A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications

Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how aspects of these problems, such as misalignment of DOAS references and uncertainty in hyperspectral endmembers, can be modeled by expanding the dictionary with grouped elements and imposing a structured sparsity assumption that the combinations within each group should be sparse or even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain good solutions using convex or greedy methods, such as non-negative least squares (NNLS) or orthogonal matching pursuit. We use penalties related to the Hoyer measure, which is the ratio of the $l_1$ and $l_2$ norms, as sparsity penalties to be added to the objective in NNLS-type models. For solving the resulting nonconvex models, we propose a scaled gradient projection algorithm that requires solving a sequence of strongly convex quadratic programs. We discuss its close connections to convex splitting methods and difference of convex programming. We also present promising numerical results for example DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure

On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy

Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.Comment: 8 pages, 9 figure

A Novel Framework of LBS Application Using Multimedia Broadcast and Multicast Services in 3G Mobile Networks

AbstractLocation-based services (LBS) provide content that is dynamically customized according to the user's location. These services are commonly delivered to mobile devices. In this paper, we propose a novel LBS application framework that Point of Interest (POI) messages are coded and embedded into the TPEG protocol (transport protocol experts group), and then TPEG Frame messages are economically and effectively broadcasted over 3GPP MBMS using the stream delivery method and download delivery method. The implementation details are explained and analyzed in terms of the design of POI Message with TPEG, The accessing of MBMS Services and delivery performance of TPEG using MBMS

Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density $\Sigma_0\propto r^{-\alpha}$, a coplanar azimuthal magnetic field $B_0\propto r^{-\gamma}$, a consistent self-gravity and a power-law rotation curve $v_0\propto r^{-\beta}$ where $v_0$ is the linear azimuthal gas rotation speed. The barotropic equation of state $\Pi\propto\Sigma^{n}$ is adopted for both MHD background equilibrium and coplanar MHD perturbations where $\Pi$ is the vertically integrated pressure and $n$ is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among $\alpha$, $\beta$, $\gamma$ and $n$ such that only one parameter (e.g., $\beta$) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For nonaxisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e., fast and slow MHD density waves) can be derived once $\beta$ is specified. To complement the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the analysis to a wider range of $-1/4<\beta<1/2$. As an example of illustration, we discuss specifically the $\beta=1/4$ case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.Comment: 25 page

Filament L1482 in the California molecular cloud

Aims. The process of gravitational fragmentation in the L1482 molecular filament of the California molecular cloud is studied by combining several complementary observations and physical estimates. We investigate the kinematic and dynamical states of this molecular filament and physical properties of several dozens of dense molecular clumps embedded therein. Methods. We present and compare molecular line emission observations of the J=2--1 and J=3--2 transitions of 12CO in this molecular complex, using the KOSMA 3-meter telescope. These observations are complemented with archival data observations and analyses of the 13CO J=1--0 emission obtained at the Purple Mountain Observatory 13.7-meter radio telescope at Delingha Station in QingHai Province of west China, as well as infrared emission maps from the Herschel Space Telescope online archive, obtained with the SPIRE and PACS cameras. Comparison of these complementary datasets allow for a comprehensive multi-wavelength analysis of the L1482 molecular filament. Results. We have identified 23 clumps along the molecular filament L1482 in the California molecular cloud. All these molecular clumps show supersonic non-thermal gas motions. While surprisingly similar in mass and size to the much better known Orion molecular cloud, the formation rate of high-mass stars appears to be suppressed in the California molecular cloud relative to that in the Orion molecular cloud based on the mass-radius threshold derived from the static Bonnor Ebert sphere. Our analysis suggests that these molecular filaments are thermally supercritical and molecular clumps may form by gravitational fragmentation along the filament. Instead of being static, these molecular clumps are most likely in processes of dynamic evolution.Comment: 10 pages, 9 figures, 2 tables, accepted to Astronomy and Astrophysic

Smart Substation Network Fault Classification Based on a Hybrid Optimization Algorithm

Accurate network fault diagnosis in smart substations is key to strengthening grid security. To solve fault classification problems and enhance classification accuracy, we propose a hybrid optimization algorithm consisting of three parts: anti-noise processing (ANP), an improved separation interval method (ISIM), and a genetic algorithm-particle swarm optimization (GA-PSO) method. ANP cleans out the outliers and noise in the dataset. ISIM uses a support vector machine (SVM) architecture to optimize SVM kernel parameters. Finally, we propose the GA-PSO algorithm, which combines the advantages of both genetic and particle swarm optimization algorithms to optimize the penalty parameter. The experimental results show that our proposed hybrid optimization algorithm enhances the classification accuracy of smart substation network faults and shows stronger performance compared with existing methods