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
May 8,2020

New York, May 8: An Indian-American father and daughter, both doctors in New Jersey, have died due to the COVID-19, with Governor Phil Murphy describing their demise as “particularly tough" and hailed them for dedicating their lives for others.

Satyender Dev Khanna, 78, was a surgeon who served both on staff and as the head of the surgical departments for multiple hospitals across New Jersey for decades.

Priya Khanna, 43, was a double board-certified in both internal medicine and nephrology. She was Chief of Residents at Union Hospital, now part of RWJ Barnabas Health.

"Dr Satyender Dev Khanna and Dr Priya Khanna were father and daughter. They both dedicated their lives to helping others. This is a family dedicated to health and medicine. Our words cannot amply express our condolences," New Jersey Governor Murphy tweeted on Thursday.

“Both dedicated their lives to helping others and we lost both of them to COVID-19,” Murphy said during a press conference on Thursday, saying their demise is a "particularly tough one.”

Satyender passed away at the Clara Maass Medical Center where he had worked for more than 35 years.

Murphy described him as a "pioneering doctor” who was one of the first surgeons to perform laparoscopic surgery in the state. He is being remembered by colleagues as a “gentle and caring physician."

“And for a doctor, I'm not one, but I would bet, I don't think there could be a more fitting way to be remembered, or a nurse or a healthcare worker of any kind,” Murphy said, adding that the doctor had a passion for bicycling, and he often found peace from the hustle of the hospital in biking along the Jersey Shore.

Priya did all of her medical training in New Jersey and then did her fellowship in nephrology in South Jersey with the Cooper Health System. Like her father, she too worked at Clara Maass, where she died.

She was also Medical Director at two dialysis centres in Essex County and “took pride” in teaching the next generation of doctors, Murphy said, adding that the ICU physician who cared for Priya Khanna was trained and taught by her as well.

Follow live developments on the coronavirus pandemic here

“Priya will be remembered as a caring and selfless person who put others first. And even while in the hospital, fighting her own battle, she continued to check up on her mom and dad and her family,” Murphy said.

“This is a family, by the way, dedicated to health and medicine,” he said.

The governor spoke with Satyender's wife Komlish Khanna, who is a paediatrician. The couple has two more daughters - Sugandha Khanna, an emergency medicine physician and Anisha Khanna, a paediatrician.

“Unbelievable. Our words cannot amply express our condolences nor, I am sure, can they express the pain that the Khanna family is feeling. But I hope that the fact that our entire state mourns with them is some small comfort. And we mourn everyone we have lost. We commit in their memory to saving as many lives as we can,” Murphy said.

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News Network
March 26,2020

London, Mar 26: British Prime Minister Boris Johnson has said that the country's NHS risks becoming "overwhelmed" by the coronavirus outbreak and that the situation in Britain is just two or three weeks behind Italy.
"The numbers are very stark, and they are accelerating. We are only a matter of weeks -- two or three -- behind Italy," Johnson said, as reported by CNN.
"The Italians have a superb health care system. And yet their doctors and nurses have been completely overwhelmed by the demand. The Italian death toll is already in the thousands and climbing.
He added, "Unless we act together unless we make the heroic and collective national effort to slow the spread -- then it is all too likely that our own NHS will be similarly overwhelmed,"
"That is why this country has taken the steps that it has, in imposing restrictions never seen before either in peace or war." He said.
The problem reached a crunch point in the UK, which has dramatically increased its response to the virus outbreak this week.
Food banks that provide a lifeline for some of the estimated 14 million in poverty are running low on volunteers, many of whom have been forced to self-isolate, as well as the food itself, which is in short supply following panic-buying.
The UK has confirmed more 9,600 cases of the deadly virus with 460 deaths.
The global tally of cases has crossed 487,000 as on Thursday with 22,030 deaths globally as per the data presented by the Johns Hopkins University.

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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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