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
July 2,2020

Jul 2: Democratic presidential candidate and former US vice-president Joe Biden has said that if he wins the November elections, strengthening the relationship with India which is America’s "natural partner", will be a high priority for his administration.

"India needs to be a partner in the region for our safety's sake and quite frankly for theirs," he said in response to a question on India-US relationship during a virtual fundraiser event on Wednesday.

At the fundraiser hosted by Chairman and CEO of Beacon Capital Partners Alan Leventhal, the former vice president said that India and the United States were natural partners.

"That partnership, a strategic partnership, is necessary and important in our security," Biden said when asked by an attendee whether India is critical to the US' national security.

Referring to his eight years as the vice president, he said, "In our administration, I was proud to play a role more than a decade ago in securing Congressional approval for the US-India Civil Nuclear Agreement, which is a big deal".

"Helping open the door to great progress in our relationship and strengthening our strategic partnership with India was a high priority in the Obama-Biden administration and will be a high priority if I'm elected president,” Biden said.

Both as the vice president and a senator from Delaware, he was a big supporter of India-US relationship.

About the November polls, Biden said that the character of the country is on the ballot. The upcoming election is the most important poll of a lifetime and that the country is currently engaged in a battle for its soul, he claimed.

Biden also slammed President Donald Trump and his administration over the handling of the coronavirus pandemic.

"Trump ignored warnings from the very beginning, refused to prepare and failed to protect the country. Not just now but throughout his presidency, undermining the very core pillars of ours, what I would argue, moral and economic strength.

"I really do believe that our country is crying out for leadership and maybe even more important, some healing. Today, we have an enormous opportunity not only to rebuild but to build back better than before. To build a better future. That's what America does," he added.

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Agencies
June 8,2020

China is aggressively pursuing a diverse range of tactics -- from cyber-attacks to recruiting insiders for economic espionage, Indian security agencies have warned. The specific alert circulated among key stakeholders suggests that Chinese operatives are not only planning to steal classified cutting-edge defense technology but also eyeing to recruit best academicians and researchers around the globe, especially from the US.

Sources said they have noticed that China has authorized an "aggressive program of stealing US science and technology information by recruiting Americans in the technology sector with access to trade secrets".

In the technology sector of the US, many Indians scientists are working at the forefront. "This is a serious matter for Indian government and security establishments," said a top source further adding that Chinese always pursue economic espionage because it suits their low cost manufacturing sector on the basis of stolen research and costly design developed by top companies across the globe.

"An alert was also issued in early January about Chinese cyber intrusion attempts at several companies where Indian researchers are working. The espionage attempt was to target UAV technology and certain top-end military equipment designs. After stealing the techniques and design, China starts producing these equipment domestically and sells at a cheaper rate, inflicting irreparable damage to the original equipment manufacturers," the sources in the security establishment observed.

Recently, the US accused China for targeting academia by sending researchers to American labs and using talent recruitment programme to steal scientific analysis. The US has also found that young recruits of the People's Liberation Army posing as students are entering into various universities across the globe to get research papers and recruit academia.

Earlier this year, the US charged a former Boston University student of visa fraud for failing to disclose the status as a lieutenant in the China's People's Liberation Army.

The US intelligence agencies have found that their "universities have become a soft target in the global espionage war with China".

In January this year, the US Department of Justice charged a leading academician at the Harvard University for hiding his alleged role in a Chinese government programme.

In July last year, the Federal Bureau of Investigation (FBI) Director Christopher Wray had revealed that the FBI is probing nearly 1,000 cases of economic espionage and attempted intellectual property theft, nearly all of them leading back to China.

Accordingly, Indian Missions have been informed about the threats being posed by Chinese spies and attempts to recruit Indian scientists and technologists working in the US and other parts of the world.

Sources further stated that security establishments in India have informed the scientist fraternity to be on alert amid threat posed by Chinese spies.

The Chinese had earlier recruited a personnel, Dongfan Chung, working at Boeing for economic espionage. Chung had stolen secret technology to benefit Chinese government and during the raid at his house more than 2.5 lakh classified pages related to Boeing were recovered.

"There has been intense debate on the international platforms regarding Chinese-sponsored theft of intellectual property. American agencies have gone on record to say that China was targeting trade secrets. In the backdrop of pandemic and global health crisis, Indian establishments in defence and technology sectors have been told to be extra cautious as China is planning to become the most advanced economy while the other countries are crippled by the highly contagious virus," the sources further added.

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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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