Showing posts with label maths. Show all posts
Showing posts with label maths. Show all posts

Thursday, 11 April 2019

That image of a black hole you saw everywhere today? Thank this grad student for making it possible

Imagine trying to take a photo of an orange that's on the moon with your smartphone. It seems impossible.

That's what it was like for scientists trying to capture an image of a black hole in space. Despite the tall order, an international team of more than 200 researchers unveiled the first-ever image of a black hole on Wednesday.

The effort wouldn't have been possible without Katie Bouman, who developed a crucial algorithm that helped devise imaging methods.


Three years ago, Bouman led the creation of an algorithm that eventually helped capture this first-of-its-kind image: a supermassive black hole and its shadow at the center of a galaxy known as M87.

She was then a graduate student in computer science and artificial intelligence at the Massachusetts Institute of Technology.

Black holes are extremely far away and compact, so taking a photo of one is no easy task. In addition, black holes by definition are supposed to be invisible -- although they can give off a shadow when they interact with the material around them.

A global network of telescopes known as the Event Horizon Telescope project collected millions of gigabytes of data about M87 using a technique known as interferometry. However, there were still large gaps in the data that needed to be filled in.

Her algorithm, and many others, helped fill in the gaps
That's where Bouman's algorithm -- along with several others -- came in. Using imaging algorithms like Bouman's, researchers created three scripted code pipelines to piece together the picture.

The Event Horizon Telescope (EHT) -- a planet-scale array of eight ground-based radio telescopes forged through international collaboration -- was designed to capture images of a black hole. Today, in coordinated press conferences across the globe, EHT researchers reveal that they have succeeded, unveiling the first direct visual evidence of a supermassive black hole and its shadow.

They took the "sparse and noisy data" that the telescopes spit out and tried to make an image. For the past few years, Bouman directed the verification of images and selection of imaging parameters.

"We developed ways to generate synthetic data and used different algorithms and tested blindly to see if we can recover an image," she told CNN.

"We didn't want to just develop one algorithm. We wanted to develop many different algorithms that all have different assumptions built into them. If all of them recover the same general structure, then that builds your confidence."

The result? A groundbreaking image of a lopsided, ring-like structure that Albert Einstein predicted more than a century ago in his theory of general relativity. In fact, the researchers had generated several photos and they all looked the same. The image of the black hole presented on Wednesday was not from any one method, but all the images from different algorithms that were blurred together.

"No matter what we did, you would have to bend over backwards crazy to get something that wasn't this ring," Bouman said.

Bouman was a crucial member of the imaging team
"(Bouman) was a major part of one of the imaging subteams," said Vincent Fish, a research scientist at MIT's Haystack Observatory.

"One of the insights Katie brought to our imaging group is that there are natural images," Fish said. "Just think about the photos you take with your camera phone -- they have certain properties. ... If you know what one pixel is, you have a good guess as to what the pixel is next to it."

For example, there are areas that are smoother and areas that have sharp boundaries. Astronomical images share these properties, and you can mathematically encode these properties, Fish said.

Junior members like Bouman made significant contributions to the project, he added. Of course, senior scientists worked on the project, but the imaging portion was mostly led by junior researchers, such as graduate students and post docs.

"No one of us could've done it alone," Bouman said. "It came together because of lots of different people from many backgrounds."

Bouman starts teaching as an assistant professor at California Institute of Technology in the fall.

(Source: CNN)

Wednesday, 12 December 2018

Puzzle solving 'won't stop mental decline'

Doing crossword puzzles and Sudoku does not appear to protect against mental decline, according to a new study.

The idea of "use it or lose it" when it comes to our brains in later life has previously been widely accepted.

The new Scottish study showed that people who regularly do intellectual activities throughout life have higher mental abilities.

This provides a "higher cognitive point" from which to decline, say the researchers.

But the study did not show that they decline any slower.

The work, published in the BMJ, was undertaken by Dr Roger Staff at Aberdeen Royal Infirmary and the University of Aberdeen.

It looked at 498 people born in 1936 who had taken part in a group intelligence test at the age of 11.

This current study started when they were about 64 years old and they were recalled for memory and mental-processing-speed testing up to five times over a 15-year period.

It found engagement in problem solving did not protect an individual from decline.

However, engaging in intellectually stimulating activities on a regular basis was linked to level of mental ability in old age.


Proof?
The study uses modelling to look at associations and cannot prove any causal link. Also, many of the participants were unable to complete the whole study - some dropped out, others died.

Previously, some studies have found that cognitive training can improve some aspects of memory and thinking, particularly for people who are middle-aged or older.

They found so-called brain training may help older people to manage their daily tasks better.

No studies have shown that brain training prevents dementia.

And last year a report from the Global Council on Brain Health recommended that people should take part in stimulating activities such as learning a musical instrument, designing a quilt or gardening rather than brain training to help their brain function in later life.

It said the younger a person started these activities, the better their brain function would be as they aged.

Dr Staff and colleagues say even though their study did not find puzzles counteracted mental decline, it doesn't mean they are a waste of time.

Dr David Reynolds, chief scientific officer at Alzheimer's Research UK, said the research added to the "ongoing 'use it or lose it' debate".

But as the research did not consider people with dementia, "we can't say from these results whether specific brain training activities could impact a person's risk of the condition".

"In addition to staying mentally active, keeping physically fit, eating a healthy balanced diet, not smoking, drinking within recommended guidelines and keeping weight, cholesterol and blood pressure in check are all good ways to support a healthy brain as we get older."

Dr James Pickett, Head of Research at Alzheimer's Society, said: "Although playing 'brain games' such as Sudoku may not prevent dementia, is has been shown that regularly challenging yourself mentally seems to build up the brain's ability to cope with disease."

(Source: BBC)

Sunday, 17 December 2017

Bad at maths in school? You might be a genius

If you were one of those unfortunate students who dreaded fractions and whose nightmares were filled with trigonometry, we have some good news for you.

You might actually be a genius in disguise.

Having 'a natural talent' for maths is a myth.

In fact, Elsbeth Stern, a professor at the Zurich Technical University, argues in a paper that maths is a fundamental human ability.


Stern wrote:

In the case of mathematics it is entirely plausible that nature has equipped human beings with intuitive number knowledge and sensitivity for magnitude.

Stern argues that bad maths grades usually stem from ineffective maths teaching - however, this assumption shifts when it comes to learning abilities such as dyscalculia.

She went on to lament that the education system may be failing those who would otherwise excel with numbers, adding:

A serious lack of conceptual understanding remains, as even the most intelligent students often cannot transfer the insights they should have gained to problems that differ from those dealt with in the classroom.

Hard work is more important than genetics

Children who have had maths introduced to them from a younger age are bound to do better on initial school tests.

Meanwhile, kids who haven't benefited from being taught maths from a young age might assume that they just don't have the brain for maths, lose confidence and fall at the first hurdle.

Believing you are bad at maths can, therefore, become a self-fulfilling prophecy. But research backs the idea that hard work, not natural ability, is more important.

A study measuring maths achievement in 3,520 students over five years concluded:

It's not how smart students are but how motivated they are and how they study that determines their growth in math achievement.

So, you may actually be an undiscovered mathematical genius after all.

(Source: Independent)