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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News Network
May 24,2020

Beijing, May 24: The Chinese virology institute in the city where COVID-19 first emerged has three live strains of bat coronavirus on-site, but none match the new contagion wreaking chaos across the world, its director has said.

Scientists think COVID-19 -- which first emerged in Wuhan and has killed some 340,000 people worldwide -- originated in bats and could have been transmitted to people via another mammal.

But the director of the Wuhan Institute of Virology told state broadcaster CGTN that claims made by US President Donald Trump and others that the virus could have leaked from the facility were "pure fabrication".

"Now we have three strains of live viruses... But their highest similarity to SARS-CoV-2 only reaches 79.8 percent," she said, referring to the coronavirus strain that causes COVID-19.

US demands immediate start to WHO review

The United States called on the World Health Organisation on Friday to begin working immediately on investigating the source of the novel coronavirus, as well as its handling of the response to the pandemic.

One of their research teams, led by Professor Shi Zhengli, has been researching bat coronaviruses since 2004 and focused on the "source tracing of SARS", the strain behind another virus outbreak nearly two decades ago.

"We know that the whole genome of SARS-CoV-2 is only 80 percent similar to that of SARS. It's an obvious difference," she said.

"So, in Professor Shi's past research, they didn't pay attention to such viruses which are less similar to the SARS virus."

Conspiracy rumours that the biosafety lab was involved in the outbreak swirled online for months before Trump and US Secretary of State Mike Pompeo brought the theory into the mainstream by claiming that there is evidence the pathogen came from the institute.

The lab has said it received samples of the then-unknown virus on December 30, determined the viral genome sequence on January 2 and submitted information on the pathogen to the WHO on January 11.

Wang said in the interview that before it received samples in December, their team had never "encountered, researched or kept the virus."

"In fact, like everyone else, we didn't even know the virus existed," she said. "How could it have leaked from our lab when we never had it?"

The World Health Organization said Washington had offered no evidence to support the "speculative" claims.

In an interview with Scientific American, Shi said the SARS-CoV-2 genome sequence did not match any of the bat coronaviruses her laboratory had previously collected and studied.

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News Network
May 20,2020

London, May 20: The current physical distancing guidelines of 6 feet may be insufficient to prevent COVID-19 transmission, according to a study which says a mild cough in low wind speeds can propel saliva droplets by as much as 18 feet.

Researchers, including those from the University of Nicosia in Cyprus, said a good baseline for studying the airborne transmission of viruses, like the one behind the COVID-19 pandemic, is a deeper understanding of how particles travel through the air when people cough.

In the study, published in the journal Physics of Fluids, they said even with a slight breeze of about four kilometres per hour (kph), saliva travels 18 feet in 5 seconds.

"The droplet cloud will affect both adults and children of different heights," said study co-author Dimitris Drikakis from the University of Nicosia.

According to the scientists, shorter adults and children could be at higher risk if they are located within the trajectory of the saliva droplets.

They said saliva is a complex fluid, which travels suspended in a bulk of surrounding air released by a cough, adding that many factors affect how saliva droplets travel in the air.

These factors, the study noted, include the size and number of droplets, how they interact with one another and the surrounding air as they disperse and evaporate, how heat and mass are transferred, and the humidity and temperature of the surrounding air.

In the study, the scientists created a computer simulation to examine the state of every saliva droplet moving through the air in front of a coughing person.

The model considered the effects of humidity, dispersion force, interactions of molecules of saliva and air, and how the droplets change from liquid to vapour and evaporate, along with a grid representing the space in front of a coughing person.

Each grid, the scientists said, holds information about variables like pressure, fluid velocity, temperature, droplet mass, and droplet position.

The study analysed the fates of nearly 1,008 simulated saliva droplets, and solved as many as 3.7 million equations.

"The purpose of the mathematical modelling and simulation is to take into account all the real coupling or interaction mechanisms that may take place between the main bulk fluid flow and the saliva droplets, and between the saliva droplets themselves," explained Talib Dbouk, another co-author of the study.

However, the researchers added that further studies are needed to determine the effect of ground surface temperature on the behaviour of saliva in air.

They also believe that indoor environments, especially ones with air conditioning, may significantly affect the particle movement through air.

This work is important since it concerns safety distance guidelines, and advances the understanding of the transmission of airborne diseases, Drikakis said.

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News Network
May 8,2020

May 8: Thousands of migrants have been stranded “all over the world” where they face a heightened risk of COVID-19 infection, the head of the UN migration agency International Organization for Migration (IOM) has said.

IOM Director-General António Vitorino said that more onerous health-related travel restrictions might discriminate disproportionately against migrant workers in future.

“Health is the new wealth,” Vitorino said, citing proposals by some countries to introduce the so-called immunity passports and use mobile phone apps designed to prevent the spread of the new coronavirus.

“In lots of countries in the world, we already have a system of screening checks to identify the health of migrants, above all malaria, tuberculosis… HIV-AIDS, and now I believe that there will be increased demands in health controls for regular migrants,” he said on Thursday.

Travel restrictions to try to limit the spread of the pandemic has left people on the move more vulnerable than ever and unable to work to support themselves, Vitorino told journalists via videoconference.

“There are thousands of stranded migrants all over the world.

 “In South-East Asia, in East Africa, in Latin America, because of the closing of the borders and with the travel restrictions, lots of migrants who were on the move; some of them wanted to return precisely because of the pandemic,” he said.

They are blocked, some in large groups, some in small, in the border areas, in very difficult conditions without access to minimal care, especially health screening, Vitorino said.

“We have been asking the governments to allow the humanitarian workers and the health workers to have access to (them),” he said.

Turning to Venezuelan migrants, who are believed to number around five million amidst a worsening economic crisis in the country, the IOM chief said “thousands… have lost their jobs in countries like Ecuador and Colombia and are returning back to Venezuela in large crowds without any health screening and being quarantined when they go back”.

In a statement, the IOM highlighted the plight of migrants left stranded in the desert in west, central and eastern Africa, either after having been deported without the due process, or abandoned by the smugglers.

The IOM’s immediate priorities for migrants include ensuring that they have access to healthcare and other basic social welfare assistance in their host country.

Among the UN agency’s other immediate concerns is preventing the spread of new coronavirus infection in more than 1,100 camps that it manages across the world.

They include the Cox’s Bazar complex in Bangladesh, home to around one million mainly ethnic Rohingya from Myanmar, the majority having fled persecution.

So far, no cases of infection have been reported there, the IOM chief said, adding that preventative measures have been communicated to the hundreds of thousands of camp residents, while medical capacity has been boosted.

Beyond the immediate health threat of COVID-19 infection, migrants also face growing stigmatization from which they need protection, Vitorino said.

Allowing hate speech and xenophobic narratives to thrive unchallenged also threatens to undermine the public health response to COVID-19, he said, before noting that migrant workers make up a significant percentage of the health sector in many developed countries including the UK, the US and Switzerland.

Populist narratives targeting migrants as carriers of disease could also destabilise national security through social upheaval and countries’ post-COVID economic recovery by removing critical workers in agriculture and service industries, he said.

Remittances have already seen a 30 per cent drop during the pandemic, Vitorino said, citing the World Bank data, meaning that some USD 20 billion has not been sent home to families in countries where up to 15 per cent of their gross domestic product comes from pay packets earned abroad.

Vitorino, in a plea, urged to give the health of migrants as much attention as that of the host populations in all countries.

“It is quite clear that health is the new wealth and that health concerns will be introduced in the mobility systems - not just for migration - but as a whole; where travelling for business or professional reasons, health will be the new gamechanger in town.

“If the current pandemic leads to a two or even three-tier mobility system, then we will have to try to solve the problem – the problem of the pandemic - but at the same time we have created a new problem of deepening the inequalities,” he said.

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