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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Agencies
June 7,2020

Boston, Jun 7: Dozens of scientists doing research funded by Mark Zuckerberg say Facebook should not be letting President Donald Trump use of the social media platform to spread both misinformation and incendiary statements.

The researchers, including 60 professors at leading US research institutions, wrote a letter to the Facebook CEO on Saturday asking that he consider stricter policies on misinformation and incendiary language that harms people," especially during the current turmoil over racial injustice.

The letter calls the spread of deliberate misinformation and divisive language the researchers' goal of using technology to prevent and eradicate disease, improving childhood education and reform the criminal justice system.

The researchers' mission "is antithetical to some of the stances that Facebook has been taking, so we're encouraging them to be more on the side of truth and on the right side of history as we've said in the letter, said Debora Marks of Harvard Medical School, one of three professors who organized the letter.

The other organisers are Martin Kampmann of the University of California-San Francisco and Jason Shepherd of the University of Utah.

All have grants from a Chan Zuckerberg Initiative program working to prevent, cure and treat neurodegenerative disorders including Alzheimer's and Parkinson's disease. The initiative is run by Zuckerberg and his wife, Priscilla Chan.

They said the letter had more than 160 signatories. Shepherd said about 10% are employees of Chan Zuckerberg foundations.

The letter objects specifically to Zuckerberg's decision not to at least flag as a violation of Facebook's community standards Trump's post that stated when the looting starts, the shooting starts after unrest in Minneapolis over the videotaped killing of George Floyd, a black man, by a white police officer.

The letter's authors called the post a clear statement of inciting violence.

Twitter had both flagged and demoted a Trump tweet using the same language.

The Associated Press emailed the Chan Zuckerberg Initiative press office for comment. It did not immediately respond.

Some Facebook employees have publicly objected to Zuckerberg's refusal to take down or label misleading or incendiary posts by Trump or other politicians. But Zuckerberg who controls a majority of voting shares in the company has so far refused.

On Friday, Zuckerberg said in a post that he would review potential options for handling violating or partially-violating content aside from the binary leave-it-up or take-it-down decisions I know many of you think we should have labeled the President's posts in some way last week, he wrote.

"Our current policy is that if content is actually inciting violence, then the right mitigation is to take that content down not let people continue seeing it behind a flag. There is no exception to this policy for politicians or newsworthiness.

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Agencies
April 17,2020

Beijing/Wuhan, Apr 17: China's coronavirus death toll mounted to 4,632 on Friday as the country revised figures in its epicentre Wuhan with 1,290 additional fatalities amid international criticism of under-reporting of COVID-19 data.

The Wuhan municipal headquarters on Friday revised the number of confirmed COVID-19 cases and deaths due to the disease, state-run Xinhua news agency reported.

As of April 16, the total number of confirmed coronavirus cases in Wuhan was increased by 325 to 50,333 and the number of fatalities up by 1,290 to 3,869.

The revised figure raised China's overall COVID-19 death toll to 4,632. The total number of cases also increased to 82,692.

The Wuhan municipal headquarters in a notification said the revisions were made in accordance with related laws and regulations as well as the principle of being responsible for history, the people and the deceased.

The revision of figures came amid sharp criticism of China by the US and other nations for its alleged under-reporting of the coronavirus cases and cover-up of the origin of the viral strain, which emerged in Wuhan in December last, reportedly from the local Hunan sea food market.

Explaining the reason for the figure revision, the Wuhan municipality said it was done to ensure that the information on the city's COVID-19 epidemic is open and transparent, and that the data are accurate.

Listing the reasons for the data discrepancies, it said the surging number of patients at the early stage of the epidemic overwhelmed medical resources and the admission capacity of medical institutions. Some patients died at home without having been treated in hospitals.

Besides, during the height of their treating efforts, hospitals were operating beyond their capacities and medical staff were preoccupied with saving and treating patients, resulting in belated, missed and mistaken reporting.

Also, due to a rapid increase of designated hospitals for treating COVID-19 patients -- including those administered by ministries, Hubei Province, Wuhan city and its districts, those affiliated to companies, as well as private hospitals and makeshift hospitals -- a few medical institutions were not linked to the epidemic information network and failed to report their data in time.

The registered information of some of the deceased patients was incomplete, and there were repetitions and mistakes in the reporting, the Wuhan authorities noted.

Citing an official of the Wuhan municipal headquarters, Xinhua reported that a group for epidemic-related big data and epidemiological investigations was established in late March.

The group used information from online systems and collected full information from all epidemic-related locations to ensure that facts about every case are accurate and every figure is objective and correct.

"What lie behind the epidemic data are the lives and health of the general public, as well as the credibility of the government," the official was quoted by the report.

The timely revision of the figures, among other things, shows respect for every single life, the official said.

Meanwhile, the revised cases were not included in the overall national figures released by China's National Commission (NHC) in its daily report on Friday as it reports previous day's cases.

As per NHC data, as of Thursday the overall confirmed cases of coronavirus was 82,367, including 3,342 deaths.

As many as 1,081 patients are being treated and 77,944 people discharged after recovery, it said.

NHC said it received reports of 26 new confirmed COVID-19 cases from the mainland on Thursday, of which 15 were imported.

The other 11 new cases were domestically transmitted, it said, noting that five cases were reported in Guangdong Province, three in Heilongjiang Province, two in Shandong Province and one in Liaoning Province.

No death was reported on Thursday on the mainland.

As of Thursday, China has a total of 1,549 imported cases, NHC said, adding that 879 were undergoing treatment with 45 in severe condition. Besides, there were 66 new asymptomatic cases, taking the tally to 1,038.

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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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