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

Joint Beamforming Design for the STAR-RIS-Enabled ISAC Systems with Multiple Targets and Multiple Users

In this paper, the sensing beam pattern gain under simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS)-enabled integrated sensing and communications (ISAC) systems is investigated, in which multiple targets and multiple users exist. However, multiple targets detection introduces new challenges, since the STAR-RIS cannot directly send sensing beams and detect targets, the dual-functional base station (DFBS) is required to analyze the echoes of the targets. While the echoes reflected by different targets through STAR-RIS come from the same direction for the DFBS, making it impossible to distinguish them. To address the issue, we first introduce the signature sequence (SS) modulation scheme to the ISAC system, and thus, the DFBS can detect different targets by the SS-modulated sensing beams. Next, via the joint beamforming design of DFBS and STAR-RIS, we develop a maxmin sensing beam pattern gain problem, and meanwhile, considering the communication quality requirements, the interference limitations of other targets and users, the passive nature constraint of STAR-RIS, and the total transmit power limitation. Then, to tackle the complex non-convex problem, we propose an alternating optimization method to divide it into two quadratic semidefinite program subproblems and decouple the coupled variables. Drawing on mathematical transformation, semidefinite programming, as well as semidefinite relaxation techniques, these two subproblems are iteratively sloved until convergence, and the ultimate solutions are obtained. Finally, simulation results are conducted to validate the benefits and efficiency of our proposed scheme

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

Deep Generative Modeling for Financial Time Series with Application in VaR: A Comparative Review

In the financial services industry, forecasting the risk factor distribution conditional on the history and the current market environment is the key to market risk modeling in general and value at risk (VaR) model in particular. As one of the most widely adopted VaR models in commercial banks, Historical simulation (HS) uses the empirical distribution of daily returns in a historical window as the forecast distribution of risk factor returns in the next day. The objectives for financial time series generation are to generate synthetic data paths with good variety, and similar distribution and dynamics to the original historical data. In this paper, we apply multiple existing deep generative methods (e.g., CGAN, CWGAN, Diffusion, and Signature WGAN) for conditional time series generation, and propose and test two new methods for conditional multi-step time series generation, namely Encoder-Decoder CGAN and Conditional TimeVAE. Furthermore, we introduce a comprehensive framework with a set of KPIs to measure the quality of the generated time series for financial modeling. The KPIs cover distribution distance, autocorrelation and backtesting. All models (HS, parametric and neural networks) are tested on both historical USD yield curve data and additional data simulated from GARCH and CIR processes. The study shows that top performing models are HS, GARCH and CWGAN models. Future research directions in this area are also discussed

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

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

Digital technology, green innovation, and the carbon performance of manufacturing enterprises

With the continuous promotion of digitalization and the global trend toward a low-carbon economy, the issue of whether enterprises can enhance their carbon performance with the assistance of digital technology has aroused widespread attention from both academia and industry. In order to explore whether digital technology can improve the carbon performance of manufacturing enterprises, this study, based on resource orchestration theory and signaling theory, utilizes data from China’s A-share manufacturing enterprises from 2012 to 2021 to empirically investigate the relationship between digital technology and the carbon performance of manufacturing firms. It also explores the mediating conduction path and boundary influencing factors between them. Its findings demonstrate that: digital technology is capable of improving carbon performance; green innovation (including green technology and green collaboration) has partially mediating effects; there is a catalytic role for environmental information disclosure in utilizing digital technology to enhance carbon performance. Building on this, we find that the impacts of digital technology, green innovation, and environmental information disclosure on carbon performance vary due to differences in the nature of industries and the strategic aggressiveness of enterprises. Specifically, the role of digital technology on carbon performance seems somewhat more pronounced among firms in the high-tech industry and those employing defensive and analytical strategies. Additionally, the effects generated by green innovation and environmental information are more pronounced in the high-tech industry and among enterprises that adopt analytical strategies. This study reveals the inherent mechanism of digital technology in enhancing the carbon performance of manufacturing enterprises, which provides empirical evidence for the development of digital technology and the improvement of carbon performance in manufacturing enterprises, thus helping promote low-carbon economic transformation