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
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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News Network
May 19,2020

Washington, May 19: As the scientists across the world are struggling to develop a vaccine for combating coronavirus, US drugmaker Moderna announced on Monday (local time) that the phase I trial of its Covid-19 vaccine has shown positive early results.

The company is hopeful that it's vaccine could be available to the public as early as January next year. Several firms across the world are in the race to develop a vaccine for the deadly virus which has claimed over 3 lakh lives worldwide.

CNN citing Dr. Tal Zaks, Moderna's chief medical officer reported that "if future studies go well, the company's vaccine could be available to the public as early as January".

"This is absolutely good news and news that we think many have been waiting for for quite some time," Zaks was quoted as saying.

Moderna, based in Cambridge, Massachusetts announced that the vaccine developed neutralising antibodies to the virus at levels reaching or exceeding the levels seen in people who have naturally recovered from Covid-19, reported CNN.

These will be followed by phase 2 trials and phase 3 trials, which Moderna plans to start in July.

President Donald Trump had on Friday said that that the United States will be able to deliver a few hundred million doses of COVID-19 vaccine, under 'Operation Warp Speed', by the end of this year.

"I have very recently seen early data from a clinical trial with a coronavirus vaccine and this data made me feel even more confident that we'll be able to deliver a few hundred million doses of vaccine by the end of 2020 and we will do the best we can," Trump had said at a press conference at the White House on Friday.

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News Network
April 6,2020

New Delhi, April 6: The United States has donated $2.9 million assistance package for India to help the Narendra Modi government brace itself against the coronavirus as countries across the world are coming together to combat the outbreak.

On March 28, the US government, via US Agency for International Development, announced $2.9 million to support India in its response to COVID-19.

"It builds on a foundation of over $1.4 billion in health assistance and nearly $3 billion in total assistance that the US provided to India over the last 20 years," the US Embassy in India said in a statement.

"These new funds will support two organisations, including $2.4 million for USAID's health strengthening project, implemented by Jhpiego, an international non-profit health organisation affiliated with Johns Hopkins University and $500,000 for the World Health Organization (WHO)," the statement said.

The funds will also help India combat the spread of COVID-19, provide care for the affected and support local communities with the tools needed to contain the disease, it added.

Moreover, being a global leader in health and humanitarian response to COVID-19, the US has provided approximately $18.3 million assistance package to ASEAN member countries to fight the contagion.

The funds will be used to prepare laboratories for large-scale testing for the lethal virus, infection prevention and control, enable risk communication, implement public-health emergency plans for border points of entry, activate case-finding and event-based surveillance for influenza-like illnesses, train and equip rapid-responders in investigation and contact-tracing and update training materials for health workers.

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