Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Microalgae biomass from swine wastewater and its conversion to bioenergy

© 2018 Elsevier Ltd Ever-increasing swine wastewater (SW) has become a serious environmental concern. High levels of nutrients and toxic contaminants in SW significantly impact on the ecosystem and public health. On the other hand, swine wastewater is considered as valuable water and nutrient source for microalgae cultivation. The potential for converting the nutrients from SW into valuable biomass and then generating bioenergy from it has drawn increasing attention. For this reason, this review comprehensively discussed the biomass production, SW treatment efficiencies, and bioenergy generation potentials through cultivating microalgae in SW. Microalgae species grow well in SW with large amounts of biomass being produced, despite the impact of various parameters (e.g., nutrients and toxicants levels, cultivation conditions, and bacteria in SW). Pollutants in SW can effectively be removed by harvesting microalgae from SW, and the harvested microalgae biomass elicits high potential for conversion to valuable bioenergy

Contextual cropping and scaling of TV productions

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11042-011-0804-3. Copyright @ Springer Science+Business Media, LLC 2011.In this paper, an application is presented which automatically adapts SDTV (Standard Definition Television) sports productions to smaller displays through intelligent cropping and scaling. It crops regions of interest of sports productions based on a smart combination of production metadata and systematic video analysis methods. This approach allows a context-based composition of cropped images. It provides a differentiation between the original SD version of the production and the processed one adapted to the requirements for mobile TV. The system has been comprehensively evaluated by comparing the outcome of the proposed method with manually and statically cropped versions, as well as with non-cropped versions. Envisaged is the integration of the tool in post-production and live workflows

ALMA Observations of Massive Clouds in the Central Molecular Zone: Jeans Fragmentation and Cluster Formation

We report ALMA Band 6 continuum observations of 2000 AU resolution toward four massive molecular clouds in the Central Molecular Zone of the Galaxy. To study gas fragmentation, we use the dendrogram method to identify cores as traced by the dust continuum emission. The four clouds exhibit different fragmentation states at the observed resolution despite having similar masses at the cloud scale ($\sim$1--5 pc). Assuming a constant dust temperature of 20 K, we construct core mass functions of the clouds and find a slightly top-heavy shape as compared to the canonical initial mass function, but we note several significant uncertainties that may affect this result. The characteristic spatial separation between the cores as identified by the minimum spanning tree method, $\sim$$10^4$ AU, and the characteristic core mass, 1--7 $M_\odot$, are consistent with predictions of thermal Jeans fragmentation. The three clouds showing fragmentation may be forming OB associations (stellar mass $\sim$$10^3$ $M_\odot$). None of the four clouds under investigation seem to be currently able to form massive star clusters like the Arches and the Quintuplet ($\sim$$10^4$ $M_\odot$), but they may form such clusters by further gas accretion onto the cores

Impacts of future climate change on water resource availability of eastern Australia: A case study of the Manning River basin

© 2019 Elsevier B.V. Hydrological responses of catchments to climate change require detailed examination to ensure sustainable management of both water resources and natural ecosystems. This study evaluated the impacts of climate change on water resource availability of a catchment in eastern Australia (i.e. the Manning River catchment) and analyzed climate-hydrology relationships. For this evaluation, the Xinanjiang (XAJ) model was used and validated to simulate monthly rainfall-runoff relationships of the catchment. Statistically downscaled climate data based on 28 global climate models (GCMs) under RCP8.5 scenarios were used to assess the impacts of climate changes on the Manning River catchment. Our results showed that the XAJ model was able to reproduce observed monthly rainfall-runoff relationships with an R 2 ≥ 0.94 and a Nash-Sutcliffe Efficiency ≥0.92. The median estimates from the ensemble of downscaled GCM projections showed a slight decrease in annual rainfall and runoff for the period 2021–2060 and an increase for the period 2061–2100. Annual actual evapotranspiration was projected to increase slightly, while annual soil moisture content was predicted to decrease in the future. Our results also demonstrated that future changes in seasonal and annual runoff, actual evapotranspiration and soil moisture are largely dominated by changes in rainfall, with a smaller influence arising from changes in temperature. An increase in the values of high runoffs and a decrease in the values of low runoffs predicted from the ensemble of the 28 GCMs suggest increased variability of water resources at monthly and seasonal time-scales in the future. A trend of decreasing values in winter runoff and soil moisture content in the future is likely to aggravate possible future reductions in water availability in eastern Australia. These results contribute to the development of adaptive strategies and future policy options for the sustainable management of water resources in eastern Australia

High-energy scale revival and giant kink in the dispersion of a cuprate superconductor

In the present photoemission study of a cuprate superconductor Bi1.74Pb0.38Sr1.88CuO6+delta, we discovered a large scale dispersion of the lowest band, which unexpectedly follows the band structure calculation very well. The incoherent nature of the spectra suggests that the hopping-dominated dispersion occurs possibly with the assistance of local spin correlations. A giant kink in the dispersion is observed, and the complete self-energy containing all interaction information is extracted for a doped cuprate in the low energy region. These results recovered significant missing pieces in our current understanding of the electronic structure of cuprates.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett. on May 21, 200

Super-resolution far-field ghost imaging via compressive sampling

Much more image details can be resolved by improving the system's imaging resolution and enhancing the resolution beyond the system's Rayleigh diffraction limit is generally called super-resolution. By combining the sparse prior property of images with the ghost imaging method, we demonstrated experimentally that super-resolution imaging can be nonlocally achieved in the far field even without looking at the object. Physical explanation of super-resolution ghost imaging via compressive sampling and its potential applications are also discussed.Comment: 4pages,4figure

Bioprocessing for elimination antibiotics and hormones from swine wastewater

© 2017 Elsevier B.V. Antibiotics and hormones in swine wastewater have become a critical concern worldwide due to the severe threats to human health and the eco-environment. Removal of most detectable antibiotics and hormones, such as sulfonamides (SAs), SMs, tetracyclines (TCs), macrolides, and estrogenic hormones from swine wastewater utilizing various biological processes were summarized and compared. In biological processes, biosorption and biodegradation are the two major removal mechanisms for antibiotics and hormones. The residuals in treated effluents and sludge of conventional activated sludge and anaerobic digestion processes can still pose risks to the surrounding environment, and the anaerobic processes’ removal efficiencies were inferior to those of aerobic processes. In contrast, membrane bioreactors (MBRs), constructed wetlands (CWs) and modified processes performed better because of their higher biodegradation of toxicants. Process modification on activated sludge, anaerobic digestion and conventional MBRs could also enhance the performance (e.g. removing up to 98% SMs, 88.9% TCs, and 99.6% hormones from wastewater). The hybrid process combining MBRs with biological or physical technology also led to better removal efficiency. As such, modified conventional biological processes, advanced biological technologies and MBR hybrid systems are considered as a promising technology for removing toxicants from swine wastewater

Problematic effects of antibiotics on anaerobic treatment of swine wastewater

© 2018 Elsevier Ltd Swine wastewaters with high levels of organic pollutants and antibiotics have become serious environmental concerns. Anaerobic technology is a feasible option for swine wastewater treatment due to its advantage in low costs and bioenergy production. However, antibiotics in swine wastewater have problematic effects on micro-organisms, and the stability and performance of anaerobic processes. Thus, this paper critically reviews impacts of antibiotics on pH, COD removal efficiencies, biogas and methane productions as well as the accumulation of volatile fatty acids (VFAs) in the anaerobic processes. Meanwhile, impacts on the structure of bacteria and methanogens in anaerobic processes are also discussed comprehensively. Furthermore, to better understand the effect of antibiotics on anaerobic processes, detailed information about antimicrobial mechanisms of antibiotics and microbial functions in anaerobic processes is also summarized. Future research on deeper knowledge of the effect of antibiotics on anaerobic processes are suggested to reduce their adverse environmental impacts