American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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
March 12,2020

Geneva, Mar 12: For the global economy, virus repercussions were profound, with increasing concerns of wealth- and job-wrecking recessions. U.S. stocks wiped out more than all the gains from a huge rally a day earlier as Wall Street continued to reel.

The Dow Jones Industrial Average dropped 1,464 points, bringing it 20% below its record set last month and putting it in what Wall Street calls a “bear market.” The broader S&P 500 is just 1 percentage point away from falling into bear territory and bringing to an end one of the greatest runs in Wall Street’s history.

WHO officials said they thought long and hard about labeling the crisis a pandemic — defined as sustained outbreaks in multiple regions of the world.

The risk of employing the term, Ryan said, is “if people use it as an excuse to give up.” But the benefit is “potentially of galvanizing the world to fight.”

Underscoring the mounting challenge: soaring numbers in the U.S. and Europe’s status as the new epicenter of the pandemic. While Italy exceeds 12,000 cases and the United States has topped 1,300, China reported a record low of just 15 new cases Thursday and three-fourths of its infected patients have recovered.

China’s totals of 80,793 cases and 3,169 deaths are a shrinking portion of the world’s more than 126,000 infections and 4,600 deaths.

“If you want to be blunt, Europe is the new China,” said Robert Redfield, the head of the U.S. Centers for Disease Control and Prevention.

With 12,462 cases and 827 deaths, Italy said all shops and businesses except pharmacies and grocery stores would be closed beginning Thursday and designated billions in financial relief to cushion economic shocks in its latest efforts to adjust to the fast-evolving crisis that silenced the usually bustling heart of the Catholic faith, St. Peter’s Square.

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Agencies
August 5,2020

Ninety per cent of a sample group of coronavirus-recovered patients from a prominent hospital in China's Wuhan city where the pandemic broke out have reported lung damage and five per cent of them are again in quarantine after testing positive for the virus, according to a media report on Wednesday.

A team at the Zhongnan Hospital of Wuhan University led by Peng Zhiyong, director of the hospital's Intensive Care Unit, has been conducting follow-up visits with '100 recovered patients' since April.

The first phase of this one-year programme finished in July. The average age of the patients in the study is 59.

According to the first phase results, 90 per cent of the patients' lungs are still in a damaged state, which means their lungs ventilation and gas exchange functions have not recovered to the level of healthy people, state-run Global Times reported.

Peng's team conducted a six-minute walking test with the patients. They found that the recovered patients could only walk 400 metres in six minutes while their healthy peers could walk 500 metres in the same period.

Some recovered patients have to rely on oxygen machines even three months after being discharged from the hospital, Liang Tengxiao, a doctor from the Dongzhimen Hospital, Beijing University of Chinese Medicine, was quoted as saying by the report.

Liang's team is also conducting follow-up visits with recovered patients aged above 65.

The results also showed that antibodies against the novel coronavirus in 10 per cent of the 100 patients have disappeared.

Five per cent of them received negative results in Covid-19 nucleic acid tests but positive results in Immunoglobulin M (IgM) tests, and thus have to be quarantined again, the report said.

IgM is usually the first antibody produced by the immune system when a virus attacks. A positive result in an IgM test usually means that a person has just been infected by the virus.

It is still unclear if this means these people have been infected again.

The 100 patients' immune systems have not fully recovered as they showed a low level of B cells -- - a primary force for killing viruses in the human body -- but a high level of T cells which only recognise viral antigens outside infected cells.

"The results revealed that the patients’ immune systems are still recovering," Peng said.

The patients also suffered from depression and a sense of stigma. Most of the recovered patients told the team that their families were not willing to have dinner with them at the same table, the report said.

Less than half of the recovered patients have returned to work, it said.

The findings are significant as the coronavirus first emerged in Wuhan city.

Hubei province for which Wuhan is the provincial capital has reported a total of 68,138 confirmed Covid-19 cases till now. The disease has claimed 4,512 lives in the province, according to the official data.

China reported 27 new confirmed Covid-19 cases on Tuesday, including 22 locally-transmitted cases, the National Health Commission (NHC) said on Wednesday.

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News Network
May 12,2020

Washington, May 12: The US Federal Bureau of Investigation and cybersecurity experts believe Chinese hackers are trying to steal research on developing a vaccine against coronavirus, two newspapers reported Monday.

The FBI and Department of Homeland Security are planning to release a warning about the Chinese hacking as governments and private firms race to develop a vaccine for COVID-19, the Wall Street Journal and New York Times reported.

The hackers are also targeting information and intellectual property on treatments and testing for COVID-19.

US officials alleged that the hackers are linked to the Chinese government, the reports say.

The official warning could come within days.

In Beijing Foreign Affairs ministry spokesman Zhao Lijian rejected the allegation, saying China firmly opposes all cyber attacks.

"We are leading the world in COVID-19 treatment and vaccine research. It is immoral to target China with rumors and slanders in the absence of any evidence," Zhao said.

Asked about the reports, President Donald Trump did not confirm them, but said: "What else is new with China? What else is new? Tell me. I'm not happy with China."

"We're watching it very closely," he added.

A US warning would add to a series of alerts and reports accusing government-backed hackers in Iran, North Korea, Russia and China of malicious activity related to the pandemic, from pumping out false news to targeting workers and scientists.

The New York Times said it could be a prelude to officially-sanctioned counterattacks by US agencies involved in cyber warfare, including the Pentagon's Cyber Command and the National Security Agency.

Last week in a joint message Britain and the United States warned of a rise in cyber attacks against health professionals involved in the coronavirus response by organised criminals "often linked with other state actors."

Britain's National Cyber Security Centre and the US Cybersecurity and Infrastructure Security Agency said they had detected large-scale "password spraying" tactics -- hackers trying to access accounts through commonly used passwords -- aimed at healthcare bodies and medical research organisations.

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