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
January 9,2020

Washington, Jan 9: The U.S. and Iran stepped back from the brink of possible war Wednesday as President Donald Trump signaled he would not retaliate militarily for Iran's missile strikes on Iraqi bases housing U.S. troops. No one was harmed in the strikes, but U.S. forces in the region remained on high alert.

Speaking from the White House, Trump seemed intent on deescalating the crisis, which spiralled after he authorized the assassination of Iran's top general, Qassem Soleimani. Iran responded overnight by firing more than a dozen missiles at two installations in Iraq, its most direct assault on America since the 1979 seizure of the U.S. Embassy in Tehran.

Trump's takeaway was that “Iran appears to be standing down, which is a good thing for all parties concerned and a very good thing for the world.”

The region remained on edge, however, and American troops including a quick-reaction force dispatched over the weekend were on high alert. Hours after Trump spoke, an ‘incoming’ siren went off in Baghdad's Green Zone after what seemed to be small rockets “impacted” the diplomatic area, a Western official said. There were no reports of casualties.

Iran's Supreme Leader Ayatollah Ali Khamenei said the overnight strike was not necessarily the totality of Iran's response. “Last night they received a slap,” Khamenei said. “These military actions are not sufficient (for revenge). What is important is that the corrupt presence of America in this region comes to an end.”

The strikes had pushed Tehran and Washington perilously close to all-out conflict and left the world waiting to see whether the American president would respond with more military force. Trump, in his nine-minute, televised address, spoke of a robust U.S. military with missiles that are “big, powerful, accurate, lethal and fast.'' But then he added: “We do not want to use it."

Iran for days had been promising to respond forcefully to Soleimani's killing, but its limited strike on two bases--one in the northern Iraqi city of Irbil and the other at Ain al-Asad in western Iraq--appeared to signal that it too was uninterested in a wider clash with the U.S. Foreign minister Mohammad Javad Zarif tweeted that the country had “concluded proportionate measures in self-defence.”

Trump said the U.S. was “ready to embrace peace with all who seek it.” That marked a sharp change in tone from his warning a day earlier that “if Iran does anything that they shouldn't be doing, they're going to be suffering the consequences, and very strongly.”

Trump opened his remarks at the White House by reiterating his promise that “Iran will never be allowed to have a nuclear weapon.” Iran had announced in the wake of Soleimani's killing that it would no longer comply with any of the limits on uranium enrichment in the 2015 nuclear deal crafted to keep it from building a nuclear device.

The president, who had earlier pulled the U.S. out of the deal, seized on the moment of calm to call for negotiations toward a new agreement that would do more to limit Iran's ballistic missile programmes and constrain regional proxy campaigns like those led by Soleimani.

Trump spoke of new sanctions on Iran, but it was not immediately clear what those would be.

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News Network
February 22,2020

Feb 22: A 20-year-old Chinese woman from Wuhan, the epicentre of the coronavirus outbreak, travelled 400 miles(675 km) north to Anyang where she infected five relatives, without ever showing signs of infection, Chinese scientists reported on Friday, offering new evidence that the virus can be spread asymptomatically.

The case study, published in the Journal of the American Medical Association, offered clues about how the coronavirus is spreading, and suggested why it may be difficult to stop.

"Scientists have been asking if you can have this infection and not be ill? The answer is apparently, yes," said Dr. William Schaffner, an infectious disease expert at Vanderbilt University Medical Center, who was not involved in the study.

China has reported a total of 75,567 cases of the virus known as COVID-19 to the World Health Organization (WHO) including 2,239 deaths, and the virus has already spread to 26 countries and territories outside of mainland China.

Researchers have reported sporadic accounts of individuals without any symptoms spreading the virus. What's different in this study is that it offers a natural lab experiment of sorts, Schaffner said.

"You had this patient from Wuhan where the virus is, travelling to where the virus wasn't. She remained asymptomatic and infected a bunch of family members and you had a group of physicians who immediately seized on the moment and tested everyone."

According to the report by Dr Meiyun Wang of the People's Hospital of Zhengzhou University and colleagues, the woman travelled from Wuhan to Anyang on Jan. 10 and visited several relatives. When they started getting sick, doctors isolated the woman and tested her for coronavirus. Initially, the young woman tested negative for the virus, but a follow-up test was positive.

All five of her relatives developed COVID-19 pneumonia, but as of Feb. 11, the young woman still had not developed any symptoms, her chest CT remained normal and she had no fever, stomach or respiratory symptoms, such as cough or sore throat.

Scientists in the study said if the findings are replicated, "the prevention of COVID-19 infection could prove challenging."

Key questions now, Schaffner said, are how often does this kind of transmission occur and when during the asymptomatic period does a person test positive for the virus.

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News Network
May 30,2020

Washington, May 30: The United States will end its relationship with the World Health Organization over the body’s handling of the coronavirus pandemic, U.S. President Donald Trump said on Friday, accusing the U.N. agency of becoming a puppet of China.

The move to quit the Geneva-based body, which the United States formally joined in 1948, comes amid growing tensions between Washington and Beijing over the coronavirus outbreak. The virus first emerged in China’s Wuhan city late last year.

Speaking in the White House Rose Garden, Trump said Chinese officials “ignored their reporting obligations” to the WHO about the virus - that has killed hundreds of thousands of people globally - and pressured the agency to “mislead the world.”

“China has total control over the World Health Organization despite only paying $40 million per year compared to what the United States has been paying which is approximately $450 million a year,” he said.

Trump’s decision follows a pledge last week by Chinese President Xi Jinping to give $2 billion to the WHO over the next two years to help combat the coronavirus. The amount almost matches the WHO’s entire annual program budget for last year.

Trump last month halted funding for the 194-member organization, then in a May 18 letter gave the WHO 30 days to commit to reforms.

“Because they have failed to make the requested and greatly needed reforms, we will be today terminating our relationship with the World Health Organization and redirecting those funds to other worldwide and deserving urgent global public health needs,” Trump said on Friday.

It was not immediately clear when his decision would come into effect. A 1948 joint resolution of Congress on U.S. membership of the WHO said the country “reserves its right to withdraw from the organization on a one-year notice.”

The World Health Organization did not immediately respond to a request for comment on Trump’s announcement. It has previously denied Trump’s assertions that it promoted Chinese “disinformation” about the virus.

“It’s important to remember that the WHO is a platform for cooperation among countries,” said Donna McKay, executive director of Physicians for Human Rights. “Walking away from this critical institution in the midst of an historic pandemic will hurt people both in the United States and around the world.”

‘ABSOLUTELY CRITICAL’

The United States currently owes the WHO more than $200 million in assessed contributions, according to the WHO website. Washington also gives several hundred million dollars annually in voluntary funding tied to specific WHO programs such as polio eradication, HIV, hepatitis and tuberculosis.

Amesh A. Adalja, a senior scholar at Johns Hopkins Center for Health Security, said that in practice Trump’s decision was unlikely to change the operations of the WHO.

“From a symbolic or moral standpoint it’s the wrong type of action to be taking in the middle of a pandemic and seems to deflect responsibility for what we in the U.S. failed to do and blame the WHO,” said Adalja.

When Trump halted funding to the WHO last month, two Western diplomats said the U.S. suspension was more harmful politically to the WHO than to the agency’s current programs, which are funded for now.

The WHO is an independent international body that works with the United Nations. U.N. Secretary-General Antonio Guterres said last month that the WHO is “absolutely critical to the world’s efforts to win the war against COVID-19.”

When asked about Trump’s decision, a U.N. spokesman said: “We have consistently called for all states to support WHO.”

Trump has long scorned multilateralism as he focuses on an “America First” agenda. Since taking office, he has quit the U.N. Human Rights Council, the U.N. cultural agency, a global accord to tackle climate change and the Iran nuclear deal. He has also cut funding for the U.N. population fund and the U.N. agency that aids Palestinian refugees.

“The WHO is the world’s early warning system for infectious diseases,” said U.S. Representative Nita Lowey, a Democrat who chairs the House Committee on Appropriations. “Now, during a global pandemic that has cost over 100,000 American lives, is not the time to put the country further at risk.”

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