Archive for the ‘mathematics’ category: Page 94

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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Mar 21, 2019

Interactomics + Super (or Quantum) Computers + Machine Learning : the Future of Medicine?

Posted by in categories: biotech/medical, mathematics, quantum physics, robotics/AI

My latest blog entry: What is INTERACTOMICS, and how it could shape the future of Medicine in the 21st century?

Science / Math blog.

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Mar 20, 2019

Founder of geometric analysis honored with Abel Prize

Posted by in category: mathematics

The Norwegian Academy of Science and Letters today announced that Karen Uhlenbeck has won the 2019 Abel Prize, a Nobel-level honor in math. Uhlenbeck won for her foundational work in geometric analysis, which combines the technical power of analysis—a branch of math that extends and generalizes calculus—with the more conceptual areas of geometry and topology. She is the first woman to receive the prize since the award of 6 million Norwegian kroner (approximately $700,000) was first given in 2003.

Karen Uhlenbeck is first woman to receive the honor.

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Mar 19, 2019

Karen Uhlenbeck Is First Woman to Win Abel Prize for Mathematics

Posted by in categories: mathematics, particle physics, quantum physics

For the first time, one of the top prizes in mathematics has been given to a woman.

On Tuesday, the Norwegian Academy of Science and Letters announced it has awarded this year’s Abel Prize — an award modeled on the Nobel Prizes — to Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin. The award cites “the fundamental impact of her work on analysis, geometry and mathematical physics.”

One of Dr. Uhlenbeck’s advances in essence described the complex shapes of soap films not in a bubble bath but in abstract, high-dimensional curved spaces. In later work, she helped put a rigorous mathematical underpinning to techniques widely used by physicists in quantum field theory to describe fundamental interactions between particles and forces.

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Mar 6, 2019

The Math That Takes Newton Into the Quantum World

Posted by in categories: information science, mathematics, quantum physics, transportation

In my 50s, too old to become a real expert, I have finally fallen in love with algebraic geometry. As the name suggests, this is the study of geometry using algebra. Around 1637, René Descartes laid the groundwork for this subject by taking a plane, mentally drawing a grid on it, as we now do with graph paper, and calling the coordinates x and y. We can write down an equation like x + y = 1, and there will be a curve consisting of points whose coordinates obey this equation. In this example, we get a circle!

It was a revolutionary idea at the time, because it let us systematically convert questions about geometry into questions about equations, which we can solve if we’re good enough at algebra. Some mathematicians spend their whole lives on this majestic subject. But I never really liked it much until recently—now that I’ve connected it to my interest in quantum physics.

If we can figure out how to reduce topology to algebra, it might help us formulate a theory of quantum gravity.

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Mar 5, 2019

Light pulses provide a new route to enhance superconductivity

Posted by in categories: energy, mathematics

Under normal electron band theory, Mott insulators ought to conduct electricity, but they do not due to interactions among their electrons. But now, scientists from the RIKEN Cluster for Pioneering Research have shown that pulses of light could be used to turn these materials beyond simple conductors to superconductors—materials that conduct electricity without energy loss. This process would happen through an unconventional type of superconductivity known as “eta pairing.”

Using , the researchers found that this unconventional type of conductivity, which is believed to take under non-equilibrium conditions in strongly correlated such as high-Tc cuprates and iron-pnictides, arises due to a known as eta pairing. This is different from the superconductivity observed in the same strongly correlated materials under equilibrium conditions, and is thought to involve repulsive interactions between certain electrons within the structure. It is also different from traditional superconductivity, where the phenomenon arises due to interactions between electrons and vibrations of the crystal structure, inducing mutual interactions between electrons through vibrations and thus overcoming the repulsion between the electrons.

Thirty years ago, the mathematical physicist Chen-Ning Yang originally proposed the idea of eta-pairing, but because it was a purely mathematical concept, it was understood as a virtual phenomenon that would not take place in the real world. But for the present study, the researchers used non-equilibrium dynamics to analyze the effect of on a Mott insulator, and found that the effect would in fact happen in the real world. “What is interesting,” says first author Tatsuya Kaneko, a postdoctoral researcher at the RIKEN Cluster for Pioneering Research, “is that our calculations showed that this takes place based on the beautiful mathematical structure that Yang and his followers formulated so many years ago.”

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