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
June 20,2020

Sao Paulo, June 20: Brazil’s government confirmed on Friday that the country has risen above 1 million confirmed coronavirus cases, second only to the United States.

The country’s health ministry said that the total now stood at 10,32,913, up more than 50,000 from Thursday. The ministry said the sharp increase was due to corrections of previous days’ underreported numbers.

Brazilian President Jair Bolsonaro still downplays the risks of the virus after nearly 50,000 deaths from COVID-19 in three months, saying the impact of social isolation measures on the economy could be worse than the disease itself.

Specialists believe the actual number of cases in Brazil could be up to seven times higher than the official statistic. Johns Hopkins University says Brazil is performing an average of 14 tests per 1,00,000 people each day, and health experts say that number is up to 20 times less than needed to track the virus.

Official data show a downward trend of the virus in Brazil’s north, including the hard-hit region of the Amazon, a plateau in cases and deaths in the countries’ biggest cities near the Atlantic coast, but a rising curve in the south.

In the Brazilian countryside, which is much less prepared to handle a crisis, the pandemic is clearly growing. Many smaller cities have weaker health care systems and basic sanitation that’s insufficient to prevent contagion.

“There is a lot of regional inequality in our public health system and a shortage of professionals in the interior,” said Miguel Lago, executive director of Brazil’s Institute for Health Policy Studies, which advises public health officials.

That creates many health care deserts, with people going long distances to get attention. When they leave the hospital, the virus can go with them.

The cattle-producing state of Mato Grosso was barely touched by the virus when it hit the nation’s biggest cities in March. Sitting far from the coast, between the Bolivian border and Brazil’s capital of Brasilia, its 33 lakh residents led a mostly normal life until May. But now its people live under lockdown and meat producers have dozens of infected workers.

In Tangará da Serra, a city of 1,03,000 people in Mato Grosso, the mayor decided Friday to forbid the sale of alcoholic drinks for two weeks as an incentive for people to stay home.

Fᢩo Junqueira said the measure was needed after a spike in COVID-19 cases that filled 80% of the city’s 54 intensive care beds. The city has had nearly 300 cases of the disease, plus three fatalities.

In Rondonópolis, only 300 miles away from Tangará da Serra and home to a thriving economy, health authorities closed the local meatpacking industry after 92 cases were confirmed there. The city of 1,44,000 inhabitants counted 21 deaths from the virus and more than 600 cases. The mayor has also decided to limit sales of alcoholic beverages.

Even regions once considered examples of successful efforts against the virus are now struggling.

Porto Alegre, home to about 14 lakh people, had success in slowing the virus’ spread over the last three months. But now its mayor is considering increasing social isolation measures after ICU occupancy in the city jumped to 80% this month.

We were already making projections for schools to come back, Mayor Nelson Marchezan Jr. told The Associated Press. Now the trend is to impose more restrictions. Outside Sao Paulo city, five regions of the state’s countryside will have to close shops starting Monday due to a rise in coronavirus cases. Governor João Doria announced the decision Friday.

Dr. Mike Ryan, the World Health Organization’s executive director, said at a news conference that Brazil needs to increase its efforts to stop the spread of infections.

“The epidemic is still quite severe in Brazil. I believe health workers are working extremely hard and under pressure to be able to deal with the number of cases that they see on a daily basis,” Dr. Ryan said.

“Certainly the rise is not as exponential as it was previously, so there are some signs that the situation is stabilising. But we’ve seen this before in other epidemics in other countries.”

Margareth Dalcolmo, a clinical researcher and professor of respiratory medicine at the state-funded Oswaldo Cruz Foundation in Rio de Janeiro, believes the reopening in major cities and the virus traveling by road into Brazil’s heartland will keep the pressure on the country’s health system.

“The risk in the interior now is very big,” she said. “Our health system just can’t solve the most serious cases of COVID in many places of the countryside.”

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News Network
April 20,2020

Washington, Apr 20: The US wants to send a team of experts to China to investigate coronavirus, President Donald Trump has said, a day after he warned Beijing of "consequences" if it was knowingly responsible for the spread of COVID-19 which has killed more than 165,000 people globally, including over 41,000 in America.

Describing the coronavirus as a plague, Trump, during his White House news conference on Sunday, said that he is not happy with China where the pandemic emerged in December last year in the central Chinese city of Wuhan.

“We spoke to them (Chinese) a long time ago about going in. We want to go in. We want to see what's going on. And we weren't exactly invited, I can tell you that,” the President told reporters.

“I was very happy with the (trade) deal (with China), very happy with everything and then we found out about the plague and since we found out about that I'm not happy,” he said.

The US has launched an investigation into whether the deadly virus "escaped" from the Wuhan Institute of Virology.

He has repeatedly expressed disappointment over China's handling of the coronavirus disease, alleged non-transparency and initial non-cooperation from Beijing with Washington on dealing with the crisis.

“Based on an investigation, we are going to find out,” Trump told reporters.

A day earlier, he warned China that it should face consequences if it was "knowingly responsible" for the spread of the novel coronavirus, upping the ante on Beijing over its handling of the COVID-19 pandemic.

“If they (China) were knowingly responsible… then there should be consequences. You're talking about, you know, potentially lives like nobody's seen since 1917,” Trump said on Saturday.

The opposition Democratic Party said that Trump has falsely claimed he acted early by restricting travel from China when it was little too late and he continued to downplay the virus throughout February.

The number of COVID-19 deaths in the US crossed 41,000 and the total infections were more than 764,000 so far.

New York, the epicentre of the deadly COVID-19 in the US, has 2,42,000 cases and over 17,600 fatalities so far. It has registered a 50-percent decline in new cases over an eight-day period.

The novel virus, which emerged in China in December last year, has killed over 160,000 and infected more than 2.3 million people worldwide.

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Agencies
July 21,2020

Washington, Jul 21: Democrat Joe Biden urged Muslim Americans on Monday to join him in the fight to defeat President Donald Trump as he addressed an online summit hosted by the advocacy organisation Emgage Action to mobilise Muslim voters ahead of the presidential election.

I want to earn your vote not just because he's not worthy of being president, the presumptive presidential nominee told participants.

I want to work in partnership with you, make sure your voices are included in the decision-making process as we work to rebuild our nation.

Biden also reiterated a pledge to overturn a Trump administration ban on travelers from several predominantly Muslim countries, calling it vile.

Wa'el Alzayat, CEO of Emgage Action, said by email that the organisation was seeking to maximise Muslim American turnout in key battleground states.

In Michigan alone one of the states where the organisation has chapters and where Trump won in 2016 by fewer than 11,000 votes he said he believed there are more than 150,000 registered Muslim voters.

Several prominent Muslim American elected officials endorsed Biden for president in a letter organised by Emgage Action ahead of the summit.

Among those who signed the letter are Minnesota Rep. Ilhan Omar, Minnesota Attorney General Keith Ellison and Indiana Rep. Andre Carson, all Democrats.

Omar, one of the first Muslim women elected to Congress, served as a high-profile surrogate for Bernie Sanders before he exited the presidential race in April making her support for Biden potentially helpful as the former vice president seeks to mobilise Muslim voters this fall.

Muslim American voices matter to our communities, to our country, Biden said.

But we all know that your voice hasn't always gotten recognised or represented.

Emgage Action has titled the event Million Muslim Votes, underscoring its emphasis on boosting Muslim turnout in November.

Joe Biden's presence serves not only to galvanise Muslim Americans to cast their ballots, but to usher in an era of engaging with Muslim American communities under a Biden administration, Alzayat said by email before the summit.

The pro-Biden letter from Muslim American elected officials decried a number of Trump's domestic and international policies, including his administration's travel ban and his pullout from the Iran nuclear deal.

A Biden administration will move the nation forward on many of the issues we care about, the letter said, citing racial justice, affordable health care, climate change and immigration.

The Muslim American officials also praised Biden's agenda for their communities.

Among other goals, Biden has vowed to rescind the travel ban affecting Muslims on Day One if he's elected.

In his address, he pledged to include Muslim American voices in his administration, if elected, and to speak out against human rights abuses against Muslim minorities around the world.

I'll continue to champion the rights of Palestinians and Israelis to have a state of their own as I have for decades, each of them a state of their own, he said.

Other state- and local-level Muslim American officials signing onto the pro-Biden letter hail from several states, including Michigan.

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