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
May 15,2020

May 15: Global tensions simmered over the race for a coronavirus vaccine Thursday, as the United States and China traded jabs, and France slammed pharmaceuticals giant Sanofi for suggesting the US would get any eventual vaccine first.

Scientists are working at breakneck speed to develop a vaccine for COVID-19, the disease caused by the virus, which has killed more than 300,000 people worldwide and pummelled economies.

From the US to Europe to Asia, national and local governments are easing lockdown orders to get people back to work -- while fretting over a possible second wave of infections.

Increased freedom of movement means an increased risk of contracting the virus, and so national labs and private firms are labouring to find the right formula for a vaccine.

The European Union's medicines agency offered some hope when it said one could be ready in a year, based on data from clinical trials already underway.

But Marco Cavaleri, the EMA's head of vaccines strategy, acknowledged that timeline was a "best-case scenario," and cautioned that "there may be delays."

The race for a vaccine has exposed a raw nerve in relations between the United States and China, where the virus was first detected late last year in the central city of Wuhan.

Two US agencies warned Wednesday that Chinese hackers were trying to steal COVID-19 vaccine research -- a claim Beijing rejected as "smearing" its reputation.

US President Donald Trump, who has ratcheted up the rhetoric against China, said he doesn't even want to engage with Chinese leader Xi Jinping -- potentially imperilling a trade deal between the world's top two economies.

"I'm very disappointed in China. I will tell you that right now," he said in an interview with Fox Business.

"There are many things we could do. We could do things. We could cut off the whole relationship."

On Capitol Hill, an ousted US health official told Congress that the Trump government had no strategy in place to find and distribute a vaccine to millions of Americans, warning of the "darkest winter" ahead.

"We don't have a single point of leadership right now for this response, and we don't have a master plan," said Rick Bright, who was removed last month as head of the US agency charged with developing a coronavirus vaccine.

The United States has registered nearly 86,000 deaths linked to COVID-19 -- the highest toll of any nation.

World leaders were among 140 signatories to a letter published Thursday saying any vaccine should not be patented and that the science should be shared among nations.

"Governments and international partners must unite around a global guarantee which ensures that, when a safe and effective vaccine is developed, it is produced rapidly at scale and made available for all people, in all countries, free of charge," it said.

But a row erupted in France after drugmaker Sanofi said it would reserve first shipments of any vaccine it discovered to the United States.

The comments prompted a swift rebuke from the French government -- President Emmanuel Macron's office said any vaccine should be treated as "a global public good, which is not submitted to market forces."

Sanofi chief executive Paul Hudson said the US had a risk-sharing model that allowed for manufacturing to start before a vaccine had been finally approved -- while Europe did not.

"The US government has the right to the largest pre-order because it's invested in taking the risk," Hudson told Bloomberg News.

Macron's top officials are scheduled to meet with Sanofi executives about the issue next week.

The search for a vaccine became even more urgent after the World Health Organization said the disease may never go away and the world would have to learn to live with it for good.

"This virus may become just another endemic virus in our communities and this virus may never go away," said Michael Ryan, the UN body's emergencies director.

The prospect of the disease lingering leaves governments facing a delicate balancing act between suppressing the pathogen and getting their economies up and running.

In the US, more grim economic data emerged Thursday, with nearly three million more Americans applying for unemployment benefits.

That takes the overall total to 36.5 million -- more than 10 percent of the US population.

Further signs of the damage to businesses emerged when Lloyd's of London forecast the pandemic will cost the global insurance industry about $203 billion.

European markets closed down, but Wall Street rallied despite the new jobless claims. In a sign of progress, the New York Stock Exchange trading floor was due to reopen on May 26.

The reopening of economies continued in earnest across Europe, where the EU has set out proposals for a phased restart of travel and the eventual lifting of border controls.

"Maybe it's a mistake, but we have no choice. Without tourists, we won't get by!" Enrico Facchetti, a 61-year-old former goldsmith, said of Venice's reopening.

Japan -- the world's third largest economy -- lifted a state of emergency across most of the country except for Tokyo and Osaka.

And Canadian Prime Minister Justin Trudeau said national parks would partially reopen on June 1.

But in Latin America, the virus continued to surge, with a 60 percent leap in cases in the Chilean capital of Santiago.

Authorities said 2,000 new graves were being dug at the main cemetery.

South Sudan reported its first COVID-19 death on Thursday.

And in Bangladesh, the first case was confirmed in the teeming Rohingya refugee camps in Bangladesh, which are home to nearly one million people.

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News Network
April 30,2020

London, Apr 30: The coronavirus is roiling global job markets, but the picture is not all gloomy. Finance, technology and consumer goods firms are hiring tens of thousands in the United States and other countries, according to data from Microsoft Corp's professional networking site LinkedIn.

Across seven countries in North America, Europe and Asia, healthcare providers are among the busiest recruiters given the ongoing battle against the novel coronavirus, which has killed over 200,000 people and infected over 3 million people worldwide, LinkedIn said. But lifestyle changes during lockdown are also driving demand for financial consultants, factory workers, animators and game designers, and delivery workers.

Overall, the hiring rate has plunged in the first quarter from the year-ago period, and in late April remains lower than a year ago across most countries surveyed by the platform. But the data offer a glimmer of hope with a gradual uptick in China, where the coronavirus emerged last year and which leads the world in surfacing from a months-long lockdown.

LinkedIn, with over 690 million users worldwide, counts new hires when people add a new employer to their profile. The rate is the number of new hires divided by the total number of LinkedIn members in a country.

The figures, tracked since mid-February, are not corroborated by official jobs data and do not represent the actual number of jobs in an economy. Government figures are usually released with a time-lag of several weeks.

"We are confident that our data is directionally correct in that there has been a huge decline in hiring in the U.S. and abroad," Guy Berger, principal economist at LinkedIn in California, told Reuters.

Hiring in China plummeted 50% during the height of its coronavirus crisis in mid-February from 12 months earlier. Since restrictions were eased in early April, the hiring rate has inched up, and for the week ending April 24 was 3% lower than the same period in 2019.

Hiring in the United States, United Kingdom, France and Italy - which lead the world in coronavirus-related deaths - remains hugely depressed, but is falling less rapidly than a few weeks ago as the countries pass the peak of their epidemics.

Retailers including Walmart Inc, Amazon.com Inc and Instacart have said they would hire a total of over 700,000 workers to meet a surge in demand for groceries and household essentials during the coronavirus outbreak.

Coronavirus state-wise India update: Total number of confirmed cases, deaths on April 30

Consumer goods manufacturers such as Unilever, whose products include soap and shampoo, confirmed on Wednesday it was hiring to fill 300 jobs globally, but declined to elaborate.

Nestle told Reuters it was looking to fill 5,000 full-time U.S. positions in "a variety of levels across corporate and frontline."

Fidelity Investments, a Boston-based financial services firm, said it had accelerated recruitment because of the pandemic and was looking to fill at least 2,000 full-time roles for financial consultants, software engineers and customer service staff in the United States in 2020.

Companies hiring in the United States and other countries also include Apple Inc; ByteDance, the Chinese parent of video-sharing social network TikTok; Takeda Pharmaceutical Co Ltd; and aerospace and defence company Lockheed Martin Corp. These companies did not immediately respond to requests for comment.

DIRE WARNINGS

The International Labour Organization warned on Wednesday that 1.6 billion workers, or nearly half of the global workforce, especially in the informal economy, could lose their livelihoods.

Record numbers of people have applied for U.S. jobless benefits since mid-March, and the unemployment rate is expected to soar to 16%, White House economic adviser Kevin Hasset said this week, from a 50-year low of 3.5% before the pandemic hit.

Both Italy and France, in lockdown for nearly two months, have seen hiring rates drop by around 70% from a year ago, according to LinkedIn.

Since China is ahead of other countries on the pandemic timeline, improvements there could suggest the same is in store elsewhere, Berger said. Several American states and European countries have begun allowing some non-essential businesses and schools to reopen in the hopes of restarting the economy and allowing a gradual return to normal life.

"It's still slightly early to call it a firm recovery," Berger said, referring to improving prospects in China. "We're not expecting a full recovery but rather it's an indication that parts of the economy will switch on as lockdowns are eased, at least relative to the worst point of the pandemic."

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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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