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
June 7,2020

Boston, Jun 7: Dozens of scientists doing research funded by Mark Zuckerberg say Facebook should not be letting President Donald Trump use of the social media platform to spread both misinformation and incendiary statements.

The researchers, including 60 professors at leading US research institutions, wrote a letter to the Facebook CEO on Saturday asking that he consider stricter policies on misinformation and incendiary language that harms people," especially during the current turmoil over racial injustice.

The letter calls the spread of deliberate misinformation and divisive language the researchers' goal of using technology to prevent and eradicate disease, improving childhood education and reform the criminal justice system.

The researchers' mission "is antithetical to some of the stances that Facebook has been taking, so we're encouraging them to be more on the side of truth and on the right side of history as we've said in the letter, said Debora Marks of Harvard Medical School, one of three professors who organized the letter.

The other organisers are Martin Kampmann of the University of California-San Francisco and Jason Shepherd of the University of Utah.

All have grants from a Chan Zuckerberg Initiative program working to prevent, cure and treat neurodegenerative disorders including Alzheimer's and Parkinson's disease. The initiative is run by Zuckerberg and his wife, Priscilla Chan.

They said the letter had more than 160 signatories. Shepherd said about 10% are employees of Chan Zuckerberg foundations.

The letter objects specifically to Zuckerberg's decision not to at least flag as a violation of Facebook's community standards Trump's post that stated when the looting starts, the shooting starts after unrest in Minneapolis over the videotaped killing of George Floyd, a black man, by a white police officer.

The letter's authors called the post a clear statement of inciting violence.

Twitter had both flagged and demoted a Trump tweet using the same language.

The Associated Press emailed the Chan Zuckerberg Initiative press office for comment. It did not immediately respond.

Some Facebook employees have publicly objected to Zuckerberg's refusal to take down or label misleading or incendiary posts by Trump or other politicians. But Zuckerberg who controls a majority of voting shares in the company has so far refused.

On Friday, Zuckerberg said in a post that he would review potential options for handling violating or partially-violating content aside from the binary leave-it-up or take-it-down decisions I know many of you think we should have labeled the President's posts in some way last week, he wrote.

"Our current policy is that if content is actually inciting violence, then the right mitigation is to take that content down not let people continue seeing it behind a flag. There is no exception to this policy for politicians or newsworthiness.

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Agencies
March 1,2020

Washington, Mar 1: Beginning April 1, Indians wishing to immigrate to America will now have to pay an additional $50,000 for the EB-5 or the US investor visa, a media report said.

Although, this additional tax would impact all visa categories, it will predominantly create a barrier for people investing in the EB-5 visa programme, the American Bazaar daily said in the report on Friday.

In 2019, the EB-5 investor visa programme, for the first time since the 1990's, increased the minimum investment amount to $900,000.

With this increase in minimum investment, the new 5 per cent additional tax would mean that applicants would have to pay the extra $50,000, when they move money to an escrow account in the US to fulfil their application criterion.

"The changes to the tax on remittances is a reminder to Indians to carefully plan their tax position before making the move to the US," the American Bazaar quoted Mark Davies, Global Chairman, Davies & Associates LLC, as saying.

"People seeking to emigrate who do not wish to pay this tax at source and rather account for it later may wish to move their money ahead of the new rules coming into effect.

"It is possible to pre-emptively move money into an escrow account in the US until such a time as they are ready to proceed with emigration process," he added.

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News Network
March 5,2020

Washington, Feb 5: Experts warned a US government panel last night that India's Muslims face risks of expulsion and persecution under the country’s new Citizenship Amendment Act (CAA) which has triggered major protests.

The hearing held inside Congress was called by the US Commission on International Freedom, which has been denounced by the Indian government as biased.

Ashutosh Varshney, a prominent scholar of sectarian violence in India, told the panel that the law championed by prime minister Narendra Modi's government amounted to a move to narrow the democracy's historically inclusive and secular definition of citizenship.

"The threat is serious, and the implications quite horrendous," said Varshney, a professor at Brown University.

"Something deeply injurious to the Muslim minority can happen once their citizenship rights are taken away," he said.

Varshney warned that the law could ultimately lead to expulsion or detention -- but, even if not, contributes to marginalization.

"It creates an enabling atmosphere for violence once you say that a particular community is not fully Indian or its Indianness in grave doubt," he said.

India's parliament in December passed a law that fast-tracks citizenship for persecuted non-Muslim minorities from neighboring countries.

Responding to criticism at the time from the US commission, which advises but does not set policy, India's External Affairs Ministry said the law does not strip anyone's citizenship and "should be welcomed, not criticized, by those who are genuinely committed to religious freedom."

Fears are particularly acute in Assam, where a citizens' register finalized last year left 1.9 million people, many of them Muslims, facing possible statelessness.

Aman Wadud, a human rights lawyer from Assam who traveled to Washington for the hearing, said that many Indians lacked birth certificates or other documentation to prove citizenship and were only seeking "a dignified life."

The hearing did not exclusively focus on India, with commissioners and witnesses voicing grave concern over Myanmar's refusal to grant citizenship to the Rohingya, the mostly Muslim minority that has faced widespread violence.

Gayle Manchin, the vice chair of the commission, also voiced concern over Bahrain's stripping of citizenship from activists of the Shiite majority as well as a new digital ID system in Kenya that she said risks excluding minorities.

More than 40 people were killed last week in New Delhi in sectarian violence sparked by the citizenship law.

India on Tuesday lodged another protest after the UN human rights chief, Michele Bachelet, sought to join a lawsuit in India that challenges the citizenship law's constitutionality.

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