American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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 30,2020

Washington, May 30: The United States will end its relationship with the World Health Organization over the body’s handling of the coronavirus pandemic, U.S. President Donald Trump said on Friday, accusing the U.N. agency of becoming a puppet of China.

The move to quit the Geneva-based body, which the United States formally joined in 1948, comes amid growing tensions between Washington and Beijing over the coronavirus outbreak. The virus first emerged in China’s Wuhan city late last year.

Speaking in the White House Rose Garden, Trump said Chinese officials “ignored their reporting obligations” to the WHO about the virus - that has killed hundreds of thousands of people globally - and pressured the agency to “mislead the world.”

“China has total control over the World Health Organization despite only paying $40 million per year compared to what the United States has been paying which is approximately $450 million a year,” he said.

Trump’s decision follows a pledge last week by Chinese President Xi Jinping to give $2 billion to the WHO over the next two years to help combat the coronavirus. The amount almost matches the WHO’s entire annual program budget for last year.

Trump last month halted funding for the 194-member organization, then in a May 18 letter gave the WHO 30 days to commit to reforms.

“Because they have failed to make the requested and greatly needed reforms, we will be today terminating our relationship with the World Health Organization and redirecting those funds to other worldwide and deserving urgent global public health needs,” Trump said on Friday.

It was not immediately clear when his decision would come into effect. A 1948 joint resolution of Congress on U.S. membership of the WHO said the country “reserves its right to withdraw from the organization on a one-year notice.”

The World Health Organization did not immediately respond to a request for comment on Trump’s announcement. It has previously denied Trump’s assertions that it promoted Chinese “disinformation” about the virus.

“It’s important to remember that the WHO is a platform for cooperation among countries,” said Donna McKay, executive director of Physicians for Human Rights. “Walking away from this critical institution in the midst of an historic pandemic will hurt people both in the United States and around the world.”

‘ABSOLUTELY CRITICAL’

The United States currently owes the WHO more than $200 million in assessed contributions, according to the WHO website. Washington also gives several hundred million dollars annually in voluntary funding tied to specific WHO programs such as polio eradication, HIV, hepatitis and tuberculosis.

Amesh A. Adalja, a senior scholar at Johns Hopkins Center for Health Security, said that in practice Trump’s decision was unlikely to change the operations of the WHO.

“From a symbolic or moral standpoint it’s the wrong type of action to be taking in the middle of a pandemic and seems to deflect responsibility for what we in the U.S. failed to do and blame the WHO,” said Adalja.

When Trump halted funding to the WHO last month, two Western diplomats said the U.S. suspension was more harmful politically to the WHO than to the agency’s current programs, which are funded for now.

The WHO is an independent international body that works with the United Nations. U.N. Secretary-General Antonio Guterres said last month that the WHO is “absolutely critical to the world’s efforts to win the war against COVID-19.”

When asked about Trump’s decision, a U.N. spokesman said: “We have consistently called for all states to support WHO.”

Trump has long scorned multilateralism as he focuses on an “America First” agenda. Since taking office, he has quit the U.N. Human Rights Council, the U.N. cultural agency, a global accord to tackle climate change and the Iran nuclear deal. He has also cut funding for the U.N. population fund and the U.N. agency that aids Palestinian refugees.

“The WHO is the world’s early warning system for infectious diseases,” said U.S. Representative Nita Lowey, a Democrat who chairs the House Committee on Appropriations. “Now, during a global pandemic that has cost over 100,000 American lives, is not the time to put the country further at risk.”

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News Network
June 4,2020

New York, Jun 4: The Minneapolis police officer who used his knee to pin down George Floyd's neck before his death was the most experienced of the four officers involved in the arrest, with a record that included medals for bravery and 17 complaints against him, including one for pulling a woman out of her car during a speeding stop.

New details about Derek Chauvin and the other now-fired officers emerged Wednesday after prosecutors upgraded Chauvin's charge to second-degree murder and charged the others with aiding and abetting in a case that has convulsed the nation with protests over race and police brutality.

Heavily redacted personnel files show that Chauvin, a 19-year veteran of the force, was initially trained as a cook and served in the Army as a military police officer.

Eleven-year veteran and native Hmong speaker Tou Thao began as a community service officer and was the subject of six complaints.

The other two officers were relative newcomers to the department, including Thomas Lane, a former juvenile detention guard who did volunteer work with Somali refugees, and J. Alexander Kueng, who got his start in law enforcement by patrolling his college campus and a department store.

The files were notable for what they didn't include. Only one of the 17 complaints against Chauvin was detailed, none of the six against Thao were mentioned and there was no further detail about a 2017 excessive force lawsuit against Thao.

Records show that the 44-year-old Chauvin initially studied cooking before taking courses in law enforcement and doing two stints in the Army as a military police officer in the late 1990s, serving at Fort Benning, Georgia, and in Germany.

Chauvin became a Minneapolis police officer in 2001 and the lone reprimand in his file involved a 2007 incident when he was accused of pulling a woman out of her car after stopping her for going 10 mph (16 kph) over the speed limit.

Investigators found it was not necessary for Chauvin to remove the woman from the car and noted that his squad car video was turned off during the stop.

But Chauvin was also singled out for bravery. Files show he won two medals of valor, one in 2006 for being part of a group of officers who opened fire on a stabbing suspect who pointed a shotgun at them, and another in 2008 for a domestic violence incident in which Chauvin broke down a bathroom door and shot a suspect in the stomach.

He also won medals of commendation in 2008 after he and his partner tackled a fleeing suspect who had a pistol in his hand, and in 2009 for single-handedly apprehending a group of gang members while working as an off-duty security guard at the El Nuevo Rodeo, a Minneapolis nightclub.

Since his arrest, the former owner of the club, Maya Santamaria, said Chauvin and Floyd both worked as security guards there at various times but that she wasn't sure if they had known one another.

She said Chauvin was unnecessarily aggressive on nights when the club had a black clientele, quelling fights by dousing the crowd with pepper spray and calling in several police squad cars as backup, a tactic she called “overkill.”

Chauvin's wife, Kellie, a Laotian immigrant who became the first Hmong winner of the Mrs. Minnesota pageant, said shortly after his arrest last week that she intends to divorce him.

Before news of the upgraded charges, an attorney for Chauvin said he was not making any statements at this time. Lawyers for the others did not return messages seeking comment.

In cellphone video of the May 25 arrest of Floyd, Chauvin is shown pressing his knee onto Floyd's neck for more than eight minutes while Floyd cries out “I can't breathe” and eventually stops moving.

During much of the arrest, Kueng and Lane were helping Chauvin restrain Floyd. Thao was standing nearby keeping onlookers back.

According the complaint, at one point during the arrest, as Chauvin held Floyd down with his knee, Lane asked Chauvin twice whether they should roll Floyd over.

“No, staying put where we got him,” Chauvin replied, “I am worried about excited delirium or whatever,” Lane said. And Chauvin replied again, “That's why we have him on his stomach.” None of the three officers moved from their positions.

Lane joined the police early last year as a 35-year-old cadet — much older than most rookies — and became a full-fledged officer last December. He had no complaints in his file during his short time on the force.

On employment forms, the University of Minnesota graduate said he done volunteer work tutoring Somali youth and as a mentor helping at-risk elementary school students with reading and homework.”

Kueng, at 26 the youngest of the four officers, was also a recent recruit to the police force. He completed his year's probation just three months before the Floyd arrest.

His personnel file, which notes that he speaks, reads and writes Russian, did not include any commendations or disciplinary actions during his short time on force.

Kueng was a 2018 graduate of the University of Minnesota, where he worked part-time as part of the campus security force. He also worked nearly three years as a theft-prevention officer at Macy's.

Thao joined the police force part-time in 2008 while attending a community college. Before that, he worked as a security guard, a supermarket stocker and trainer at McDonald's.

City records show six complaints were filed against Thao, but there was no mention of that in the records released Wednesday. There also was no mention of a 2017 federal lawsuit accusing him and another officer of excessive force.

According to the lawsuit, Lamar Ferguson claimed that in 2014, Thao and his partner stopped him and beat him up while he was on his way to his girlfriend's house. The lawsuit was settled for $25,000 ___

Richmond reported from Madison, Wisconsin. Associated Press writer Scott Bauer in Madison and researcher Rhonda Shafner in New York contributed to this report.

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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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