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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Agencies
March 8,2020

Washington, Mar 8: An attendee at last week's Conservative Political Action Conference (CPAC), which also saw the participation of US President Donald Trump, has tested positive for COVID-19, the American Conservative Union (ACU) said.

The exposure occurred prior to the conference held in National Harbor, Maryland, just south of Washington D.C., Xinhua news agency quoted the ACU as saying in a statement on Saturday.

A New Jersey hospital tested the person, and the Centers for Disease Control and Prevention (CDC) confirmed the positive result, said the statement.

"The individual is under the care of medical professionals in the state of New Jersey, and has been quarantined," it said.

Trump and Vice President Mike Pence spoke at the gathering, which took place from February 26-29.

Also present at the event were a number of administration and cabinet officials, including Secretary of State Mike Pompeo, Health and Human Services Secretary Alex Azar, and newly-appointed White House Chief of Staff Mark Meadows.

White House Press Secretary Stephanie Grisham said in a statement Saturday that the White House was aware of the development.

"At this time there is no indication that either President Trump or Vice President Pence met with or were in close proximity to the attendee," Grisham said in a statement.

"The President's physician and US Secret Service have been working closely with White House Staff and various agencies to ensure every precaution is taken to keep the First Family and the entire White House Complex safe and healthy."

The news emerged as Washington D.C. and neighbouring state of Virginia respectively confirmed their first cases of COVID-19 on Saturday.

In a press conference on Saturday night, Washington D.C. Mayor Muriel Bowser said a resident in his 50s showed symptoms of a respiratory virus in February. He was admitted to a hospital in the District on March 5.

The patient had no history of recent international travel, nor had he been exposed to anyone who was confirmed to be infected, according to Bowser.

The Mayor said D.C. health authorities were investigating the man's contact with other people before he went to the hospital.

A US Marine assigned to Fort Belvoir in Fairfax County, Virginia, tested positive on Saturday for COVID-19 and is currently being treated at Fort Belvoir Community Hospital, according to a Pentagon spokesman.

"The Marine recently returned from overseas where he was on official business," tweeted Jonathan Rath Hoffman, adding that Secretary of Defence Mark Esper and the White House have been briefed.

As of Saturday night, more than 420 cases of COVID-19 were reported in the US with 17 deaths, according to the Center for Systems Science and Engineering at Johns Hopkins University.

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News Network
February 18,2020

Beijing, Feb 18: Police in China have arrested a prominent activist who had been a fugitive for weeks and criticised President Xi Jinping's handling of the coronavirus epidemic while in hiding, a rights group said Tuesday.

Anti-corruption activist Xu Zhiyong was arrested on Saturday after being on the run since December, according to Amnesty International.

China's ruling Communist Party has severely curtailed civil liberties since Xi took power in 2012, rounding up rights lawyers, labour activists and even Marxist students.

The death this month of a whistleblowing doctor who was reprimanded by police for raising the alarm about the deadly new virus before dying of it himself triggered rare calls for political reform and freedom of speech.

The "Chinese government's battle against the coronavirus has in no way diverted it from its ongoing general campaign to crush all dissenting voices," said Patrick Poon, China researcher at Amnesty International, in an emailed statement.

Another source, who spoke to news agency on the condition of anonymity, said Xu had been arrested in the southern city of Guangzhou.

Guangzhou police did not respond to requests for comment.

Xu went into hiding after authorities broke up a December gathering of intellectuals discussing political reform in the eastern coastal city of Xiamen in Fujian province, prior to the coronavirus crisis.

Over a dozen lawyers and activists were detained or disappeared after the Xiamen gathering, according to rights groups -- and Xu's detention appears linked to his presence at the meeting, explained Poon.

But while on the run, Xu continued to post information on Twitter about rights issues.

On February 4 Xu released an article calling on Xi to step down and criticised his leadership across a range of issues including the US-China trade war, Hong Kong's pro-democracy protests and the coronavirus epidemic, which has now killed nearly 1,900 people.

"Medical supplies are tight, hospitals are filled with patients, and a large number of infected people have no way to be diagnosed," he wrote. "It's a mess."

"The coronavirus outbreak shows just how important values like freedom of expression and transparency are -- the exact values that Xu has long advocated," Yaqiu Wang, China researcher at Human Rights Watch, told news agency.

But the disappearance of Xu illustrates how the Chinese state "persists in its old ways" by "silencing its critics", she said.

Xu -- who founded a movement calling for greater transparency among high-ranking officials -- previously served a four-year prison sentence from 2013 to 2017 for organising an "illegal gathering".

"That he was a fugitive for so many days while continuing to speak out, that in itself was... a kind of challenge to (Chinese authorities)," said Hua Ze, a long-time friend of Xu who told AFP she lost contact with the Chinese activist on Saturday morning.

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News Network
May 14,2020

May 14: The UN’s children agency has warned that an additional 6,000 children could die daily from preventable causes over the next six months as the COVID-19 pandemic weakens the health systems and disrupts routine services, the first time that the number of children dying before their fifth birthday could increase worldwide in decades.

As the coronavirus outbreak enters its fifth month, the UN Children’s Fund (UNICEF) requested USD 1.6 billion to support its humanitarian response for children impacted by the pandemic.

The health crisis is “quickly becoming a child rights crisis. And without urgent action, a further 6,000 under-fives could die each day,” it said.

With a dramatic increase in the costs of supplies, shipment and care, the agency appeal is up from a USD 651.6 million request made in late March – reflecting the devastating socioeconomic consequences of the disease and families’ rising needs.

"Schools are closed, parents are out of work and families are under strain," UNICEF Executive Director Henrietta Fore said on Tuesday.

 “As we reimagine what a post-COVID world would look like, these funds will help us respond to the crisis, recover from its aftermath, and protect children from its knock-on effects.”

The estimate of the 6,000 additional deaths from preventable causes over the next six months is based on an analysis by researchers from the Johns Hopkins Bloomberg School of Public Health, published on Wednesday in the Lancet Global Health Journal.

UNICEF said it was based on the worst of three scenarios analysing 118 low and middle-income countries, estimating that an additional 1.2 million deaths could occur in just the next six months, due to reductions in routine health coverage, and an increase in so-called child wasting.

Around 56,700 more maternal deaths could also occur in just six months, in addition to the 144,000 likely deaths across the same group of countries. The worst case scenario, of children dying before their fifth birthdays, would represent an increase "for the first time in decades,” Fore said.

"We must not let mothers and children become collateral damage in the fight against the virus. And we must not let decades of progress on reducing preventable child and maternal deaths, be lost,” she said.

Access to essential services, like routine immunisation, has already been compromised for hundreds of millions of children and threatens a significant increase in child mortality.

According to a UNICEF analysis, some 77 per cent of children under the age of 18 worldwide are living in one of 132 countries with COVID-19 movement restrictions.

The UN agency also spotlighted that the mental health and psychosocial impact of restricted movement, school closures and subsequent isolation are likely to intensify already high levels of stress, especially for vulnerable youth.

At the same time, they maintained that children living under restricted movement and socio-economic decline are in greater jeopardy of violence and neglect. Girls and women are at increased risk of sexual and gender-based violence.

The UNICEF pointed out that in many cases, refugee, migrant and internally displaced children are experiencing reduced access to protection and services while being increasingly exposed to xenophobia and discrimination.

“We have seen what the pandemic is doing to countries with developed health systems and we are concerned about what it would do to countries with weaker systems and fewer available resources,” Fore said.

In countries suffering from humanitarian crises, UNICEF is working to prevent transmission and mitigate the collateral impacts on children, women and vulnerable populations – with a special focus on access to health, nutrition, water and sanitation, education and protection.

To date, the UN agency said it has received USD 215 million to support its pandemic response, and additional funding will help build upon already-achieved results.

Within its response, UNICEF has reached more than 1.67 billion people with COVID-19 prevention messaging around hand washing and cough and sneeze hygiene; over 12 million with critical water, sanitation and hygiene supplies; and nearly 80 million children with distance or home-based learning.

The UN agency has also shipped to 52 countries, more than 6.6 million gloves, 1.3 million surgical masks, 428,000 N95 respirators and 34,500 COVID-19 diagnostic tests, among other items.

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