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
June 13,2020

Washington, Jun 13: America's first-ever Hindu lawmaker Tulsi Gabbard has said that in this chaotic time, one can find certainty, strength, and peace in Bhagavad Gita.

In her message during a virtual commencement address, the 39-year-old Congresswoman from Hawaii said that it is a chaotic time and no one can say with certainty what tomorrow looks like.

"... but we find certainty, strength, and peace in the practice of Bhakti Yoga and Karma Yoga taught to us by Krishna in the Bhagavad Gita," Tulsi Gabbard told the 'Class of 2020 for Hindu students''.

Her address came amidst protests in the US against the killing of African-American George Floyd by a white police officer in Minneapolis.

The country has been swept by protests since George Floyd's custodial death on May 25 with thousands of people mounting pressure for changes to the law enforcement practices.

The first-ever virtual Hindu commencement was organised by the Hindu Students Council on June 7, which drew thousands of viewers on Facebook and YouTube Live, all coming together in solidarity during the ongoing COVID-19 crisis.

According to Johns Hopkins Coronavirus Resource Center, the contagion has infected over 76,00,000 people and killed more than 4,25,000 across the world. The US is the worst affected country with over 2.04 million cases and more than 1,14,000 deaths.

The COVID-19, which originated in China''s Wuhan city in December last year, has also battered the world economy with the International Monetary Fund saying that the global economy is bound to suffer a "severe recession".

Scientists are racing against time to find a vaccine or medicine for its treatment.

Hundreds of graduates from the US, Canada, the UK, India and Australia attended to commemorate their graduation in a unique way - by celebrating their shared Hindu values.

Professor Subhash Kak served as the ceremony's Grand Marshall.

"As you think about this new chapter in your lives, ask yourself what is my purpose in life? It is a deep question that if you can recognise now that your purpose is to serve God and God''s children, practicing Karma Yoga, then you can lead a truly successful life," Tulsi Gabbard said.

"Success is not defined by temporary material things, trinkets, glittery objects or accomplishments - but a deeply successful and happy life centered around service," she added.

The Iraq war veteran ended her presidential campaign in March and offered her full support to former vice president Joe Biden, 77, who is all set to challenge Republican incumbent Donald Trump, 73, in November elections.

The commencement address focused heavily on themes from the Bhagavad Gita, a timeless historical text that many Hindus consider their moral framework.

Professor Kak, Regent Professor at Oklahoma State University and 2019 Padma Shri recipient, read out the names of the graduating students.

"I exhort you - the graduating students - to be the leaders of the new world where education is less of the mind of a vessel to be filled with information (usually forgotten after the semester is over), and more of a flame that is lit as envisioned by our Vedic sages," he said.

The student speakers were from many university campuses, including the Massachusetts Institute of Technology, Princeton, and Stanford.

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The programme included offerings of Hindu prayers, recitation of a traditional graduation message from the Upanishads, and a symbolic conferral of degrees to high school and college graduate.

Founded in 1990, Hindu Students Council is North America''s largest pan-Hindu youth organisation. 

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News Network
May 24,2020

Beijing, May 24: The Chinese virology institute in the city where COVID-19 first emerged has three live strains of bat coronavirus on-site, but none match the new contagion wreaking chaos across the world, its director has said.

Scientists think COVID-19 -- which first emerged in Wuhan and has killed some 340,000 people worldwide -- originated in bats and could have been transmitted to people via another mammal.

But the director of the Wuhan Institute of Virology told state broadcaster CGTN that claims made by US President Donald Trump and others that the virus could have leaked from the facility were "pure fabrication".

"Now we have three strains of live viruses... But their highest similarity to SARS-CoV-2 only reaches 79.8 percent," she said, referring to the coronavirus strain that causes COVID-19.

US demands immediate start to WHO review

The United States called on the World Health Organisation on Friday to begin working immediately on investigating the source of the novel coronavirus, as well as its handling of the response to the pandemic.

One of their research teams, led by Professor Shi Zhengli, has been researching bat coronaviruses since 2004 and focused on the "source tracing of SARS", the strain behind another virus outbreak nearly two decades ago.

"We know that the whole genome of SARS-CoV-2 is only 80 percent similar to that of SARS. It's an obvious difference," she said.

"So, in Professor Shi's past research, they didn't pay attention to such viruses which are less similar to the SARS virus."

Conspiracy rumours that the biosafety lab was involved in the outbreak swirled online for months before Trump and US Secretary of State Mike Pompeo brought the theory into the mainstream by claiming that there is evidence the pathogen came from the institute.

The lab has said it received samples of the then-unknown virus on December 30, determined the viral genome sequence on January 2 and submitted information on the pathogen to the WHO on January 11.

Wang said in the interview that before it received samples in December, their team had never "encountered, researched or kept the virus."

"In fact, like everyone else, we didn't even know the virus existed," she said. "How could it have leaked from our lab when we never had it?"

The World Health Organization said Washington had offered no evidence to support the "speculative" claims.

In an interview with Scientific American, Shi said the SARS-CoV-2 genome sequence did not match any of the bat coronaviruses her laboratory had previously collected and studied.

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