Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery

In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which enforces orthonormality among most of the factors. To ensure the orthonormal structure, we utilize the Riemannian gradient descent (RGD) for optimizing those factors over the Stiefel manifold. We first delve into the TT factorization problem and establish the local linear convergence of RGD. Notably, the rate of convergence only experiences a linear decline as the tensor order increases. We then study the sensing problem that aims to recover a TT format tensor from linear measurements. Assuming the sensing operator satisfies the restricted isometry property (RIP), we show that with a proper initialization, which could be obtained through spectral initialization, RGD also converges to the ground-truth tensor at a linear rate. Furthermore, we expand our analysis to encompass scenarios involving Gaussian noise in the measurements. We prove that RGD can reliably recover the ground truth at a linear rate, with the recovery error exhibiting only polynomial growth in relation to the tensor order. We conduct various experiments to validate our theoretical findings

A Validation Approach to Over-parameterized Matrix and Image Recovery

In this paper, we study the problem of recovering a low-rank matrix from a number of noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a prior and use an overspecified factored representation of the matrix variable, where the global optimal solutions overfit and do not correspond to the underlying ground-truth. We then solve the associated nonconvex problem using gradient descent with small random initialization. We show that as long as the measurement operators satisfy the restricted isometry property (RIP) with its rank parameter scaling with the rank of ground-truth matrix rather than scaling with the overspecified matrix variable, gradient descent iterations are on a particular trajectory towards the ground-truth matrix and achieve nearly information-theoretically optimal recovery when stop appropriately. We then propose an efficient early stopping strategy based on the common hold-out method and show that it detects nearly optimal estimator provably. Moreover, experiments show that the proposed validation approach can also be efficiently used for image restoration with deep image prior which over-parameterizes an image with a deep network.Comment: 29 pages and 9 figure

Immediate Antiretroviral Therapy Decreases Mortality Among Patients With High CD4 Counts in China: A Nationwide, Retrospective Cohort Study.

BackgroundClinical trials have demonstrated that immediate initiation of antiretroviral therapy (ART) reduces AIDS-related morbidity and mortality. We tested the hypothesis that initiating ART ≤30 days after human immunodeficiency virus (HIV) diagnosis would be associated with reduced mortality among people living with HIV (PLWH) with CD4 counts >500 cells/μL.MethodsPLWH enrolled in the Chinese National HIV Information System between January 2012 and June 2014 with CD4 counts >500 cells/μL were followed for 12 months. Cox proportional hazards model was used to determine hazard ratios (HRs) for PLWH who initiated ART after HIV diagnosis. ART initiation was treated as a time-dependent variable.ResultsWe enrolled 34581 PLWH with CD4 >500 cells/μL; 1838 (5.3%) initiated ART ≤30 days after diagnosis (immediate ART group), and 19 deaths were observed with a mortality rate of 1.04 per 100 person-years (PY). Fifty-eight deaths were documented among the 5640 PLWH in the delayed ART group with a mortality rate of 2.25 per 100 PY. There were 713 deaths among the 27103 PLWH in the no ART group with a mortality rate of 2.39 per 100 PY. After controlling for potential confounding factors, ART initiation at ≤30 days (adjusted HR, 0.37 [95% confidence interval, .23-.58]) was a statistically significant protective factor.ConclusionsWe found that immediate ART is associated with a 63% reduction in overall mortality among PLWH with CD4 counts >500 cells/μL in China, supporting the recommendation to initiate ART immediately following HIV diagnosis

Feasibility of Terahertz Time-Domain Spectroscopy to Detect Carbendazim Mixtures Wrapped in Paper

The purpose of this work was to detect carbendazim mixtures wrapped in paper. Unlike previous reports of THz-TDS for detecting pesticide residue, this work focused on detecting pesticide residue in packaged foods. Different weight ratios of carbendazim in polyethylene and in rice powder were detected qualitatively and quantitatively. Results show that pure carbendazim, polyethylene, and rice powder can be easily distinguished from each other. However, when the weight ratio was low, the absorbance of the mixture was similar with that of pure polyethylene and rice powder. With the help of SVM, carbendazim could be qualitatively detected in low weight ratio mixture successfully. Moreover, PLS and SVR were selected to quantitatively detect carbendazim mixtures. SVR has higher R and lower RMSECV, RMSEC, and RMSEP than PLS model. Lasty, the results also indicate that THz-TDS is a potential tool to detect pesticide residue in packaged foods qualitatively and quantitatively

Design and Synthesis of Neuroprotective Methylthiazoles and Modification as NO-Chimeras for Neurodegenerative Therapy

Learning and memory deficits in Alzheimer’s disease (AD) result from synaptic failure and neuronal loss, the latter caused in part by excitotoxicity and oxidative stress. A therapeutic approach is described that uses NO-chimeras directed at restoration of both synaptic function and neuroprotection. 4-Methylthiazole (MZ) derivatives were synthesized, based upon a lead neuroprotective pharmacophore acting in part by GABAA receptor potentiation. MZ derivatives were assayed for protection of primary neurons against oxygen−glucose deprivation and excitotoxicity. Selected neuroprotective derivatives were incorporated into NO-chimera prodrugs, coined nomethiazoles. To provide proof of concept for the nomethiazole drug class, selected examples were assayed for restoration of synaptic function in hippocampal slices from AD-transgenic mice, reversal of cognitive deficits, and brain bioavailability of the prodrug and its neuroprotective MZ metabolite. Taken together, the assay data suggest that these chimeric nomethiazoles may be of use in treatment of multiple components of neurodegenerative disorders, such as AD

Two-dimensional germanium islands with Dirac signature on Ag2Ge surface alloy

Two-dimensional (2D) Dirac materials have attracted intense research efforts due to their promise for applications ranging from field-effect transistors and low-power electronics to fault-tolerant quantum computation. One key challenge is to fabricate 2D Dirac materials hosting Dirac electrons. Here, monolayer germanene is successfully fabricated on a Ag2Ge surface alloy. Scanning tunneling spectroscopy measurements revealed a linear energy dispersion relation. The latter was supported by density functional theory calculations. These results demonstrate that monolayer germanene can be realistically fabricated on a Ag2Ge surface alloy. The finding opens the door to exploration and study of 2D Dirac material physics and device applications