Smoothing algorithms for nonsmooth and nonconvex minimization over the stiefel manifold

We consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with an linear mapping. We propose three numerical algorithms for solving this problem, by combining smoothing methods and some existing algorithms for smooth optimization over the Stiefel manifold. In particular, we approximate the aforementioned nonsmooth convex function by its Moreau envelope in our smoothing methods, and prove that the Moreau envelope has many favorable properties. Thanks to this and the scheme for updating the smoothing parameter, we show that any accumulation point of the solution sequence generated by the proposed algorithms is a stationary point of the original optimization problem. Numerical experiments on building graph Fourier basis are conducted to demonstrate the efficiency of the proposed algorithms.Comment: 22 page

Tin-graphene tubes as anodes for lithium-ion batteries with high volumetric and gravimetric energy densities.

Limited by the size of microelectronics, as well as the space of electrical vehicles, there are tremendous demands for lithium-ion batteries with high volumetric energy densities. Current lithium-ion batteries, however, adopt graphite-based anodes with low tap density and gravimetric capacity, resulting in poor volumetric performance metric. Here, by encapsulating nanoparticles of metallic tin in mechanically robust graphene tubes, we show tin anodes with high volumetric and gravimetric capacities, high rate performance, and long cycling life. Pairing with a commercial cathode material LiNi0.6Mn0.2Co0.2O2, full cells exhibit a gravimetric and volumetric energy density of 590 W h Kg-1 and 1,252 W h L-1, respectively, the latter of which doubles that of the cell based on graphite anodes. This work provides an effective route towards lithium-ion batteries with high energy density for a broad range of applications

High-quality mesoporous graphene particles as high-energy and fast-charging anodes for lithium-ion batteries.

The application of graphene for electrochemical energy storage has received tremendous attention; however, challenges remain in synthesis and other aspects. Here we report the synthesis of high-quality, nitrogen-doped, mesoporous graphene particles through chemical vapor deposition with magnesium-oxide particles as the catalyst and template. Such particles possess excellent structural and electrochemical stability, electronic and ionic conductivity, enabling their use as high-performance anodes with high reversible capacity, outstanding rate performance (e.g., 1,138 mA h g-1 at 0.2 C or 440 mA h g-1 at 60 C with a mass loading of 1 mg cm-2), and excellent cycling stability (e.g., >99% capacity retention for 500 cycles at 2 C with a mass loading of 1 mg cm-2). Interestingly, thick electrodes could be fabricated with high areal capacity and current density (e.g., 6.1 mA h cm-2 at 0.9 mA cm-2), providing an intriguing class of materials for lithium-ion batteries with high energy and power performance

Multi-functional anodes boost the transient power and durability of proton exchange membrane fuel cells.

Proton exchange membrane fuel cells have been regarded as the most promising candidate for fuel cell vehicles and tools. Their broader adaption, however, has been impeded by cost and lifetime. By integrating a thin layer of tungsten oxide within the anode, which serves as a rapid-response hydrogen reservoir, oxygen scavenger, sensor for power demand, and regulator for hydrogen-disassociation reaction, we herein report proton exchange membrane fuel cells with significantly enhanced power performance for transient operation and low humidified conditions, as well as improved durability against adverse operating conditions. Meanwhile, the enhanced power performance minimizes the use of auxiliary energy-storage systems and reduces costs. Scale fabrication of such devices can be readily achieved based on the current fabrication techniques with negligible extra expense. This work provides proton exchange membrane fuel cells with enhanced power performance, improved durability, prolonged lifetime, and reduced cost for automotive and other applications

Role of T2 mapping of magnetic resonance imaging in the differentiation of endometrial cancer and benign endometrial lesions

PURPOSEThe T2 mapping of magnetic resonance imaging (MRI) in endometrial cancer (EC), benign endometrial lesions (BELs), and normal endometrium (NE) has rarely been reported. This study aimed to determine the T2 values of MRI in EC, BELs, and NE to investigate whether the T2 values can differentiate them and to assess the aggressiveness of EC.METHODSIn total, 73 patients [EC, 51 (age, 57.4 ± 5.4 years); BELs, 22 (age, 57.8 ± 11.8 years)] and 23 normal volunteers (age, 56.1 ± 6.6 years) were included. The T2 values of MRI of the EC (type I and II), BEL, and NE groups were described and compared. The relationships between the T2 values of MRI in EC and the pathological characteristics [International Federation of Gynecology and Obstetrics (FIGO) stage and grade] were analyzed.RESULTSThe median T2 values of NE, BEL, and EC were 197.5 (142.9–324.0) ms, 131.1 (103.2–247.9) ms, and 103.0 (71.6–243.5) ms (P < 0.001), respectively. The median T2 values of type I and type II EC were 100.8 (71.62–130.44) ms and 125.7 (119.7–243.5) ms, respectively. There were significant differences in the T2 values among the NE, BEL, type I EC, and type II EC groups (P < 0.001) except for between the type II EC and BEL groups (P = 0.938). The T2 value of MRI in type I EC was significantly lower than that in type II EC (P = 0.001). There were no significant differences in patients with type I EC having different FIGO stages (P = 0.273) or tumor grades (P = 0.686).CONCLUSIONT2 mapping of MRI has the potential to quantitatively differentiate between EC, BELs, and NE as well as between type I and type II EC