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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Agencies
February 11,2020

The head of the World Health Organisation on Tuesday warned the novel coronavirus was a "very grave threat" for the world as he opened a conference to combat the epidemic.

"With 99% of cases in China, this remains very much an emergency for that country, but one that holds a very grave threat for the rest of the world," Tedros Adhanom Ghebreyesus said in Geneva.

Some 400 scientists will review how the virus is transmitted and possible vaccines at the two-day forum.

"What matters most is stopping the outbreak and saving lives. With your support, that's what we can do together," Tedros said.

The virus, first identified in China on December 31, has killed more than 1,000 people, infected over 42,000 and reached some 25 countries.

Participants will also discuss the source of the virus, which is thought to have originated in bats and reached humans via another animal such as snakes or pangolins.

There is no specific treatment or vaccine against the virus, which can cause respiratory failure.

Tedros, who has repeatedly urged countries affected to share their data, called for global "solidarity".

"That is especially true in relation to the sharing of samples and sequences. To defeat this outbreak, we need open and equitable sharing, according to the principles of fairness and equity," he said.

"We hope that one of the outcomes of this meeting will be an agreed roadmap for research around which researchers and donors will align," Tedros said.

Several companies and institutes in Australia, China, France, Germany and the United States are racing to develop a vaccine -- a process that normally takes years.

Asked whether scientists from Taiwan would be allowed to take part in this week's Geneva conference, WHO officials said that they would do so but only online -- along with colleagues from other parts of China.

While the WHO does not deal with Taiwan directly and only recognises Beijing, Taiwan was often allowed to attend annual assemblies and sideline meetings as an observer.

But in recent years it has been frozen out as Beijing takes an increasingly combative stance towards democratic Taiwan, which it considers its own territory.

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News Network
July 1,2020

Tehran, Jul 1 As many as 19 people have been killed in an explosion and fire at a medical facility in Tehran.

A total of 19 people, including 15 men and 4 women, were killed in the explosion, the emergency services confirmed, RT reported citing KhabarOnline website.

According to a regional official, a gas leak caused the incident. Sputnik quoted a deputy head of Tehran police as saying to YJC news outlet that oxygen tanks exploded in the semi-basement of the clinic.

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News Network
May 30,2020

May 30: Warning of the tightrope walk ahead as governments battle the coronavirus crisis, Nobel laureate Peter Charles Doherty has expressed concern about densely populated countries such as India relaxing lockdown norms while also describing a complete shutdown as “an economic and social impossibility”.

The Australian immunologist, who cautioned that the number of COVID-19 cases will rise in the coming days, said the earliest time frame for an effective vaccine “going into large numbers of people” is nine to 12 months.

"If all goes well with testing, we could know if some of the candidate vaccines are both safe and effective as early as September/October. Then, rolling a vaccine out will depend on the type of product and how quickly it can be made, put in vials and so forth," Doherty told PTI in an email interview from Melbourne.

The novel coronavirus, he added, does not change fast like influenza and, from what is known so far, “the same vaccine should work everywhere”.

Doherty, who is with the Department of Microbiology and Immunology at the Doherty Institute, University of Melbourne, won the Nobel Prize for Medicine in 1996 for his discovery of how the body’s immune system distinguishes virus-infected cells from normal ones.

Discussing the lockdown, he said, "If it was purely a matter of hard science, everywhere should stay locked down. But that’s pretty much an economic and social impossibility.”

The expectation, he said, is the numbers will rise and limiting spread will depend on people acting responsibly and the capacity for rapid response and extensive contact testing.

“And in a densely populated country like India I think that it will be very difficult," the scientist said.

Several countries, including India, began relaxing lockdown norms in mid-May despite the WHO’s warning about a second wave. India’s lockdown began on March 25 and has since been extended. The fourth phase ends on Sunday.

Asked whether there are any alternatives to a lockdown, the 79-year-old said, "There is no other option other than closing borders. South Korea, for example, conducted massive, intensive testing and contact tracing in a wealthy country with a very disciplined population. Otherwise, not till we have effective vaccines."

He added that he personally doesn’t see the point of closing borders for people coming in if there’s already a high incidence of disease in the community, “unless it’s to avoid the need to care for them and use scarce hospital beds".

According to Doherty, the coronavirus "is a new virus which has come straight out of nature".

“It (the virus) has moved so rapidly across the world because of people travelling on international planes as well as tourist ships," he added.

The immunologist also warned against the use of hydroxychloroquine to treat COVID-19, and said current and planned trials of the anti-malaria drug should be stopped.

“My understanding is that the use of the drug in severe disease is definitely contra-indicated, but it’s not yet clear whether, if taken under medical supervision, it could have some useful effect if taken early on, or as a preventive. Those trials just haven’t been done properly," Doherty noted.

The Indian Council of Medical Research (ICMR) has backed the use of hydroxychloroquine as a preventive against COVID-19 even after the WHO suspended clinical trials of the drug citing safety concerns.

Asked whether plasma therapy can be an effective treatment for COVID-19, Doherty said, "We lack good properly controlled trials but, especially if the plasma has been tested for antibody levels and there’s evidence of good activity, it could be helpful. If I had the disease and was offered plasma therapy I would certainly accept, but I would not take hydroxychloroquine."

Doherty is also very optimistic about herd immunity developing against the SARS-CoV-2 infection.

"We think that (herd immunity) will cut in and have an obvious effect when, say, 60 per cent of people have been infected. Best hope is to boost herd immunity with a vaccine," he stated.

Herd immunity is a form of indirect protection from infectious disease that occurs when a large percentage of a population has become immune to an infection, whether through vaccination or previous infections.

The number of COVID-19 cases have crossed 5.9 million and the fatalities 3,65,000, according to the Johns Hopkins University on Saturday. 

In India, the death toll has risen to 4,971 and the number of cases to 1,73,763, according to the Union Health Ministry on Saturday.

Several states, including Bihar, Uttar Pradesh, Madhya Pradesh, Jharkhand and Chhattisgarh, have reported a rise in number since lockdown norms were relaxed in early May and migrant workers reached home.

In Uttar Pradesh, for instance, the number of infections rose from around 3,000 on May 4 to 6,532 on May 26. Similarly, Bihar’s numbers increased from around 500 to over 2,700 in the period.

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