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
July 8,2020

Washington D.C, Jul 8:  US Secretary of State, Mike Pompeo on Tuesday (local time) announced visa restrictions on some Chinese officials under the Reciprocal Access to Tibet Act, 2018.

"Today I am announcing visa restrictions on PRC government and Chinese Communist Party officials determined to be "substantially involved in the formulation or execution of policies related to access for foreigners to Tibetan areas," pursuant to the Reciprocal Access to Tibet Act of 2018," Pompeo said.

"Access to Tibetan areas is increasingly vital to regional stability, given the PRC's human rights abuses there, as well as Beijing's failure to prevent environmental degradation near the headwaters of Asia's major rivers," he said.

The US Secretary of State pointed out that Beijing has continued "systematically to obstruct travel to the Tibetan Autonomous Region (TAR) and other Tibetan areas" by U.S. diplomats and other officials, journalists, and tourists, while PRC officials and other citizens enjoy far greater access to the United States.

"The United States will continue to work to advance the sustainable economic development, environmental conservation, and humanitarian conditions of Tibetan communities within the People's Republic of China and abroad," he said.

Pompeo said US also remains "committed to supporting meaningful autonomy for Tibetans, respect for their fundamental and unalienable human rights, and the preservation of their unique religious, cultural, and linguistic identity".

"In the spirit of true reciprocity, we will work closely with the U.S. Congress to ensure U.S. citizens have full access to all areas of the People's Republic of China, including the TAR and other Tibetan areas," he said.

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News Network
May 22,2020

May 22: A Pakistan International Airlines (PIA) flight on its way from Lahore to Karachi, crashed in the area near Jinnah International Airport on Friday, according to Civil Aviation Authority officials.

Geo News reported that the plane crashed at the Jinnah Ground area near the airport as it was approaching for landing. There were more than 90 passengers on board the Airbus aircraft. Black smoke could be seen from afar at the crash site, say eye witnesses.

There were no immediate reports on the number of casualties. The aircraft arriving from the eastern city of Lahore was carrying 99 passengers and 8 crew members, news agency AP said, quoting Abdul Sattar Kokhar, spokesman for the country’s civil aviation authority.

Witnesses said the Airbus A320 appeared to attempt to land two or three times before crashing in a residential area near Jinnah International Airport.

Flight PK-303 from Lahore was about to land in Karachi when it crashed at the Jinnah Garden area near Model Colony in Malir, just a minute before its landing, Geo News reported.

Local television reports showed smoke coming from the direction of the airport. Ambulances were on their way to the airport.

News agency said Sindh’s Ministry of Health and Population Welfare has declared emergency in all major hospitals of Karachi due to the plane crash.

It’s the second plane crash for Pakistani carrier in less than four years. The airline’s chairman resigned in late 2016, less than a week after the crash of an ATR-42 aircraft killed 47 people. The incident comes as Pakistan was slowly resuming domestic flights in the wake of the coronavirus pandemic, Bloomberg reported.

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Agencies
January 6,2020

The Cambridge Analytica scandal is far from over. New explosive details leaked by a whistleblower shows that the extent of the rot is far deeper than previously thought.

An anonymous Twitter account, @HindsightFiles, has started releasing the documents, apparently on behalf of Brittany Kaiser, a former employee of the now defunct British data analytics and consulting company Cambridge Analytica.

"Democracies around the world are being auctioned to the highest bidder. We release the documents that explain how," reads the biography of the @HindsightFiles.

The document will reveal previously unreleased emails, project plans, case studies, negotiations and more spanning over 60 countries.

"Over the past two years I have given evidence to investigators, journalists and academics to analyse what happened at Cambridge Analytica, and how our data was used to influence democracies around the world. In the name of shedding light on these dark practices, I am releasing documents and emails in full for the public good," Kaiser, who worked with Cambridge Analytica from 2014 to 208, was quoted as saying.

"I do this to strengthen the case for data rights and enforcement of our electoral laws online globally. We should all be seeking more ethical digital future for ourselves and our children," added Kaiser who starred in the Oscar-shortlisted Netflix documentary "The Great Hack".

The details released so far includes links to material on the firm's activities in Malaysia, Kenya, Brazil and Iran, an addition to the John Bolton archive.

Over the next months, more than 100,000 documents relating to work in 68 countries are set to be released, according to a report in The Guardian.

More than one and a half year after the Cambridge Analytica scandal first became public, US regulators last month said that the now-defunct British data analytics and consulting company engaged in deceptive practices to harvest personal information from tens of millions of Facebook users for voter profiling and targeting.

According to Kaiser, the Facebook data scandal was part of a much bigger global operation designed to manipulate people in collaboration with governments, intelligence agencies, commercial companies and political campaigns.

The unpublished documents contain material that suggests the firm collaborated with a political party in Ukraine in 2017 even while under investigation as part of Robert Mueller's investigation into Russian interference in the 2016 US presidential election, said The Guardian report.

"There are emails between these major Trump donors discussing ways of obscuring the source of their donations through a series of different financial vehicles. These documents expose the entire dark money machinery behind US politics," Kaiser was quoted as saying.

Similar tactics were deployed in other countries that Cambridge Analytica operated in, including Britain, she claimed.

The files released by Kaiser suggest that Cambridge Analytica offered to help United Malays National Organisation (Umno), the party of Malaysia's Former Prime Minister Najib Razak, to influence the voting of 40 parliamentary constituencies in the 14th General Election (GE14) in 2013.

Umno, according to the leaks, requested the company to prepare a proposal to regain 13 seats, The South China Morning Post reported on Saturday.

In 2018, Razak claimed that he had never engaged Cambridge Analytica in any way.

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