American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

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London, December 30: American researchers claim to have solved a cryptic formula that renowned mathematician Srinivasa Ramanujan believed came to him in dreams while on his deathbed, the Daily Mail reported on Saturday.

The formula was contained in a letter he wrote to his mentor, the English mathematician G.H. Hardy, from his deathbed in 1920 outlining several new mathematical functions that had never been heard of before, together with a theory about how they worked. It had baffled mathematicians for more than 90 years, but new findings — presented at a conference at the University of Florida last month — reportedly show that Ramanujan's “hunch” about his formula was right — that it could explain the behaviour of black holes.

“We've solved the problems from his last mysterious letters,” said the well-known American mathematician Ken Ono of Emory University.

“For people who work in this area of math, the problem has been open for 90 years … Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died.”

He said the so-called “deathbed puzzle” which, according to Ramanujan, was revealed to him by the goddess Namagiri, may unlock secrets about black holes. “We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess. No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” said Professor Ono.

The Mail said that Ramanujan's letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

“Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value. Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1,” it said. Nobody at the time understood what the Indian mathematical genius was talking about.

“It wasn't until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Prof. Ono said.

His team, which used modern mathematical tools to solve the puzzle, was “stunned” to find the function could be used even today.

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News Network
June 13,2020

Jun 13: Requiring the wearing of masks to prevent the spread of the novel coronavirus in areas at the epicenter of the global pandemic may have prevented tens of thousands of infections, a new study suggests.

Mask-wearing is even more important for preventing the virus' spread and the sometimes deadly COVID-19 illness it causes than social distancing and stay-at-home orders, researchers said, in the study published in PNAS: The Proceedings of the National Academy of Sciences of the USA.

Infection trends shifted dramatically when mask-wearing rules were implemented on April 6 in northern Italy and April 17 in New York City - at the time among the hardest hit areas of the world by the health crisis - the study found.

"This protective measure alone significantly reduced the number of infections, that is, by over 78,000 in Italy from April 6 to May 9 and over 66,000 in New York City from April 17 to May 9," researchers calculated.

When mask-wearing went into effect in New York, the daily new infection rate fell by about 3% per day, researchers said. In the rest of the country, daily new infections continued to increase.

Direct contact precautions - social distancing, quarantine and isolation, and hand sanitizing - were all in place before mask-wearing rules went into effect in Italy and New York City. But they only help minimize virus transmission by direct contact, while face covering helps prevent airborne transmission, the researchers say.

"The unique function of face covering to block atomization and inhalation of virus-bearing aerosols accounts for the significantly reduced infections," they said. That would indicate "that airborne transmission of COVID-19 represents the dominant route for infection."

The U.S. Center for Disease Control and Prevention on Friday urged organizers of large gatherings that involve "shouting, chanting or singing to strongly encourage the use of cloth face coverings to lower the risk of spreading the coronavirus."

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News Network
June 4,2020

Jun 4: A malaria drug President Donald Trump took to try to prevent COVID-19 proved ineffective for that in the first large, high-quality study to test it in people in close contact with someone with the disease.

Results published Wednesday by the New England Journal of Medicine show that hydroxychloroquine was no better than placebo pills at preventing illness from the coronavirus.

The drug did not seem to cause serious harm, though -- about 40% on it had side effects, mostly mild stomach problems.

 “We were disappointed. We would have liked for this to work,” said the study leader, Dr. David Boulware, an infectious disease specialist at the University of Minnesota.

“But our objective was to answer the question and to conduct a high-quality study,” because the evidence on the drug so far has been inconclusive, he said.

Hydroxychloroquine and a similar drug, chloroquine, have been the subject of much debate since Trump started promoting them in March.

Hydroxychloroquine has long been used for malaria, lupus, and rheumatoid arthritis, but no large studies have shown it or chloroquine to be safe or effective for much sicker patients with coronavirus, and some studies have suggested the drugs may do harm.

Trump took a two-week course of hydroxychloroquine, along with zinc and Vitamin D, after two staffers tested positive for COVID-19, and had no ill effects, according to results of his latest physical released by his doctor Wednesday.

Federal regulators have warned against hydroxychloroquine's use except in hospitals and formal studies because of the risk of side effects, especially heart rhythm problems.

Boulware's study involved 821 people in the United States and Canada living with someone diagnosed with COVID-19 or at high risk of getting it because of their job -- doctors, nurses, ambulance workers who had significant exposure to a sick patient while not wearing full protective gear.

They were randomly assigned to get either the nutrient folate as a placebo or hydroxychloroquine for five days, starting within four days of their exposure. Neither they nor others involved in the research knew who was getting which pills.

After 14 days in the study, 12 per cent on the drug developed COVID-19 symptoms versus 14 per cent in the placebo group, but the difference is so small it could have occurred by chance, Boulware said.

“There's basically no effect. It does not prevent infection,” he said of the drug. Even if it were to give some slim advantage, “we'd want a much larger effect” to justify its use and risk of side effects for preventing illness, he said.

Results were no different among a subgroup of participants who were taking zinc or vitamin C, which some people believe might help make hydroxychloroquine more effective or fight the coronavirus.

There are some big caveats: The study enrolled people through the Internet and social media, relying on them to report their own symptoms rather than having them tracked in a formal way by doctors.

Participants were not all tested for the coronavirus but were diagnosed as COVID-19 cases based on symptoms in many cases. And not all took their medicines as directed.

The results “are more provocative than definitive,” and the drug may yet have prevention benefits if tried sooner or in a different way, Dr. Myron Cohen of the University of North Carolina at Chapel Hill wrote in a commentary in the journal.

Others were glad to see a study that had a comparison group and good scientific methods after so many weaker reports on hydroxychloroquine.

“This fits with everything else we've seen so far which suggests that it's not beneficial," said Dr. Peter Bach, director of a health policy center at Memorial Sloan Kettering Cancer Center in New York.

This study was in younger relatively healthy people, but the results “would make me very discouraged about trying to use this in older people” who are most vulnerable to serious illness from the coronavirus, Bach said.

“If it does work, it doesn't work very well.” Dr. Dan Culver, a lung specialist at the Cleveland Clinic, said there's still a chance that giving the drug sooner than four days after someone's exposure to the virus may help prevent illness.

But the study “takes 'home run' off the table” as far as hopes for the drug, he said.

The study was mostly funded by David Baszucki, founder of Roblox, a California-based game software company, and other private donors and the Minnesota university.

Boulware also is leading a study testing hydroxychloroquine for treating COVID-19. The study is finished and results are being analyzed now.

On Tuesday, the journal Lancet posted an “expression of concern” about a study it published earlier this month of nearly 15,000 COVID-19 patients on the malaria drugs that tied their use to a higher risk of dying in the hospital or developing a heartbeat problem.

Scientists have raised serious questions about the database used for that study, and its authors have launched an independent audit.

That work had a big impact: the World Health Organization suspended use of hydroxychloroquine in a study it is leading, and French officials stopped the drug's use in hospitals. On Wednesday, the WHO said experts who reviewed safety information decided that its study could resume.

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Agencies
May 23,2020

Washington, May 23: President Donald Trump has labeled churches and other houses of worship as “essential" and called on governors nationwide to let them reopen this weekend even though some areas remain under coronavirus lockdown.

The president threatened Friday to “override” governors who defy him, but it was unclear what authority he has to do so.

“Governors need to do the right thing and allow these very important essential places of faith to open right now — for this weekend," Trump said at a hastily arranged press conference at the White House. Asked what authority Trump might have to supersede governors, White House press secretary Kayleigh McEnany said she wouldn't answer a theoretical question.

Trump has been pushing for the country to reopen as he tries to reverse an economic free fall playing out months before he faces reelection. White evangelical Christians have been among the president's most loyal supporters, and the White House has been careful to attend to their concerns throughout the crisis.

Following Trump's announcement, the Centers for Disease Control and Prevention released new guidelines for communities of faith on how to safely reopen, including recommendations to limit the size of gatherings and consider holding services outdoors or in large, well-ventilated areas.

Public health agencies have generally advised people to avoid gatherings of more than 10 people and encouraged Americans to remain 6 feet (1.8 meters) away from others when possible. Some parts of the country remain under some version of remain-at-home orders.

In-person religious services have been vectors for transmission of the virus. A person who attended a Mother's Day service at a church in Northern California that defied the governor's closure orders later tested positive, exposing more than 180 churchgoers. And a choir practice at a church in Washington state was labeled by the CDC as an early “superspreading" event.

But Trump on Friday stressed the importance of churches in many communities and said he was “identifying houses of worship — churches, synagogues and mosques — as essential places that provide essential services.”

“Some governors have deemed liquor stores and abortion clinics as essential” but not churches, he said. “It's not right. So I'm correcting this injustice and calling houses of worship essential." “These are places that hold our society together and keep our people united,” he added.

Dr. Deborah Birx, coordinator of the White House coronavirus task force, said faith leaders should be in touch with local health departments and can take steps to mitigate risks, including making sure those who are at high risk of severe complications remain protected.

“There's a way for us to work together to have social distancing and safety for people so we decrease the amount of exposure that anyone would have to an asymptomatic," she said.

A person familiar with the White House's thinking who spoke on condition of anonymity to discuss internal deliberations said Trump had called the news conference, which had not been on his public schedule, because he wanted to be the face of church reopenings, knowing how well it would play with his political base.

Churches around the country have filed legal challenges opposing virus closures.

In Minnesota, after Democratic Gov. Tim Walz this week declined to lift restrictions on churches, Roman Catholic and some Lutheran leaders said they would defy his ban and resume worship services. They called the restrictions unconstitutional and unfair since restaurants, malls and bars were allowed limited reopening.

Some hailed the president's move, including Kelly Shackelford, president of the conservative First Liberty Institute.

“The discrimination that has been occurring against churches and houses of worship has been shocking," he said in a statement. "Americans are going to malls and restaurants. They need to be able to go to their houses of worship.” But Rabbi Jack Moline, president of Interfaith Alliance, said it was “completely irresponsible” for Trump to call for a mass reopening of houses of worship.

“Faith is essential and community is necessary; however, neither requires endangering the people who seek to participate in them,” he said.

“The virus does not discriminate between types of gatherings, and neither should the president." Rhode Island Gov. Gina Raimondo, a Democrat, made clear that churches and other houses of worship will not resume in-person services in her state until at least next weekend and said she was skeptical Trump had the authority to impose such a requirement.

“It's reckless to force them to reopen this weekend. They're not ready,” she said. “We've got a good plan. I'm going to stick with it.” New Hampshire Gov. Chris Sununu, a Republican, said he would review the federal guidance, while maintaining a decision rests with him.

"Obviously we'd love to get to the point where we can get those open, but we'll look at the guidance documents and try to make some decisions rather quickly, depending on what it might say,” he said. “It's the governor's decision, of course.”

The CDC more than a month ago sent the Trump administration documents the agency had drafted outlining specific steps various kinds of organizations, including houses of worship, could follow as they worked to reopen safely.

But the White House dragged its feet, concerned that the recommendations were too specific and could give the impression the administration was interfering in church operations.

The guidance posted Friday contains most of the same advice as the draft guidance. It calls for the use of face coverings and recommends keeping worshippers 6 feet from one another and cutting down on singing, which can spread aerosolized drops that carry the virus.

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