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 15,2020

Washington, Jul 15: The Trump administration has agreed to rescind its July 6 rule, which temporarily barred international students from staying in the United States unless they attend at least one in-person course, a federal district court judge said on Tuesday.

The U-turn by the Trump administration comes following a nationwide outrage against its July 6 order and a series of lawsuits filed by a large number of educational institutions, led by the prestigious Harvard University and Massachusetts Institute of Technology (MIT), seeking a permanent injunctive relief to bar the Department of Homeland Security (DHS) and the US Immigration and Customs Enforcement (ICE) from enforcing the federal guidelines barring international students attending colleges and universities offering only online courses from staying in the country.

As many as 17 US states and the District of Columbia, along with top American IT companies such as Google, Facebook and Microsoft, joined MIT and Harvard in the US District Court in Massachusetts against the DHS and the ICE in seeking an injunction to stop the entire rule from going into effect.

"I have been informed by the parties that they have come to a resolution. They will return to the status quo," Judge Allison Burroughs, the federal district judge in Boston, said in a surprise statement at the top of the hearing on the lawsuit.

The announcement comes as a big relief to international students, including those from India. In the 2018-2019 academic year, there were over 10 lakh international students in the US. According to a recent report of the Student and Exchange Visitor Program (SEVP), 1,94,556 Indian students were enrolled in various academic institutions in the US in January.

Judge Burroughs said the policy would apply nationwide.

"Both the policy directive and the frequently asked questions would not be enforced anyplace," she said, referring to the agreement between the US government and MIT and Harvard.

Congressman Brad Scneider said this is a great win for international students, colleges and common sense.

"The Administration needs to give us a plan to tackle our public health crisis - it can't be recklessly creating rules one day and rescinding them the next," he said in a tweet.

Last week, more than 136 Congressmen and 30 senators wrote to the Trump administration to rescind its order on international students.

"This is a major victory for the students, organisers and institutions of higher education in the #MA7 and all across the country that stood up and fought back against this racist and xenophobic rule," said Congresswoman Ayanna Pressley.

"Taking online classes shouldn't force international students out of our country," Congressman Mikie Sherrill said in a tweet.

In its July 6 notice, the ICE had said all student visa holders, whose university curricula were only offered online, "must depart the country or take other measures, such as transferring to a school with in-person instruction to remain in lawful status".

"If not, they may face immigration consequences, including but not limited to the initiation of removal proceedings," it had said.

In their lawsuit, the 17 states and the District of Columbia said for many international students, remote learning in the countries and communities they come from would impede their studies or be simply impossible.

The lawsuit alleged that the new rule imposes a significant economic harm by precluding thousands of international students from coming to and residing in the US and finding employment in fields such as science, technology, biotechnology, healthcare, business and finance, and education, and contributing to the overall economy.

In a separate filing, companies like Google, Facebook and Microsoft, along with the US Chamber of Commerce and other IT advocacy groups, asserted that the July 6 ICE directive will disrupt their recruiting plans, making it impossible to bring on board international students that businesses, including the amici, had planned to hire, and disturb the recruiting process on which the firms have relied on to identify and train their future employees.

The July 6 directive will make it impossible for a large number of international students to participate in the CPT and OPT programmes. The US will "nonsensically be sending...these graduates away to work for our global competitors and compete against us...instead of capitalising on the investment in their education here in the US", they said.

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News Network
June 20,2020

Sao Paulo, June 20: Brazil’s government confirmed on Friday that the country has risen above 1 million confirmed coronavirus cases, second only to the United States.

The country’s health ministry said that the total now stood at 10,32,913, up more than 50,000 from Thursday. The ministry said the sharp increase was due to corrections of previous days’ underreported numbers.

Brazilian President Jair Bolsonaro still downplays the risks of the virus after nearly 50,000 deaths from COVID-19 in three months, saying the impact of social isolation measures on the economy could be worse than the disease itself.

Specialists believe the actual number of cases in Brazil could be up to seven times higher than the official statistic. Johns Hopkins University says Brazil is performing an average of 14 tests per 1,00,000 people each day, and health experts say that number is up to 20 times less than needed to track the virus.

Official data show a downward trend of the virus in Brazil’s north, including the hard-hit region of the Amazon, a plateau in cases and deaths in the countries’ biggest cities near the Atlantic coast, but a rising curve in the south.

In the Brazilian countryside, which is much less prepared to handle a crisis, the pandemic is clearly growing. Many smaller cities have weaker health care systems and basic sanitation that’s insufficient to prevent contagion.

“There is a lot of regional inequality in our public health system and a shortage of professionals in the interior,” said Miguel Lago, executive director of Brazil’s Institute for Health Policy Studies, which advises public health officials.

That creates many health care deserts, with people going long distances to get attention. When they leave the hospital, the virus can go with them.

The cattle-producing state of Mato Grosso was barely touched by the virus when it hit the nation’s biggest cities in March. Sitting far from the coast, between the Bolivian border and Brazil’s capital of Brasilia, its 33 lakh residents led a mostly normal life until May. But now its people live under lockdown and meat producers have dozens of infected workers.

In Tangará da Serra, a city of 1,03,000 people in Mato Grosso, the mayor decided Friday to forbid the sale of alcoholic drinks for two weeks as an incentive for people to stay home.

Fᢩo Junqueira said the measure was needed after a spike in COVID-19 cases that filled 80% of the city’s 54 intensive care beds. The city has had nearly 300 cases of the disease, plus three fatalities.

In Rondonópolis, only 300 miles away from Tangará da Serra and home to a thriving economy, health authorities closed the local meatpacking industry after 92 cases were confirmed there. The city of 1,44,000 inhabitants counted 21 deaths from the virus and more than 600 cases. The mayor has also decided to limit sales of alcoholic beverages.

Even regions once considered examples of successful efforts against the virus are now struggling.

Porto Alegre, home to about 14 lakh people, had success in slowing the virus’ spread over the last three months. But now its mayor is considering increasing social isolation measures after ICU occupancy in the city jumped to 80% this month.

We were already making projections for schools to come back, Mayor Nelson Marchezan Jr. told The Associated Press. Now the trend is to impose more restrictions. Outside Sao Paulo city, five regions of the state’s countryside will have to close shops starting Monday due to a rise in coronavirus cases. Governor João Doria announced the decision Friday.

Dr. Mike Ryan, the World Health Organization’s executive director, said at a news conference that Brazil needs to increase its efforts to stop the spread of infections.

“The epidemic is still quite severe in Brazil. I believe health workers are working extremely hard and under pressure to be able to deal with the number of cases that they see on a daily basis,” Dr. Ryan said.

“Certainly the rise is not as exponential as it was previously, so there are some signs that the situation is stabilising. But we’ve seen this before in other epidemics in other countries.”

Margareth Dalcolmo, a clinical researcher and professor of respiratory medicine at the state-funded Oswaldo Cruz Foundation in Rio de Janeiro, believes the reopening in major cities and the virus traveling by road into Brazil’s heartland will keep the pressure on the country’s health system.

“The risk in the interior now is very big,” she said. “Our health system just can’t solve the most serious cases of COVID in many places of the countryside.”

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News Network
July 3,2020

Islamabad, Jul 3: The US embassy here in a statement on Friday said the Trump administration through the US Agency for International Development (USAID) “donated a shipment of 100 brand-new, state-of-the-art ventilators” to Pakistan.

The ventilators arrived in Karachi on July 2 and will be sent to hospitals across Pakistan.

“This donation delivers on President Donald Trump’s generous offer of these critically-needed supplies and supports Pakistan’s urgent response to the pandemic,” the embassy said.

Made in America, the ventilators are valued at about $3 million and reflect the latest in cutting-edge medical design and technology, it said.

They are compact, easily deployable, and will enable Pakistan to more effectively treat patients suffering from Covid-19.

The US-Pakistan health partnership to curb the spread of the novel coronavirus is helping to improve and expand laboratory testing, disease monitoring, case tracking, infection prevention and control and patient care, the embassy said.

The US has contributed nearly $27 million in new funding so far to this vital partnership that is growing every day. "We are also thankful for Pakistan's contribution of medical supplies to help fight coronavirus in the US," the embassy said in the statement.

Ambassador Paul Jones said, “The US stands with Pakistan in its fight against the coronavirus. These American-made ventilators will help Pakistani patients in the most acute need of medical care."

The announcement comes days after Pakistan said it had started producing locally designed ventilators.

Pakistan reported 78 more deaths from the coronavirus in the past 24 hours, raising virus-related fatalities to 4,551 while the total number of confirmed cases has increased to 221,896.

On Friday, the health authorities said 1,13,623 persons have recovered from the coronavirus, surpassing the number of active Covid-19 infections in the country for the first time.

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