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
August 7,2020

Russia boasts that it's about to become the first country to approve a Covid-19 vaccine, with mass vaccinations planned as early as October using shots that are yet to complete clinical trials -- and scientists worldwide are sounding the alarm that the headlong rush could backfire.

Moscow sees a Sputnik-like propaganda victory, recalling the Soviet Union's launch of the world's first satellite in 1957.

But the experimental Covid-19 shots began first-in-human testing on a few dozen people less than two months ago, and there's no published scientific evidence yet backing Russia's late entry to the global vaccine race, much less explaining why it should be considered a front-runner.

“I'm worried that Russia is cutting corners so that the vaccine that will come out may be not just ineffective, but also unsafe,” said Lawrence Gostin, a global public health law expert at Georgetown University. “It doesn't work that way... Trials come first. That's really important.”

According to Kirill Dmitriev, head of Russia's Direct Investment Fund that bankrolled the effort, a vaccine developed by the Gamaleya research institute in Moscow may be approved in days, before scientists complete what's called a Phase 3 study.

That final-stage study, usually involving tens of thousands of people, is the only way to prove if an experimental vaccine is safe and really works.

Health Minister Mikhail Murashko said members of “risk groups,” such as medical workers, may be offered the vaccine this month.

He didn't clarify whether they would be part of the Phase 3 study that is said to be completed after the vaccine receives “conditional approval.”

Deputy Prime Minister Tatyana Golikova promised to start “industrial production” in September, and Murashko said mass vaccination may begin as early as October.

Dr Anthony Fauci, the top US infectious disease specialist, questioned the fast-track approach last week.

“I do hope that the Chinese and the Russians are actually testing a vaccine before they are administering the vaccine to anyone, because claims of having a vaccine ready to distribute before you do testing I think is problematic at best," he said.

Questions about this vaccine candidate come after the US, Britain and Canada last month accused Russia of using hackers to steal vaccine research from Western labs.

Delivering a vaccine first is a matter of national prestige for the Kremlin as it tries to assert the image of Russia as a global power capable of competing with the US and China.

The notion of being “the first in the world” dominated state news coverage of the effort, with government officials praising reports of the first-step testing.

In April, President Vladimir Putin ordered state officials to shorten the time of clinical trials for a variety of drugs, including potential coronavirus vaccines.

According to Russia's Association of Clinical Trials Organizations, the order set “an unattainable bar” for scientists who, as a result, "joined in on the mad race, hoping to please those at power.”

The association first raised concern in late May, when professor Alexander Gintsburg, head of the Gamaleya institute, said he and other researchers tried the vaccine on themselves.

The move was a “crude violation of the very foundations of clinical research, Russian law and universally accepted international regulations" the group said in an open letter to the government, urging scientists and health officials to adhere to clinical research standards.

But a month later, the Health Ministry authorized clinical trials of the Gamaleya product, with what appeared to be another ethical issue.

Human studies started June 17 among 76 volunteers. Half were injected with a vaccine in liquid form and the other half with a vaccine that came as soluble powder.

Some in the first half were recruited from the military, which raised concerns that servicemen may have been pressured to participate.

Some experts said their desire to perform well would affect the findings. “It's no coincidence media reports we see about the trials among the military said no one had any side effects, while the (other group) reported some," said Vasily Vlassov, a public health expert with Moscow's Higher School of Economics.

As the trials were declared completed and looming regulatory approval was announced last week, questions arose about the vaccine's safety and effectiveness.

Government assurances the drug produced the desired immune response and caused no significant side effects were hardly convincing without published scientific data describing the findings.

The World Health Organization said all vaccine candidates should go through full stages of testing before being rolled out.

“There are established practices and there are guidelines out,” WHO spokesman Christian Lindmeier said Tuesday.

“Between finding or having a clue of maybe having a vaccine that works, and having gone through all the stages, is a big difference.”

Offering an unsafe compound to medical workers on the front lines of the outbreak could make things worse, Georgetown's Gostin said, adding: “What if the vaccine started killing them or making them very ill?”

Vaccines that are not properly tested can cause harm in many ways — from a negative impact on health to creating a false sense of security or undermining trust in vaccinations, said Thomas Bollyky, director of the global health program at the Council on Foreign Relations. 

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Agencies
May 8,2020

United Nations, May 8: UN Secretary-General Antonio Guterres said Friday the coronavirus pandemic keeps unleashing a tsunami of hate and xenophobia, scapegoating and scare-mongering. 

The UN chief said anti-foreigner sentiment has surged online and in the streets, anti-Semitic conspiracy theories have spread, and COVID-19-related anti-Muslim attacks have occurred. 

Guterres said migrants and refugees have been vilified as a source of the virus -- and then denied access to medical treatment. 

With older persons among the most vulnerable, contemptible memes have emerged suggesting they are also the most expendable, he said. 

And journalists, whistleblowers, health professionals, aid workers and human rights defenders are being targeted simply for doing their jobs. 

Guterres appealed for an all-out effort to end hate speech globally. The secretary-general called on political leaders to show solidarity with all people, on educational institutions to focus on digital literacy at a time when extremists are seeking to prey on captive and potentially despairing audiences. 

He called on the media, especially social media, to remove racist, misogynist and other harmful content, on civil society to strengthen their outreach to vulnerable people, and on religious figures to serve as models of mutual respect. 

And I ask everyone, everywhere, to stand up against hate, treat each other with dignity and take every opportunity to spread kindness, Guterres said.

The secretary-general stressed that COVID-19 does not care who we are, where we live, what we believe or about any other distinction. His global appeal to address and counter COVID-19-related hate speech follows his April 23 message calling the coronarivus pandemic a human crisis that is fast becoming a human rights crisis. 

Guterres said then that the pandemic has seen disproportionate effects on certain communities, the rise of hate speech, the targeting of vulnerable groups, and the risks of heavy-handed security responses undermining the health response. 

With rising ethno-nationalism, populism, authoritarianism and a push back against human rights in some countries, the crisis can provide a pretext to adopt repressive measures for purposes unrelated to the pandemic, he warned.

In February, Guterres issued a call to action to countries, businesses and people to help renew and revive human rights across the globe, laying out a seven-point plan amid concerns about climate change, conflict and repression.

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News Network
April 2,2020

United Nations, Apr 2: The global economy could shrink by up to one per cent in 2020 due to the coronavirus pandemic, a reversal from the previous forecast of 2.5 per cent growth, the UN has said, warning that it may contract even further if restrictions on the economic activities are extended without adequate fiscal responses.

The analysis by the UN Department of Economic and Social Affairs (DESA) said the COVID-19 pandemic is disrupting global supply chains and international trade. With nearly 100 countries closing national borders during the past month, the movement of people and tourism flows have come to a screeching halt.

"Millions of workers in these countries are facing the bleak prospect of losing their jobs. Governments are considering and rolling out large stimulus packages to avert a sharp downturn of their economies which could potentially plunge the global economy into a deep recession. In the worst-case scenario, the world economy could contract by 0.9 per cent in 2020," the DESA said, adding that the world economy had contracted by 1.7 per cent during the global financial crisis in 2009.

It added that the contraction could be even higher if governments fail to provide income support and help boost consumer spending.

The analysis noted that before the outbreak of the COVID-19, world output was expected to expand at a modest pace of 2.5 per cent in 2020, as reported in the World Economic Situation and Prospects 2020.

Taking into account rapidly changing economic conditions, the UN DESA's World Economic Forecasting Model has estimated best and worst-case scenarios for global growth in 2020.

In the best-case scenario with moderate declines in private consumption, investment and exports and offsetting increases in government spending in the G-7 countries and China global growth would fall to 1.2 per cent in 2020.

"In the worst-case scenario, the global output would contract by 0.9 per cent instead of growing by 2.5 per cent in 2020," it said, adding that the scenario is based on demand-side shocks of different magnitudes to China, Japan, South Korea, the US and the EU, as well as an oil price decline of 50 per cent against our baseline of USD 61 per barrel.

The severity of the economic impact will largely depend on two factors - the duration of restrictions on the movement of people and economic activities in major economies; and the actual size and efficacy of fiscal responses to the crisis.

A well-designed fiscal stimulus package, prioritising health spending to contain the spread of the virus and providing income support to households most affected by the pandemic would help to minimise the likelihood of a deep economic recession, it said.

According to the forecast, lockdowns in Europe and North America are hitting the service sector hard, particularly industries that involve physical interactions such as retail trade, leisure and hospitality, recreation and transportation services. Collectively, such industries account for more than a quarter of all jobs in these economies.

The DESA said as businesses lose revenue, unemployment is likely to increase sharply, transforming a supply-side shock to a wider demand-side shock for the economy.

Against this backdrop, the UN-DESA is joining a chorus of voices across the UN system calling for well-designed fiscal stimulus packages which prioritize health spending and support households most affected by the pandemic.

Urgent and bold policy measures are needed, not only to contain the pandemic and save lives, but also to protect the most vulnerable in our societies from economic ruin and to sustain economic growth and financial stability, Under-Secretary-General for Economic and Social Affairs Liu Zhenmin said.

The analysis also warns that the adverse effects of prolonged economic restrictions in developed economies will soon spill over to developing countries via trade and investment channels.

A sharp decline in consumer spending in the European Union and the United States will reduce imports of consumer goods from developing countries.

Developing countries, particularly those dependent on tourism and commodity exports, face heightened economic risks. Global manufacturing production could contract significantly, and the plummeting number of travellers is likely to hurt the tourism sector in small island developing States, which employs millions of low-skilled workers, it said.

Meanwhile, the decline in commodity-related revenues and a reversal of capital flows are increasing the likelihood of debt distress for many nations. Governments may be forced to curtail public expenditure at a time when they need to ramp up spending to contain the pandemic and support consumption and investment.

UN Chief Economist and Assistant Secretary-General for Economic Development Elliot Harris said the collective goal must be a resilient recovery which puts the planet back on a sustainable track. We must not lose sight how it is affecting the most vulnerable population and what that means for sustainable development, he said.

The alarms raised by UN-DESA echo another report, released on March 31, in which UN experts issued a broad appeal for a large-scale, coordinated, comprehensive multilateral response amounting to at least 10 per cent of global gross domestic product (GDP).

According to estimates by the Johns Hopkins University, confirmed coronavirus cases across the world now stand at over 932,600 and over 42,000 deaths.

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