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 12,2020

Jun 12: The global number of COVID-19 cases has increased to over 7.5 million, while the death toll was nearing 421,000, according to the Johns Hopkins University.

As of Friday morning, the overall number of cases stood at 7,500,777, while the deaths increased to 420,993, the University's Center for Systems Science and Engineering (CSSE) revealed in its latest update.

The US continues with the world's highest number of confirmed cases and deaths at 2,022,488 and 113,803, respectively, according to the CSSE.

In terms of cases, Brazil comes in the second place with 802,828 infections.

This was followed by Russia (501,800), the UK (292,860), India (286,605), Spain (242,707), Italy (236,142), Peru (214,788), France (192,493), Germany (186,691), Iran (180,156), Turkey (174,023), Chile (154,092), Mexico (133,974), Pakistan (125,933) and Saudi Arabia (116,021), the CSSE figures showed.

Regarding fatalities, the UK continues in the second position after the US with 41,364 COVID-19 deaths, which also accounts for the highest number of fatalities in Europe.

The other countries with over 10,000 deaths are Brazil (40,919), Italy (34,167), France (29,349), Spain (27,136) and Mexico (15,944).

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April 5,2020

Washington, Apr 5: US President Donald Trump on Saturday said that he has requested Prime Minister Narendra Modi to supply Hydroxychloroquine tablets that can be used to treat COVID-19 patients.

"After call today with Indian Prime Minister Narendra Modi, India is giving serious consideration to releasing the hold it put on a US order for hydroxychloroquine," Trump announced at the White House Coronavirus task force briefing that he requested PM Narendra Modi for more Hydroxychloroquine tablets.

President Trump did not shy away from saying he too will take a tablet of hydroxychloroquine after announcing that he has requested Prime Minister during his telephonic conversation earlier today to lift a hold on the US order of the medicine.

"I may take it too, will have to talk to my doctors," he added.

"India makes a lot of it. They need a lot too for their billion-plus people. 

The hydroxychloroquine, the anti-malaria drug will be released through the Strategic National Stockpile for treatment," he said.

"I said I would appreciate if they would release the amounts that we ordered" of hydroxychloroquine, he said.

The Indian government has put on hold the export of anti-malarial drug hydroxychloroquine and its formulations.

Prime Minister Narendra Modi said on Twitter, "Had an extensive telephone conversation with President @realDonaldTrump. 

We had a good discussion, and agreed to deploy the full strength of the India-US partnership to fight COVID-19."

Prime Minister conveyed deep condolences for the loss of lives in the United States and his prayers for the early recovery of those still suffering from the disease.

As on Sunday, the United States has at least 301,902 cases of coronavirus according to Johns Hopkins University's tally. 

At least 8,175 people have died in the US from coronavirus.

There was a steep rise in the number of cases in the last 24 hours. At least 23,949 new cases were reported, and at least 1,023 new deaths in the US have been reported in the last 24 hours.

US Secretary of State Michael Pompeo had discussions with External Affairs Minister S Jaishankar about the importance of continued close cooperation between the United States and India to combat coronavirus by strengthening global pharmaceutical supply chains.

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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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