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
May 23,2020

Washington, May 23: President Donald Trump has labeled churches and other houses of worship as “essential" and called on governors nationwide to let them reopen this weekend even though some areas remain under coronavirus lockdown.

The president threatened Friday to “override” governors who defy him, but it was unclear what authority he has to do so.

“Governors need to do the right thing and allow these very important essential places of faith to open right now — for this weekend," Trump said at a hastily arranged press conference at the White House. Asked what authority Trump might have to supersede governors, White House press secretary Kayleigh McEnany said she wouldn't answer a theoretical question.

Trump has been pushing for the country to reopen as he tries to reverse an economic free fall playing out months before he faces reelection. White evangelical Christians have been among the president's most loyal supporters, and the White House has been careful to attend to their concerns throughout the crisis.

Following Trump's announcement, the Centers for Disease Control and Prevention released new guidelines for communities of faith on how to safely reopen, including recommendations to limit the size of gatherings and consider holding services outdoors or in large, well-ventilated areas.

Public health agencies have generally advised people to avoid gatherings of more than 10 people and encouraged Americans to remain 6 feet (1.8 meters) away from others when possible. Some parts of the country remain under some version of remain-at-home orders.

In-person religious services have been vectors for transmission of the virus. A person who attended a Mother's Day service at a church in Northern California that defied the governor's closure orders later tested positive, exposing more than 180 churchgoers. And a choir practice at a church in Washington state was labeled by the CDC as an early “superspreading" event.

But Trump on Friday stressed the importance of churches in many communities and said he was “identifying houses of worship — churches, synagogues and mosques — as essential places that provide essential services.”

“Some governors have deemed liquor stores and abortion clinics as essential” but not churches, he said. “It's not right. So I'm correcting this injustice and calling houses of worship essential." “These are places that hold our society together and keep our people united,” he added.

Dr. Deborah Birx, coordinator of the White House coronavirus task force, said faith leaders should be in touch with local health departments and can take steps to mitigate risks, including making sure those who are at high risk of severe complications remain protected.

“There's a way for us to work together to have social distancing and safety for people so we decrease the amount of exposure that anyone would have to an asymptomatic," she said.

A person familiar with the White House's thinking who spoke on condition of anonymity to discuss internal deliberations said Trump had called the news conference, which had not been on his public schedule, because he wanted to be the face of church reopenings, knowing how well it would play with his political base.

Churches around the country have filed legal challenges opposing virus closures.

In Minnesota, after Democratic Gov. Tim Walz this week declined to lift restrictions on churches, Roman Catholic and some Lutheran leaders said they would defy his ban and resume worship services. They called the restrictions unconstitutional and unfair since restaurants, malls and bars were allowed limited reopening.

Some hailed the president's move, including Kelly Shackelford, president of the conservative First Liberty Institute.

“The discrimination that has been occurring against churches and houses of worship has been shocking," he said in a statement. "Americans are going to malls and restaurants. They need to be able to go to their houses of worship.” But Rabbi Jack Moline, president of Interfaith Alliance, said it was “completely irresponsible” for Trump to call for a mass reopening of houses of worship.

“Faith is essential and community is necessary; however, neither requires endangering the people who seek to participate in them,” he said.

“The virus does not discriminate between types of gatherings, and neither should the president." Rhode Island Gov. Gina Raimondo, a Democrat, made clear that churches and other houses of worship will not resume in-person services in her state until at least next weekend and said she was skeptical Trump had the authority to impose such a requirement.

“It's reckless to force them to reopen this weekend. They're not ready,” she said. “We've got a good plan. I'm going to stick with it.” New Hampshire Gov. Chris Sununu, a Republican, said he would review the federal guidance, while maintaining a decision rests with him.

"Obviously we'd love to get to the point where we can get those open, but we'll look at the guidance documents and try to make some decisions rather quickly, depending on what it might say,” he said. “It's the governor's decision, of course.”

The CDC more than a month ago sent the Trump administration documents the agency had drafted outlining specific steps various kinds of organizations, including houses of worship, could follow as they worked to reopen safely.

But the White House dragged its feet, concerned that the recommendations were too specific and could give the impression the administration was interfering in church operations.

The guidance posted Friday contains most of the same advice as the draft guidance. It calls for the use of face coverings and recommends keeping worshippers 6 feet from one another and cutting down on singing, which can spread aerosolized drops that carry the virus.

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Agencies
June 27,2020

Washington, Jun 27: Facebook has said that it will flag all "newsworthy" posts from politicians that break its rules, including those from President Donald Trump.

Separately, Facebook's stock dropped more than 8 per cent, erasing roughly USD 50 billion from its market valuation, after the European company behind brands such as Ben & Jerry's and Dove announced it would boycott Facebook ads through the end of the year over the amount of hate speech and divisive rhetoric on its platform.

Later in the day, Coca-Cola also announced it joined the boycott for at least 30 days.

CEO Mark Zuckerberg had previously refused to take action against Trump posts suggesting that mail-in ballots will lead to voter fraud, saying that people deserved to hear unfiltered statements from political leaders.

Twitter, by contrast, slapped a "get the facts" label on them.

Until Friday, Trump's posts with identical wording to those labelled on Twitter remained untouched on Facebook, sparking criticism from Trump's opponents as well as current and former Facebook employees.

Now, Facebook is all but certain to face off with the president the next time he posts something the company deems to be violating its rules.

"The policies we're implementing today are designed to address the reality of the challenges our country is facing and how they're showing up across our community," Zuckerberg wrote on his Facebook page announcing the changes.

Zuckerberg said the social network is taking additional steps to counter election-related misinformation.

In particular, the social network will begin adding new labels to all posts about voting that will direct users to authoritative information from state and local election officials.

Facebook is also banning false claims intended to discourage voting, such as stories about federal agents checking legal status at polling places.

The company also said it is increasing its enforcement capacity to remove false claims about local polling conditions in the 72 hours before the US election.

Ethan Zuckerman, director of the Massachusetts Institute of Technology's Center for Civic Media, said the changes are a "reminder of how powerful Facebook may be in terms of spreading disinformation during the upcoming election".

He said the voting labels will depend on how good Facebook's artificial intelligence is at identifying posts to label.

"If every post that mentions voting links, people will start ignoring those links. If they're targeted to posts that say things like 'Police will be checking warrants and unpaid traffic tickets at polls' a classic voter suppression disinfo tactic and clearly mark posts as disinfo, they might be useful," he said.

But Zuckerman noted that Facebook "has a history of trying hard not to alienate right-leaning users, and given how tightly President Trump has aligned himself with voter-suppressing misinfo, it seems likely that Facebook will err on the side of non-intrusive and ignorable labels, which would minimize impact of the campaign."

Earlier in the day, shares of Facebook and Twitter dropped sharply after consumer-product maker Unilever announced a new ad boycott on Facebook, Twitter and Instagram through at least the end of the year.

The European company said it took the move to protest the amount of hate speech online.

Unilever said the polarised atmosphere in the United States ahead of November's presidential election placed responsibility on brands to act.

In addition to the decline in Facebook shares, Twitter ended the day more than 7 per cent lower.

Unilever, which is based in the Netherlands and Britain, joins a raft of other advertisers pulling back from online platforms.

Facebook in particular has been the target of an escalating movement to withhold advertising dollars to pressure it to do more to prevent racist and violent content from being shared on its platform.

"We have decided that starting now through at least the end of the year, we will not run brand advertising in social media newsfeed platforms Facebook, Instagram and Twitter in the U.S.," Unilever said.

"Continuing to advertise on these platforms at this time would not add value to people and society."

Facebook did not immediately respond to a request for comment. On Thursday, Verizon joined others in the Facebook boycott.

Unilever "has enough influence to persuade other brand advertisers to follow its lead," said eMarketer analyst Nicole Perrin.

She noted that Unilever pulled back spending "for longer, on more platforms (including Twitter) and for more expansive reasons" in particular, by citing problems with "divisiveness" as well as hate speech.

Sarah Personette, vice president of global client solutions at Twitter, said the company's "mission is to serve the public conversation and ensure Twitter is a place where people can make human connections, seek and receive authentic and credible information, and express themselves freely and safely."

She added that Twitter is "respectful of our partners' decisions and will continue to work and communicate closely with them during this time."

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News Network
June 15,2020

Stockholm, Jun 15: Nuclear powers continue to modernise their arsenals, researchers said Monday, warning that tensions were rising and the outlook for arms control was "bleak".

"The loss of key channels of communication between Russia and the USA... could potentially lead to a new nuclear arms race," said Shannon Kile, director of the nuclear arms control programme at the Stockholm International Peace Research Institute (SIPRI) and co-author of the report.

Russia and the US account for more than 90 percent of the world's nuclear weapons.

Kile was referring to the future of the New START treaty between the US and Russia, which is set to expire in February 2021.

It is the final nuclear deal still in force between the two superpowers, aimed at maintaining their nuclear arsenals below Cold War levels.

"Discussions to extend New START or to negotiate a new treaty made no progress in 2019," the SIPRI researchers noted.

At the same time, nuclear powers continue to modernise their weapons while China and India are increasing the size of their arsenals.

"China is in the middle of a significant modernisation of its nuclear arsenal. It is developing a so-called nuclear triad for the first time, made up of new land- and sea-based missiles and nuclear-capable aircraft," SIPRI said.

The country has repeatedly rejected Washington's insistence that it join any future nuclear arms reduction talks.

The number of nuclear warheads declined in the past year.

At the start of 2020, the United States, Russia, Britain, China, India, Pakistan, Israel and North Korea together had 13,400 nuclear arms, according to SIPRI's estimates, 465 fewer than at the start of 2019.

The decline was attributed mainly to the United States and Russia.

While the future of the New START treaty remains uncertain, Washington and Moscow have continued to respect their obligations under the accord.

"In 2019, the forces of both countries remained below the limits specified by the treaty," the report said. But both nations "have extensive and expensive programmes underway to replace and modernise their nuclear warheads, missile and aircraft delivery systems, and nuclear weapon production facilities," it added.

"Both countries have also given new or expanded roles to nuclear weapons in their military plans and doctrines, which marks a significant reversal of the post-Cold War trend towards the gradual marginalisation of nuclear weapons."

The Treaty on the Non-Proliferation of Nuclear Weapons (NPT), a cornerstone of the global nuclear non-proliferation regime, celebrates its 50th anniversary this year.

The number of nuclear arms worldwide has declined since hitting a peak of almost 70,000 in the mid-1980s.

The five original nuclear powers -- Washington, Beijing, Moscow, Paris and London -- in March reiterated their commitment to the treaty.

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