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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News Network
June 19,2020

United Nations, Jun 19: Half of the world's children -- one billion every year -- are affected by physical, sexual or psychological violence, suffering injuries and death because countries have failed to follow established strategies to protect them, the first report of its kind from the UN has said, with experts noting that the coronavirus-related lockdowns have left far too many youngsters stuck with their abusers.

While nearly all countries (88 per cent) have laws in place to protect minors, less than half (47 per cent) say they strongly enforce them, said the Global Status Report on Preventing Violence Against Children 2020 launched on Thursday.

Because countries have failed to follow established strategies to protect children, about one billion are affected each year by physical, sexual or psychological violence, it said.

"There is never any excuse for violence against children," WHO Director-General Tedros Adhanom Ghebreyesus said.

"We have evidence-based tools to prevent it, which we urge all countries to implement. Protecting the health and well-being of children is central to protecting our collective health and well-being, now and for the future," he said.

The report -- launched by the World Health Organisation, the UNICEF, the UNESCO, the Special Representative of the UN Secretary-General on Violence against Children and the End Violence Partnership -- charted progress in 155 countries against the "INSPIRE" framework, a set of seven strategies for preventing and responding to violence against children.

The report signaled a clear need in all countries to scale up efforts to implement them. It included the first ever global homicide estimates specifically for children under 18 years of age -- previous estimates were based on data that included 18 to 19-year olds.

According to the findings, in 2017, around 40,000 children were victims of homicide.

"Violence against children has always been pervasive, and now things could be getting much worse," UNICEF Executive Director Henrietta Fore said.

"Lockdowns, school closures and movement restrictions have left far too many children stuck with their abusers, without the safe space that school would normally offer. It is urgent to scale up efforts to protect children during these times and beyond, including by designating social service workers as essential and strengthening child helplines," she said.

UNESCO Director-General Audrey Azoulay said during the COVID-19 pandemic, and the related school closures, "we have seen a rise in violence and hate online – and this includes bullying".

"Now, as schools begin to re-open, children are expressing their fears about going back to school. It is our collective responsibility to ensure that schools are safe environments for all children. We need to think and act collectively to stop violence at school and in our societies at large," Azoulay said.

Stay-at-home measures including school closures have limited the usual sources of support for families and individuals such as friends, extended family or professionals.

This further erodes victims’ ability to successfully cope with crises and the new routines of daily life. Spikes in calls to helplines for child abuse and intimate partner violence have been observed, the report said.

While online communities have become central to maintain many children's learning, support and play, an increase in harmful online behaviors including cyberbullying, risky online behavior and sexual exploitation have been identified.

“Whilst this report was being finalised, confinement measures and the disrupted provision of already limited child protection services exacerbated the vulnerability of children to various forms of violence," said Najat Maalla M’jid, Special Representative of the UN Secretary-General on Violence against Children.

Of the INSPIRE strategies, only access to schools through enrolment showed the most progress with 54 per cent of the countries reporting that a sufficient number of children in need were being reached in this way.

Between 32 per cent and 37 per cent of the countries considered that victims of violence could access support services, while 26 per cent of the countries provided programmes on parent and caregiver support; 21 per cent of the countries had programmes to change harmful norms; and 15 per cent of the countries had modifications to provide safe physical environments for children, the report said.

Although a majority of countries (83 per cent) have national data on violence against children, only 21 per cent used these to set baselines and national targets to prevent and respond to violence against children, it added.

The report said about 80 per cent of countries have national plans of action and policies but only one-fifth have plans that are fully funded or have measurable targets. A lack of funding combined with inadequate professional capacity are likely contributing factors and a reason why implementation has been slow.

"Ending violence against children is the right thing to do, a smart investment to make - and it's possible. We can and must create a world where every child can thrive," Howard Taylor of the End Violence Partnership said.

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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
July 1,2020

Jul 1: Hong Kong police moved swiftly on Wednesday against protesters gearing up for the first rally since the introduction of sweeping security legislation, making their first arrest under it and warning of punishment for pro-independence material.

Beijing on Tuesday unveiled the details of the much-anticipated law after weeks of uncertainty, pushing China's freest city and one of the world's most glittering financial hubs onto a more authoritarian path.

As hundreds of protesters gathered downtown for an annual rally marking the 23rd anniversary of the former British colony's handover to China, riot police used pepper spray to arrest at least two people, while one metro station closed.

Police, who earlier banned the rally, cited the law for the first time in confronting protesters and they also made their first arrest under it - a man holding a flag advocating independence.

"You are displaying flags or banners/chanting slogans/or conducting yourselves with an intent such as secession or subversion, which may constitute offences under the ... national security law," police said in a message displayed on a purple banner.

The law will punish crimes of secession, subversion, terrorism and collusion with foreign forces with up to life in prison, heralding a more authoritarian era for the Asian financial hub.

China's parliament adopted it in response to months of pro-democracy protests last year triggered by fears that Beijing was stifling the city's freedoms, guaranteed by a "one country, two systems" formula agreed when it returned to Chinese rule.

Authorities in Beijing and Hong Kong have repeatedly said the legislation is aimed at a few "troublemakers" and will not affect rights and freedoms, nor investor interests.

But critics fear it will crush the freedoms that are seen as key to Hong Kong's success as a financial centre.

"With the release of the full detail of the law, it should be clear to those in any doubt that this is not the Hong Kong they grew up in," said Hasnain Malik, head of equity research, Tellimer in Dubai.

"The difference is that U.S. and China relations are far worse and this could be used as a pretext to impede the role of Hong Kong as a finance hub."

In Beijing, Zhang Xiaoming, executive deputy director of Beijing's Hong Kong and Macau Affairs Office, told reporters suspects arrested by Beijing's new security office in Hong Kong could be tried on the mainland.

He said the mainland's national security office abided by Chinese law and that Hong Kong's legal system could not be expected to implement the laws of the mainland. Article 55 of the law states that Beijing's national security office in Hong Kong could exercise jurisdiction over "complex" or "serious" cases.

Mainland security agencies will also be based in Hong Kong officially for the first time, with powers that go beyond city laws.

"The law is a birthday gift to (Hong Kong) and will show its precious value in the future," Zhang said, adding the law would not be applied retroactively.

On July 1 last year, hundreds of protesters stormed and vandalised the city's legislature to protest against a now-scrapped bill that would have allowed extraditions to mainland China.

Those protests evolved into calls for greater democracy, paralysing parts of the city and paving the way for Beijing's imposition of the law this week.

'INEVITABLE'

Speaking at a flag-raising ceremony to mark the handover anniversary, the city's Beijing-backed leader, Carrie Lam, said the law was the most important development since the city's return to Chinese rule.

"It is also an inevitable and prompt decision to restore stability," Lam said at the same harbour-front venue where 23 years ago the last colonial governor, Chris Patten, a staunch critic of the security law, tearfully handed back Hong Kong to Chinese rule.

Some pro-Beijing officials and political commentators say the law is aimed at sealing Hong Kong's "second return" to the motherland after the first failed to bring residents to heel.

Luo Huining, the head of Beijing's top representative office in Hong Kong, said at the ceremony the law was a "common aspiration" of Hong Kong citizens.

Critics denounced the lack of transparency surrounding the details of the legislation until it was unveiled. It came into force at 11 p.m. (1500 GMT) on Tuesday.

Some pro-democracy activists gave up membership of their groups just before the law came into force, though calling for the campaign for democracy to go on offshore.

"I saw this morning there are celebrations for Hong Kong's handover, but to me it is a funeral, a funeral for 'one country two systems'," said democracy lawmaker Kwok Ka-ki.

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