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
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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News Network
April 17,2020

Paris, Apr 17: The number of coronavirus-related deaths in France has increased by 753 to 17,920 over the past 24 hours, with the total case count now standing at 108,847, Jerome Salomon, the head of the state health agency, said on Thursday.

On Wednesday, the country reported a total of 106,206 cases, including a record 1,438 new fatalities. Salomon specified that it was not the daily death toll, as the data had been compiled over the last three-day weekend.

"The total number of victims since March 1 is 17,920," Salomon said at a briefing on Thursday.
He noted that 11,060 of them had died in hospitals, and 6,860 others in social and medical-social facilities.

President Emmanuel Macron on Monday extended nationwide movement restrictions, which had been introduced due to the epidemic, until May 11. Afterwards, the country is set to gradually reopen kindergartens, schools and universities.

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Agencies
May 8,2020

United Nations, May 8: UN Secretary-General Antonio Guterres said Friday the coronavirus pandemic keeps unleashing a tsunami of hate and xenophobia, scapegoating and scare-mongering. 

The UN chief said anti-foreigner sentiment has surged online and in the streets, anti-Semitic conspiracy theories have spread, and COVID-19-related anti-Muslim attacks have occurred. 

Guterres said migrants and refugees have been vilified as a source of the virus -- and then denied access to medical treatment. 

With older persons among the most vulnerable, contemptible memes have emerged suggesting they are also the most expendable, he said. 

And journalists, whistleblowers, health professionals, aid workers and human rights defenders are being targeted simply for doing their jobs. 

Guterres appealed for an all-out effort to end hate speech globally. The secretary-general called on political leaders to show solidarity with all people, on educational institutions to focus on digital literacy at a time when extremists are seeking to prey on captive and potentially despairing audiences. 

He called on the media, especially social media, to remove racist, misogynist and other harmful content, on civil society to strengthen their outreach to vulnerable people, and on religious figures to serve as models of mutual respect. 

And I ask everyone, everywhere, to stand up against hate, treat each other with dignity and take every opportunity to spread kindness, Guterres said.

The secretary-general stressed that COVID-19 does not care who we are, where we live, what we believe or about any other distinction. His global appeal to address and counter COVID-19-related hate speech follows his April 23 message calling the coronarivus pandemic a human crisis that is fast becoming a human rights crisis. 

Guterres said then that the pandemic has seen disproportionate effects on certain communities, the rise of hate speech, the targeting of vulnerable groups, and the risks of heavy-handed security responses undermining the health response. 

With rising ethno-nationalism, populism, authoritarianism and a push back against human rights in some countries, the crisis can provide a pretext to adopt repressive measures for purposes unrelated to the pandemic, he warned.

In February, Guterres issued a call to action to countries, businesses and people to help renew and revive human rights across the globe, laying out a seven-point plan amid concerns about climate change, conflict and repression.

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