A study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform"

This article is a study guide for "Trilinear smoothing inequalities and a variant of the triangular Hilbert transform" by Christ, Durcik, and Roos. We first present the standard techniques in the study of oscillatory integrals with the simpler toy model of a Hilbert transform along a parabola. These standard techniques prove to be insufficient in the study of the triangular Hilbert transform with curvature. The central and novel idea in their proof of the $L^p$-boundedness of the triangular Hilbert transform with curvature is a trilinear smoothing inequality which we also examine in this article.Comment: 55 pages, 2 figures, Study guide writing workshop in UPenn(https://sites.google.com/view/studyguideworkshop2023/home

A sharp H\"{o}rmander condition for bilinear Fourier multipliers with Lipschitz singularities

This paper studies the $L^{p}$ boundedness of bilinear Fourier multipliers in the local $L^{2}$ range. We assume a H\"{o}rmander condition relative to a singular set that is a finite union of Lipschitz curves. The H\"{o}rmander condition is sharp with respect to the Sobolev exponent. Our setup generalizes the non-degenerate bilinear Hilbert transform but avoids issues of uniform bounds near degeneracy

MiniSUPERB: Lightweight Benchmark for Self-supervised Speech Models

Self-supervised learning (SSL) is a popular research topic in speech processing. Successful SSL speech models must generalize well. SUPERB was proposed to evaluate the ability of SSL speech models across many speech tasks. However, due to the diversity of tasks, the evaluation process requires huge computational costs. We present MiniSUPERB, a lightweight benchmark that efficiently evaluates SSL speech models with comparable results to SUPERB while greatly reducing the computational cost. We select representative tasks and sample datasets and extract model representation offline, achieving 0.954 and 0.982 Spearman's rank correlation with SUPERB Paper and SUPERB Challenge, respectively. In the meanwhile, the computational cost is reduced by 97% in regard to MACs (number of Multiply-ACcumulate operations) in the tasks we choose. To the best of our knowledge, this is the first study to examine not only the computational cost of a model itself but the cost of evaluating it on a benchmark

Metastatic Gallbladder Cancer Presenting as a Gingival Tumor and Deep Neck Infection

Gallbladder cancer has an extremely poor prognosis because it is often diagnosed at an advanced stage. We describe a 63-year-old woman who was treated 4 years previously for gallbladder cancer, with laparoscopic cholecystectomy and secondary hepatectomy after presenting with acute cholecystitis and gallbladder rupture. At her second presentation, she had a left lower gingival tumor and deep neck infection. Incision and drainage and tumor biopsies were performed, and pathology at both sites revealed adenocarcinoma. Positron emission tomography revealed other tumors in the left breast and left lower lung field, which were both proven to be adenocarcinoma by biopsy. The patient's presentation with a metastatic oral tumor was rare. Although the incidence is very low, physicians should consider the possibility of metastatic cancer in a patient with a history of cancer, who presents with new oral tumor or deep neck infection

106GBaud (200G PAM4) CWDM EML for 800G/1.6T Optical Networks and AI Applications

We report ultrahigh speed 106GBaud (200G PAM4) electro-absorption modulated laser (EML) for 800G and 1.6T optical transmission. Four CWDM EMLs of 1271, 1291, 1311 and 1331nm in 800G FR4 optical transceivers show clear eye diagram after 2km. Our 106GBaud EMLs show high bandwidth, high extinction ratio, low threshold current and high power, making it a suitable source laser for 800G/1.6T and AI applications.&nbsp

Strong association of lumbar disk herniation with diabetes mellitus: a 12-year nationwide retrospective cohort study

BackgroundDespite reports on the association between diabetes mellitus (DM) and lumbar disk herniation (LDH), large-scale, nationwide studies exploring this relationship are lacking. We aimed to examine the profiles of DM in individuals with LDH and explore the potential mechanisms underlying the development of these disorders.MethodsThis retrospective, population-based study was conducted between 2008 and 2019 using data from the National Health Insurance (NHI) research database in Taiwan. The primary outcome was the date of initial LDH diagnosis, death, withdrawal from the NHI program, or end of the study period.ResultsIn total, 2,662,930 individuals with and 16,922,546 individuals without DM were included in this study; 719,068 matched pairs were established following propensity score matching (1:1 ratio) for sex, age, comorbidities, smoking, alcohol consumption, antihyperglycemic medications, and index year. The adjusted risk for developing LDH was 2.33-fold (95% confidence interval: 2.29−2.37; P<0.001), age-stratified analysis revealed a significantly greater risk of LDH in every age group, and both males and females were approximately twice as likely to develop LDH in the DM compared with non-DM cohort. Individuals with DM and comorbidities had a significantly higher risk of developing LDH than those without, and the serial models yielded consistent results. Treatment with metformin, sulfonylureas, meglitinides, thiazolidinediones, dipeptidyl peptidase-4 inhibitors, or alpha-glucosidase inhibitors was associated with a more than 4-fold increased risk of LDH in the DM cohort. DM was strongly associated with the long-term development of LDH; over the 12-year follow-up period, the cumulative risk of LDH was significantly higher in patients with than without DM (log-rank P<0.001).ConclusionDM is associated with an increased risk of LDH, and advanced DM may indicate a higher risk of LDH

Enhancing the Insulation of Wide-Range Spectrum in the PVA/N Thin Film by Doping ZnO Nanowires

In this study, polyvinyl alcohol/nitrogen (PVA/N) hybrid thin films doped with sharp-sword ZnO nanowires with insulating effect and wide-range spectrum are demonstrated for the first time. PVA/N doped ZnO nanocomposites were developed by blending PVA and N-doped ZnO nanowires in water at room temperature. Measurements from the field emission scanning electron microscopy (FE-SEM), X-ray diffraction (XRD), Raman, and photoluminescence emission (PL) spectra of the products show that nitrogen is successfully doped into the ZnO wurtzite crystal lattice. In addition, the refractive index of PVA/N doped ZnO hybrid thin films can be controlled by varying the doped ZnO nanowires under different NH3 concentrations. It is believed that PVA/N doped ZnO hybrid thin films are a suitable candidate for emerging applications like heat-shielding coatings on smart windows

Emotion and Concentration Integrated System: Applied to the Detection and Analysis of Consumer Preference

With the expansion of consumer market, the appearance becomes an important issue when consumers make decisions under the situation of similar qualities and contents. Accordingly, to attract consumers, companies cost and take much attention on product appearance. Compared to using questionnaires individually, obtaining humans’ thoughts directly from their brains can accurately grasp the actual preference of consumers, which can provide effective and precious decisions for companies. \ In this study, consumers’ brainwaves which are related to concentration and emotion are extracted by wearing a portable and wireless Electroencephalography (EEG) device. The extracted EEG data are then trained by using perceptron learning algorithm (PLA) to make the judgments of concentration and emotion work well with each subject. They are then applied to the detection and analysis of consumer preference. Finally, the questionnaires are also performed and used as the reference on training process. They are integrated with brainwaves data to create one prediction model which can improve the accuracy significantly. The Partial Least Squares is used to compare the correlation between different factors in the model, to ensure the test can accurately meet consumers’ thoughts