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 2,2020

London/Milan, Jun 2: World Health Organization experts and a range of other scientists said on Monday there was no evidence to support an assertion by a high profile Italian doctor that the coronavirus causing the COVID-19 pandemic has been losing potency.

Professor Alberto Zangrillo, head of intensive care at Italy's San Raffaele Hospital in Lombardy, which bore the brunt of Italy's COVID-19 epidemic, on Sunday told state television that the new coronavirus "clinically no longer exists".

But WHO epidemiologist Maria Van Kerkhove, as well as several other experts on viruses and infectious diseases, said Zangrillo's comments were not supported by scientific evidence.

There is no data to show the new coronavirus is changing significantly, either in its form of transmission or in the severity of the disease it causes, they said.

"In terms of transmissibility, that has not changed, in terms of severity, that has not changed," Van Kerkhove told reporters.

It is not unusual for viruses to mutate and adapt as they spread, and the debate on Monday highlights how scientists are monitoring and tracking the new virus. The COVID-19 pandemic has so far killed more than 370,000 people and infected more than 6 million.

Martin Hibberd, a professor of emerging infectious disease at the London School of Hygiene & Tropical Medicine, said major studies looking at genetic changes in the SARS-CoV-2 virus that causes COVID-19 did not support the idea that it was becoming less potent, or weakening in any way.

"With data from more than 35,000 whole virus genomes, there is currently no evidence that there is any significant difference relating to severity," he said in an emailed comment.

Zangrillo, well known in Italy as the personal doctor of former Prime Minister Silvio Berlusconi, said his comments were backed up by a study conducted by a fellow scientist, Massimo Clementi, which Zangrillo said would be published next week.

Zangrillo told Reuters: "We have never said that the virus has changed, we said that the interaction between the virus and the host has definitely changed."

He said this could be due either to different characteristics of the virus, which he said they had not yet identified, or different characteristics in those infected.

The study by Clementi, who is director of the microbiology and virology laboratory of San Raffaele, compared virus samples from COVID-19 patients at the Milan-based hospital in March with samples from patients with the disease in May.

"The result was unambiguous: an extremely significant difference between the viral load of patients admitted in March compared to" those admitted last month, Zangrillo said.

Oscar MacLean, an expert at the University of Glasgow's Centre for Virus Research, said suggestions that the virus was weakening were "not supported by anything in the scientific literature and also seem fairly implausible on genetic grounds."

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News Network
July 11,2020

Jul 11: UK’s Prince Charles, at the ongoing India Global week 2020, has praised India’s sustainable way of life, as he emphasised on sustainable development amid the ongoing coronavirus pandemic. Addressing the summit through a video link from London, Prince Charles said, “The country’s (India’s) diversity and resilience is a personal inspiration for him and much to teach all,” reported the All India Radio.

The three-day summit is getting held on a virtual platform from July 9 to July 11 due to the ongoing COVID-19 pandemic. Around 75 sessions on subjects such as geopolitics, business, emerging technologies, banking, finance, pharmaceuticals, defence and security, and arts and culture are getting held. The summit is expected to bring together over 250 speakers and more than 5,000 participants for incisive discussion and lively debate over the three days.

During his address, Prince Charles said India’s philosophies and values have emphasised a sustainable way of life and a harmonious relationship between humanity and nature, the AIR report said.

He also informed that he spoke to Prime Minister Narendra Modi about the importance of sustainable living.

In his address, he also spoke about the ancient yogic concept of ‘Aparigraha’. “It’s the time when the world learnt this ancient wisdom from India as it seeks revival amid the pandemic, he said as reported by the AIR news.

As the countries across the globe are reeling under the corornavirus pandemic, he emphasised on sustainable development to overcome the crisis. He said, “We have an unparalleled opportunity to put people and planet at the heart of global value creation and move to sustainable markets for long-term value, balancing natural, social, and physical capital.”

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News Network
February 16,2020

Munich, Feb 16: Iran's foreign minister said Saturday that US President Donald Trump is receiving bad advice if he believes an American "maximum pressure" campaign against his country will cause the government in Tehran to collapse.

Foreign Minister Mohammad Javad Zarif told a group of top defense officials and diplomats at the Munich Security Conference that the information provided to the president has dissuaded Trump from accepting offers from other leaders to mediate between Washington and Tehran.

"President Trump has been convinced that we are about to collapse so he doesn't want to talk to a collapsing regime," Zarif said.

To support his argument, the Iranian minister cited Trump's decision to pull out unilaterally in 2018 from Iran's nuclear deal with the US and other world powers. Trump said the landmark 2015 accord didn't address Iran's ballistic missile program or regional activities and needed to be renegotiated.

Since then, the Trump administration's re-imposition of US sanctions in a campaign of so-called "maximum pressure" have taken a severe toll on the Iranian economy and sent Iran's currency plunging.

"I believe President Trump, unfortunately, does not have good advisers," Zarif said. "He's been wanting for Iran to collapse since he withdrew from the nuclear deal." Zarif also said the killing of Iranian Gen. Qassem Soleimani in a US drone strike in Iraq on January 3 was a miscalculation by Washington that has galvanized support for Iran instead of increasing pressure on the regime.

The Iran nuclear deal, known as the Joint Comprehensive Plan of Action or JCPOA, promised Iran economic incentives in exchange for curbs on its nuclear program. It was intended to prevent Tehran from developing a nuclear bomb, which Iran insists it does not want to do.

Since the US withdrawal, the deal's other signatories - Germany, France, Britain, Russia and China - have unsuccessfully struggled to come up with ways to offset the effects of the new American sanctions.

Washington has pressured the other countries - so far without success - to abandon the deal entirely US Secretary of State Mike Pompeo said at the Munich Security Conference earlier Saturday that while there may be disagreements on what to do with the JCPOA, "when I talk to my counterparts here in Europe, everybody gets it."

"Everyone understands that these are folks who continue to build out their nuclear program," Pompeo said. "So there's a common understanding about the threat; we have tactical differences on how to proceed."

In recent months, Iran has steadily violated the limitations the deal placed on the amount of enriched uranium and heavy water it can stockpile, the number and type of centrifuges it can operate, and the purity of the uranium it enriches.

Iranian officials insist the moves are intended only to put pressure on the countries that remain part of the deal to provide economic help to Iran and that all the measures taken are fully reversible.

Zarif rejected Trump's suggestion of negotiating a new deal, saying the one negotiated during the Obama administration was the only vehicle for talks on Iran's nuclear program.

"There is no point in talking over something you already talked about. You don't buy a horse twice," he said.

"It's not about opening talks with the United States. It's about bringing the United States to the negotiating table that's already there," Zarif said.

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