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
July 18,2020

Days after Twitter accounts of several billionaires were hacked to engineer a crypto scam, Twitter on Saturday said it is embarrassed, disappointed and, more than anything, sorry for what happened with some of its high-profile users as attackers successfully manipulated its employees and used their credentials to access internal systems, including getting through the two-factor protections.

In the first detailed summary of the "social engineering attack" via a crypto scam that hit at least 130 users this week, Twitter said for 45 of those accounts, the attackers were able to initiate a password reset, login to the account and send Tweets.

"We are continuing our forensic review of all of the accounts to confirm all actions that may have been taken. In addition, we believe they may have attempted to sell some of the usernames," the micro-blogging platform said in a statement.

For up to eight of the Twitter accounts involved, the attackers took the additional step of downloading the account's information via "Your Twitter Data" tool.

This is a tool that is meant to provide an account owner with a summary of their Twitter account details and activity.

"We are reaching out directly to any account owner where we know this to be true. None of the eight were verified accounts," said Twitter.

The company said the attackers were not able to view previous account passwords, as those are not stored in plain text or available through the tools used in the attack.

"Attackers were able to view personal information including email addresses and phone numbers, which are displayed to some users of our internal support tools," informed Twitter.

In cases where an account was taken over by the attacker, they may have been able to view additional information, Twitter added, saying its forensic investigation of these activities was still ongoing.

"We are actively working on communicating directly with the account-holders that were impacted".

The company said it will soon restore access for all account owners who may still be locked out as a result of the remediation efforts.

The New York Times reported on Friday that the Twitter crypto scam can be traced back to a group of hackers who congregate online at OGusers.com, a username-swapping community where people buy and sell coveted online handles.

The report said that the Twitter hack is not from Russian, Chinese or North Korean hackers but was done by a group of young people, "one of whom says he lives at home with his mother".

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News Network
June 24,2020

Jun 24: The coronavirus tally in Pakistan reached 188,926 with the detection of 3,892 new cases in the last 24 hours, the health ministry said on Wednesday.

Sixty more people died due to the viral infection, taking the death toll to 3,755.

As many as 3,337 patients are in critical condition across the country, the ministry said.

With the detection of 3,892 new cases in the last 24 hours, the coronavirus tally in the country now stands at 188,926, it said.

Sindh reported the maximum number of 72,656 cases, followed by 69,536 in Punjab, 23,388 in Khyber-Pakhtunkhwa, 11,483 in Islamabad, 9,634 in Balochistan, 1,337 in Gilgit-Baltistan and 892 in Pakistan-occupied Kashmir (Pok).

Health authorities have so far conducted 1,150,141 coronavirus tests, including 23,380 in the last 24 hours.

A total of 77,754 patients have recovered so far from the disease.

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Agencies
March 24,2020

Beijing, Mar 24:  China reported 78 new confirmed cases, including 74 imported infections, while the death toll from the novel coronavirus increased to 3,277 after seven more fatalities were confirmed from the COVID-19, health officials said on Tuesday.

The overall confirmed cases on the Chinese mainland have reached 81,171 by the end of Monday. This included 3,277 people who died of the disease, 4,735 patients who were still being treated and 73,159 patients discharged after recovery, the National Health Commission (NHC) said on Tuesday.

The NHC said, 78 new confirmed COVID-19 cases were reported on the Chinese mainland on Monday, of which 74 were imported from abroad taking the number of overseas cases to 427.

Also on Monday, seven deaths and 35 new suspected cases were reported on the mainland with all the deaths in Hubei Province.

The total COVID-19 cases in Beijing climbed to 522 with eight deaths prompting local governments of Beijing as well as Shanghai to announce that all overseas arrivals will be subjected to nucleic acid tests to ensure proper detection.

Of the 74 newly imported cases, 31 were reported in Beijing, 14 in Guangdong, nine in Shanghai, five in Fujian, four in Tianjin, three in Jiangsu, two in Zhejiang and Sichuan respectively, and one in Shanxi, Liaoning, Shandong and Chongqing respectively, the NHC said.

Beijing is already diverting all international flights to different cities where the passengers will be quarantined for 14 days before arriving in the city.

The NHC said 132 people were still suspected of being infected with the virus.

Coronavirus epicentre Wuhan has reported one confirmed case after a gap of five days prompting officials to begin to ease restrictions.

Wuhan also reported seven new deaths, bringing the total number of deaths in the city and Hubei province for which Wuhan is the capital to 3,160.

The province also saw 444 patients discharged from hospital after recovery on Monday. Among the 4,200 patients being treated in hospital, 1,203 were still in severe condition and another 336 in critical condition, the local health commission said.

By the end of Monday, 356 confirmed cases, including four deaths have been reported in Hong Kong, which has restricted the entry of foreigners into the city. Also a total of 25 confirmed cases were reported in Macao and 195 in Taiwan including two deaths, state-run Xinhua news agency reporrted.

After days of decline in coronavirus cases, China on Monday said that COVID-19 has effectively been "stemmed" in the country and it started easing severe restrictions imposed on Wuhan's 11 million people who were under lockdown since January 23.

The authorities began relaxing restrictions in Wuhan as it reported no new case for the fifth consecutive day on Monday.

Significantly, the Central Leading Group (CLP), headed by Premier Li Keqiang which is coordinating efforts to contain the virus since January 23, said the virus has been curtailed in the country as well as in Wuhan.

"The meeting noted that the spread of the virus nationwide, particularly in the epicentre of Wuhan, has been effectively stemmed," an official statement said on Monday.

The meeting, however, warned that the risks for sporadic infections and localised outbreaks have not gone away. With the pandemic rampaging across the world, the situation remains complex and challenging.

"Wuhan city and Hubei province should stay focused on medical treatment and community-level containment as the two key priorities. They should continue to treat the severe cases, promptly admit new cases, and advance epidemiological investigations," the meeting said.

In Wuhan, officials said people are allowed to go back to work while restrictions on the public transport are gradually being eased.

The Hubei province and its capital Wuhan with over 56 million people were under lockdown since January 23. The vicious virus broke out in city, reportedly at a live animal market in December last year and became virulent inflicting thousands of people in the city and province catching the government off guard.

As the country saw a surge in imported infections, the Chinese government announced that all international flights scheduled to arrive in Beijing will be redirected to airports in 12 other Chinese cities from Monday.

International passengers flying to Beijing will instead land at airports in 12 cities including Shanghai, Tianjin, Nanjing and Shenyang as their first points of entry, the Civil Aviation Administration of China (CAAC) said in a statement.

On Monday, China said international travellers should "think twice" about choosing Beijing for flight transfer in view of the restrictions.

Starting from Monday, all international flights scheduled to arrive in Beijing will be redirected to airports in 12 other Chinese cities, Liu Haitao, an official with China's National Immigration Administration said.

Passengers would go through entry procedures and quarantine measures at the designated cities' airports before they continue their flights to Beijing, Liu said, urging travellers to reserve enough time for their next flights to make sure that they do not miss their outbound flights.

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