The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery without Regularization

Low-rank matrix recovery is a fundamental problem in signal processing and machine learning. A recent very popular approach to recovering a low-rank matrix X is to factorize it as a product of two smaller matrices, i.e., X = UV^T, and then optimize over U, V instead of X. Despite the resulting non-convexity, recent results have shown that many factorized objective functions actually have benign global geometry---with no spurious local minima and satisfying the so-called strict saddle property---ensuring convergence to a global minimum for many local-search algorithms. Such results hold whenever the original objective function is restricted strongly convex and smooth. However, most of these results actually consider a modified cost function that includes a balancing regularizer. While useful for deriving theory, this balancing regularizer does not appear to be necessary in practice. In this work, we close this theory-practice gap by proving that the unaltered factorized non-convex problem, without the balancing regularizer, also has similar benign global geometry. Moreover, we also extend our theoretical results to the field of distributed optimization

Magnet bioreporter device for ecological toxicity assessment on heavy metal contamination of coal cinder sites

A novel magnet bioreporter device was developed in this research for soil toxicity assessment, via magnetic nanoparticles functionalized whole-cell bioreporters. The whole-cell bioreporter ADPWH-recA kept response capability to DNA damage after magnetic nanoparticles (MNPs) functionalization, and could be harvested from soil samples by permanent magnet to reduce the soil particle disturbance. Compared to conventional treatments applying bioreporter directly in soil-water mixture (SW-M treatment) or supernatant (SW-S treatment), MNPs functionalized bioreporter via the magnet device (MFB) treatment achieved high sensitivity to evaluate the toxicity and bioavailability of chromium contamination in soils from 10 mg/kg to 5000 mg/kg soil dry weight. The MNPs functionalized bioreporter also achieved high reproducibility with pH value from 5.0 to 9.0, salinity from 0% to 3% and temperature from 20 °C to 37 °C. A case study was carried out on the ecological toxicity assessment of heavy metal contamination at the coal cinder site via the magnet bioreporter device. The heavy metal toxicity declined with the increasing distance to the coal cinder point, and a significant accumulation of heavy metal toxicity was observed along the vertical distribution. No direct link was found between the pollution load index (PLI) and heavy metal toxicity, and the results suggested the bioreporter test monitored the toxicity of heavy metals in soils and was an important approach for ecological risk assessment. Magnet bioreporter device also offered the high throughput biological measurement and was feasible for in situ monitoring

1-(1,3-Benzothia­zol-2-yl)-3-phenyl-2-pyrazoline

In the title compound, C16H13N3S, the pyrazoline ring forms dihedral angles of 6.89 (14) and 4.96 (11)° with the benzene ring and the benzothia­zole group, respectively. In the crystal, weak C—H⋯N inter­actions link the mol­ecules into chains extending along the b-axis direction

Large‐area integrated triboelectric sensor array for wireless static and dynamic pressure detection and mapping

Large-area flexible pressure sensors are of paramount importance for various future applications, such as electronic skin, human-machine interfacing, and health-monitoring devices. Here, we report a self-powered and large-area integrated triboelectric sensor array (ITSA) based on coupling a triboelectric sensor array (TSA) and an array chip of CD4066 through a traditional connection way. Enabled by a simple and cost-effective fabrication process, the size of the ITSA can be scaled up to 38 × 38 cm2. In addition, unlike the proposed triboelectric sensors array before which can only react to the dynamic interaction, this ITSA is able to detect static and dynamic pressure. Moreover, through integrating the ITSA with a signal processing circuit, a complete wireless sensing system is present. Diverse applications of the system are demonstrated in details, including detecting pressure, identifying position, tracking trajectory and recognizing the profile of external contact objects. Thus, the ITSA in this work opens a new route in the direction of large-area, self-powered, and wireless triboelectric sensing system

A novel mutation outside homeodomain of HOXD13 causes synpolydactyly in a Chinese family

AbstractIntroductionHuman synpolydactyly (SPD), belonging to syndactyly (SD) II, is caused by mutations in homeobox d13 (HOXD13). Here, we describe the study of a two-generation Chinese family with a variant form of synpolydactyly.Materials and methodsThe sequence of the HOXD13 gene was analyzed. Luciferase assays were conducted to determine whether the mutation affected the function of the HOXD13 protein.ResultsWe identified a novel c.659G>C (p.Gly220Ala) mutation outside the HOXD13 homeodomain responsible for the disease in this family. This mutation was not found in any of the unaffected family members and healthy control. Luciferase assays demonstrated that this mutation affected the transcriptional activation ability of HOXD13 (only approximately 84.7% of wild type, p<0.05).ConclusionPhenotypes displayed by individuals carrying the novel mutation present additional features, such as the fifth finger clinodactyly, which is not always associated with canonical SPD. This finding enhances our understanding about the phenotypic spectrum associated with HOXD13 mutations and advances our understanding of human limb development