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
March 26,2020

London, Mar 26: British Prime Minister Boris Johnson has said that the country's NHS risks becoming "overwhelmed" by the coronavirus outbreak and that the situation in Britain is just two or three weeks behind Italy.
"The numbers are very stark, and they are accelerating. We are only a matter of weeks -- two or three -- behind Italy," Johnson said, as reported by CNN.
"The Italians have a superb health care system. And yet their doctors and nurses have been completely overwhelmed by the demand. The Italian death toll is already in the thousands and climbing.
He added, "Unless we act together unless we make the heroic and collective national effort to slow the spread -- then it is all too likely that our own NHS will be similarly overwhelmed,"
"That is why this country has taken the steps that it has, in imposing restrictions never seen before either in peace or war." He said.
The problem reached a crunch point in the UK, which has dramatically increased its response to the virus outbreak this week.
Food banks that provide a lifeline for some of the estimated 14 million in poverty are running low on volunteers, many of whom have been forced to self-isolate, as well as the food itself, which is in short supply following panic-buying.
The UK has confirmed more 9,600 cases of the deadly virus with 460 deaths.
The global tally of cases has crossed 487,000 as on Thursday with 22,030 deaths globally as per the data presented by the Johns Hopkins University.

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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
May 4,2020

Washington, May 4: Anxious for an economic recovery, President Donald Trump fielded Americans' questions about decisions by some states to allow nonessential businesses to reopen while other states are on virtual lockdown due to the coronavirus.

After more than a month of being cooped up at the White House, Trump returned from a weekend at the Camp David presidential retreat in Maryland and participated in a “virtual” town hall, hosted Sunday night by Fox News Channel, from inside the Lincoln Memorial.

He pushed for an economic reopening, one his advisers believe will be essential for his reelection chances this November.

“We have to get it back open safely but as quickly as possible," Trump said.

The president acknowledged fear on both sides of the issue, some Americans worried about getting sick while others are concerned about losing jobs.

Though the administration's handling of the pandemic, particularly its ability to conduct widespread testing, has come under fierce scrutiny, the president defended the response and said the nation was ready to begin reopening.

“I'll tell you one thing. We did the right thing and I really believe we saved a million and a half lives,” the president said.

But he also broke with the assessment of his senior adviser and son-in-law, Jared Kushner, saying it was “too soon to say" if the federal government was overseeing a “success story."

Trump's impatience also flashed. While noting that states would go at their own pace in returning to normal, with ones harder hit by the coronavirus going slower, he said that “some states frankly I think aren't going fast enough" and singled out Virginia, which has a Democratic governor and legislature.

And he urged the nation's schools and universities to return to classes this fall.

But many public health experts believe that cannot be done safely until a vaccine is developed.

Trump declared Sunday that he believed one could be available by year's end although his own pandemic task force has predicated it could be another 18 months.

Federal guidelines that encouraged people to stay at home and practice social distancing expired late last week.

Debate continued over moves by governors to start reopening state economies that tanked after shopping malls, salons and other nonessential businesses were ordered closed in attempt to slow a virus that has killed more than 66,000 Americans, according to a tally of reported deaths by Johns Hopkins University.

The U.S. economy has suffered, shrinking at a 4.8 per cent annual rate from January through March, the government estimated last week. It was the sharpest quarterly drop since the 2008 financial crisis.

Roughly 30.3 million people have filed for unemployment aid in the six weeks since the outbreak forced employers to shut down and slash their workforces. It was the worst string of layoffs on record.

Larry Kudlow, Trump's top economic adviser, on Sunday predicted a “spectacular 2021” — with “the right set of policies” — on top of a rebound from July through December of this year.

He said on CNN's "State of the Union" that the administration would "pause” to review the effectiveness of trillions in economic relief spending before making any decision on whether additional aid is needed.

House Speaker Nancy Pelosi, D-Calif., said Thursday that state and local governments are seeking up to USD 1 trillion for coronavirus costs, The Senate planned to reopen Monday, despite the Washington area's continued status as a virus hot spot and with the region still under stay-at-home orders.

The House remains shuttered. The pandemic is forcing big changes at the tradition-bound Supreme Court: The justices will hear arguments, beginning Monday, by telephone for the first time since Alexander Graham Bell patented his invention in 1876.

Congressional Republicans are resisting calls by Democrats for emergency spending for states and local governments whose revenue streams all but dried up in recent weeks.

The GOP is counting on the country's reopening and the rebound promised by Trump as their best hope to forestall another big round of virus aid.

The leaders of California and Michigan are among governors under public pressure over lockdowns still in effect while states such as Florida, Georgia and Ohio are reopening.

Michigan Governor Gretchen Whitmer, a Democrat, said Sunday that the armed protesters who demonstrated inside her state's Capitol “depicted some of the worst racism” and “awful parts” of US history by showing up with Confederate flags, nooses and swastikas.

Trump had tweeted “LIBERATE” and named Michigan and other states in mid-April. In a new tweet Friday, he urged Whitmer to “make a deal” with the protesters. “These are very good people, but they are angry.

They want their lives back again, safely!” Trump said.

Despite the opposition of Michigan's Republican-controlled Legislature, Whitmer has extended a state of emergency declaration and directed most businesses statewide to remain closed.

Some people participating in other public protests across the US have not kept their distance from one another and have rallied without masks, not heeding public health recommendations.

Deborah Birx, coordinator of the White House coronavirus task force, called that behavior “devastatingly worrisome.”

She said people will feel guilty for the rest of their lives if they end up infected and unwittingly spread the virus to vulnerable family members.

“We need to protect each other at the same time we're voice our discontent,” she told CNN's “State of the Union.”

An overwhelming majority of Americans support stay-at-home orders and other efforts to slow the virus' spread, according to a recent survey from The Associated Press-NORC Center for Public Affairs Research.

Asked about states that are reopening before they meet benchmarks laid out in federal guidelines she helped write, Birx said the guidelines “are a pretty firm policy of what we think is important from a public health standpoint.”

She added that she and others have made it clear that people must continue practising social distancing, “scrupulous” hand washing and other measures to protect themselves and others.

Fox News Channel said it asked viewers to submit questions about reopening the country on the network's Twitter, Facebook and Instagram accounts for a chance to appear on the rare broadcast from the Lincoln Memorial. Trump spoke from the memorial's steps last July Fourth.

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