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
April 15,2020

Wuhan, Apr 15: In the six days after top Chinese officials secretly determined they likely were facing a pandemic from a new coronavirus, the city of Wuhan at the epicenter of the disease hosted a mass banquet for tens of thousands of people; millions began traveling through for Lunar New Year celebrations.

President Xi Jinping warned the public on the seventh day, Janaury 20. But by that time, more than 3,000 people had been infected during almost a week of public silence, according to internal documents obtained by The Associated Press and expert estimates based on retrospective infection data.

That delay from Jan 14 to Jan. 20 was neither the first mistake made by Chinese officials at all levels in confronting the outbreak, nor the longest lag, as governments around the world have dragged their feet for weeks and even months in addressing the virus.

But the delay by the first country to face the new coronavirus came at a critical time — the beginning of the outbreak. China's attempt to walk a line between alerting the public and avoiding panic set the stage for a pandemic that has infected almost 2 million people and taken more than 126,000 lives.

A This is tremendous, a said Zuo-Feng Zhang, an epidemiologist at the University of California, Los Angeles. If they took action six days earlier, there would have been much fewer patients and medical facilities would have been sufficient. We might have avoided the collapse of Wuhan's medical system.

Other experts noted that the Chinese government may have waited on warning the public to stave off hysteria, and that it did act quickly in private during that time.

But the six-day delay by China's leaders in Beijing came on top of almost two weeks during which the national Center for Disease Control did not register any cases from local officials, internal bulletins obtained by the AP confirm. Yet during that time, from Jan 5 to Jan 17, hundreds of patients were appearing in hospitals not just in Wuhan but across the country.

It's uncertain whether it was local officials who failed to report cases or national officials who failed to record them. It's also not clear exactly what officials knew at the time in Wuhan, which only opened back up last week with restrictions after its quarantine.

But what is clear, experts say, is that China's rigid controls on information, bureaucratic hurdles and a reluctance to send bad news up the chain of command muffled early warnings. The punishment of eight doctors for rumor-mongering, broadcast on national television on Jan. 2, sent a chill through the city's hospitals.

Doctors in Wuhan were afraid, said Dali Yang, a professor of Chinese politics at the University of Chicago. It was truly intimidation of an entire profession. Without these internal reports, it took the first case outside China, in Thailand on Jan 13, to galvanize leaders in Beijing into recognising the possible pandemic before them. It was only then that they launched a nationwide plan to find cases distributing CDC-sanctioned test kits, easing the criteria for confirming cases and ordering health officials to screen patients, all without telling the public.

The Chinese government has repeatedly denied suppressing information in the early days, saying it immediately reported the outbreak to the World Health Organization.

Allegations of a cover-up or lack of transparency in China are groundless, said foreign ministry spokesman Zhao Lijian at a Thursday press conference.

The documents show that the head of China's National Health Commission, Ma Xiaowei, laid out a grim assessment of the situation on Jan. 14 in a confidential teleconference with provincial health officials.

A memo states that the teleconference was held to convey instructions on the coronavirus from President Xi Jinping, Premier Li Keqiang and Vice Premier Sun Chunlan, but does not specify what those instructions were.

The epidemic situation is still severe and complex, the most severe challenge since SARS in 2003, and is likely to develop into a major public health event, the memo cites Ma as saying.

The National Health Commission is the top medical agency in the country. In a faxed statement, the Commission said it had organised the teleconference because of the case reported in Thailand and the possibility of the virus spreading during New Year travel. It added that China had published information on the outbreak in an open, transparent, responsible and timely manner," in accordance with important instructions repeatedly issued by President Xi.

The documents come from an anonymous source in the medical field who did not want to be named for fear of retribution. The AP confirmed the contents with two other sources in public health familiar with the teleconference. Some of the memo's contents also appeared in a public notice about the teleconference, stripped of key details and published in February.

Under a section titled sober understanding of the situation, the memo said that clustered cases suggest that human-to-human transmission is possible. It singled out the case in Thailand, saying that the situation had changed significantly because of the possible spread of the virus abroad.

With the coming of the Spring Festival, many people will be traveling, and the risk of transmission and spread is high, the memo continued.

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News Network
April 2,2020

Washington, Apr 2: The total US death toll from the coronavirus pandemic topped 4,000 early Wednesday, more than double the number from three days earlier, according to a tally by Johns Hopkins University.

The number of deaths was 4,076 -- more than twice the 2,010 recorded late Saturday.

More than 40 percent of recorded deaths nationally were in New York state, the Johns Hopkins data showed.

On Tuesday the United States exceeded the number of deaths in China, where the pandemic emerged in December before spreading worldwide.

The number of confirmed US cases has reached 189,510, the most in the world, though Italy and Spain have recorded more fatalities.

After initially downplaying the threat from new coronavirus in the early stages of the US outbreak, President Donald Trump warned of "a very, very painful two weeks" to come for the country on Tuesday.

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News Network
June 2,2020

Oakland, Jun 2: Facebook employees are using Twitter to register their frustration over CEO Mark Zuckerberg's decision to leave up posts by President Donald Trump that suggested protesters in Minneapolis could be shot.

While Twitter demoted and placed a warning on a tweet about the protests that read, in part, that “when the looting starts the shooting starts,” Facebook has let it stand, with Zuckerberg laying out his reasoning in a Facebook post Friday.

“I know many people are upset that we've left the President's posts up, but our position is that we should enable as much expression as possible unless it will cause imminent risk of specific harms or dangers spelled out in clear policies,” Zuckerberg wrote.

Trump's comment evoked the civil-rights era by borrowing a phrase used in 1967 by Miami's police chief to warn of an aggressive police response to unrest in black neighborhoods.

On Monday, Facebook employees staged a virtual “walkout” to protest the company's decision not to touch the Trump posts according to a report in the New York Times, which cited anonymous senior employees at Facebook.

The Times report says “dozens” of Facebook workers “took the day off by logging into Facebook's systems and requesting time off to support protesters across the country." “I work at Facebook and I am not proud of how we're showing up.

The majority of coworkers I've spoken to feel the same way. We are making our voice heard,” tweeted Jason Toff, a director of product management at Facebook who's been at the company for a year.

Toff, who has a verified Twitter account, had 131,400 “likes” and thousands of retweets of his comment. He did not immediately respond to a message seeking comment on Monday.

“I don't know what to do, but I know doing nothing is not acceptable. I'm a FB employee that completely disagrees with Mark's decision to do nothing about Trump's recent posts, which clearly incite violence. I'm not alone inside of FB.

There isn't a neutral position on racism,” tweeted another employee, design manager Jason Stirman.

Stirman did not immediately respond to a request for comment on Monday. Sara Zhang, a product designer at the company, tweeted that Facebook's “decision to not act on posts that incite violence ignores other options to keep our community safe.

The policy pigeon holes us into addressing harmful user-facing content in two ways: keep content up or take it down.” “I believe that this is a self-imposed constraint and implore leadership to revisit the solution,” she continued. Zhang declined to comment to The Associated Press.

Representatives for Facebook did not immediately respond to messages for comment.

Twitter has historically taken stronger stances than its larger rival, including a complete ban on political advertisements that the company announced last November.

That's partly because Facebook, a much larger company with a broader audience,targeted by regulators over its size and power, has more to lose. And partly because the companies' CEOs don't always see eye to eye on their role in society.

Over the weekend, Twitter changed the background and logo if its main Twitter account to black from its usual blue in support of the Black Lives Matter protesters and added a #blacklivesmatter hashtag. Facebook did the same with its own logo on its site, though without the hashtag.

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