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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News Network
May 13,2020

Islamabad, May 13 : The number of confirmed COVID-19 cases in Pakistan rose to 34,370 on Wednesday after new infections were confirmed in the country.

As per province-wise breakup of the total tally cited by Radio Pakistan, so far 13,225 cases have been registered in Punjab, 12,610 in Sindh, 5,021 in Khyber Pakhtunkhwa, 2,158 in Balochistan, 759 in Islamabad, 475 in Gilgit Baltistan and 88 in Pakistan-occupied Kashmir.

As many as 2,255 cases positive were confirmed, while 31 deaths reported during the last 24 hours.

At least 737 patients have died so far while 8,812 stand recovered, the media reported further.

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News Network
January 30,2020

Jan 30: The death toll rose to 170 in the new virus outbreak in China on Thursday as foreign evacuees from the worst-hit region begin returning home under close observation and world health officials expressed “great concern” that the disease is starting to spread between people outside of China.

Thursday’s figures cover the previous 24 hours and represent an increase of 38 deaths and 1,737 cases for a total of 7,711. Of the new deaths, 37 were in the epicenter of the outbreak in Hubei province and one in the southwestern province of Sichuan.

The news comes as the 195 Americans evacuated from Wuhan, the Hubei province city of 11 million where the outbreak originated, are undergoing three days of testing and monitoring at a Southern California military base to make sure they do not show signs of the virus.

A group of 210 Japanese evacuees from Wuhan landed Thursday at Tokyo’s Haneda airport on a second government chartered flight, according to the foreign ministry. Reports said nine of those aboard the flight showed signs of cough and fever. Three of the 206 Japanese who returned on Wednesday tested positive for the new coronavirus, Prime Minister Shinzo Abe said during a parliamentary session. Two of them showed no symptoms of the disease.

France, New Zealand, Australia and other countries are also pulling out their citizens or making plans to do so.

The World Health Organization emergencies chief said the few cases of human-to-human spread of the virus outside China — in Japan, Germany, Canada and Vietnam — were of “great concern” and were part of the reason the U.N. health agency’s director-general was reconvening a committee of experts on Thursday to assess whether the outbreak should be declared a global emergency.

The new virus has now infected more people in China than were sickened there during the 2002-2003 SARS outbreak.

Dr. Michael Ryan spoke at a news conference in Geneva on Wednesday after returning from a trip to Beijing to meet with Chinese President Xi Jinping and other senior government leaders. He said China was taking “extraordinary measures in the face of an extraordinary challenge” posed by the outbreak.

To date, about 99% of the cases are in China. Ryan estimated the death rate of the new virus at 2%, but said the figure was very preliminary. With fluctuating numbers of cases and deaths, scientists are only able to produce a rough estimate of the fatality rate and it’s likely many milder cases of the virus are being missed.

In comparison, the SARS virus killed about 10% of people who caught it. The new virus is from the coronavirus family, which includes those that can cause the common cold as well as more serious illnesses such as SARS and MERS.

Scientists say there are many questions to be answered about the new virus, including just how easily it spreads and how severe it is.

In a report published Wednesday, Chinese researchers suggested that person-to-person spread among close contacts occurred as early as mid-December.

“Considerable efforts” will be needed to control the spread if this ratio holds up elsewhere, researchers wrote in the report, published in the New England Journal of Medicine.

More than half of the cases in which symptoms began before Jan. 1 were tied to a seafood market, but only 8% of cases after that have been, researchers found. They reported the average incubation period was five days.

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News Network
April 10,2020

Melbourne, Apr 10: Scientists have identified six drug candidates from more than 10,000 compounds that may help treat COVID-19.

The research, published in the journal Nature, tested the efficacy of approved drugs, drug candidates in clinical trials and other compounds.

"Currently there are no targeted therapeutics or effective treatment options for COVID-19," said Professor Luke Guddat from the University of Queensland in Australia.

"In order to rapidly discover lead compounds for clinical use, we initiated a programme of high-throughput drug screening, both in laboratories and also using the latest computer software to predict how different drugs bind to the virus," Guddat said.

The project targeted the main COVID-19 virus enzyme, known as the main protease or Mpro, which plays a pivotal role in mediating viral replication, the researchers said.

This makes it an attractive drug target for this virus, and as people don't naturally have this enzyme, compounds that target it are likely to have low toxicity, they said.

"We add the drugs directly to the enzyme or to cell cultures growing the virus and assess how much of each compound is required to stop the enzyme from working or to kill the virus. If the amount is small, then we have a promising compound for further studies," said Guddat.

After assaying thousands of drugs, researchers found of the six that appear to be effective in inhibiting the enzyme, one is of particular interest.

"We're particularly looking at several leads that have been subjected to clinical trials including for the prevention and treatment of various disorders such as cardiovascular diseases, arthritis, stroke, atherosclerosis and cancer," Guddat said.

Researchers said compounds that are already along the pipeline to drug discovery are preferred, as they can be further tested as antivirals at an accelerated rate compared to new drug leads that would have to go through this process from scratch.

"With continued and up-scaled efforts we are optimistic that new candidates can enter the COVID-19 drug discovery pipeline in the near future," Guddat said.

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