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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Agencies
May 8,2020

United Nations, May 8: UN Secretary-General Antonio Guterres said Friday the coronavirus pandemic keeps unleashing a tsunami of hate and xenophobia, scapegoating and scare-mongering. 

The UN chief said anti-foreigner sentiment has surged online and in the streets, anti-Semitic conspiracy theories have spread, and COVID-19-related anti-Muslim attacks have occurred. 

Guterres said migrants and refugees have been vilified as a source of the virus -- and then denied access to medical treatment. 

With older persons among the most vulnerable, contemptible memes have emerged suggesting they are also the most expendable, he said. 

And journalists, whistleblowers, health professionals, aid workers and human rights defenders are being targeted simply for doing their jobs. 

Guterres appealed for an all-out effort to end hate speech globally. The secretary-general called on political leaders to show solidarity with all people, on educational institutions to focus on digital literacy at a time when extremists are seeking to prey on captive and potentially despairing audiences. 

He called on the media, especially social media, to remove racist, misogynist and other harmful content, on civil society to strengthen their outreach to vulnerable people, and on religious figures to serve as models of mutual respect. 

And I ask everyone, everywhere, to stand up against hate, treat each other with dignity and take every opportunity to spread kindness, Guterres said.

The secretary-general stressed that COVID-19 does not care who we are, where we live, what we believe or about any other distinction. His global appeal to address and counter COVID-19-related hate speech follows his April 23 message calling the coronarivus pandemic a human crisis that is fast becoming a human rights crisis. 

Guterres said then that the pandemic has seen disproportionate effects on certain communities, the rise of hate speech, the targeting of vulnerable groups, and the risks of heavy-handed security responses undermining the health response. 

With rising ethno-nationalism, populism, authoritarianism and a push back against human rights in some countries, the crisis can provide a pretext to adopt repressive measures for purposes unrelated to the pandemic, he warned.

In February, Guterres issued a call to action to countries, businesses and people to help renew and revive human rights across the globe, laying out a seven-point plan amid concerns about climate change, conflict and repression.

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News Network
July 6,2020

Beijing, Jul 6: A city in northern China on Sunday sounded an alert after a suspected case of bubonic plague was reported, according to official media here.

Bayannur, Inner Mongolia Autonomous Region, announced a level III warning of plague prevention and control, state-run People’s Daily Online reported.

The suspected bubonic plague case was reported on Saturday by a hospital in Bayannur. The local health authority announced that the warning period will continue until the end of 2020.

"At present, there is a risk of a human plague epidemic spreading in this city. The public should improve its self-protection awareness and ability, and report abnormal health conditions promptly,” the local health authority said.

On July 1, state-run Xinhua news agency said that two suspected cases of bubonic plague reported in Khovd province in western Mongolia have been confirmed by lab test results.

The confirmed cases are a 27-year-old resident and his 17-year-old brother, who are being treated at two separate hospitals in their province, it quoted a health official as saying.

The brothers ate marmot meat, the health official said, warning people not to eat marmot meat.

A total of 146 people who had contact with them have been isolated and treated at local hospitals, according to Narangerel.

Bubonic plague is a bacterial disease that is spread by fleas living on wild rodents such as marmots. It can kill an adult in less than 24 hours if not treated in time, according to the World Health Organization (WHO).

A couple died of bubonic plague in the western Mongolian province of Bayan-Ulgii last year after eating raw marmot meat.

The news of bubonic plague came after Chinese researchers issued an early warning over another potential pandemic caused by an influenza virus in pigs.

Scientists from China Agricultural University, the Chinese Centre for Disease Control and Prevention and other institutes detected a pig influenza virus bearing genotype 4 (G4), which is contagious among pigs and has the possibility of jumping to humans, as the G4 virus is able to bind with human cells, state-run Global Times reported last week.

The researchers are concerned that it could mutate further so that it can spread easily from person to person, and trigger a global outbreak, BBC reported.

"Controlling the prevailing G4 EA H1N1 viruses in pigs and close monitoring in human populations, especially workers in the swine industry, should be urgently implemented," Chinese researchers warned in the paper.

The new diseases were reported even as China grappled with the second attack of Covid-19 in Beijing after controlling it in Wuhan where it was first reported in December last year.

On Saturday, Beijing reported a single-digit Covid-19, local authorities said Sunday.

The number of newly confirmed Covid-19 cases reached a peak in Beijing on June 13 and 14 and then started declining in general, Xinhua quoted local officials as saying.

From June 11 to July 4, the city reported 334 confirmed locally transmitted cases, 47 per cent of whom are workers of the Xinfadi wholesale food market, the official said.

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Agecnies
July 13,2020

Moscow, Jul 13: Russia has become the first nation to complete clinical trials of a COVID-19 vaccine on humans. Chief researcher Elena Smolyarchuk, who heads the Center for Clinical Research on Medications at Sechenov University, told Russian news agency TASS on Sunday that the human trials for the vaccine have been completed at the university and the volunteers will be discharged soon.

"The research has been completed and it proved that the vaccine is safe. The volunteers will be discharged on July 15 and July 20," Smolyarchuk was quoted as saying in the report.

Though the results have been favourable with respect to the medication’s effectiveness, no further information was provided on when this vaccine would enter commercial production stage.

Russia had allowed clinical trials of two forms of a potential COVID-19 vaccine developed by the Gamaleya National Research Center for Epidemiology and Microbiology on June 18.

The first vaccine, in the form of a solution for intramuscular administration, was carried out at the Burdenko Military Hospital.

Another vaccine, in the form of a powder for the preparation of a solution for intramuscular administration, was carried out at Sechenov First Moscow State Medical University.

The first stage of research on the vaccine at Sechenov University involved a group of 18 volunteers and the second group involved 20 volunteers.

After vaccination, all volunteers were expected to remain in isolation in a hospital for 28 days.

Earlier, results of the COVID-19 vaccine tests performed on a group of volunteers in Russia showed that they were developing immunity to the coronavirus.

"The data obtained by the Gamalei National Research Center for Epidemiology and Microbiology, proves that volunteers of the first and second groups are forming an immune response after injections of the vaccine against the coronavirus," according to an earlier statement from the Russian Defense Ministry.

Russia has reported 719,449 cases and 11,188 deaths to date.

There are at least 21 vaccines currently under key trials, according to the World Health Organisation (WHO).

The overall number of global COVID-19 cases crossed 12.9 million, while the deaths have increased to more than 5,69,000, according to Johns Hopkins University in the US.

As of Monday morning, the total number of cases stood at 1,29,10,357, while the fatalities rose to 5,69,128.

The US accounted for the world's highest number of infections at over 33 lakh. Brazil came in the second place with over 18 lakh infections. India is third worst affected with over 8.7 lakh people reported to have COVID-19.

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