Almost-Tight Distributed Minimum Cut Algorithms

We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let $\lambda$ be the minimum cut, $n$ be the number of nodes in the network, and $D$ be the network diameter. Our algorithm can compute $\lambda$ exactly in $O((\sqrt{n} \log^{*} n+D)\lambda^4 \log^2 n)$ time. To the best of our knowledge, this is the first paper that explicitly studies computing the exact minimum cut in the distributed setting. Previously, non-trivial sublinear time algorithms for this problem are known only for unweighted graphs when $\lambda\leq 3$ due to Pritchard and Thurimella's $O(D)$-time and $O(D+n^{1/2}\log^* n)$-time algorithms for computing $2$-edge-connected and $3$-edge-connected components. By using the edge sampling technique of Karger's, we can convert this algorithm into a $(1+\epsilon)$-approximation $O((\sqrt{n}\log^{*} n+D)\epsilon^{-5}\log^3 n)$-time algorithm for any $\epsilon>0$. This improves over the previous $(2+\epsilon)$-approximation $O((\sqrt{n}\log^{*} n+D)\epsilon^{-5}\log^2 n\log\log n)$-time algorithm and $O(\epsilon^{-1})$-approximation $O(D+n^{\frac{1}{2}+\epsilon} \mathrm{poly}\log n)$-time algorithm of Ghaffari and Kuhn. Due to the lower bound of $\Omega(D+n^{1/2}/\log n)$ by Das Sarma et al. which holds for any approximation algorithm, this running time is tight up to a $\mathrm{poly}\log n$ factor. To get the stated running time, we developed an approximation algorithm which combines the ideas of Thorup's algorithm and Matula's contraction algorithm. It saves an $\epsilon^{-9}\log^{7} n$ factor as compared to applying Thorup's tree packing theorem directly. Then, we combine Kutten and Peleg's tree partitioning algorithm and Karger's dynamic programming to achieve an efficient distributed algorithm that finds the minimum cut when we are given a spanning tree that crosses the minimum cut exactly once

STABITY INDICATING DISSOLUTION METHOD DEVELOPMENT FOR ESTIMATION OF METHYLDOPA AND HYDROCHLOROTHIAZIDE IN COMBINE DOSAGE FORM

The aim of this work was to develop validate a dissolution test for Methyldopa and Hydrochlorothiazide in combination tablets using spectrophotometric method. The dissolution established conditions were 900 mL of 0.1M HCl pH 1.0 as dissolution medium, using a paddle apparatus at a stirring rate of 50 rpm. The drug release was evaluated by UV spectrophotometric method the areas of solution were recorded at 274-284 nm and266-276 nm for Methyldopa and Hydrochlorothiazide respectively. It can be concluded that the method developed consists in an efficient alternative for assay of dissolution for tablets. The method was validated to meet requirements for a global regulatory filing which includes linearity, precision, accuracy robustness and ruggedness. In addition, filter suitability and drug stability in medium were demonstrated Keywords: In vitro release, Stability, Dissolution study of methyldopa and Hydrochlorothiazide, Spectrophotometry, Area under curve method, Validation

Muon anomalous magnetic moment, lepton flavor violation, and flavor changing neutral current processes in SUSY GUT with right-handed neutrino

Motivated by the large mixing angle solutions for the atmospheric and solar neutrino anomalies, flavor changing neutral current processes and lepton flavor violating processes as well as the muon anomalous magnetic moment are analyzed in the framework of SU(5) SUSY GUT with right-handed neutrino. In order to explain realistic mass relations for quarks and leptons, we take into account effects of higher dimensional operators above the GUT scale. It is shown that the supersymmetric (SUSY) contributions to the CP violation parameter in $K^0-\bar{K}^0$ mixing, $\epsilon_K$, the $\mu \to e \gamma$ branching ratio, and the muon anomalous magnetic moment become large in a wide range of parameter space. We also investigate correlations among these quantities. Within the current experimental bound of $\text{B}(\mu \to e \gamma)$, large SUSY contributions are possible either in the muon anomalous magnetic moment or in $\epsilon_K$. In the former case, the favorable value of the recent muon anomalous magnetic moment measurement at the BNL E821 experiment can be accommodated. In the latter case, the allowed region of the Kobayashi-Maskawa phase can be different from the prediction within the Standard Model (SM) and therefore the measurements of the CP asymmetry of $B\to J/\psi K_S$ mode and $\Delta m_{B_s}$ could discriminate this case from the SM. We also show that the $\tau \to \mu \gamma$ branching ratio can be close to the current experimental upperbound and the mixing induced CP asymmetry of the radiative B decay can be enhanced in the case where the neutrino parameters correspond to the Mikheyev-Smirnov-Wolfenstein small mixing angle solution.Comment: 70 pages, 14 figure

Tracking development assistance for health and for COVID-19 : a review of development assistance, government, out-of-pocket, and other private spending on health for 204 countries and territories, 1990-2050

Background The rapid spread of COVID-19 renewed the focus on how health systems across the globe are financed, especially during public health emergencies. Development assistance is an important source of health financing in many low-income countries, yet little is known about how much of this funding was disbursed for COVID-19. We aimed to put development assistance for health for COVID-19 in the context of broader trends in global health financing, and to estimate total health spending from 1995 to 2050 and development assistance for COVID-19 in 2020. Methods We estimated domestic health spending and development assistance for health to generate total health-sector spending estimates for 204 countries and territories. We leveraged data from the WHO Global Health Expenditure Database to produce estimates of domestic health spending. To generate estimates for development assistance for health, we relied on project-level disbursement data from the major international development agencies' online databases and annual financial statements and reports for information on income sources. To adjust our estimates for 2020 to include disbursements related to COVID-19, we extracted project data on commitments and disbursements from a broader set of databases (because not all of the data sources used to estimate the historical series extend to 2020), including the UN Office of Humanitarian Assistance Financial Tracking Service and the International Aid Transparency Initiative. We reported all the historic and future spending estimates in inflation-adjusted 2020 US$, 2020 US$ per capita, purchasing-power parity-adjusted US$per capita, and as a proportion of gross domestic product. We used various models to generate future health spending to 2050. Findings In 2019, health spending globally reached$8. 8 trillion (95% uncertainty interval [UI] 8.7-8.8) or $1132 (1119-1143) per person. Spending on health varied within and across income groups and geographical regions. Of this total,$40.4 billion (0.5%, 95% UI 0.5-0.5) was development assistance for health provided to low-income and middle-income countries, which made up 24.6% (UI 24.0-25.1) of total spending in low-income countries. We estimate that $54.8 billion in development assistance for health was disbursed in 2020. Of this,$13.7 billion was targeted toward the COVID-19 health response. $12.3 billion was newly committed and$1.4 billion was repurposed from existing health projects. $3.1 billion (22.4$2.4 billion (17.9%) was for supply chain and logistics. Only $714.4 million (7.7$1519 (1448-1591) per person in 2050, although spending across countries is expected to remain varied. Interpretation Global health spending is expected to continue to grow, but remain unequally distributed between countries. We estimate that development organisations substantially increased the amount of development assistance for health provided in 2020. Continued efforts are needed to raise sufficient resources to mitigate the pandemic for the most vulnerable, and to help curtail the pandemic for all. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

All-sky search for long-duration gravitational wave transients with initial LIGO

We present the results of a search for long-duration gravitational wave transients in two sets of data collected by the LIGO Hanford and LIGO Livingston detectors between November 5, 2005 and September 30, 2007, and July 7, 2009 and October 20, 2010, with a total observational time of 283.0 days and 132.9 days, respectively. The search targets gravitational wave transients of duration 10-500 s in a frequency band of 40-1000 Hz, with minimal assumptions about the signal waveform, polarization, source direction, or time of occurrence. All candidate triggers were consistent with the expected background; as a result we set 90% confidence upper limits on the rate of long-duration gravitational wave transients for different types of gravitational wave signals. For signals from black hole accretion disk instabilities, we set upper limits on the source rate density between 3.4×10-5 and 9.4×10-4 Mpc-3 yr-1 at 90% confidence. These are the first results from an all-sky search for unmodeled long-duration transient gravitational waves. © 2016 American Physical Society