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Archive for the ‘mathematics’ category: Page 7

Apr 24, 2019

A faster method for multiplying very big numbers

Posted by in categories: computing, education, information science, mathematics

The multiplication of integers is a problem that has kept mathematicians busy since Antiquity. The “Babylonian” method we learn at school requires us to multiply each digit of the first number by each digit of the second one. But when both numbers have a billion digits each, that means a billion times a billion or 1018 operations.

At a rate of a billion operations per second, it would take a computer a little over 30 years to finish the job. In 1971, the mathematicians Schönhage and Strassen discovered a quicker way, cutting calculation time down to about 30 seconds on a modern laptop. In their article, they also predicted that another algorithm—yet to be found—could do an even faster job. Joris van der Hoeven, a CNRS researcher from the École Polytechnique Computer Science Laboratory LIX, and David Harvey from the University of New South Wales (Australia) have found that algorithm.

They present their work in a new article that is available to the through the online HAL archive. But one problem raised by Schönhage et Strassen remains to be solved: proving that no quicker method exists. This poses a new challenge for theoretical science.

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Apr 16, 2019

Optimizing network software to advance scientific discovery

Posted by in categories: mathematics, particle physics, supercomputing

High-performance computing (HPC)—the use of supercomputers and parallel processing techniques to solve large computational problems—is of great use in the scientific community. For example, scientists at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory rely on HPC to analyze the data they collect at the large-scale experimental facilities on site and to model complex processes that would be too expensive or impossible to demonstrate experimentally.

Modern science applications, such as simulating , often require a combination of aggregated computing power, high-speed networks for data transfer, large amounts of memory, and high-capacity storage capabilities. Advances in HPC hardware and software are needed to meet these requirements. Computer and computational scientists and mathematicians in Brookhaven Lab’s Computational Science Initiative (CSI) are collaborating with physicists, biologists, and other domain scientists to understand their data analysis needs and provide solutions to accelerate the scientific discovery process.

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Apr 15, 2019

Gravitational echo phenomenon will become a key to the new physics, physicist says

Posted by in categories: cosmology, mathematics, neuroscience, physics

Gravitational echoes may be caused by the collision of two black holes, and may indicate that these objects have completely new physical properties. This conclusion was made by RUDN physicists after a series of mathematical calculations. The scientists state that if the existence of the echo phenomenon is confirmed, astrophysicists would have to reconsider their view of compact space objects. The results of the study were published in Physical Review D.

According to the theory of general relativity (GR), any massive object distorts space-time. A similar effect is observed when a heavy metal ball is placed on stretched elastic fabric. The heavier is the ball, the deeper is the depression in the fabric. Similarly, the higher the mass of an object, the more it distorts space-time. Black holes are among the heaviest objects in the universe, and therefore distort space-time the most. When two black holes collide, gravitational waves spread out from the site of collision. They can be compared to rings on the water, or sound waves, but there is one important peculiar feature. Gravitational waves do not propagate spatially—they are themselves the oscillations of space-time.

Gravitational waves from the collision of two black holes decay with time, but on their final stage, they can cause the so-called echo—additional wave scattering. It can be compared to regular acoustic echo. The existence of such gravitational echo has not been confirmed yet, and there are different opinions about its possible source. A RUDN physicist, together with colleagues from the Czech Republic and Russia, assumed that if the existence of gravitational echo is experimentally confirmed, it would be the beginning of the new physics adding to GR.

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Apr 15, 2019

Too much information? Sure looks like it

Posted by in category: mathematics

Mathematicians have confirmed that humanity’s collective attention span is getting shorter. And it’s not just social media that’s to blame.


Research reveals ‘social acceleration’ occurring across different domains. Samantha Page reports.

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Apr 10, 2019

Event horizon shadow of supermassive black hole candidates are now possible via electromagnetic waves, thus transforming this elusive boundary from a mathematical concept to a physical entity that can be studied and tested via repeated astronomical observations

Posted by in categories: cosmology, mathematics

https://iopscience.iop.org/article/10.3847/2041-8213/ab0ec7

No photo description available.

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Apr 8, 2019

In Bubbles, She Sees a Mathematical Universe

Posted by in category: mathematics

For Karen Uhlenbeck, winner of the Abel Prize for math, a whimsical phenomenon offers a window onto higher dimensions.

Credit Credit Kym Cox/Science Source

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Apr 4, 2019

Building a Hardware Store Faraday Cage

Posted by in categories: habitats, health, mathematics

Most Hackaday readers are no doubt familiar with the Faraday cage, at least in name, and nearly everyone owns one: if you’ve ever stood watching a bag of popcorn slowly revolve inside of a microwave, you’be seen Michael Faraday’s 1836 invention in action. Yet despite being such a well known device, the average hacker still doesn’t have one in their arsenal. But why?

It could be that there’s a certain mystique about Faraday cages, an assumption that their construction requires techniques or materials outside the realm of the home hacker. While it’s true that building a perfect Faraday cage for a given frequency involves math and careful attention to detail, putting together a simple model for general purpose use and experimentation turns out to be quick and easy.

As an exercise in minimalist hacking I recently built a basic Faraday cage out of materials sourced from Home Depot, and thought it would be interesting to not only describe its construction but give some ideas as to how one can put it to practical use in the home lab. While it’s hardly a perfect specimen, it clearly works, and it didn’t take anything that can’t be sourced locally pretty much anywhere in the world.

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Mar 31, 2019

I ran across this post and thought it interesting

Posted by in category: mathematics

I am not too sure the math is solid, obviously, but the fact that its been shared over 100k times means people are paying attention and starting to think about the impact.

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Mar 24, 2019

The Mysterious Math of How Cells Determine Their Own Fate

Posted by in category: mathematics

During development, cells seem to use statistics to figure out what identities they should take on.

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Mar 23, 2019

Blue Brain solves a century-old neuroscience problem

Posted by in categories: information science, mathematics, neuroscience

A team led by Lida Kanari now reports a new system for distinguishing cell types in the brain, an algorithmic classification method that the researchers say will benefit the entire field of neuroscience. Blue Brain founder Professor Henry Markram says, “For nearly 100 years, scientists have been trying to name cells. They have been describing them in the same way that Darwin described animals and trees. Now, the Blue Brain Project has developed a mathematical algorithm to objectively classify the shapes of the neurons in the brain. This will allow the development of a standardized taxonomy [classification of cells into distinct groups] of all cells in the brain, which will help researchers compare their data in a more reliable manner.”

The team developed an algorithm to distinguish the shapes of the most common type of neuron in the neocortex, the . Pyramidal are distinctively tree-like cells that make up 80 percent of the in the neocortex, and like antennas, collect information from other neurons in the . Basically, they are the redwoods of the brain forest. They are excitatory, sending waves of electrical activity through the network, as people perceive, act, and feel.

The father of modern neuroscience, Ramón y Cajal, first drew pyramidal cells over 100 years ago, observing them under a microscope. Yet up until now, scientists have not reached a consensus on the types of pyramidal neurons. Anatomists have been assigning names and debating the different types for the past century, while neuroscience has been unable to tell for sure which types of neurons are subjectively characterized. Even for visibly distinguishable neurons, there is no common ground to consistently define morphological types.

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