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 27,2020

Washington, May 27: Most viruses and other germs do not spread easily on flights, the US Center for Disease Control and Prevention has said in its COVID-19 guidelines which do not recommend following social distancing between two passengers inside a plane or keeping the middle seat unoccupied.

As a result of coronavirus pandemic, air traffic inside the US has come to a near halt. Air traffic is said to be down to about 90 per cent. For all travellers coming from overseas, the Center for Disease Control and Prevention (CDC) has recommended 14 days quarantine.

"Most viruses and other germs do not spread easily on flights because of how air circulates and is filtered on aeroplanes," the CDC has said in its set of COVID-19 guidelines for air travellers.

However, it noted that the air travellers were not risk-free especially in the time of the coronavirus pandemic and recommended Americans to avoid travel as far as possible.

"Air travel requires spending time in security lines and airport terminals, which can bring you in close contact with other people and frequently touched surfaces," it said.

"Social distancing is difficult on crowded flights, and you may have to sit near others (within six feet), sometimes for hours. This may increase your risk for exposure to the virus that causes COVID-19," the CDC said.

But instead of recommended social distancing inside commercial planes, the CDC has advised a series of preventive and hygienic measures to be taken by the airlines pilot and crew to prevent the spread of coronavirus.

The US Department of Transportation and Federal Aviation Administration in its latest safety alerts for operators on May 11 said that air carriers and crews conducting flight operations having a nexus to the US, including both domestic and foreign air carriers, should follow CDC's occupational health and safety guidance.

The CDC issued its guidelines in first guidelines for the airlines and airline crew on March and again in May.

The CDC, which has issued an exhaustive social guideline measures in various sections, is silent on keeping the middle seat of a plane unoccupied so as to maintain the six feet distance between two passengers.

It calls for the plane crew to report to the CDC a traveller with specific COVID-19 symptoms like fever, persistent cough, difficulty in breathing and appearing unwell.

Asking the airlines and cabin crew to review infection control guidelines for cabin crew, the CDC recommends several measures for cabin crew to protect themselves and others, manage a sick traveller, clean contaminated areas, and take actions after a flight.

Prominent among them include washing hands often with soap and water for at least 20 seconds, particularly after assisting sick travellers or touching potentially contaminated body fluids or surfaces and use of alcohol-based hand sanitizer (containing at least 60 per cent alcohol) if soap and water are not available.

Airlines should consider providing alcohol-based hand sanitizer to cabin and flight crews for their personal use, it said.

The CDC guidelines do not recommend following social distancing inside a plane between two passengers or keeping the middle seat unoccupied. But it asks to minimise contact between passengers and cabin crew and the sick person.

"If possible, separate the sick person from others (by a distance of 2 meters or 6 feet, ideally) and designate one crew member to serve the sick person. Offer a facemask, if available and if the sick person can tolerate it. If a facemask is not available or cannot be tolerated, ask the sick person to cover their mouth and nose with tissues when coughing or sneezing," said the CDC guidelines.

If no symptomatic passengers were identified during or immediately after the flight, the CDC recommends airlines to follow routine operating procedures for cleaning aircraft, managing solid waste, and wearing PPE.

"If symptomatic passengers are identified during or immediately after the flight, routine cleaning procedures should be followed, and enhanced cleaning procedures should also be used," it said.

Clean porous (soft) surfaces (e.g, cloth seats, cloth seat belts) at the seat of the symptomatic passengers and within 6 feet of the symptomatic passengers in all directions, it added.

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News Network
February 28,2020

Washington, Feb 28: US intelligence agencies are monitoring the global spread of coronavirus and the ability of governments to respond, sources familiar with the matter said on Thursday, warning that there were concerns about how India would cope with a widespread outbreak.

While there are only a few known cases in India, one source said the country's available countermeasures and the potential for the virus to spread given India's dense population was a focus of serious concern.

US intelligence agencies are also focusing on Iran, where the country's deputy health minister has fallen ill during a worsening outbreak.

US Secretary of State Mike Pompeo said on Tuesday the United States was "deeply concerned" Tehran may have covered up details about the spread of coronavirus. A US government source said Iran's response was considered ineffective because the government only has minimal capabilities to respond to the outbreak.

Another source said US agencies were also concerned about the weak ability of governments in some developing countries to respond to an outbreak.

The US House of Representatives Intelligence Committee has received a briefing on the virus from the spy agencies. "The Committee has received a briefing from the IC (intelligence community) on coronavirus, and continues to receive updates on the outbreak on a daily basis," an official of the House Intelligence Committee told Reuters.

"Addressing the threat has both national security and economic dimensions, requiring a concerted government-wide effort and the IC is playing an important role in monitoring the spread of the outbreak, and the worldwide response," the official added.

A source familiar with the activities of the Senate Intelligence Committee, led by Republican Senator Richard Burr and Democratic Senator Mark Warner, said the panel was receiving daily updates. The role of US intelligence agencies in responding to the coronavirus epidemic at this point principally involves monitoring the spread of the illness around the world and assessing the responses of governments.

They are working closely with health agencies, such as the US Center for Disease Control, in sharing information they collect and targeting further intelligence gathering.

One source said US agencies would use a wide range of intelligence tools, ranging from undercover informants to electronic eavesdropping tools, to track the virus' impact.

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News Network
February 26,2020

Feb 26: Looking out over the world’s largest cricket stadium, the seats jammed with more than 100,000 people, India’s prime minister heaped praise on his American visitor.

“The leadership of President Trump has served humanity,” Prime Minister Narendra Modi said Monday, highlighting Trump’s fight against terrorism and calling his 36-hour visit to India a watershed in India-U.S. relations.

The crowds cheered. Trump beamed.

“The ties between India and the U.S. are no longer just any other partnership,” Modi said. “It is a far greater and closer relationship.”

India, it seems, loves Donald Trump. It seemed obvious from the thousands who turned out to wave as his motorcade snaked through the city of Ahmedabad, and from the tens of thousands who filled the city’s new stadium. It seemed obvious from the hug that Modi gave Trump after he descended from Air Force One, and from the hundreds of billboards proclaiming Trump’s visit.

But it’s not so simple.

Because while Trump is genuinely popular in India, his clamorous and carefully choreographed welcome was also about Asian geopolitics, China’s growing power and a masterful Indian politician who gave his American visitor exactly what he wanted.

Modi “is doing this not necessarily because he loves Trump,” said Tanvi Madan, the director of the India Project at the Brookings Institution in Washington, D.C. “It’s very much about Trump as the leader of the U.S. and recognizing what it is that Trump himself likes.”

Trump likes crowds — big crowds — and the foot soldiers of India’s political parties have long known how to corral enough people to make any politician look popular. In a city like Ahmedabad, the capital of Modi’s home state of Gujarat and the center of his power base, it wouldn’t take much effort to fill a cavernous sports stadium. It was more surprising that a handful of seats remained empty, and that some in the stands had left even before Trump had finished his speech.

For India, good relations with the U.S. are deeply important: They signal that India is a serious global player, an issue that has long been important to New Delhi, and help cement an alliance that both nations see as a counterweight to China’s rise.

“For both countries, their biggest rival is China,” said John Echeverri-Gent, a professor at the University of Virginia whose research often focuses on India. “China is rapidly expanding its presence in the Indian Ocean, which India has long considered its backyard and its exclusive realm for security concerns.”

“It’s very clearly a major concern for both India and the United States,” he said.

Trump isn’t the first U.S. president that Modi has courted. In 2015, then-President Barack Obama was the first American chief guest at India’s Republic Day parade, a powerful symbolic gesture. Obama also got a Modi hug, and the media in both countries were soon writing about the two leaders’ “bromance.”

Trump is popular in India, even if some of that is simply because he’s the U.S. president. A 2019 Pew Research Center poll showed that 56% of Indians had confidence in Trump’s abilities in world affairs, one of only a handful of countries where he has that level of approval. But Obama was also popular: Before he left office, he had 58% approval in world affairs among Indians.

The Pew poll also indicated that Trump’s support was higher among supporters of Modi’s Hindu nationalist party.

That’s not surprising. Both men have fired up their nationalist bases with anti-Muslim rhetoric and government policies, from Trump’s travel bans to Modi’s crackdown in Kashmir, India’s only Muslim-majority state.

And Trump’s Indian support is far from universal. Protests against his trip roiled cities from New Delhi to Hyderabad to the far northeastern city of Gauhati, although those demonstrations were mostly overshadowed by protests over a new Indian citizenship law that Modi backs.

Modi, who is widely popular in India, has faced weeks of protests over the law, which provides fast track naturalization for some foreign-born religious minorities — but not Muslims. While Trump talked about ties with India on Tuesday, Hindus and Muslims fought in violent clashes that left at least 10 people dead over two days.

In some ways, Modi and Trump are powerful echoes of each other.

They have overlapping political styles. Both are populists who see themselves as brash, rule-breaking outsiders who disdain their countries’ traditional elites. Both are seen by their critics as having authoritarian leanings. Both surround themselves with officials who rarely question their decisions.

But are they friends?

Trump says yes. “Really, we feel very strongly about each other,” he said at a New Delhi press briefing.

But many observers aren’t so sure.

“The question is how much of this is real chemistry, as opposed to what I’d call planned chemistry” orchestrated for diplomatic reasons, said Madan. “It’s so hard to know if you’re not in the room.”

Certainly, Modi understands America’s importance to India. While the two countries continue to bicker about trade issues, the prime minister organized a welcome that impressed even India’s news media, which have watched countless choreographed mass political rallies.

“There is no other country for whose leader India would hold such an event, and for which an Indian prime minister would lavish such rhetoric,” the Hindustan Times said in an editorial.

“The spectacle and the sound were worth a thousand agreements.”

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