiCNWs all increase with temperature increasing.These results contribute to the electronic application of nanodevices.     

Response surface methodology toward the optimization of high-energy carotenoid extraction from Aristeus antennatus shrimp

High-energy assisted extraction techniques, like ultrasound assisted extraction (UAE) and microwave assisted extraction (MAE), are widely applied over the last years for the recovery of bioactive compounds such as carotenoids, antioxidants and phenols from foods, animals and herbal natural sources. Especially for the case of xanthophylls, the main carotenoid group of crustaceans, they can be extracted in a rapid and quantitative way with the use of UAE and MAE.     

Synthesis of self‐healing polyurethane urea‐based supramolecular materials

Supramolecular polyurethane ureas are expected to have superior mechanical properties primarily due to the reversible, noncovalent interactions such as hydrogen bonding interactions. We synthesized polyurethane prepolymers from small molecular weight of poly(tetramethylene ether)glycol and isophorone diisocyanates, which were end capped with propylamine to synthesize polyurethane ureas with high contents of urea and urethane groups for hydrogen‐bonding formations to facilitate self‐healing. The effects of polyurethane urea molecular weight (3000 ≤ M_n ≤ 9000), crosslinking, and cutting direction were studied in terms of thermal, mechanical, and morphological properties with an emphasis on the self‐healing efficiency. It was found that the thermal self‐healability was more pronounced as the molecular weight of polyurethane urea decreased, showing a maximum of more than 96% with 3000 M_n when the sample was cut along the stretch direction. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 468–474