Generalization Ability of Wide Residual Networks

In this paper, we study the generalization ability of the wide residual network on $\mathbb{S}^{d-1}$ with the ReLU activation function. We first show that as the width $m\rightarrow\infty$, the residual network kernel (RNK) uniformly converges to the residual neural tangent kernel (RNTK). This uniform convergence further guarantees that the generalization error of the residual network converges to that of the kernel regression with respect to the RNTK. As direct corollaries, we then show $i)$ the wide residual network with the early stopping strategy can achieve the minimax rate provided that the target regression function falls in the reproducing kernel Hilbert space (RKHS) associated with the RNTK; $ii)$ the wide residual network can not generalize well if it is trained till overfitting the data. We finally illustrate some experiments to reconcile the contradiction between our theoretical result and the widely observed ``benign overfitting phenomenon''Comment: 28 pages, 3 figure

Functional Slicing-free Inverse Regression via Martingale Difference Divergence Operator

Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR is critical but challenging. In this paper, we propose a new method called functional slicing-free inverse regression (FSFIR) to estimate the central subspace in FSDR. FSFIR is based on the martingale difference divergence operator, which is a novel metric introduced to characterize the conditional mean independence of a functional predictor on a multivariate response. We also provide a specific convergence rate for the FSFIR estimator. Compared with existing functional sliced inverse regression methods, FSFIR does not require the selection of a slice number. Simulations demonstrate the efficiency and convenience of FSFIR

Statistical Optimality of Deep Wide Neural Networks

In this paper, we consider the generalization ability of deep wide feedforward ReLU neural networks defined on a bounded domain $\mathcal X \subset \mathbb R^{d}$. We first demonstrate that the generalization ability of the neural network can be fully characterized by that of the corresponding deep neural tangent kernel (NTK) regression. We then investigate on the spectral properties of the deep NTK and show that the deep NTK is positive definite on $\mathcal{X}$ and its eigenvalue decay rate is $(d+1)/d$. Thanks to the well established theories in kernel regression, we then conclude that multilayer wide neural networks trained by gradient descent with proper early stopping achieve the minimax rate, provided that the regression function lies in the reproducing kernel Hilbert space (RKHS) associated with the corresponding NTK. Finally, we illustrate that the overfitted multilayer wide neural networks can not generalize well on $\mathbb S^{d}$. We believe our technical contributions in determining the eigenvalue decay rate of NTK on $\mathbb R^{d}$ might be of independent interests

Blood glucose variance measured by continuous glucose monitors across the menstrual cycle

Past studies on how blood glucose levels vary across the menstrual cycle have largely shown inconsistent results based on limited blood draws. In this study, 49 individuals wore a Dexcom G6 continuous glucose monitor and a Fitbit Sense smartwatch while measuring their menstrual hormones and self-reporting characteristics of their menstrual cycles daily. The average duration of participation was 79.3 ± 21.2 days, leading to a total of 149 cycles and 554 phases in our dataset. We use periodic restricted cubic splines to evaluate the relationship between blood glucose and the menstrual cycle, after which we assess phase-based changes in daily median glucose level and associated physiological parameters using mixed-effects models. Results indicate that daily median glucose levels increase and decrease in a biphasic pattern, with maximum levels occurring during the luteal phase and minimum levels occurring during the late-follicular phase. These trends are robust to adjustments for participant characteristics (e.g., age, BMI, weight) and self-reported menstrual experiences (e.g., food cravings, bloating, fatigue). We identify negative associations between each of daily estrogen level, step count, and low degrees of fatigue with higher median glucose levels. Conversely, we find positive associations between higher food cravings and higher median glucose levels. This study suggests that blood glucose could be an important parameter for understanding menstrual health, prompting further investigation into how the menstrual cycle influences glucose fluctuation

Targeted therapy of RET fusion-positive non-small cell lung cancer

Lung cancer has very high morbidity and mortality worldwide, and the prognosis is not optimistic. Previous treatments for non-small cell lung cancer (NSCLC) have limited efficacy, and targeted drugs for some gene mutations have been used in NSCLC with considerable efficacy. The RET proto-oncogene is located on the long arm of chromosome 10 with a length of 60,000 bp, and the expression of RET gene affects cell survival, proliferation, growth and differentiation. This review will describe the basic characteristics and common fusion methods of RET genes; analyze the advantages and disadvantages of different RET fusion detection methods; summarize and discuss the recent application of non-selective and selective RET fusion-positive inhibitors, such as Vandetanib, Selpercatinib, Pralsetinib and Alectinib; discuss the mechanism and coping strategies of resistance to RET fusion-positive inhibitors

Enhanced energy density with a wide thermal stability in epitaxial Pb0.92La0.08Zr0.52Ti0.48O3 thin films

High-quality epitaxial Pb0.92La0.08Zr0.52Ti0.48O3 (PLZT) films of thickness of 880 nm were fabricated using pulsed laser deposition on (001) Nb doped SrTiO3 (Nb:STO) substrates. Besides a confirmation of the epitaxial relationship [100]PLZT//[100]Nb:STO and (001)PLZT//(001)Nb:STO using X-ray diffraction, a transmission electron microscopy study has revealed a columnar structure across the film thickness. The recoverable energy density (Wrec) of the epitaxial PLZT thin film capacitors increases linearly with the applied electric field and the best value of 31 J/cm3 observed at 2.27 MV/cm is considerably higher by 41% than that of the polycrystalline PLZT film of a comparable thickness. In addition to the high Wrec value, an excellent thermal stability as illustrated in a negligible temperature dependence of the Wrec in the temperature range from room temperature to 180 C is achieved. The enhanced Wrec and the thermal stability are attributed to the reduced defects and grain boundaries in epitaxial PLZT thin films, making them promising for energy storage applications that require both high energy density, power density, and wide operation temperatures

Peeling of graphene/molybdenum disulfide heterostructure at different angles: A continuum model with accommodations for van der Waals interaction

Being the key process of a promising scalable production method, mechanical peeling is often used to construct high-quality van der Waals (vdW) heterostructures. By combining molecular dynamics (MD) studies and theoretical analysis, the investigation of the process of peeling heterostructures at different angles is reported. Taking vdW interaction into account, we present a theory that considers the effects of peeling angles on peeling forces. The theory is verified with results of MD simulations and found to describe the stable peeling stage well. Furthermore, there is a characteristic length at the initial stage of peeling, which reflects the bending and interfacial properties of the layered materials during peeling and indicates the influence of peeling angles on transition from unstable peeling to stable peeling. Our findings could help to understand the peeling mechanisms of 2D material interfaces and may give a guidance for the construction of better-quality and more complex vdW heterostructures

Generation of mode-locked states of conventional solitons and bright-dark solitons in graphene mode-locked fiber laser

Abstract This paper proposes a mode-locked fiber laser based on graphene-coated microfiber. The total length of the fiber laser resonant cavity is 31.34 m. Under the condition of stable output of bright-dark soliton pairs from the fiber laser, dual-wavelength tuning is realized by adjusting the polarization controller (PC), and the wavelength tuning range is 11 nm. Furthermore, the effects of polarization states on bright-dark solitons are studied. It is demonstrated that the mode-locking state can be switched between conventional solitons and bright-dark solitons in the graphene mode-locked fiber laser. Bright-dark soliton pairs with different shapes and nanosecond pulse width can be obtained by adjusting the PC and pump power. Graphical Abstrac

Nuciferine Effectively Protects Mice against Acetaminophen-Induced Liver Injury

Acetaminophen (APAP) overdose still poses a major clinical challenge and is a leading cause of acute liver injury (ALI). N-acetylcysteine (NAC) is the only approved antidote to treat APAP toxicity while NAC therapy can trigger side effects including severe vomiting and even shock. Thus, new insights in developing novel therapeutic drugs may pave the way for better treatment of APAP poisoning. Previous research has reported that nuciferine (Nuci) possesses anti-inflammatory and antioxidant properties. Therefore, the objective of this study was proposed to investigate the hepatoprotective effects of Nuci and explore its underlying mechanisms. Mice were intraperitoneally (i.p.) administered with APAP (300 mg/kg) and subsequently injected with Nuci (25, 50, and 100 mg/kg, i.p.) at 30 min after APAP overdose. Then, all mice were sacrificed at 12 h after APAP challenge for further analysis. Nuci-treated mice did not show any side effects and our results revealed that treating Nuci significantly attenuated APAP-induced ALI, as confirmed by histopathological examinations, biochemical analysis, and diminished hepatic oxidative stress and inflammation. The in silico prediction and mRNA-sequencing analysis were performed to explore the underlying mechanisms of Nuci. GO and KEGG enrichment of the predicted target proteins of Nuci includes reactive oxygen species, drug metabolism of cytochrome P450 (CYP450) enzymes, and autophagy. Furthermore, the mRNA-sequencing analyses indicated that Nuci can regulate glutathione metabolic processes and anti-inflammatory responses. Consistently, we found that Nuci increased the hepatic glutathione restoration but decreased APAP protein adducts in damaged livers. Western blot analysis further confirmed that Nuci effectively promoted hepatic autophagy in APAP-treated mice. However, Nuci could not affect the expression levels of the main CYP450 enzymes (CYP1A2, CYP2E1, and CYP3A11). These results demonstrated that Nuci may be a potential therapeutic drug for APAP-induced ALI via amelioration of the inflammatory response and oxidative stress, regulation of APAP metabolism, and activation of autophagy