Adaptive Reduced Rank Regression

We study the low rank regression problem $\mathbf{y} = M\mathbf{x} + \epsilon$, where $\mathbf{x}$ and $\mathbf{y}$ are $d_1$ and $d_2$ dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations $n$ is less than $d_1 + d_2$. Existing algorithms are designed for settings where $n$ is typically as large as $\mathrm{rank}(M)(d_1+d_2)$. This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix denoising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baselines, and is always at least competitive.Comment: 40 page

Gaussian process machine learning-based surface extrapolation method for improvement of the edge effect in surface filtering

Filtering for signal and data is an important technology to reduce and/or remove noise signal for further extraction of desired information. However, it is well known that significant distortions may occur in the boundary areas of the filtered data because there is no sufficient data to be processed. This drawback largely affects the accuracy of topographic measurements and characterizations of precision freeform surfaces, such as freeform optics. To address this issue, a Gaussian process machine learning-based method is presented for extrapolation of the measured surface to an extended measurement area with high accuracy prior to filtering the surface. With the extrapolated data, the edge distortion can be effectively reduced. The effectiveness of this method was evaluated using both simulated and experimental data. Successful implementation of the proposed method not only addresses the issue in surface filtering but also provides a promising solution for numerous applications involving filtering processes

Climatic and biogeographic processes underlying the diversification of the pantropical flowering plant family Annonaceae

Tropical forests harbor the richest biodiversity among terrestrial ecosystems, but few studies have addressed the underlying processes of species diversification in these ecosystems. We use the pantropical flowering plant family Annonaceae as a study system to investigate how climate and biogeographic events contribute to diversification. A super-matrix phylogeny comprising 835 taxa (34% of Annonaceae species) based on eight chloroplast regions was used in this study. We show that global temperature may better explain the recent rapid diversification in Annonaceae than time and constant models. Accelerated accumulation of niche divergence (around 15 Ma) lags behind the increase of diversification rate (around 25 Ma), reflecting a heterogeneous transition to recent diversity increases. Biogeographic events are related to only two of the five diversification rate shifts detected. Shifts in niche evolution nevertheless appear to be associated with increasingly seasonal environments. Our results do not support the direct correlation of any particular climatic niche shifts or historical biogeographical event with shifts in diversification rate. Instead, we suggest that Annonaceae diversification can lead to later niche divergence as a result of increasing interspecific competition arising from species accumulation. Shifts in niche evolution appear to be associated with increasingly seasonal environments. Our results highlight the complexity of diversification in taxa with long evolutionary histories

Frustrated magnetic interactions in a Wigner-Mott insulator

Two-dimensional semiconductor moir\'e materials have emerged as a highly controllable platform to simulate and explore quantum condensed matter. Compared to real solids, electrons in semiconductor moir\'e materials are less strongly attracted to the moir\'e lattice sites, making the nonlocal contributions to the magnetic interactions as important as the Anderson super-exchange. It provides a unique platform to study the effects of competing magnetic interactions. Here, we report the observation of strongly frustrated magnetic interactions in a Wigner-Mott insulating state at 2/3 filling of the moir\'e lattice in angle-aligned WSe2/WS2 heterobilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at 2/3 filling. The suppression is lifted upon screening of the long-range Coulomb interactions and melting of the Wigner-Mott insulator by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model with an antiferromagnetic nearest-neighbor coupling and a ferromagnetic second-neighbor coupling. Our study establishes semiconductor moir\'e materials as a model system for the lattice-spin physics and frustrated magnetism

Surgical intervention combined with weight-bearing walking training improves neurological recoveries in 320 patients with clinically complete spinal cord injury: a prospective self-controlled study

Although a large number of trials in the SCI field have been conducted, few proven gains have been realized for patients. In the present study, we determined the efficacy of a novel combination treatment involving surgical intervention and long-term weight-bearing walking training in spinal cord injury (SCI) subjects clinically diagnosed as complete or American Spinal Injury Association Impairment Scale (AIS) Class A (AIS-A). A total of 320 clinically complete SCI subjects (271 male and 49 female), aged 16-60 years, received early (≤ 7 days, n = 201) or delayed (8-30 days, n = 119) surgical interventions to reduce intraspinal or intramedullary pressure. Fifteen days post-surgery, all subjects received a weight-bearing walking training with the "Kunming Locomotion Training Program (KLTP)" for a duration of 6 months. The neurological deficit and recovery were assessed using the AIS scale and a 10-point Kunming Locomotor Scale (KLS). We found that surgical intervention significantly improved AIS scores measured at 15 days post-surgery as compared to the pre-surgery baseline scores. Significant improvement of AIS scores was detected at 3 and 6 months and the KLS further showed significant improvements between all pair-wise comparisons of time points of 15 days, 3 or 6 months indicating continued improvement in walking scores during the 6-month period. In conclusion, combining surgical intervention within 1 month post-injury and weight-bearing locomotor training promoted continued and statistically significant neurological recoveries in subjects with clinically complete SCI, which generally shows little clinical recovery within the first year after injury and most are permanently disabled. This study was approved by the Science and Research Committee of Kunming General Hospital of PLA and Kunming Tongren Hospital, China and registered at ClinicalTrials.gov (Identifier: NCT04034108) on July 26, 2019

A human in vitro model system for investigating genome-wide host responses to SARS coronavirus infection

10.1186/1471-2334-4-34BMC Infectious Diseases4-BIDM