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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Agencies
August 4,2020

Washington, Aug 4: US President Donald Trump gave popular Chinese-owned video app TikTok six weeks to sell its US operations to an American company, saying Monday it would be "out of business" otherwise, and that the government wanted a financial benefit from the deal.

"It's got to be an American company... it's got to be owned here," Trump said. "We don't want to have any problem with security."

Trump said that Microsoft was in talks to buy TikTok, which has as many as one billion worldwide users who make quirky 60-second videos with its smartphone app.

But US officials say the app constitutes a national security risk because it could share millions of Americans' personal data with Chinese intelligence.

Trump gave the company's Chinese parent ByteDance until mid-September to strike a deal.

"I set a date of around September 15, at which point it's going to be out of business in the United States," he said.

Whatever the price is, he said, "the United States should get a very large percentage of that price because we're making it possible."

Trump compared the demand for a piece of the pie to a landlord demanding under-the-table "key money" from a new tenant, a practice widely illegal including in New York, where the billionaire president built his real estate empire.

"TikTok is a big success, but a big portion of it is in the country," he said. "I think it's very fair."

But Trump also threw a surprise new condition in any deal, saying the sale of TikTok's US business would have to result in a significant payout to the US Treasury for initiating it.

"A very substantial portion of that price is going to have to come into the Treasury of the United States, because we're making it possible for this deal to happen," Trump told reporters.

"They don't have any rights unless we give it to them," he said.

Sell or shut down

The pressure for a sale of TikTok's US and international business, based in Los Angeles, left the company and ByteDance facing tough decisions.

Trump has made TikTok the latest front in the ongoing political and trade battles between Washington and Beijing.

The app has been under formal investigation on US national security grounds because it collects large amounts of personal data on all its users and is legally bound to share that with authorities in Beijing if they demand it.

Both its huge user base and its algorithm for collecting data make it hugely valuable.

But being forced by the US government to sell at least its US business or be shut down -- and to then split the sale price with the US Treasury as Trump is demanding -- was an almost unheard-of tactic.

Shutting down could force users to switch to competitors, and many content creators are already encouraging followers to follow them on other social media platforms.

"The most obvious beneficiaries are Snapchat, Facebook and Twitter, with Snapchat likely being the biggest beneficiary," said investment analysts at Lightshed Partners.

Earlier Monday, ByteDance founder Zhang Yiming acknowledged the hefty pressure and said in a letter to staff, reported by Chinese media, that they were working around-the-clock "for the best outcome."

"We have always been committed to ensuring user data security, as well as the platform neutrality and transparency," Zhang said.

However, he said, the company faces "mounting complexities across the geopolitical landscape and significant external pressure."

He said the company must confront the challenge from the United States, though "without giving up exploring any possibilities."

According to Britain's The Sun newspaper Monday, as a possible consequence of the pressure, ByteDance is planning to relocate TikTok's global operations to Britain.

Pushing back

China's foreign ministry pushed back Monday, calling Washington hypocritical for demanding TikTok be sold.

"The US is using an abused concept of national security and, without providing any evidence, is making presumptions of guilt and issuing threats to relevant companies," said spokesman Wang Wenbin.

"This goes against the principle of market economy and exposes the hypocrisy and typical double standards of the US in upholding so-called fairness and freedom," he added.

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News Network
May 5,2020

May 5: Global coronavirus deaths reached 250,000 on Monday after recorded infections topped 3.5 million, a news agency tally of official government data showed, although the rate of fatalities has slowed.

North America and European countries accounted for most of the new deaths and cases reported in recent days, but numbers were rising from smaller bases in Latin America, Africa and Russia.

Globally, there were 3,062 new deaths and 61,923 new cases over the past 24 hours, taking total cases to 3.58 million.

That easily exceeds the estimated 140,000 deaths worldwide in 2018 caused by measles, and compares with around 3 million to 5 million cases of severe illness caused annually by seasonal influenza, according to the World Health Organization (WHO).

While the current trajectory of COVID-19 falls far short of the 1918 Spanish flu, which infected an estimated 500 million people, killing at least 10% of patients, experts worry the available data is underplaying the true impact of the pandemic.

The concerns come as several countries begin to ease strict lockdowns that have been credited with helping contain the spread of the virus.

"We could easily have a second or a third wave because a lot of places aren't immune," Peter Collignon, an infectious diseases physician and microbiologist at Canberra Hospital, told Reuters. He noted the world was well short of herd immunity, which requires around 60% of the population to have recovered from the disease.

The first death linked to COVID-19 was reported on Jan. 10 in Wuhan, China after the coronavirus first emerged there in December. Global fatalities grew at a rate of 1-2% in recent days, down from 14% on March 21, according to the Reuters data.

DEATH RATE ANOMALIES

Mortality rates from recorded infections vary greatly from country to country.

Collignon said any country with a mortality rate of more than 2% almost certainly had underreported case numbers. Health experts fear those ratios could worsen in regions and countries less prepared to deal with the health crisis.

"If your mortality rate is higher than 2%, you've missed a lot of cases," he said, noting that countries overwhelmed by the outbreak were less likely to conduct testing in the community and record deaths outside of hospitals.

In the United States, around half the country's state governors partially reopened their economies over the weekend, while others, including New York Governor Andrew Cuomo, declared the move was premature.

In Britain, Prime Minister Boris Johnson, who battled COVID-19 last month, has said the country was over the peak but it was still too early to relax lockdown measures.

Even in countries where the suppression of the disease has been considered successful, such as Australia and New Zealand which have recorded low daily rates of new infections for weeks, officials have been cautious.

Australian Prime Minister Scott Morrison has predicated a full lifting of curbs on widespread public adoption of a mobile phone tracking app and increased testing levels.

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Agencies
February 11,2020

The head of the World Health Organisation on Tuesday warned the novel coronavirus was a "very grave threat" for the world as he opened a conference to combat the epidemic.

"With 99% of cases in China, this remains very much an emergency for that country, but one that holds a very grave threat for the rest of the world," Tedros Adhanom Ghebreyesus said in Geneva.

Some 400 scientists will review how the virus is transmitted and possible vaccines at the two-day forum.

"What matters most is stopping the outbreak and saving lives. With your support, that's what we can do together," Tedros said.

The virus, first identified in China on December 31, has killed more than 1,000 people, infected over 42,000 and reached some 25 countries.

Participants will also discuss the source of the virus, which is thought to have originated in bats and reached humans via another animal such as snakes or pangolins.

There is no specific treatment or vaccine against the virus, which can cause respiratory failure.

Tedros, who has repeatedly urged countries affected to share their data, called for global "solidarity".

"That is especially true in relation to the sharing of samples and sequences. To defeat this outbreak, we need open and equitable sharing, according to the principles of fairness and equity," he said.

"We hope that one of the outcomes of this meeting will be an agreed roadmap for research around which researchers and donors will align," Tedros said.

Several companies and institutes in Australia, China, France, Germany and the United States are racing to develop a vaccine -- a process that normally takes years.

Asked whether scientists from Taiwan would be allowed to take part in this week's Geneva conference, WHO officials said that they would do so but only online -- along with colleagues from other parts of China.

While the WHO does not deal with Taiwan directly and only recognises Beijing, Taiwan was often allowed to attend annual assemblies and sideline meetings as an observer.

But in recent years it has been frozen out as Beijing takes an increasingly combative stance towards democratic Taiwan, which it considers its own territory.

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