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 28,2020

Washington, Apr 28: After nearly three weeks in an intensive care unit in Los Angeles, doctors treating 41-year-old Broadway actor Nick Cordero for COVID-19 were forced to amputate his right leg.

The flow of blood had been impeded by a blood clot: yet another dangerous complication of the disease that has been bubbling up in frontline reports from China, Europe and the United States.

To be sure, so-called "thrombotic events" occur for a variety of reasons among intensive care patients, but the rates among COVID-19 patients are far higher than would be otherwise expected.

"I have had 40-year-olds in my ICU who have clots in their fingers that look like they'll lose the finger, but there's no other reason to lose the finger than the virus," Shari Brosnahan, a critical care doctor at NYU Langone said.

One of these patients is suffering from a lack of blood flow to both feet and both hands, and she predicts an amputation may be necessary, or the blood vessels may get so damaged that an extremity could drop off by itself.

Blood clots aren't just dangerous for our limbs, but can make their way to the lungs, heart or brain, where they may cause lethal pulmonary embolisms, heart attacks, and strokes.

A recent paper from the Netherlands in the journal Thrombosis Research found that 31 percent of 184 patients suffered thrombotic complications, a figure that the researchers called "remarkably high" -- even if extreme consequences like amputation are rare.

Behnood Bikdeli, a doctor at New York-Presbyterian Hospital, assembled an international consortium of experts to study the issue. Their findings were published in the Journal of The American College of Cardiology.

The experts found the risks were so great that COVID-19 patients "may need to receive blood thinners, preventively, prophylactically," even before imaging tests are ordered, said Bikdeli.

What exactly is causing it? The reasons aren't fully understood, but he offered several possible explanations.

People with severe forms of COVID-19 often have underlying medical conditions like heart or lung disease -- which are themselves linked to higher rates of clotting.

Next, being in intensive care makes a person likelier to develop a clot because they are staying still for so long. That's why for example people are encouraged to stretch and move around on long haul flights.

It's also now clear the COVID-19 illness is associated with an abnormal immune reaction called "cytokine storm" -- and some research has indicated this too is linked to higher rates of clotting.

There could also be something about the virus itself that is causing coagulation, which has some precedent in other viral illnesses.

A paper in the journal The Lancet last week showed that the virus can infect the inner cell layer of organs and of blood vessels, called the endothelium. This, in theory, could interfere with the clotting process.

According to Brosnahan, while thinners like Heparin are effective in some patients, they don't work for all patients because the clots are at times too small.

"There are too many microclots," she said. "We're not sure exactly where they are."

Autopsies have in fact shown some people's lungs filled with hundreds of microclots.

The arrival of a new mystery however helps solve a slightly older one.

Cecilia Mirant-Borde, an intensive care doctor at a military veterans hospital in Manhattan, told AFP that lungs filled with microclots helped explain why ventilators work poorly for patients with low blood oxygen.

Earlier in the pandemic doctors were treating these patients according to protocols developed for acute respiratory distress syndrome, sometimes known as "wet lung."

But in some cases, "it's not because the lungs are occupied with water" -- rather, it's that the microclotting is blocking circulation and blood is leaving the lungs with less oxygen than it should.

It has just been a little under five months since the virus emerged in Wuhan, China, and researchers are learning more about its impact every day.

"While we react surprised, we shouldn't be as surprised as we were. Viruses tend to do weird things," said Brosnahan.

While the dizzying array of complications may seem daunting, "it's possible there'll be one or a couple of unifying mechanisms that describe how this damage happens," she said.

"It's possible it's all the same thing, and that there'll be the same solution."

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Agencies
January 4,2020

Stockholm, Jan 4: “I’m not the kind of person who celebrates birthdays,” Greta Thunberg said as she turned 17 on Friday, marking the occasion in inimitable style - with a seven-hour hour protest outside the Swedish parliament.

The climate activist braved winter conditions in her native Stockholm to continue the weekly Friday School Strike for the Climate campaign that helped catapult her to international fame.

“I stand here striking from 8am until 3pm as usual ... then I’ll go home,” Thunberg, Time magazine’s Person of the Year for 2019, told Reuters.

“I won’t have a birthday cake but we’ll have a dinner.”

It’s been a busy 12 months for Thunberg, who crisscrossed the globe by car, train and boat - but not plane - to demand action on climate change.

“It has been a strange and busy year, but also a great one because I have found something I want to do with my life and what I am doing is having an impact,” she said.

When she was 15, Thunberg began skipping school on Fridays to demonstrate outside the Swedish parliament to push her government to curb carbon emissions. Her campaign gave rise to a grassroots movement that has gone global, inspiring millions of people to take action.

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News Network
February 21,2020

Washington, Feb 21: US President Donald Trump has made yet another tall claim about the size of the crowd that will welcome him in Ahmedabad, saying Prime Minister Narendra Modi has told him that there will 10 million(1 crore) people to greet him on his arrival for his maiden visit to India.

President Trump and First Lady Melania are scheduled to travel to Ahmedabad, Agra and New Delhi on February 24 and 25.

Speaking to reporters at the Joint Base Andrews in Maryland on Tuesday, Trump said that Modi told him that "we'll have 7 million people between the airport and the event."

"So it's going to be very exciting. But he says between the stadium and the airport, we'll have about 7 million people. So it's going to be very exciting. I hope you all enjoy it," he said.

On Thursday, Trump upped the crowd size by three million at a 'Keep America Great' rally in Colorado.

"I hear, they are going to have 10 million people. They say anywhere from six to 10 million people are going to be showing up along the route to one of the largest stadiums in the world, the largest cricket stadium in the world, which is brand new and beautiful," said Trump, who is seeking reelection in the November presidential polls.

But according to a top civic official in Ahmedabad, the total population of the city is only around 70 lakh.

The authorities believe that between one to two lakh people are expected to line up along the 22-km route of the road show by Modi and Trump from the airport to the Motera cricket stadium, said to be the world's largest.

"We believe that around one to two lakh people will gather to welcome the dignitaries during the road show," Ahmedabad Municipal Commissioner Vijay Nehra said on Thursday, contradicting the claims made by the US President.

As per the road show route plan, Trump and Modi will first reach the Sabarmati Ashram, a place closely associated with Mahatma Gandhi, from Ahmedabad airport.

Addressing his supporters, Trump spoke about his India visit and said the "Namaste Trump" rally in Ahmedabad would spoil him.

"Prime Minister Modi said, we will have 10 million people greet you. Here's my problem. We have a packed house. We have a lot of people, thousands of people that couldn't get in. It's going to look like peanuts from now on," he said.

"I'll never be satisfied with the crowd. If we have 10 million people in India, how can I be satisfied when we fill up like a 60,000-seat stadium? I am getting spoiled," Trump said.

One of Trump's supporters from the audience then suggested that he build a bigger stadium.

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