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 12,2020

May 12: Several Indians in the US, either on the H-1B work visa or Green Card having children who are American citizens by birth, are being prevented from travelling to India aboard the special repatriation flights being run by Air India amidst the coronavirus-linked global travel restrictions.

According to the regulations issued by the Indian government last month and updated last week, visas of foreign nationals and OCI cards, that provide visa-free travel privileges to the people of Indian-origin, have been suspended as part of the new international travel restrictions.

For some of the Indian citizens like the Pandey couple in New Jersey (name and place changed at request), it's a double whammy. Having lost their H-1B job, they have to go back to India within the stipulated 60 days as required by law. The couple has two kids aged one and six years who are American citizens.

In the wee hours of Monday, they had to return from Newark airport as Air India refused to give their kids a ticket to fly to India along with them, despite them having a valid Indian visa. The young mother and father are Indian citizens.

They said that the officials from Air India and (Indian) Consulate (in New York) were very cooperative.

Also Read: COVID-19: Top senators urge Trump to temporarily suspend all new guest worker visas, including H-1B

But they could not do anything as their hands were tied by the latest regulation issued by the Indian government, a shocked Ratna Pandey told PTI.

"I would like to urge the Indian government to reconsider their decision on the humanitarian basis," said the Indian national who has lost her job but could not leave the US within the stipulated 60 days to avoid any future visa complications.

She now plans to make an appeal to the US Citizenship and Immigration Services (USCIS) to extend their stay.

Last month, H-1B visa holders, mostly Indians, launched a White House petition urging US President Donald Trump to extend their permissible stay from 60 to 180 days after job loss. However, there has been no decision from the White House so far.

While there is no official statistics of how many Indian H-1B visa holders have lost their jobs, it is believed to be substantial.

The US, due to the coronavirus pandemic, is experiencing an unprecedented unemployment rate and more than 33 million Americans have lost their jobs in the last two months. Given this massive job loss, Indians, who have lost their jobs, are unlikely to get one and thus many would have no other option but to travel back home.

In the case of single mother Mamta (name changed), the situation is graver as her son is just three-month old. Only she was given the ticket and the infant was not allowed to fly along with her because he carried an American passport.

"I would like to request the Indian government to let us fly back home. I don't want to stay in the US any longer," she told PTI hours after being prevented from boarding her hometown Ahmedabad-bound flight from Newark on Sunday.

"I am alone here. I don't have a relative here. It's a difficult situation," she said.

"Vande Bharat Mission is a humanitarian mission. But this is certainly inhuman," said Rakesh Gupta (name changed) from Washington DC.

An H-1B professional, Gupta has lost his job and needs to return to India within the stipulated 60 days. He and his wife, Geeta (name changed) being Indian citizens, received the confirmation of their seats in the flight but have been told that their two-and-a-half-year-old daughter cannot travel with them as she carried an OCI card.

"I don't believe this," he said.

Unlike the Pandey couple and Mamta, who had made the payment of USD 1,361 per ticket for their flight back home, Rakesh has not made the payment. Air India has said that the money would be refunded.

All the three Indian citizens requested the Indian government to help them travel back home by making necessary changes in the current regulations.

As per a recent government notification, all existing Indian visa holders, and visa-free travel facility, granted to OCI card holders who are not in India, have been suspended till restrictions on international air travel remains.

New York-based community leader Prem Bhandari said that the May 5 travel advisory has created multiple painful issues for the OCI card holders in the US and also to Indian citizens who are either on Green Card or H-1B visas and want to travel back home, but cannot leave their kids who are Americans by birth.

"We would like to express our disappointment with the discrimination between OCIs and citizens in respect of entering India at this critical stage when many OCIs have lawfully built their homes, families and businesses in India," Bhandari said in a letter to Union Home Secretary Ajay Kumar Bhalla on Monday.

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News Network
May 27,2020

Washington, May 27: Most viruses and other germs do not spread easily on flights, the US Center for Disease Control and Prevention has said in its COVID-19 guidelines which do not recommend following social distancing between two passengers inside a plane or keeping the middle seat unoccupied.

As a result of coronavirus pandemic, air traffic inside the US has come to a near halt. Air traffic is said to be down to about 90 per cent. For all travellers coming from overseas, the Center for Disease Control and Prevention (CDC) has recommended 14 days quarantine.

"Most viruses and other germs do not spread easily on flights because of how air circulates and is filtered on aeroplanes," the CDC has said in its set of COVID-19 guidelines for air travellers.

However, it noted that the air travellers were not risk-free especially in the time of the coronavirus pandemic and recommended Americans to avoid travel as far as possible.

"Air travel requires spending time in security lines and airport terminals, which can bring you in close contact with other people and frequently touched surfaces," it said.

"Social distancing is difficult on crowded flights, and you may have to sit near others (within six feet), sometimes for hours. This may increase your risk for exposure to the virus that causes COVID-19," the CDC said.

But instead of recommended social distancing inside commercial planes, the CDC has advised a series of preventive and hygienic measures to be taken by the airlines pilot and crew to prevent the spread of coronavirus.

The US Department of Transportation and Federal Aviation Administration in its latest safety alerts for operators on May 11 said that air carriers and crews conducting flight operations having a nexus to the US, including both domestic and foreign air carriers, should follow CDC's occupational health and safety guidance.

The CDC issued its guidelines in first guidelines for the airlines and airline crew on March and again in May.

The CDC, which has issued an exhaustive social guideline measures in various sections, is silent on keeping the middle seat of a plane unoccupied so as to maintain the six feet distance between two passengers.

It calls for the plane crew to report to the CDC a traveller with specific COVID-19 symptoms like fever, persistent cough, difficulty in breathing and appearing unwell.

Asking the airlines and cabin crew to review infection control guidelines for cabin crew, the CDC recommends several measures for cabin crew to protect themselves and others, manage a sick traveller, clean contaminated areas, and take actions after a flight.

Prominent among them include washing hands often with soap and water for at least 20 seconds, particularly after assisting sick travellers or touching potentially contaminated body fluids or surfaces and use of alcohol-based hand sanitizer (containing at least 60 per cent alcohol) if soap and water are not available.

Airlines should consider providing alcohol-based hand sanitizer to cabin and flight crews for their personal use, it said.

The CDC guidelines do not recommend following social distancing inside a plane between two passengers or keeping the middle seat unoccupied. But it asks to minimise contact between passengers and cabin crew and the sick person.

"If possible, separate the sick person from others (by a distance of 2 meters or 6 feet, ideally) and designate one crew member to serve the sick person. Offer a facemask, if available and if the sick person can tolerate it. If a facemask is not available or cannot be tolerated, ask the sick person to cover their mouth and nose with tissues when coughing or sneezing," said the CDC guidelines.

If no symptomatic passengers were identified during or immediately after the flight, the CDC recommends airlines to follow routine operating procedures for cleaning aircraft, managing solid waste, and wearing PPE.

"If symptomatic passengers are identified during or immediately after the flight, routine cleaning procedures should be followed, and enhanced cleaning procedures should also be used," it said.

Clean porous (soft) surfaces (e.g, cloth seats, cloth seat belts) at the seat of the symptomatic passengers and within 6 feet of the symptomatic passengers in all directions, it added.

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News Network
May 8,2020

New York, May 8: An Indian-American father and daughter, both doctors in New Jersey, have died due to the COVID-19, with Governor Phil Murphy describing their demise as “particularly tough" and hailed them for dedicating their lives for others.

Satyender Dev Khanna, 78, was a surgeon who served both on staff and as the head of the surgical departments for multiple hospitals across New Jersey for decades.

Priya Khanna, 43, was a double board-certified in both internal medicine and nephrology. She was Chief of Residents at Union Hospital, now part of RWJ Barnabas Health.

"Dr Satyender Dev Khanna and Dr Priya Khanna were father and daughter. They both dedicated their lives to helping others. This is a family dedicated to health and medicine. Our words cannot amply express our condolences," New Jersey Governor Murphy tweeted on Thursday.

“Both dedicated their lives to helping others and we lost both of them to COVID-19,” Murphy said during a press conference on Thursday, saying their demise is a "particularly tough one.”

Satyender passed away at the Clara Maass Medical Center where he had worked for more than 35 years.

Murphy described him as a "pioneering doctor” who was one of the first surgeons to perform laparoscopic surgery in the state. He is being remembered by colleagues as a “gentle and caring physician."

“And for a doctor, I'm not one, but I would bet, I don't think there could be a more fitting way to be remembered, or a nurse or a healthcare worker of any kind,” Murphy said, adding that the doctor had a passion for bicycling, and he often found peace from the hustle of the hospital in biking along the Jersey Shore.

Priya did all of her medical training in New Jersey and then did her fellowship in nephrology in South Jersey with the Cooper Health System. Like her father, she too worked at Clara Maass, where she died.

She was also Medical Director at two dialysis centres in Essex County and “took pride” in teaching the next generation of doctors, Murphy said, adding that the ICU physician who cared for Priya Khanna was trained and taught by her as well.

Follow live developments on the coronavirus pandemic here

“Priya will be remembered as a caring and selfless person who put others first. And even while in the hospital, fighting her own battle, she continued to check up on her mom and dad and her family,” Murphy said.

“This is a family, by the way, dedicated to health and medicine,” he said.

The governor spoke with Satyender's wife Komlish Khanna, who is a paediatrician. The couple has two more daughters - Sugandha Khanna, an emergency medicine physician and Anisha Khanna, a paediatrician.

“Unbelievable. Our words cannot amply express our condolences nor, I am sure, can they express the pain that the Khanna family is feeling. But I hope that the fact that our entire state mourns with them is some small comfort. And we mourn everyone we have lost. We commit in their memory to saving as many lives as we can,” Murphy said.

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