Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search methods can find the ground truth with a small error. By analyzing the landscape of the non-convex problem, we first propose a global guarantee on the maximum distance between an arbitrary local minimizer and the ground truth under the assumption that the RIP constant is smaller than $1/2$. We show that this distance shrinks to zero as the intensity of the noise reduces. Our new guarantee is sharp in terms of the RIP constant and is much stronger than the existing results. We then present a local guarantee for problems with an arbitrary RIP constant, which states that any local minimizer is either considerably close to the ground truth or far away from it. Next, we prove the strict saddle property, which guarantees the global convergence of the perturbed gradient descent method in polynomial time. The developed results demonstrate how the noise intensity and the RIP constant of the problem affect the landscape of the problem

Repression of the Glucocorticoid Receptor Aggravates Acute Ischemic Brain Injuries in Adult Mice.

Strokes are one of the leading causes of mortality and chronic morbidity in the world, yet with only limited successful interventions available at present. Our previous studies revealed the potential role of the glucocorticoid receptor (GR) in the pathogenesis of neonatal hypoxic-ischemic encephalopathy (HIE). In the present study, we investigate the effect of GR knockdown on acute ischemic brain injuries in a model of focal cerebral ischemia induced by middle cerebral artery occlusion (MCAO) in adult male CD1 mice. GR siRNAs and the negative control were administered via intracerebroventricular (i.c.v.) injection 48 h prior to MCAO. The cerebral infarction volume and neurobehavioral deficits were determined 48 h after MCAO. RT-qPCR was employed to assess the inflammation-related gene expression profiles in the brain before and after MCAO. Western Blotting was used to evaluate the expression levels of GR, the mineralocorticoid receptor (MR) and the brain-derived neurotrophic factor/tropomyosin receptor kinase B (BDNF/TrkB) signaling. The siRNAs treatment decreased GR, but not MR, protein expression, and significantly enhanced expression levels of pro-inflammatory cytokines (IL-6, IL-1β, and TNF-α) in the brain. Of interest, GR knockdown suppressed BDNF/TrkB signaling in adult mice brains. Importantly, GR siRNA pretreatment significantly increased the infarction size and exacerbated the neurobehavioral deficits induced by MCAO in comparison to the control group. Thus, the present study demonstrates the important role of GR in the regulation of the inflammatory responses and neurotrophic BDNF/TrkB signaling pathway in acute ischemic brain injuries in adult mice, revealing a new insight into the pathogenesis and therapeutic potential in acute ischemic strokes

Ordered GeSi nanorings grown on patterned Si (001) substrates

An easy approach to fabricate ordered pattern using nanosphere lithography and reactive iron etching technology was demonstrated. Long-range ordered GeSi nanorings with 430 nm period were grown on patterned Si (001) substrates by molecular beam epitaxy. The size and shape of rings were closely associated with the size of capped GeSi quantum dots and the Si capping processes. Statistical analysis on the lateral size distribution shows that the high growth temperature and the long-term annealing can improve the uniformity of nanorings

Multi-variable weakening buffer operator and its application

To weaken the disturbances of multi-variable and reveal the real situation, it is proved that the essence of the weakening buffer operator (abbreviated as WBO) can weaken the disturbance of one variable. According to this, the multi-variable weakening buffer operator is put forward. The multi-variable weakening buffer operator can satisfy the desire to use the freshest data and its buffer effect is obvious when the sample size is small. Four real cases show that the proposed multi-variable weakening buffer operator has higher forecasting performances

CO2 capture performance of calcium-based synthetic sorbent with hollow core-shell structure under calcium looping conditions

A novel calcium-based synthetic CO2 sorbent with hollow core-shell structure was prepared by a carbon microsphere template route where carbide slag, alumina cement and glucose were employed as the low-cost calcium precursor, support and carbon source, respectively. The effects of the alumina cement addition, the pre-calcination temperature during the preparation process, the carbon template addition and calcination conditions on CO2 capture performances of the calcium-based synthetic sorbents were studied during calcium looping cycles. The synthetic sorbent containing 5 wt.% alumina cement possesses the highest CO2 capture capacity during calcium looping cycles, which is mainly composed of CaO and Ca12Al14O33. The CO2 capture capacities of the synthetic sorbent under mild and severe calcination conditions can retain 0.37 and 0.29 g/g after 20 cycles, which are 57% and 99% higher than those of carbide slag under the same conditions, respectively. The synthetic sorbent possesses a hollow micro-sphere morphology with a nano-structured shell and meso-porous structure, which decreases the diffusion resistance of CO2. Periodic density functional theory (DFT) calculations are used to explain why Ca12Al14O33 can effectively retard both agglomeration and sintering of the synthetic sorbent. The hollow core-shell model is proposed to explain the CO2 capture mechanism of the synthetic sorbent. For the same CO2 capture efficiency, the energy consumption in the calciner using the synthetic sorbent is much lower than those using carbide slag and natural limestone. This work designs a good method to prepare the hollow sphere-structured synthetic sorbents with high CO2 capture capacity and provides a promising way to integrate efficient CO2 capture with the utilization of industrial waste

Conflating point of interest (POI) data: A systematic review of matching methods

Point of interest (POI) data provide digital representations of places in the real world, and have been increasingly used to understand human-place interactions, support urban management, and build smart cities. Many POI datasets have been developed, which often have different geographic coverages, attribute focuses, and data quality. From time to time, researchers may need to conflate two or more POI datasets in order to build a better representation of the places in the study areas. While various POI conflation methods have been developed, there lacks a systematic review, and consequently, it is difficult for researchers new to POI conflation to quickly grasp and use these existing methods. This paper fills such a gap. Following the protocol of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), we conduct a systematic review by searching through three bibliographic databases using reproducible syntax to identify related studies. We then focus on a main step of POI conflation, i.e., POI matching, and systematically summarize and categorize the identified methods. Current limitations and future opportunities are discussed afterwards. We hope that this review can provide some guidance for researchers interested in conflating POI datasets for their research

A No-Reference Quality Assessment Method for Digital Human Head

In recent years, digital humans have been widely applied in augmented/virtual reality (A/VR), where viewers are allowed to freely observe and interact with the volumetric content. However, the digital humans may be degraded with various distortions during the procedure of generation and transmission. Moreover, little effort has been put into the perceptual quality assessment of digital humans. Therefore, it is urgent to carry out objective quality assessment methods to tackle the challenge of digital human quality assessment (DHQA). In this paper, we develop a novel no-reference (NR) method based on Transformer to deal with DHQA in a multi-task manner. Specifically, the front 2D projections of the digital humans are rendered as inputs and the vision transformer (ViT) is employed for the feature extraction. Then we design a multi-task module to jointly classify the distortion types and predict the perceptual quality levels of digital humans. The experimental results show that the proposed method well correlates with the subjective ratings and outperforms the state-of-the-art quality assessment methods