Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces

In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calder\'{o}n-Zygmund operators.Comment: 31 pages,added one sentence in page 3 and a referenc

Multi-scale characterisation of the 3D microstructure of a thermally-shocked bulk metallic glass matrix composite

Bulk metallic glass matrix composites (BMGMCs) are a new class of metal alloys which have significantly increased ductility and impact toughness, resulting from the ductile crystalline phases distributed uniformly within the amorphous matrix. However, the 3D structures and their morphologies of such composite at nano and micrometre scale have never been reported before. We have used high density electric currents to thermally shock a Zr-Ti based BMGMC to different temperatures, and used X-ray microtomography, FIB-SEM nanotomography and neutron diffraction to reveal the morphologies, compositions, volume fractions and thermal stabilities of the nano and microstructures. Understanding of these is essential for optimizing the design of BMGMCs and developing viable manufacturing methods

Serum high-sensitivity C-reactive protein levels in comorbid patients with type-2 diabetes mellitus and periodontal disease

Purpose: To investigate the relationship between serum levels of high-sensitivity C-reactive protein (hs-CRP) and the severity of periodontal disease in diabetics with periodontitis.Methods: Ninety patients were recruited for this study. They were divided into three groups, namely, group 1 (30 patients with type 2 diabetes mellitus (T2DM) and periodontal disease), group II (30 patients with T2DM only) and control (30 healthy individuals). Serum levels of hs-CRP and glycosylated hemoglobin (HbAc) were determined. Moreover, blood glucose (BG) and insulin (FNS) levels were determined in the fasted state, and their values used to compute insulin resistance index (Homa-IR).Results: Serum levels of FNS, FPG, HbAc and Homa-IR in group I patients were significantly higher (p < 0.05) than those of control group. While the levels of BG and Homa-IR in the serum of patients in groups I and II were significantly higher (p < 0.05) than those of control, marked reductions were seen in their values in group II, relative to group I. The serum levels of hs-CRP in group I and II were significantly increased (p < 0.05) relative to control, but were lower in group II than in group I (p < 0.05). Homa-IR was positively correlated with serum hs-CRP, FNS, BG, HbAc, and Homa-IR in groups I and II. Results from multiple regression analysis revealed significant effects of hs-CRP and HbAc on Homa-IR.Conclusion: Serum levels of hs-CRP in patients with T2DM and periodontitis are closely related to disease severity, insulin resistance and blood glucose level.Keywords: Type-2 diabetes mellitus, Periodontal disease, High-sensitivity C-reactive protein, Blood glucose, Insulin resistance, Correlatio

In situ synchrotron x-ray study of ultrasound cavitation and its effect on solidification microstructures

Considerable progress has been made in studying the mechanism and effectiveness of using ultrasound waves to manipulate the solidification microstructures of metallic alloys. However, uncertainties remain in both the underlying physics of how microstructures evolve under ultrasonic waves, and the best technological approach to control the final microstructures and properties. We used the ultrafast synchrotron X-ray phase contrast imaging facility housed at the Advanced Photon Source, Argonne National Laboratory, US to study in situ the highly transient and dynamic interactions between the liquid metal and ultrasonic waves/bubbles. The dynamics of ultrasonic bubbles in liquid metal and their interactions with the solidifying phases in a transparent alloy were captured in situ. The experiments were complemented by the simulations of the acoustic pressure field, the pulsing of the bubbles, and the associated forces acting onto the solidifying dendrites. The study provides more quantitative understanding on how ultrasonic waves/bubbles influence the growth of dendritic grains and promote the grain multiplication effect for grain refinement

Strategic Analysis of Dual Sourcing and Dual Channel with an Unreliable Alternative Supplier

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148383/1/poms12938_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148383/2/poms12938.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148383/3/poms12938-sup-0001-AppendixS1.pd

Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation

Model-based deep learning has achieved astounding successes due in part to the availability of large-scale realworld data. However, processing such massive amounts of data comes at a considerable cost in terms of computations, storage, training and the search for good neural architectures. Dataset distillation has thus recently come to the fore. This paradigm involves distilling information from large real-world datasets into tiny and compact synthetic datasets such that processing the latter yields similar performances as the former. State-of-the-art methods primarily rely on learning the synthetic dataset by matching the gradients obtained during training between the real and synthetic data. However, these gradient-matching methods suffer from the accumulated trajectory error caused by the discrepancy between the distillation and subsequent evaluation. To alleviate the adverse impact of this accumulated trajectory error, we propose a novel approach that encourages the optimization algorithm to seek a flat trajectory. We show that the weights trained on synthetic data are robust against the accumulated errors perturbations with the regularization towards the flat trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to boost the performance of gradient-matching methods by up to 4.7% on a subset of images of the ImageNet dataset with higher resolution images. We also validate the effectiveness and generalizability of our method with datasets of different resolutions and demonstrate its applicability to neural architecture search

Efficient Sharpness-aware Minimization for Improved Training of Neural Networks

Overparametrized Deep Neural Networks (DNNs) often achieve astounding performances, but may potentially result in severe generalization error. Recently, the relation between the sharpness of the loss landscape and the generalization error has been established by Foret et al. (2020), in which the Sharpness Aware Minimizer (SAM) was proposed to mitigate the degradation of the generalization. Unfortunately, SAM s computational cost is roughly double that of base optimizers, such as Stochastic Gradient Descent (SGD). This paper thus proposes Efficient Sharpness Aware Minimizer (ESAM), which boosts SAM s efficiency at no cost to its generalization performance. ESAM includes two novel and efficient training strategies-StochasticWeight Perturbation and Sharpness-Sensitive Data Selection. In the former, the sharpness measure is approximated by perturbing a stochastically chosen set of weights in each iteration; in the latter, the SAM loss is optimized using only a judiciously selected subset of data that is sensitive to the sharpness. We provide theoretical explanations as to why these strategies perform well. We also show, via extensive experiments on the CIFAR and ImageNet datasets, that ESAM enhances the efficiency over SAM from requiring 100% extra computations to 40% vis-a-vis base optimizers, while test accuracies are preserved or even improved

OpenGSL: A Comprehensive Benchmark for Graph Structure Learning

Graph Neural Networks (GNNs) have emerged as the de facto standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node connections, resulting from the complex and contingent formation process of graphs, presents significant challenges in modeling them effectively. To tackle this issue, Graph Structure Learning (GSL), a family of data-centric learning approaches, has garnered substantial attention in recent years. The core concept behind GSL is to jointly optimize the graph structure and the corresponding GNN models. Despite the proposal of numerous GSL methods, the progress in this field remains unclear due to inconsistent experimental protocols, including variations in datasets, data processing techniques, and splitting strategies. In this paper, we introduce OpenGSL, the first comprehensive benchmark for GSL, aimed at addressing this gap. OpenGSL enables a fair comparison among state-of-the-art GSL methods by evaluating them across various popular datasets using uniform data processing and splitting strategies. Through extensive experiments, we observe that existing GSL methods do not consistently outperform vanilla GNN counterparts. However, we do observe that the learned graph structure demonstrates a strong generalization ability across different GNN backbones, despite its high computational and space requirements. We hope that our open-sourced library will facilitate rapid and equitable evaluation and inspire further innovative research in the field of GSL. The code of the benchmark can be found in https://github.com/OpenGSL/OpenGSL.Comment: 9 pages, 4 figure