Sticky Brownian Rounding and its Applications to Constraint Satisfaction Problems

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively studied for more than two decades, resulting in various extensions to the original technique and beautiful algorithms for a wide range of applications. Despite the fact that this approach yields tight approximation guarantees for some problems, e.g., Max-Cut, for many others, e.g., Max-SAT and Max-DiCut, the tight approximation ratio is still unknown. One of the main reasons for this is the fact that very few techniques for rounding semidefinite relaxations are known. In this work, we present a new general and simple method for rounding semi-definite programs, based on Brownian motion. Our approach is inspired by recent results in algorithmic discrepancy theory. We develop and present tools for analyzing our new rounding algorithms, utilizing mathematical machinery from the theory of Brownian motion, complex analysis, and partial differential equations. Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut, Max-2SAT, and MaxDiCut, and derive new algorithms that are competitive with the best known results. To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration results for the Sticky Brownian Motion, a feature missing from hyperplane rounding and its generalization

Management of stripe rust of barley (Hordeum vulgare L.) using fungicides

Under field conditions, various fungicide molecules were validated for their effectiveness on barley (Hordeum vulgare L.) stripe rust Puccinia striiformis f. sp. consecutively for three years under artificial field epiphytotic conditions. Seven fungicides viz., propiconazole 25%EC (tilt @ 0.1%), tebuconazole 25.9% m/m EC (folicur @ 0.1%), triademefon 25%WP (bayleton @ 0.1%), propiconazole 25%EC (tilt @ 0.05%), tebuconazole 25.9% m/m EC (folicur @ 0.05%), triademefon 25%WP (bayleton@ 0.05%), and mancozeb 75%WP (dithane M45 @ 0.2%) with variousconcentrations were tested for their effectiveness in controlling barley stripe rust severity. All fungicide applications resulted in lower disease severity and higher grain yields than untreated check plots. All the fungicides @ 0.1% concentrations reduced disease severity ranging from 87.8% to 95.6% except Mancozeb @ 0.2% (34.4%). Significant higher yield was obtained with Propiconazole @ 0.1% (26.7 q/ha) followed by Tebuconazole @ 0.1% (25.2 q/ha) and Triademefon @ 0.1% (24.5 q/ha). The present study revealed propiconazole as the most effective fungicide for the control of stripe rust of barley under epiphytotic conditions

Upcoming Aeon of Cryptocurrency

The virtual sector requires laws and regulation, and prohibiting cryptocurrencies would limit their growth potential. We are living in an age of exponential technological breakthroughs. We've progressed from mobile banking to stock exchange to cryptocurrency. These technological advancements have already made life more manageable and feasible. According to some sources, India's largest cryptocurrency exchanges - WazirX, CoinDCX, and Unocoin - estimate that the nation has between 60 lakh and one crore cryptocurrency holders with combined balances of more than Rs 10,000 crore1. Globally, cryptocurrency has gained traction. We are technologically advanced age, and any progress will undoubtedly represent a danger. There is tremendous potential for investors, but it also carries risk. The phrase "virtual money" refers to an intangible means of trade that is not legal money; "cryptocurrency" is a subset of virtual money. As cryptocurrencies gained popularity, governments, central banks, and regulators started to show curiosity, curiosity, and skepticism

A Comparative Study of Masanumasik Garbha Vikas Krama according to Ayurveda with Its Clinical Importance

In universe human is the best creation of Nature. It is a miracle and wonder of the nature which have proper shape, size and weight of human body. Procuring a baby is a lifetime dream of every female in the society. A malformed alive fetus is one of the worst aspects of pregnancy. Ayurveda gives precise description of Garbha Vriddhi and Vikas Kram, though there were no modern imaging techniques like sonography, MRI etc. Different Texts of Ayurveda gives various views regarding Garbha Utpattiand Garbha Vriddhi. Ayurveda has   also mentioned Garbhini Lakshana which are helpful in diagnosis of early pregnancy and prevents the fetal anamolies. This study is an attempt to elaborate and compare both ancient and modern concept of embryogenesis and its clinical significance.&nbsp

Sticky Brownian rounding and its applications to constraint satisfaction problems

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson [23] has been extensively studied for more than two decades, resulting in various extensions to the original technique and beautiful algorithms for a wide range of applications. Despite the fact that this approach yields tight approximation guarantees for some problems, e.g., Max-Cut, for many others, e.g., Max-SAT and Max-DiCut, the tight approximation ratio is still unknown. One of the main reasons for this is the fact that very few techniques for rounding semidefinite relaxations are known. In this work, we present a new general and simple method for rounding semi-definite programs, based on Brownian motion. Our approach is inspired by recent results in algorithmic discrepancy theory. We develop and present tools for analyzing our new rounding algorithms, utilizing mathematical machinery from the theory of Brownian motion, complex analysis, and partial differential equations. Focusing on constraint satisfaction problems, we apply our method to several classical problems, including Max-Cut, Max-2SAT, and Max-DiCut, and derive new algorithms that are competitive with the best known results. To illustrate the versatility and general applicability of our approach, we give new approximation algorithms for the Max-Cut problem with side constraints that crucially utilizes measure concentration results for the Sticky Brownian Motion, a feature missing from hyperplane rounding and its generalizations

Evolution and Growth of Alternative Dispute Resolution in India with Special Emphasis on Mediation

The Constitution of India charges the state to verify social, financial and political equity to every one of its residents, in this manner making the established command for expedient equity certain through Article 141 which ensures correspondence under the watchful eye of the law and the equivalent assurance of the laws and through article 39A2 the constitution orders the State to verify the task of the lawful framework so that it advances equity on a premise of equivalent chance and guarantees that the equivalent isn't denied to any native by reason of monetary or different handicaps further equivalent open door must be managed for access to equity as it isn't adequate that the law treats all people similarly, regardless of the predominant imbalances it must be ensured that the law must capacity so that every one of the general population approach equity notwithstanding monetary difference

Section 3 of The Competition Act: Selective Distribution Agreements and Luxury Goods

Through this Research Paper, the author aims to establish that it may be vital for luxury brands to develop an elaborate selective distribution system in order to choose its authorized sellers and distributors. This distribution system cannot be said to be a violation of Sec. 3 of the Competition act, as such a distribution system is necessary to promote its brand image as well as to preserve its aura of luxury, that it delivers or promises to deliver to its consumers

The effect of total arterial grafting on medium-term outcomes following coronary artery bypass grafting

<p>Abstract</p> <p>Background</p> <p>While it is believed that total arterial grafting (TAG) for coronary artery bypass grafting (CABG) confers improved long-term outcomes when compared to conventional grafting with left internal mammary artery and saphenous vein grafts (LIMA+SVG), to date, this has not become the standard of care. In this study, we assessed the impact of TAG on medium-term outcomes after CABG.</p> <p>Methods</p> <p>Peri-operative data was prospectively collected on consecutive first-time, isolated CABG patients between 1995 and 2005. Patients were divided into two groups based on grafting strategy: TAG (all arterial grafts no saphenous veins) or LIMA+SVG. Patients who had an emergent status or underwent fewer than two distal bypasses were excluded. Medium term univariate and risk-adjusted comparisons between TAG and LIMA+SVG cases were performed.</p> <p>Results</p> <p>A total of 4696 CABG patients were included with 1019 patients undergoing TAG (22%). Unadjusted in-hospital mortality was 1.5% for TAG patients compared to 2.0% for LIMA+SVG (p = 0.31). The mean follow-up was 4.8 ± 2.0 years for TAG patients compared to 6.1 ± 3.0 years for LIMA+SVG patients (p < 0.0001). At follow-up total mortality (8% vs 19%; p < 0.0001), and the incidence of readmission to hospital for cardiac reasons (29% vs 38%; p < 0.0001) were significantly lower in TAG compared to LIMA+SVG patients. However, after adjusting for clinical covariates, TAG did not emerge as a significant independent predictor of long-term mortality (HR 0.92; CI 0.71–1.18), readmission to hospital (HR 1.02; CI 0.89–1.18) or the composite outcome of mortality and readmission (HR 1.00; CI 0.88–1.15). Risk adjusted survival was better than 88% in both TAG and LIMA-SVG patients at 5 years follow-up.</p> <p>Conclusion</p> <p>Patients undergoing TAG appear to experience lower rates of medium-term all-cause mortality and readmission to hospital for any cardiac cause when compared to patients undergoing LIMA+SVG. However, after adjusting for clinical variables, this difference no longer persists suggesting that at median follow-up there are no mortality or morbidity benefit based on the choice of conduit.</p

Crossing boundaries:bras, lingerie and rape myths in postcolonial urban middle-class India

With the processes of modernization, urbanization and the entry of women in the formal labour market in Indian metropolitan spaces, this paper examines how the modern middle-class woman’s sartorial choices become enmeshed in popular rape myths (false beliefs) that serve to blame her for the wearing of western clothing. The paper articulates the ways in which middle-class women’s social realities are shaped by historical, colonial and nationalist ideologies of modernization, constructed and mediated through moral codes of dressing. By drawing upon original and contemporary empirical narratives from the urban spaces of Delhi and Mumbai, we emphasise how everyday sartorial choices, in relation to particularly the bra and lingerie, can reveal the nuanced ways in which Urban Indian Professional Women (UIPW) seek to understand, negotiate, and resist patriarchal power. Our findings shed light on conflicting and contradictory spatial experiences, where some women internalize and negotiate moral codes of dressing, out of fear, and others who transgress are subject to sanctions. Given the paucity of scholarly literature in this area, the paper makes an important theoretical and empirical contribution with its focus on postcoloniality and everyday discursive material spaces of gendered and sexualized dress practices. It argues for the consciousness raising of everyday urban geographies of dress that reveal complicated structures of power that are often deemed hidden