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
February 22,2020

Washington, Feb 22: US President Donald Trump will raise the issue of religious freedom with Prime Minister Narendra Modi during his visit to India next week, the White House said on Friday, noting that the US has great respect for India's democratic traditions and institutions.

"President Trump will talk about our shared tradition of democracy and religious freedom both in his public remarks and then certainly in private. He will raise these issues, particularly the religious freedom issue, which is extremely important to this administration," a senior official told reporters in a conference call.

The official was responding to a question on whether the president was planning to speak to Modi on the Citizenship (Amendment) Act or the National Register of Citizens.

"We do have this shared commitment to upholding our universal values, the rule of law. We have great respect for India's democratic traditions and institutions, and we will continue to encourage India to uphold those traditions," the official said, requesting anonymity.

"And we are concerned with some of the issues that you have raised," the senior administration official said, in response to the question on CAA and NRC.

"I think the President will talk about these issues in his meetings with Prime Minister Modi and note that the world is looking to India to continue to uphold its democratic traditions, respect for religious minorities," the official said.

"Of course, it's in the Indian constitution -- religious freedom, respect for religious minorities, and equal treatment of all religions. So this is something that is important to the president and I'm sure it will come up," said the official.

Pointing out that India has a strong democratic foundation, the official said India is a country rich in religious, linguistic, and cultural diversity.

"In fact, it's the birthplace of four major world religions," the official noted.

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News Network
May 8,2020

New York, May 8: An Indian-American father and daughter, both doctors in New Jersey, have died due to the COVID-19, with Governor Phil Murphy describing their demise as “particularly tough" and hailed them for dedicating their lives for others.

Satyender Dev Khanna, 78, was a surgeon who served both on staff and as the head of the surgical departments for multiple hospitals across New Jersey for decades.

Priya Khanna, 43, was a double board-certified in both internal medicine and nephrology. She was Chief of Residents at Union Hospital, now part of RWJ Barnabas Health.

"Dr Satyender Dev Khanna and Dr Priya Khanna were father and daughter. They both dedicated their lives to helping others. This is a family dedicated to health and medicine. Our words cannot amply express our condolences," New Jersey Governor Murphy tweeted on Thursday.

“Both dedicated their lives to helping others and we lost both of them to COVID-19,” Murphy said during a press conference on Thursday, saying their demise is a "particularly tough one.”

Satyender passed away at the Clara Maass Medical Center where he had worked for more than 35 years.

Murphy described him as a "pioneering doctor” who was one of the first surgeons to perform laparoscopic surgery in the state. He is being remembered by colleagues as a “gentle and caring physician."

“And for a doctor, I'm not one, but I would bet, I don't think there could be a more fitting way to be remembered, or a nurse or a healthcare worker of any kind,” Murphy said, adding that the doctor had a passion for bicycling, and he often found peace from the hustle of the hospital in biking along the Jersey Shore.

Priya did all of her medical training in New Jersey and then did her fellowship in nephrology in South Jersey with the Cooper Health System. Like her father, she too worked at Clara Maass, where she died.

She was also Medical Director at two dialysis centres in Essex County and “took pride” in teaching the next generation of doctors, Murphy said, adding that the ICU physician who cared for Priya Khanna was trained and taught by her as well.

Follow live developments on the coronavirus pandemic here

“Priya will be remembered as a caring and selfless person who put others first. And even while in the hospital, fighting her own battle, she continued to check up on her mom and dad and her family,” Murphy said.

“This is a family, by the way, dedicated to health and medicine,” he said.

The governor spoke with Satyender's wife Komlish Khanna, who is a paediatrician. The couple has two more daughters - Sugandha Khanna, an emergency medicine physician and Anisha Khanna, a paediatrician.

“Unbelievable. Our words cannot amply express our condolences nor, I am sure, can they express the pain that the Khanna family is feeling. But I hope that the fact that our entire state mourns with them is some small comfort. And we mourn everyone we have lost. We commit in their memory to saving as many lives as we can,” Murphy said.

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News Network
May 8,2020

May 8: Thousands of migrants have been stranded “all over the world” where they face a heightened risk of COVID-19 infection, the head of the UN migration agency International Organization for Migration (IOM) has said.

IOM Director-General António Vitorino said that more onerous health-related travel restrictions might discriminate disproportionately against migrant workers in future.

“Health is the new wealth,” Vitorino said, citing proposals by some countries to introduce the so-called immunity passports and use mobile phone apps designed to prevent the spread of the new coronavirus.

“In lots of countries in the world, we already have a system of screening checks to identify the health of migrants, above all malaria, tuberculosis… HIV-AIDS, and now I believe that there will be increased demands in health controls for regular migrants,” he said on Thursday.

Travel restrictions to try to limit the spread of the pandemic has left people on the move more vulnerable than ever and unable to work to support themselves, Vitorino told journalists via videoconference.

“There are thousands of stranded migrants all over the world.

 “In South-East Asia, in East Africa, in Latin America, because of the closing of the borders and with the travel restrictions, lots of migrants who were on the move; some of them wanted to return precisely because of the pandemic,” he said.

They are blocked, some in large groups, some in small, in the border areas, in very difficult conditions without access to minimal care, especially health screening, Vitorino said.

“We have been asking the governments to allow the humanitarian workers and the health workers to have access to (them),” he said.

Turning to Venezuelan migrants, who are believed to number around five million amidst a worsening economic crisis in the country, the IOM chief said “thousands… have lost their jobs in countries like Ecuador and Colombia and are returning back to Venezuela in large crowds without any health screening and being quarantined when they go back”.

In a statement, the IOM highlighted the plight of migrants left stranded in the desert in west, central and eastern Africa, either after having been deported without the due process, or abandoned by the smugglers.

The IOM’s immediate priorities for migrants include ensuring that they have access to healthcare and other basic social welfare assistance in their host country.

Among the UN agency’s other immediate concerns is preventing the spread of new coronavirus infection in more than 1,100 camps that it manages across the world.

They include the Cox’s Bazar complex in Bangladesh, home to around one million mainly ethnic Rohingya from Myanmar, the majority having fled persecution.

So far, no cases of infection have been reported there, the IOM chief said, adding that preventative measures have been communicated to the hundreds of thousands of camp residents, while medical capacity has been boosted.

Beyond the immediate health threat of COVID-19 infection, migrants also face growing stigmatization from which they need protection, Vitorino said.

Allowing hate speech and xenophobic narratives to thrive unchallenged also threatens to undermine the public health response to COVID-19, he said, before noting that migrant workers make up a significant percentage of the health sector in many developed countries including the UK, the US and Switzerland.

Populist narratives targeting migrants as carriers of disease could also destabilise national security through social upheaval and countries’ post-COVID economic recovery by removing critical workers in agriculture and service industries, he said.

Remittances have already seen a 30 per cent drop during the pandemic, Vitorino said, citing the World Bank data, meaning that some USD 20 billion has not been sent home to families in countries where up to 15 per cent of their gross domestic product comes from pay packets earned abroad.

Vitorino, in a plea, urged to give the health of migrants as much attention as that of the host populations in all countries.

“It is quite clear that health is the new wealth and that health concerns will be introduced in the mobility systems - not just for migration - but as a whole; where travelling for business or professional reasons, health will be the new gamechanger in town.

“If the current pandemic leads to a two or even three-tier mobility system, then we will have to try to solve the problem – the problem of the pandemic - but at the same time we have created a new problem of deepening the inequalities,” he said.

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