Strictly Balancing Matrices in Polynomial Time Using Osborne\u27s Iteration

Osborne\u27s iteration is a method for balancing n x n matrices which is widely used in linear algebra packages, as balancing preserves eigenvalues and stabilizes their numeral computation. The iteration can be implemented in any norm over R^n, but it is normally used in the L_2 norm. The choice of norm not only affects the desired balance condition, but also defines the iterated balancing step itself. In this paper we focus on Osborne\u27s iteration in any L_p norm, where p < infty. We design a specific implementation of Osborne\u27s iteration in any L_p norm that converges to a strictly epsilon-balanced matrix in O~(epsilon^{-2}n^{9} K) iterations, where K measures, roughly, the number of bits required to represent the entries of the input matrix. This is the first result that proves a variant of Osborne\u27s iteration in the L_2 norm (or any L_p norm, p < infty) strictly balances matrices in polynomial time. This is a substantial improvement over our recent result (in SODA 2017) that showed weak balancing in L_p norms. Previously, Schulman and Sinclair (STOC 2015) showed strict balancing of another variant of Osborne\u27s iteration in the L_infty norm. Their result does not imply any bounds on strict balancing in other norms

Developmental screening of children with congenital hypothyroidism using Ages & Stages Questionnaires test.

 Abstract:Objectives: Congenital hypothyroidism (CH) is one of the most common causes of mental retardation in children. This study investigated the developmental status of children with CH screened by Ages &amp; Stages Questionnaires (ASQ) measurement scores.Materials &amp; Methods: In this retrospective study, neurodevelopmental status of 78 children diagnosed with CH who being followed up at the outpatient Pediatric Endocrinology Clinic of Besat Hospital, Hamadan, Iran, was evaluated by ASQ method. Data on age, sex, birth body weight, height and head circumference, residency location, parental education level, primary venous TSH and T4 level, diagnosis age, treatment start age and initial levothyroxine dosage were extracted from medical records .Data analyzed using statistical software SPSS v16. P-value less than 0.05 was considered statistically significant.Results: Of the 78 patients (34=43.6% female), 32 patients (41%) had developmental disorder. 56 cases (71.8%) were living in urban areas. In terms of type of developmental impairment, global delay: 13 patients (40.6%), problem solving: 11 patients (34.3%), communication: 5 patients (15.6%), fine motor: 2 patients (6.2%) and personal-social: 1 patient (3.1%) were detected. The average of diagnosis and treatment age was 25.65 days in patients with developmental impairment and 17.99 days in those without delay. ASQ results had significant statistical correlation with initial dose of levothyroxine (p=0.017), hypothyroidism diagnosis age (p=0.002) and age of treatment initiation (p=0.018).Conclusions: Early diagnosis and treatment along with initial L-thyroxin dose were most important factor of ASQ scores of children with CH. Higher amounts of the LT4 is required at onset

On a Linear Program for Minimum-Weight Triangulation

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial- time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: for an LP formulation due to Dantzig et al. (1985): (i) the integrality gap is bounded by a constant; (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201

Third-harmonic generation and imaging with resonant Si membrane metasurface

Dielectric metasurfaces play an increasingly important role in enhancing optical nonlinear generations owing to their ability to support strong light-matter interactions based on Mie-type multipolar resonances. Compared to metasurfaces composed of the periodic arrangement of nanoparticles, inverse, so-called, membrane metasurfaces offer unique possibilities for supporting multipolar resonances, while maintaining small unit cell size, large mode volume and high field enhancement for enhancing nonlinear frequency conversion. Here, we theoretically and experimentally investigate the formation of bound states in the continuum (BICs) from silicon dimer-hole membrane metasurfaces. We demonstrate that our BIC-formed resonance features a strong and tailorable electric near-field confinement inside the silicon membrane films. Furthermore, we show that by tuning the gap between the holes, one can open a leaky channel to transform these regular BICs into quasi-BICs, which can be excited directly under normal plane wave incidence. To prove the capabilities of such metasurfaces, we demonstrate the conversion of an infrared image to the visible range, based on the Third-harmonic generation (THG) process with the resonant membrane metasurfaces. Our results suggest a new paradigm for realising efficient nonlinear photonics metadevices and hold promise for extending the applications of nonlinear structuring surfaces to new types of all-optical near-infrared imaging technologies

Species Composition and Spatial Distribution of Medically Important Scorpions in the Northern Part of Kerman Province, Iran

Background: Kerman Province is one of the endemic foci of scorpionism in southeastern Iran. Totally 17 species are reported for Kerman Province fauna. The current study seeks to determine the fauna of medically important scorpions in northern parts of this province. Methods: A descriptive cross-sectional study was conducted from January 2019 to March 2021. The specimens were captured from different areas, by rock-rolling during day and using Ultraviolet light at night. The specimens were pre­served in ethanol (80%) and then identified using reliable identification keys for scorpions. Results: Totally, 499 specimens were captured from eight cities in northern Kerman. In total, 11 species belonging to three families were identified. Buthacus sp. is reported for the first time from Kerman Province. Buthacus sp., Hotten­totta cf. juliae, and Hottentotta cf. schach, were the lowest in frequency of occurrence, against Mesobuthus navidpouri as the highest frequency. Conclusion: The results of this study are useful for the preparation of regional or monovalent antivenom for the Razi Vaccine and Serum Research Institute. Additionally, the obtained data are useful for the effective planning of scorpion control programs in the northern parts of Kerman Province, Iran

Global injury morbidity and mortality from 1990 to 2017 : results from the Global Burden of Disease Study 2017

Correction:Background Past research in population health trends has shown that injuries form a substantial burden of population health loss. Regular updates to injury burden assessments are critical. We report Global Burden of Disease (GBD) 2017 Study estimates on morbidity and mortality for all injuries. Methods We reviewed results for injuries from the GBD 2017 study. GBD 2017 measured injury-specific mortality and years of life lost (YLLs) using the Cause of Death Ensemble model. To measure non-fatal injuries, GBD 2017 modelled injury-specific incidence and converted this to prevalence and years lived with disability (YLDs). YLLs and YLDs were summed to calculate disability-adjusted life years (DALYs). Findings In 1990, there were 4 260 493 (4 085 700 to 4 396 138) injury deaths, which increased to 4 484 722 (4 332 010 to 4 585 554) deaths in 2017, while age-standardised mortality decreased from 1079 (1073 to 1086) to 738 (730 to 745) per 100 000. In 1990, there were 354 064 302 (95% uncertainty interval: 338 174 876 to 371 610 802) new cases of injury globally, which increased to 520 710 288 (493 430 247 to 547 988 635) new cases in 2017. During this time, age-standardised incidence decreased non-significantly from 6824 (6534 to 7147) to 6763 (6412 to 7118) per 100 000. Between 1990 and 2017, age-standardised DALYs decreased from 4947 (4655 to 5233) per 100 000 to 3267 (3058 to 3505). Interpretation Injuries are an important cause of health loss globally, though mortality has declined between 1990 and 2017. Future research in injury burden should focus on prevention in high-burden populations, improving data collection and ensuring access to medical care.Peer reviewe