A Generalization of the Doubling Construction for Sums of Squares Identities

The doubling construction is a fast and important way to generate new solutions to the Hurwitz problem on sums of squares identities from any known ones. In this short note, we generalize the doubling construction and obtain from any given admissible triple $[r,s,n]$ a series of new ones $[r+\rho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m$, where $\rho$ is the Hurwitz-Radon function

Frugal Optimization for Cost-related Hyperparameters

The increasing demand for democratizing machine learning algorithms calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters which can cause a large variation in the training cost. But this effect is largely ignored in existing HPO methods, which are incapable to properly control cost during the optimization process. To address this problem, we develop a new cost-frugal HPO solution. The core of our solution is a simple but new randomized direct-search method, for which we prove a convergence rate of $O(\frac{\sqrt{d}}{\sqrt{K}})$ and an $O(d\epsilon^{-2})$-approximation guarantee on the total cost. We provide strong empirical results in comparison with state-of-the-art HPO methods on large AutoML benchmarks.Comment: 29 pages (including supplementary appendix

How to Fine-Tune BERT for Text Classification?

Language model pre-training has proven to be useful in learning universal language representations. As a state-of-the-art language model pre-training model, BERT (Bidirectional Encoder Representations from Transformers) has achieved amazing results in many language understanding tasks. In this paper, we conduct exhaustive experiments to investigate different fine-tuning methods of BERT on text classification task and provide a general solution for BERT fine-tuning. Finally, the proposed solution obtains new state-of-the-art results on eight widely-studied text classification datasets

ANALYSES OF MULTIVITAMINS IN NUTRACEUTICALS BY REVERSE PHASE HPLC WITH DAD, ELSD AND MS

ABSTRACT Vitamins are essential to human beings and support long-term healthy lifestyle. They exist widely in food, but in small amount. Hence, dietary supplements and fortified food products are more and more popular in the nutritional markets. According to the Infant Formula Act of 1980, the range of each of the nutrients should fall within a specific range or above the required minimum, so there is an increasing interest of accurate measurement of vitamins, particularly the B-group vitamins. However, traditional methods for vitamin B analyses are time-consuming and often in poor accuracy. As a result, rapid and reliable analytical methods for simultaneous determination of water-soluble vitamins in multivitamin and supplemented foods are important, indispensible and needed by food and nutraceutical industries for quality control during production, and for accurate evaluation of data and label clams. Due to low concentrations of B8 and B9 in nature, there is a critical need for preconcentration to facilitate their isolation and purification from a complex matrix like food. In order to minimize the consumption of solvents, solid phase extraction (SPE) has been introduced for sample preparation. In this study, two types of SPE, i.e., reversed-phase C18 and strong anion-exchange phase, were used for sample clean-up and pre-concentration. The average recoveries for vitamin B3, B5, B7 and B9 were 101.3%, 102.9%, 92.8% and 102.6%, respectively, by using C18 SPE. In contrast, the strong anion-exchange SPE provided the average recoveries of B3, B5, B7 and B9 in 91.5%, 93.0%, 109.1% and 106.7%, respectively. Furthermore, simultaneous determination of water-soluble vitamins was developed by a HPLC system installed with a ZORBAX Eclipse XDB-C18 (250mm x 4.6mm, 5 μm particle size, Aglient Technologies, Inc., Loveland, CO, USA) with a guard column (12.5mm x 4.6mm, 5 μm particle size), and compared by three detectors, including DAD, ELSD and MS. The B-complex supplement, multivitamin/multimineral tablets and powder and vitamin drink were tested to verify HPLC method. According to the results, LC-MS is the best to do the simultaneous determination of the B-group vitamins in lights of its analytical accuracy, precision, sensitivity and versatility

The production of textile fibers from soy proteins

The use of soy protein presently is limited mostly to animal feeds, but the markets for soy protein could be expanded by industrial applications. In these studies, soy fibers were produced from soy protein isolate using both wet spinning and extrusion methods. The wet spinning process consisted of forcing an aged alkaline protein solution through a spinnerette having 368-[mu] openings into an acid coagulating bath. The extrusion process employed a twin screw extruder to force a protein-water mixture with dough-like consistency through a die also with 368-[mu] openings. The physical properties of the fibers were measured at 11% and 65% relative humidity and wet conditions using an Instron Universal Testing Machine. The fibers produced by both methods initially were brittle and very weak. The addition of glycerol reduced brittleness in extruded fibers and the inorganic ions zinc and calcium decreased the brittleness of wet-spun fibers. Modification of soy proteins by acylation with acetic anhydride or esterification with low molecular weight alcohols prior to extrusion to block the polar groups of soy proteins decreased the tenacity of the fibers. The tenacity of soy fibers was significantly improved by finishing treatments after extrusion using reagents such as acetic anhydride, glyoxal, glutaraldehyde or a combination of glutaraldehyde and acetic anhydride. The fibers finished with acetic anhydride or glutaraldehyde after extrusion became less polar by blocking the polar groups or cross-linking protein molecules. The conditions of finishing fibers and stretching fibers were studied to improve fiber properties. Scanning electron micrographs of the fibers revealed that strong fibers were smooth and continuous while weak fibers often contained cracks and voids

Cardiovascular magnetic resonance and right ventricular angiography in assessment of right ventricular volumes, function and wall motion abnormalities in arrhythmogenic right ventricular cardiomyopathy: a comparative study

Background: Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited cardiomyopathy characterised by structural changes to mostly the right ventricle (RV) that predisposes to ventricular arrhythmias heart failure and sudden cardiac death. ARVC is diagnosed using the 2010 Task Force Criteria which include RV angiography (RVA) and cardiovascular magnetic resonance (CMR). There has been a dearth of studies to document the comparison of the performance of CMR and RVA, and none undertaken in Africa. The aim of this study was to compare CMR and RVA in the assessment of ARVC in the South African ARVC registry. Methods: The study is a retrospective analysis of definite, possible and borderline ARVC cases from the South African ARVC registry and the African Cardiomyopathy and Myocarditis Registry Program (IMHOTEP) that have both CMR and RVA data. RV end-systolic and diastolic volumes, RV ejection fractions and the presence of absence of structural abnormalities derived from RVA and CMR are compared. Sensitivity of CMR and RVA for the diagnosis of definite, possible and borderline ARVC was also calculated. Results: A total of 11 patients out of 62 from the registry met the inclusion criteria. The Spearman’s coefficient for RV end-systolic volume was 0.48 (p=0.12). The Spearman’s coefficient for RV enddiastolic volume was 0.28 (p=0.4). The Spearman’s coefficient for RV ejection fraction was 0.06 (p=0.85). CMR detected regional wall abnormalities in 4 out of 11 patients while RVA did not detect any regional wall abnormalities. Sensitivity of CMR and RVA for the diagnosis of definite, possible and borderline ARVC was 48% and 55%, respectively. Conclusions: We show that South African ARVC patients had poor correlation between CMR and RVA parameters, and CMR was also more likely to reveal RV free wall regional wall motion abnormalities