American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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
February 26,2020

Feb 26: China’s massive travel restrictions, house-to-house checks, huge isolation wards and lockdowns of entire cities bought the world valuable time to prepare for the global spread of the new virus.

But with troubling outbreaks now emerging in Italy, South Korea and Iran, and U.S. health officials warning Tuesday it’s inevitable it will spread more widely in America, the question is: Did the world use that time wisely and is it ready for a potential pandemic?

“It’s not so much a question of if this will happen anymore, but rather more a question of exactly when this will happen — and how many people in this country will have severe illness,” said Dr. Nancy Messonnier of the U.S. Centers for Disease Control and Prevention.

Some countries are putting price caps on face masks to combat price gouging, while others are using loudspeakers on trucks to keep residents informed. In the United States and many other nations, public health officials are turning to guidelines written for pandemic flu and discussing the possibility of school closures, telecommuting and canceling events.

Countries could be doing even more: training hundreds of workers to trace the virus’ spread from person to person and planning to commandeer entire hospital wards or even entire hospitals, said Dr. Bruce Aylward, the World Health Organization’s envoy to China, briefing reporters Tuesday about lessons learned by the recently returned team of international scientists he led.

“Time is everything in this disease,” Aylward said. “Days make a difference with a disease like this.”

The U.S. National Institutes of Health’s infectious disease chief, Dr. Anthony Fauci, said the world is “teetering very, very close” to a pandemic. He credits China’s response for giving other nations some breathing room.

China locked down tens of millions of its citizens and other nations imposed travel restrictions, reducing the number of people who needed health checks or quarantines outside the Asian country.

It “gave us time to really brush off our pandemic preparedness plans and get ready for the kinds of things we have to do,” Fauci said. “And we’ve actually been quite successful because the travel-related cases, we’ve been able to identify, to isolate” and to track down those they came in contact with.

With no vaccine or medicine available yet, preparations are focused on what’s called “social distancing” — limiting opportunities for people to gather and spread the virus.

That played out in Italy this week. With cases climbing, authorities cut short the popular Venice Carnival and closed down Milan’s La Scala opera house. In Japan, Prime Minister Shinzo Abe called on companies to allow employees to work from home, while the Tokyo Marathon has been restricted to elite runners and other public events have been canceled.

Is the rest of the world ready?

In Africa, three-quarters of countries have a flu pandemic plan, but most are outdated, according to authors of a modeling study published last week in The Lancet medical journal. The slightly better news is that the African nations most connected to China by air travel — Egypt, Algeria and South Africa — also have the most prepared health systems on the continent.

Elsewhere, Thailand said it would establish special clinics to examine people with flu-like symptoms to detect infections early. Sri Lanka and Laos imposed price ceilings for face masks, while India restricted the export of personal protective equipment.

India’s health ministry has been framing step-by-step instructions to deal with sustained transmissions that will be circulated to the 250,000 village councils that are the most basic unit of the country’s sprawling administration.

Vietnam is using music videos on social media to reach the public. In Malaysia, loudspeakers on trucks blare information through the streets.

In Europe, portable pods set up at United Kingdom hospitals will be used to assess people suspected of infection while keeping them apart from others. France developed a quick test for the virus and has shared it with poorer nations. German authorities are stressing “sneezing etiquette” and Russia is screening people at airports, railway stations and those riding public transportation.

In the U.S., hospitals and emergency workers for years have practiced for a possible deadly, fast-spreading flu. Those drills helped the first hospitals to treat U.S. patients suffering from COVID-19, the disease caused by the virus.

Other hospitals are paying attention. The CDC has been talking to the American Hospital Association, which in turn communicates coronavirus news daily to its nearly 5,000 member hospitals. Hospitals are reviewing infection control measures, considering using telemedicine to keep potentially infectious patients from making unnecessary trips to the hospital and conserving dwindling supplies of masks and gloves.

What’s more, the CDC has held 17 different calls reaching more than 11,000 companies and organizations, including stadiums, universities, faith leaders, retailers and large corporations. U.S. health authorities are talking to city, county and state health departments about being ready to cancel mass gathering events, close schools and take other steps.

The CDC’s Messonnier said Tuesday she had contacted her children’s school district to ask about plans for using internet-based education should schools need to close temporarily, as some did in 2009 during an outbreak of H1N1 flu. She encouraged American parents to do the same, and to ask their employers whether they’ll be able to work from home.

“We want to make sure the American public is prepared,” Messonnier said.

How prepared are U.S. hospitals?

“It depends on caseload and location. I would suspect most hospitals are prepared to handle one to two cases, but if there is ongoing local transmission with many cases, most are likely not prepared just yet for a surge of patients and the ‘worried well,’” Dr. Jennifer Lighter, a pediatric infectious diseases specialist at NYU Langone in New York, said in an email.

In the U.S., a vaccine candidate is inching closer to first-step safety studies in people, as Moderna Inc. has delivered test doses to Fauci’s NIH institute. Some other companies say they have candidates that could begin testing in a few months. Still, even if those first safety studies show no red flags, specialists believe it would take at least a year to have something ready for widespread use. That’s longer than it took in 2009, during the H1N1 flu pandemic — because that time around, scientists only had to adjust regular flu vaccines, not start from scratch.

The head of the World Health Organization, Tedros Adhanom Ghebreyesus, said the U.N. health agency’s team in China found the fatality rate between 2% and 4% in the hard-hit city of Wuhan, the virus’ epicenter, and 0.7% elsewhere.

The world is “simply not ready,” said the WHO’s Aylward. “It can get ready very fast, but the big shift has to be in the mindset.”

Aylward advised other countries to do “really practical things” now to get ready.

Among them: Do you have hundreds of workers lined up and trained to trace the contacts of infected patients, or will you be training them after a cluster pops up?

Can you take over entire hospital wards, or even entire hospitals, to isolate patients?

Are hospitals buying ventilators and checking oxygen supplies?

Countries must improve testing capacity — and instructions so health workers know which travelers should be tested as the number of affected countries rises, said Johns Hopkins University emergency response specialist Lauren Sauer. She pointed to how Canada diagnosed the first traveler from Iran arriving there with COVID-19, before many other countries even considered adding Iran to the at-risk list.

If the disease does spread globally, everyone is likely to feel it, said Nancy Foster, a vice president of the American Hospital Association. Even those who aren’t ill may need to help friends and family in isolation or have their own health appointments delayed.

“There will be a lot of people affected even if they never become ill themselves,” she said.

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Agencies
March 8,2020

Panic gripped big tech firms like Facebook and Twitter which decided to close their offices from Seattle to London as more employees tested positive for the new coronavirus.

Facebook shut its three London offices till Monday after an employee was diagnosed with COVID-19.

The social networking giant told nearly 3,000 employees in London to work from home after an employee, who is based in Singapore but visited the London offices between February 24-26, was diagnosed with the new coronavirus, Sky News reported on Friday.

"An employee based in our Singapore office who has been diagnosed with COVID-19 visited our London offices on February 24-26.

"We are therefore closing our London offices until Monday for deep cleaning and employees are working from home until then," the company said in a statement.

There have been 163 cases of coronavirus so far in the UK.

Earlier, Facebook recommended all its Bay Area employees in the US to work from home. The latest precautions come after San Francisco announced its first two coronavirus cases on Thursday.

Facebook has also shut its Seattle office until Monday after one of its contractors was confirmed to be infected with the virus. The infected contractor last visited the Facebook office on February 21. King County health officials said all Facebook sites should work from home until March 31.

Twitter shut its Seattle office for a 'deep clean' after an employee developed COVID-19 like symptoms though final result was still awaited.

"A Seattle-based employee has been advised by doctor about likely COVID-19, though still awaiting the final testing," Twitter said in a tweet on Friday.

"While the employee has not been at a Twitter office for several weeks and hasn't been in contact w/others, we're closing our Seattle office to deep clean," the company added.

According to The Seattle Times, at least 14 people have died due to COVID-19 in Washington State till date.

Amazon, Microsoft, Google and Facebook have advised their employees in Washington State to work from home.

Apple has reportedly suggested its employees at California campuses to work from home as an "extra precaution" while new coronavirus cases spread on the west coast in the US, especially Seattle area.

Apple's flagship developers' conference WWDC 2020 in June is also at the risk of getting cancelled as the Santa Clara public health department has warned against large public gatherings. The event draws nearly 5,000 developers from across the world.

The US death toll from the new coronavirus has climbed to 14, according to Johns Hopkins' tracker, with 329 cases reported across the country.

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News Network
February 10,2020

New Delhi, Feb 10: Former Jammu and Kashmir chief minister Omar Abdullah's sister on Monday moved the Supreme Court to challenge his detention under the Public Safety Act.

Senior advocate Kapil Sibal, appearing for the petitioner, mentioned the matter for urgent listing before a bench headed by Justice N V Ramana.

Sibal told the bench that they have filed a habeas corpus petition challenging the detention of Abdullah under the PSA and the matter should be heard this week.

The bench agreed for urgent listing of the matter.

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