Directional Differentiability of the Generalized Metric Projection in Hilbert spaces and Hilbertian Bochner spaces

Let $H$ be a real Hilbert space and $C$ a nonempty closed and convex subset of $H$. Let $P_C: H\rightarrow C$ denote the (standard) metric projection operator. In this paper, we study the G\^ateaux directional differentiability of $P_C$ and investigate some of its properties. The G\^ateaux directionally derivatives of $P_C$ are precisely given for the following cases of the considered subset $C$: 1. closed and convex subsets; 2. closed balls; 3. closed and convex cones (including proper closed subspaces). For special Hilbert spaces, we consider directional differentiability of $P_C$ for some Hilbert spaces with orthonormal bases and the real Hilbert space $L^2([-\pi,\pi])$ with the trigonometric orthonormal basis.Comment: This article has been accepted for publicatio

Origins of Large Voltage Hysteresis in High Energy-Density Metal Fluoride Lithium-Ion Battery Conversion Electrodes

Metal fluoride and oxides can store multiple lithium-ions through conversion chemistry to enable high energy-density lithium-ion batteries. However, their practical applications have been hindered by an unusually large voltage hysteresis between charge and discharge voltage-profiles and the consequent low energy efficiency (< 80%). The physical origins of such hysteresis are rarely studied and poorly understood. Here we employ in situ X-ray absorption spectroscopy (XAS), transmission electron microscopy (TEM), density-functional-theory (DFT) calculations, and galvanostatic intermittent titration technique (GITT) to first correlate the voltage profile of iron fluoride ($FeF_3$), a representative conversion electrode material, with evolution and spatial distribution of intermediate phases in the electrode. The results reveal that, contrary to conventional belief, the phase evolution in the electrode is symmetrical during discharge and charge. However, the spatial evolution of the electrochemically active phases, which is controlled by reaction kinetics, is different. We further propose that the voltage hysteresis in the $FeF_3$ electrode is kinetic in nature. It is the result of Ohmic voltage drop, reaction overpotential, and different spatial distributions of electrochemically-active phases (i.e. compositional inhomogeneity). Therefore, the large hysteresis can be expected to be mitigated by rational design and optimization of material microstructure and electrode architecture to improve the energy efficiency of lithium-ion batteries based on conversion chemistry

Stability and Generalization of ℓp\ell_p-Regularized Stochastic Learning for GCN

Graph convolutional networks (GCN) are viewed as one of the most popular representations among the variants of graph neural networks over graph data and have shown powerful performance in empirical experiments. That $\ell_2$-based graph smoothing enforces the global smoothness of GCN, while (soft) $\ell_1$-based sparse graph learning tends to promote signal sparsity to trade for discontinuity. This paper aims to quantify the trade-off of GCN between smoothness and sparsity, with the help of a general $\ell_p$-regularized $(1<p\leq 2)$ stochastic learning proposed within. While stability-based generalization analyses have been given in prior work for a second derivative objectiveness function, our $\ell_p$-regularized learning scheme does not satisfy such a smooth condition. To tackle this issue, we propose a novel SGD proximal algorithm for GCNs with an inexact operator. For a single-layer GCN, we establish an explicit theoretical understanding of GCN with the $\ell_p$-regularized stochastic learning by analyzing the stability of our SGD proximal algorithm. We conduct multiple empirical experiments to validate our theoretical findings.Comment: Accepted to IJCAI 202

Design Principles for Self-forming Interfaces Enabling Stable Lithium Metal Anodes

The path toward Li-ion batteries with higher energy-densities will likely involve use of thin lithium metal (Li) anode (<50 $\mu$m in thickness), whose cyclability today remains limited by dendrite formation and low Coulombic efficiency. Previous studies have shown that the solid-electrolyte-interface (SEI) of Li metal plays a crucial role in Li electrodeposition and stripping. However, design rules for optimal SEIs on lithium metal are not well-established. Here, using integrated experimental and modeling studies on a series of structurally-similar SEI-modifying compounds as model systems, we reveal the relationship between SEI compositions, Li deposition morphology and coulombic efficiency, and identify two key descriptors (ionicity and compactness) for high performance SEIs through integrated experimental and modeling studies. Using this understanding, we design a highly ionic and compact SEI that shows excellent cycling performance in LiCoO$_2$-Li full cells at practical current densities. Our results provide guidance for the rational selection and optimization of SEI modifiers to further improve Li metal anodes.Comment: 21 pages, 6 figures and Supplementary Informatio

Far-Infrared Spectroscopy of Cationic Polycyclic Aromatic Hydrocarbons: Zero Kinetic Energy Photoelectron Spectroscopy of Pentacene Vaporized from Laser Desorption

doi:10.1088/0004-637X/715/1/485The distinctive set of infrared (IR) emission bands at 3.3, 6.2, 7.7, 8.6, and 11.3 μm are ubiquitously seen in a wide variety of astrophysical environments. They are generally attributed to polycyclic aromatic hydrocarbon (PAH) molecules. However, not a single PAH species has yet been identified in space, as the mid-IR vibrational bands are mostly representative of functional groups and thus do not allow one to fingerprint individual PAH molecules. In contrast, the far-IR (FIR) bands are sensitive to the skeletal characteristics of a molecule, hence they are important for chemical identification of unknown species. With an aim to offer laboratory astrophysical data for the Herschel Space Observatory, Stratospheric Observatory for Infrared Astronomy, and similar future space missions, in this work we report neutral and cation FIR spectroscopy of pentacene (C22H14), a five-ring PAH molecule. We report three IR active modes of cationic pentacene at 53.3, 84.8, and 266 μm that may be detectable by space missions such as the SAFARI instrument on board SPICA. In the experiment, pentacene is vaporized from a laser desorption source and cooled by a supersonic argon beam. We have obtained results from two-color resonantly enhanced multiphoton ionization and two-color zero kinetic energy photoelectron (ZEKE) spectroscopy. Several skeletal vibrational modes of the first electronically excited state of the neutral species and those of the cation are assigned, with the aid of ab initio and density functional calculations. Although ZEKE is governed by the Franck-Condon principle different from direct IR absorption or emission, vibronic coupling in the long ribbon-like molecule results in the observation of a few IR active modes. Within the experimental resolution of ~7 cm-1, the frequency values from our calculation agree with the experiment for the cation, but differ for the electronically excited intermediate state. Consequently, modeling of the intensity distribution is difficult and may require explicit inclusion of vibronic interactions.This work is supported by the National Aeronautics and Space Administration under award No. NNX09AC03G. A.L. is supported in part by the NSF grant AST 07-07866, a Spitzer Theory grant and a Herschel Theory grant

Molecular characterization, polymorphism of growth differentiation factor 5 gene and association with ultrasound measurement traits in native Chinese cattle breeds

Growth differentiation factor 5 (GDF5), involved in the development and maintenance of bone andcartilage, is a n important candidate gene for growth and carcass traits selection through markerassisted selection (MAS). Genomic structural analysis showed that bovine GDF5 shares much similarity with human GDF5. The latest findings demonstrate that the single nucleotide polymorphism (SNP) T586C in exon 1 is significantly associated with ultrasound marbling score (UMAR) and ultrasound backfat thickness (UBF). Furthermore, the analysis of T586C SNP marker shows there are significant effects on the UBF (P = 0.0498) and on the UMAR (P = 0.0058) in 465 individuals. These results clearly suggest that the GDF5 gene is among target genes for carcass traits in bovine reproduction and breeding.Keywords: Cattle, GDF5 gene, ultrasound measurement, polymorphism, association analysisAfrican Journal of Biotechnology Vol. 9(33), pp. 5269-5273, 16 August, 201

Effect of the of remazolam toluenesulfonate and IPACK on postoperative rehabilitation and sedation in elderly patients undergoing knee arthroplasty

Purpose: To investigate the effect of the combination of remazolam toluenesulfonate and infiltration between the popliteal artery and capsule of the knee (IPACK) on the rehabilitation and sedation of elderly patients undergoing knee arthroplasty. Methods: A total of 84 elderly patients who underwent knee arthroplasty in Quzhou Affiliated Hospital of Wenzhou Medical University between January 2021 and December 2021 were given IPACK in combination with adductor canal block under ultrasound guidance. Forty (40) patients were given anesthesia with propofol + sufentanil + cis-benzene sulfonic acid atracurium (control group), while 44 patients received anesthesia with remazolam toluenesulfonate + sufentanil + cis-benzene sulfonic acid atracurium (study group). Various clinical indices in the patients were assessed Results: Relative to control, there were significantly lower visual analog scale (VAS) scores at 6 and 12 h after operation, lower frequency of post-operation pumping with PCA pump, lower frequency of remedial analgesia within 48 h after operation (p &lt; 0.05). Moreover, the time taken for spontaneous recovery of breathing, recovery time, and extubation time were similar in the two groups (p &gt; 0.05). The muscle strength of quadriceps femoris of the affected knee joint was higher in the study group than in the control group at 12, 24, and 48 h, after operation (p &lt; 0.05). Conclusion: The combination of remazolam toluenesulfonate with IPACK effectively alleviate pain in elderly patients undergoing knee arthroplasty and improves sedation without increasing cognitive dysfunction. This treatment strategy has potentials for further investigation for possible large-scale application

Electrical Tuning of Neutral and Charged Excitons with 1-nm Gate

Electrical control of individual spins and photons in solids is key for quantum technologies, but scaling down to small, static systems remains challenging. Here, we demonstrate nanoscale electrical tuning of neutral and charged excitons in monolayer WSe2 using 1-nm carbon nanotube gates. Electrostatic simulations reveal a confinement radius below 15 nm, reaching the exciton Bohr radius limit for few-layer dielectric spacing. In situ photoluminescence spectroscopy shows gate-controlled conversion between neutral excitons, negatively charged trions, and biexcitons at 4 K. Important for quantum information processing applications, our measurements indicate gating of a local 2D electron gas in the WSe2 layer, coupled to photons via trion transitions with binding energies exceeding 20 meV. The ability to deterministically tune and address quantum emitters using nanoscale gates provides a pathway towards large-scale quantum optoelectronic circuits and spin-photon interfaces for quantum networking.Comment: 21 pages, 11 figure