M-estimation in Low-rank Matrix Factorization: a General Framework

Many problems in science and engineering can be reduced to the recovery of an unknown large matrix from a small number of random linear measurements. Matrix factorization arguably is the most popular approach for low-rank matrix recovery. Many methods have been proposed using different loss functions, for example the most widely used L_2 loss, more robust choices such as L_1 and Huber loss, quantile and expectile loss for skewed data. All of them can be unified into the framework of M-estimation. In this paper, we present a general framework of low-rank matrix factorization based on M-estimation in statistics. The framework mainly involves two steps: firstly we apply Nesterov's smoothing technique to obtain an optimal smooth approximation for non-smooth loss function, such as L_1 and quantile loss; secondly we exploit an alternative updating scheme along with Nesterov's momentum method at each step to minimize the smoothed loss function. Strong theoretical convergence guarantee has been developed for the general framework, and extensive numerical experiments have been conducted to illustrate the performance of proposed algorithm

Wnt-5a Promotes Neural Development and Differentiation by Regulating CDK5 via Ca2+/Calpain Pathway

Background/Aims: The Wnt signaling pathway has essential functions in the central nervous system, where it regulates the major physiological functions of neurons, including development, differentiation, and plasticity. Wnt signaling controls these cellular events; however, how Wnt pathways integrate into a coherent developmental program remains unclear. Methods: The expression and secretion of different WNT ligands (Wnt-1, Wnt-3a, Wnt-4, Wnt-5a, Wnt-11), and the levels and activities of cyclin-dependent kinases (CDK2, CDK4, CDK6/cyclin D, cyclin E) or CDK5 (CDK5/p35 and p25) were measured in Rat cortex at different embryonic stages, and in RA/BDNF-induced differentiated SH-SY5Y cell model, by Quantitative real-time PCR (qPCR), western blotting, ELISA, and in vitro CDK5 kinase assays. MAP2-BrdU double staining was used to assess cell differentiation and cell cycle exit in an RA/BDNF-induced differentiated SH-SY5Y cell model. The effects of CDK5 and Ca2+/calpain signaling were assessed using specific chemical inhibitors. Results: We found that Wnt-1 was unchanged and Wnt-3a was attenuated, whereas Wnt-4, Wnt-5a, and Wnt-11 were markedly up-regulated, during the development of neurons and differentiated SH-SY5Y cells. Simultaneously, the activity of CDK5 was elevated. Furthermore, we describe crosstalk between non-canonical Wnt signaling and CDK5 in the development of neurons and differentiated SH-SY5Y cells. Wnt-5a, a non-canonical Wnt ligand, regulated CDK5 via Ca2+/calpain signaling in both neuronal development and differentiation. Inhibition of Wnt-5a diminished CDK5 kinase activity via the Ca2+/calpain pathway, thereby attenuating RA-BDNF induced SH-SY5Y cell differentiation. Conclusion: Wnt-5a signaling is a significant regulator of neuronal development and differentiation and upregulates CDK5 kinase activity via Ca2+/calpain signaling

Superconducting Diode Effect and Large Magnetochiral Anisotropy in Td_d-MoTe2_2 Thin Film

In the absence of time-reversal invariance, metals without inversion symmetry may exhibit nonreciprocal charge transport -- a magnetochiral anisotropy that manifests as unequal electrical resistance for opposite current flow directions. If superconductivity also sets in, the charge transmission may become dissipationless in one direction while remaining dissipative in the opposite, thereby realizing a superconducting diode. Through both direct-current and alternating-current measurements, we study the nonreciprocal effects in thin films of the noncentrosymmetric superconductor T$_d$-MoTe\textsubscript{2} with disorders. We observe nonreciprocal superconducting critical currents with a diode efficiency close to 20\%~, and a large magnetochiral anisotropy coefficient up to \SI{5.9e8}{\per\tesla\per\ampere}, under weak out-of-plane magnetic field in the millitesla range. The great enhancement of rectification efficiency under out-of-plane magnetic field is likely abscribed to the vortex ratchet effect, which naturally appears in the noncentrosymmetric superconductor with disorders. Intriguingly, unlike the finding in Rashba systems, the strongest in-plane nonreciprocal effect does not occur when the field is perpendicular to the current flow direction. We develop a phenomenological theory to demonstrate that this peculiar behavior can be attributed to the asymmetric structure of spin-orbit coupling in T$_d$-MoTe\textsubscript{2}. Our study highlights how the crystallographic symmetry critically impacts the nonreciprocal transport, and would further advance the research for designing the superconducting diode with the best performance.Comment: 7 pages, 5figure

Special Issue: Mechanical Properties of Advanced Multifunctional Coatings

Coatings are found almost anywhere in the modern world [...

Effect of Forced Air Cooling on the Microstructures, Tensile Strength, and Hardness Distribution of Dissimilar Friction Stir Welded AA5A06-AA6061 Joints

Friction stir welding (FSW) is a promising welding method for welding dissimilar materials without using welding flux. In the present work, 5A06-H112 and 6061-T651 aluminium alloys were successfully welded by friction stir welding with forced air cooling (FAC) and natural cooling (NC). Nanoindentation tests and microstructure characterisations revealed that forced air cooling, which can accelerate the cooling process and suppress the coarsening of grains and the dissolution of precipitate phases, contributes to strengthening and narrowing the weakest area of the joint. The tensile strength of joints with FAC were commonly improved by 10% compared to those with NC. Scanning electron microscopy (SEM) images of the fracture surface elucidated that FSW with FAC tended to increase the number and reduce the size of the dimples. These results demonstrated the advantages of FSW with FAC in welding heat-sensitive materials and provide fresh insight into welding industries

Quantification of occlusions influencing the tree stem curve retrieving from single-scan terrestrial laser scanning data

Background The stem curve of standing trees is an essential parameter for accurate estimation of stem volume. This study aims to directly quantify the occlusions within the single-scan terrestrial laser scanning (TLS) data, evaluate its correlation with the accuracy of the retrieved stem curves, and subsequently, to assess the capacity of single-scan TLS to estimate stem curves. Methods We proposed an index, occlusion rate, to quantify the occlusion level in TLS data. We then analyzed three influencing factors for the occlusion rate: the percentage of basal area near the scanning center, the scanning distance and the source of occlusions. Finally, we evaluated the effects of occlusions on stem curve estimates from single-scan TLS data. Results The results showed that the correlations between the occlusion rate and the stem curve estimation accuracies were strong (r = 0.60–0.83), so was the correlations between the occlusion rate and its influencing factors (r = 0.84–0.99). It also showed that the occlusions from tree stems were the main factor of the low detection rate of stems, while the non-stem components mainly influenced the completeness of the retrieved stem curves. Conclusions Our study demonstrates that the occlusions significantly affect the accuracy of stem curve retrieval from the single-scan TLS data in a typical-size (32 m × 32 m) forest plot. However, the single-scan mode has the capacity to accurately estimate the stem curve in a small forest plot (< 10 m × 10 m) or a plot with a lower occlusion rate, such as less than 35% in our tested datasets. The findings from this study are useful for guiding the practice of retrieving forest parameters using single-scan TLS data

Me Sarah Bernhardt. [Porte Saint-Martin. Jeanne d'Arc] : [photographie, tirage de démonstration] / [Atelier Nadar]

The finite element method (FEM) and scratch sliding test were combined to investigate the tribological behaviors of Chromium Aluminum Silicon Nitride (CrAlSiN) coatings with various Si contents. The tribological behavior was evaluated through sliding tests using a conventional ball-on-disc wear apparatus. It was found that the coefficient of friction (COF) of CrAlSiN was lower than CrAlN coating and it reached a minimum value of 0.56 for CrAlSi3.7N. Energy-dispersive Scanning Electron Microscopy (SEM) with X-ray spectroscopy (EDX) was employed to reveal the compositions of wear debris formed during the scratch sliding experiments. As a reasonable approximation, a static condition was applied, and the scratch behavior was modeled by a sphere indenter scratching on a thin coating coated on a thick substrate. A three-dimensional finite element model was constructed with the help of the ABAQUS to describe the mechanical response during scratch. (C) 2019 Author(s)