Archive for the ‘mathematics’ category: Page 73

Feb 3, 2020

Garrett Lisi on “The Portal”, Ep. #015 — My Arch-nemesis, Myself. (with host Eric Weinstein)

Posted by in categories: alien life, employment, mathematics, physics

Complex cognitive dissonance disorder guaranteed. 😬.

Garrett Lisi, the so called “Surf Bum with a Theory of Everything (or T.O.E.)”, is a PhD theoretical physicist who has refused to be captured by the theoretical physics community. By making shrewd investments, he has avoided holding meaningful employment for his entire adult life. Instead, he lives in Maui and travels the world chasing the perfect wave.

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Jan 31, 2020

Researchers find evidence for metallic hydrogen at 425 gigapascals

Posted by in categories: materials, mathematics

A team of researchers, two with the French Atomic Energy Commission (AEC) and a third with the Soleil synchrotron, have found evidence of a phase change for hydrogen at a pressure of 425 gigapascals. In their paper published in the journal Nature, Paul Loubeyre, Florent Occelli and Paul Dumas describe testing hydrogen at such a high pressure and what they learned from it.

Researchers long ago theorized that if gas were exposed to enough pressure, it would transition into a metal. But the theories were not able to derive how much pressure is required. Doubts about the theories began to arise when scientists developed tools capable of exerting the high pressures that were believed necessary to squeeze hydrogen into a metal. Theorists simply moved the number higher.

In the past several years, however, theorists have come to a consensus—their math showed that hydrogen should transition at approximately 425 gigapascals—but a way to generate that much pressure did not exist. Then, last year, a team at the AEC improved on the diamond anvil cell, which for years has been used to create intense pressure in experiments. In a diamond anvil cell, two opposing diamonds are used to compress a sample between highly polished tips—the pressure generated is typically measured using a reference material. With the new design, called a toroidal diamond anvil cell, the tip was made into a donut shape with a grooved dome. When in use, the dome deforms but does not break at high pressures. With the new design, the researchers were able to exert pressures up to 600 GPa. That still left the problem of how to test a sample of hydrogen as it was being squeezed.

Jan 30, 2020

Female mathematicians who changed the world

Posted by in category: mathematics

Read more.

Jan 30, 2020

We Spent All Day Arguing About This Triangle Brain Teaser. Can You Solve It?

Posted by in categories: internet, mathematics, neuroscience

There’s nothing quite like a maddening math problem, mind-bending optical illusion, or twisty logic puzzle to halt all productivity in the Popular Mechanics office. We’re curious people by nature, but we also collectively share a stubborn insistence that we’re right, dammit, and so we tend to throw work by the wayside whenever we come upon a problem with several seemingly possible solutions.

This triangle brain teaser isn’t new—shoutout to Popsugar for unearthing it a couple years ago—but based on some shady Internet magic, the tweet below reappeared in my feed today and kick-started a new debate on our staff-wide Slack channel, a place traditionally reserved for workshopping ideas, but instead mostly used for yelling about other stuff that we occasionally turn into content.

Jan 29, 2020

Mathematicians Have Developed a Computing Problem That AI Can Never Solve

Posted by in categories: information science, mathematics, robotics/AI

Not everything is knowable. In a world where it seems like artificial intelligence and machine learning can figure out just about anything, that might seem like heresy – but it’s true.

At least, that’s the case according to a new international study by a team of mathematicians and AI researchers, who discovered that despite the seemingly boundless potential of machine learning, even the cleverest algorithms are nonetheless bound by the constraints of mathematics.

“The advantages of mathematics, however, sometimes come with a cost… in a nutshell… not everything is provable,” the researchers, led by first author and computer scientist Shai Ben-David from the University of Waterloo, write in their paper.

Jan 21, 2020

Computational Biology

Posted by in categories: biological, chemistry, computing, genetics, mathematics

Computational biology is the combined application of math, statistics and computer science to solve biology-based problems. Examples of biology problems are: genetics, evolution, cell biology, biochemistry. [1].

Jan 20, 2020

How (Relatively) Simple Symmetries Underlie Our Expanding Universe

Posted by in categories: cosmology, information science, mathematics, physics

Isaac Newton and other premodern physicists saw space and time as separate, absolute entities — the rigid backdrops against which we move. On the surface, this made the mathematics behind Newton’s 1687 laws of motion look simple. He defined the relationship between force, mass and acceleration, for example, as $latex \vec{F} = m \vec{a}$.

In contrast, when Albert Einstein revealed that space and time are not absolute but relative, the math seemed to get harder. Force, in relativistic terms, is defined by the equation $latex \vec {F} =\gamma (\vec {v})^{3}m_{0}\,\vec {a} _{\parallel }+\gamma (\vec {v})m_{0}\,\vec {a} _{\perp }$.

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Jan 15, 2020

Hidden Computational Power Found in the Arms of Neurons

Posted by in categories: mathematics, neuroscience, robotics/AI

The information-processing capabilities of the brain are often reported to reside in the trillions of connections that wire its neurons together. But over the past few decades, mounting research has quietly shifted some of the attention to individual neurons, which seem to shoulder much more computational responsibility than once seemed imaginable.

The latest in a long line of evidence comes from scientists’ discovery of a new type of electrical signal in the upper layers of the human cortex. Laboratory and modeling studies have already shown that tiny compartments in the dendritic arms of cortical neurons can each perform complicated operations in mathematical logic. But now it seems that individual dendritic compartments can also perform a particular computation — “exclusive OR” — that mathematical theorists had previously categorized as unsolvable by single-neuron systems.

“I believe that we’re just scratching the surface of what these neurons are really doing,” said Albert Gidon, a postdoctoral fellow at Humboldt University of Berlin and the first author of the paper that presented these findings in Science earlier this month.

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Jan 13, 2020

Tuning optical resonators gives researchers control over transparency

Posted by in categories: mathematics, quantum physics

In the quantum realm, under some circumstances and with the right interference patterns, light can pass through opaque media.

This feature of is more than a mathematical trick; optical quantum memory, optical storage and other systems that depend on interactions of just a few photons at a time rely on the process, called electromagnetically induced transparency, also known as EIT.

Because of its usefulness in existing and emerging quantum and optical technologies, researchers are interested in the ability to manipulate EIT without the introduction of an outside influence, such as additional photons that could perturb the already delicate system. Now, researchers at the McKelvey School of Engineering at Washington University in St. Louis have devised a fully contained optical system that can be used to turn transparency on and off, allowing for a measure of control that has implications across a wide variety of applications.

Jan 12, 2020

CS221: Artificial Intelligence: Principles and Techniques | Stanford University

Posted by in categories: mathematics, robotics/AI

Recent AI lecture by Stanford University.

What do web search, speech recognition, face recognition, machine translation, autonomous driving, and automatic scheduling have in common? These are all complex real-world problems, and the goal of artificial intelligence (AI) is to tackle these with rigorous mathematical tools.

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