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.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
May 15,2020

May 15: Global tensions simmered over the race for a coronavirus vaccine Thursday, as the United States and China traded jabs, and France slammed pharmaceuticals giant Sanofi for suggesting the US would get any eventual vaccine first.

Scientists are working at breakneck speed to develop a vaccine for COVID-19, the disease caused by the virus, which has killed more than 300,000 people worldwide and pummelled economies.

From the US to Europe to Asia, national and local governments are easing lockdown orders to get people back to work -- while fretting over a possible second wave of infections.

Increased freedom of movement means an increased risk of contracting the virus, and so national labs and private firms are labouring to find the right formula for a vaccine.

The European Union's medicines agency offered some hope when it said one could be ready in a year, based on data from clinical trials already underway.

But Marco Cavaleri, the EMA's head of vaccines strategy, acknowledged that timeline was a "best-case scenario," and cautioned that "there may be delays."

The race for a vaccine has exposed a raw nerve in relations between the United States and China, where the virus was first detected late last year in the central city of Wuhan.

Two US agencies warned Wednesday that Chinese hackers were trying to steal COVID-19 vaccine research -- a claim Beijing rejected as "smearing" its reputation.

US President Donald Trump, who has ratcheted up the rhetoric against China, said he doesn't even want to engage with Chinese leader Xi Jinping -- potentially imperilling a trade deal between the world's top two economies.

"I'm very disappointed in China. I will tell you that right now," he said in an interview with Fox Business.

"There are many things we could do. We could do things. We could cut off the whole relationship."

On Capitol Hill, an ousted US health official told Congress that the Trump government had no strategy in place to find and distribute a vaccine to millions of Americans, warning of the "darkest winter" ahead.

"We don't have a single point of leadership right now for this response, and we don't have a master plan," said Rick Bright, who was removed last month as head of the US agency charged with developing a coronavirus vaccine.

The United States has registered nearly 86,000 deaths linked to COVID-19 -- the highest toll of any nation.

World leaders were among 140 signatories to a letter published Thursday saying any vaccine should not be patented and that the science should be shared among nations.

"Governments and international partners must unite around a global guarantee which ensures that, when a safe and effective vaccine is developed, it is produced rapidly at scale and made available for all people, in all countries, free of charge," it said.

But a row erupted in France after drugmaker Sanofi said it would reserve first shipments of any vaccine it discovered to the United States.

The comments prompted a swift rebuke from the French government -- President Emmanuel Macron's office said any vaccine should be treated as "a global public good, which is not submitted to market forces."

Sanofi chief executive Paul Hudson said the US had a risk-sharing model that allowed for manufacturing to start before a vaccine had been finally approved -- while Europe did not.

"The US government has the right to the largest pre-order because it's invested in taking the risk," Hudson told Bloomberg News.

Macron's top officials are scheduled to meet with Sanofi executives about the issue next week.

The search for a vaccine became even more urgent after the World Health Organization said the disease may never go away and the world would have to learn to live with it for good.

"This virus may become just another endemic virus in our communities and this virus may never go away," said Michael Ryan, the UN body's emergencies director.

The prospect of the disease lingering leaves governments facing a delicate balancing act between suppressing the pathogen and getting their economies up and running.

In the US, more grim economic data emerged Thursday, with nearly three million more Americans applying for unemployment benefits.

That takes the overall total to 36.5 million -- more than 10 percent of the US population.

Further signs of the damage to businesses emerged when Lloyd's of London forecast the pandemic will cost the global insurance industry about $203 billion.

European markets closed down, but Wall Street rallied despite the new jobless claims. In a sign of progress, the New York Stock Exchange trading floor was due to reopen on May 26.

The reopening of economies continued in earnest across Europe, where the EU has set out proposals for a phased restart of travel and the eventual lifting of border controls.

"Maybe it's a mistake, but we have no choice. Without tourists, we won't get by!" Enrico Facchetti, a 61-year-old former goldsmith, said of Venice's reopening.

Japan -- the world's third largest economy -- lifted a state of emergency across most of the country except for Tokyo and Osaka.

And Canadian Prime Minister Justin Trudeau said national parks would partially reopen on June 1.

But in Latin America, the virus continued to surge, with a 60 percent leap in cases in the Chilean capital of Santiago.

Authorities said 2,000 new graves were being dug at the main cemetery.

South Sudan reported its first COVID-19 death on Thursday.

And in Bangladesh, the first case was confirmed in the teeming Rohingya refugee camps in Bangladesh, which are home to nearly one million people.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
January 27,2020

Kabul, Jan 27: A passenger plane crashed on Monday in a Taliban-held area of Afghanistan's Ghazni province, local officials said.

Arif Noori, spokesman for the provincial governor, said the plane went down around 1:10 p.m. local time in Deh Yak district, which is held by the Taliban. Two provincial council members also confirmed the crash.

The number of people on board and their fate was not immediately known, nor was the cause of the crash.

Ariana Airlines, Afghanistan's national carrier, dismissed the claim that one of their planes had crashed in a statement on their website, saying all their aircraft were operational and safe.

The mountainous Ghazni province sits in the foothills of the Hindu Kush mountains and is bitterly cold in winter.

The last major commercial air crash in Afghanistan occurred in 2005 when a Kam Air flight from western Herat to the capital Kabul crashed into the mountains as it tried to land in snowy weather.

The war however has seen a number of deadly crashes of military aircraft. One of the most spectacular occurred in 2013 when an American Boeing 747 cargo jet crashed shortly after takeoff from Bagram air base north of Kabul en route to Dubai in the United Arab Emirates. All seven crew member were killed.

Afghanistan's aviation industry suffered desperately during the rule of the Taliban when its only airline Ariana was subject to punishing sanctions and allowed to fly only to Saudi Arabia for Hajj flights.

Since the overthrow of the religious regime smaller private airlines have emerged but the industry is still a nascent one.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
August 5,2020

Ninety per cent of a sample group of coronavirus-recovered patients from a prominent hospital in China's Wuhan city where the pandemic broke out have reported lung damage and five per cent of them are again in quarantine after testing positive for the virus, according to a media report on Wednesday.

A team at the Zhongnan Hospital of Wuhan University led by Peng Zhiyong, director of the hospital's Intensive Care Unit, has been conducting follow-up visits with '100 recovered patients' since April.

The first phase of this one-year programme finished in July. The average age of the patients in the study is 59.

According to the first phase results, 90 per cent of the patients' lungs are still in a damaged state, which means their lungs ventilation and gas exchange functions have not recovered to the level of healthy people, state-run Global Times reported.

Peng's team conducted a six-minute walking test with the patients. They found that the recovered patients could only walk 400 metres in six minutes while their healthy peers could walk 500 metres in the same period.

Some recovered patients have to rely on oxygen machines even three months after being discharged from the hospital, Liang Tengxiao, a doctor from the Dongzhimen Hospital, Beijing University of Chinese Medicine, was quoted as saying by the report.

Liang's team is also conducting follow-up visits with recovered patients aged above 65.

The results also showed that antibodies against the novel coronavirus in 10 per cent of the 100 patients have disappeared.

Five per cent of them received negative results in Covid-19 nucleic acid tests but positive results in Immunoglobulin M (IgM) tests, and thus have to be quarantined again, the report said.

IgM is usually the first antibody produced by the immune system when a virus attacks. A positive result in an IgM test usually means that a person has just been infected by the virus.

It is still unclear if this means these people have been infected again.

The 100 patients' immune systems have not fully recovered as they showed a low level of B cells -- - a primary force for killing viruses in the human body -- but a high level of T cells which only recognise viral antigens outside infected cells.

"The results revealed that the patients’ immune systems are still recovering," Peng said.

The patients also suffered from depression and a sense of stigma. Most of the recovered patients told the team that their families were not willing to have dinner with them at the same table, the report said.

Less than half of the recovered patients have returned to work, it said.

The findings are significant as the coronavirus first emerged in Wuhan city.

Hubei province for which Wuhan is the provincial capital has reported a total of 68,138 confirmed Covid-19 cases till now. The disease has claimed 4,512 lives in the province, according to the official data.

China reported 27 new confirmed Covid-19 cases on Tuesday, including 22 locally-transmitted cases, the National Health Commission (NHC) said on Wednesday.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.