Archive for the ‘mathematics’ category: Page 84

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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Jan 10, 2020

Trippy maths program could help figure out the shape of the universe

Posted by in categories: mathematics, space

By Donna Lu

A trippy maths program that visualises the inside of strange 3D spaces could help us figure out the shape of the universe.

Henry Segerman at Oklahoma State University and his colleagues have been working to interactively map the inside of mathematical spaces known as 3-manifolds using a program called SnapPy.

Dec 31, 2019

Scientists have developed a new concept of mathematical modeling

Posted by in categories: energy, mathematics, nanotechnology

A team of scientists from the Research Center “Fundamental Problems of Thermophysics and Mechanics,” of Samara Polytech is engaged in the construction of new mathematical models and the search for methods for their study in relation to a wide range of local nonequilibrium transport processes in various physical systems. An innovative approach developed not so long ago is based on a modern version of third-generation thermodynamics. The project of these scientists, “Development, theoretical research and experimental verification of mathematical models of oscillatory processes, heat and mass transfer and thermomechanics with two- and multiphase delays” was among the winners of the RFBR contest. Recent research results are published in the journal Physica A: Statistical Mechanics and its Applications.

An interest in studying local nonequilibrium processes that take into account the specifics of transport processes at the molecular level (the mean free path of a molecule, the momentum transfer rate, relaxation time, etc.) is dictated by the need to conduct various physical processes under —for example, femtosecond concentrated exposure to energy flows on matter, ultra-low and ultra-high temperatures and pressures, shock waves, etc. Such physical processes are widely used to create new technologies for producing nanomaterials and coatings with unique physicochemical properties that cannot be obtained by traditional methods (binary and multicomponent metal alloys, ceramics, polymeric materials, metal and semiconductor glasses, nanofilms, graphene, composite nanomaterials, etc.).

“Classical thermodynamics is not suitable for describing processes that occur under local nonequilibrium conditions, since it is based on the principle of local equilibrium. Our project is important both for and for practical applications,” explains the project manager, Professor Igor Kudinov. “To accomplish the tasks, we plan to create a new, unparalleled software package designed for 3D modeling of high-speed local nonequilibrium processes of heat, mass and momentum transfer. Thus, our method opens up wide possibilities for studying processes that are practically significant from the point of view of modern nanotechnology.”

Dec 25, 2019

The ‘Quantum Computing’ Decade Is Coming—Here’s Why You Should Care

Posted by in categories: computing, encryption, internet, mathematics, quantum physics

The ability to process qubits is what allows a quantum computer to perform functions a binary computer simply cannot, like computations involving 500-digit numbers. To do so quickly and on demand might allow for highly efficient traffic flow. It could also render current encryption keys mere speedbumps for a computer able to replicate them in an instant. #QuantumComputing

Multiply 1,048,589 by 1,048,601, and you’ll get 1,099,551,473,989. Does this blow your mind? It should, maybe! That 13-digit prime number is the largest-ever prime number to be factored by a quantum computer, one of a series of quantum computing-related breakthroughs (or at least claimed breakthroughs) achieved over the last few months of the decade.

An IBM computer factored this very large prime number about two months after Google announced that it had achieved “quantum supremacy”—a clunky term for the claim, disputed by its rivals including IBM as well as others, that Google has a quantum machine that performed some math normal computers simply cannot.

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Dec 21, 2019

Discovering a new fundamental underwater force

Posted by in categories: biological, food, mathematics, particle physics, space

A team of mathematicians from the University of North Carolina at Chapel Hill and Brown University has discovered a new phenomenon that generates a fluidic force capable of moving and binding particles immersed in density-layered fluids. The breakthrough offers an alternative to previously held assumptions about how particles accumulate in lakes and oceans and could lead to applications in locating biological hotspots, cleaning up the environment and even in sorting and packing.

How matter settles and aggregates under gravitation in systems, such as lakes and oceans, is a broad and important area of scientific study, one that greatly impacts humanity and the planet. Consider “marine snow,” the shower of organic matter constantly falling from upper waters to the deep ocean. Not only is nutrient-rich essential to the global food chain, but its accumulations in the briny deep represent the Earth’s largest carbon sink and one of the least-understood components of the planet’s carbon cycle. There is also the growing concern over microplastics swirling in ocean gyres.

Ocean particle accumulation has long been understood as the result of chance collisions and adhesion. But an entirely different and unexpected phenomenon is at work in the , according to a paper published Dec. 20 in Nature Communications by a team led by professors Richard McLaughlin and Roberto Camassa of the Carolina Center for Interdisciplinary Applied Mathematics in the College of Arts & Sciences, along with their UNC-Chapel Hill graduate student Robert Hunt and Dan Harris of the School of Engineering at Brown University.

Dec 15, 2019

Mathematician Terence Tao Cracks a ‘Dangerous’ Problem

Posted by in category: mathematics

Tao has made huge progress on the Collatz conjecture, a simple-seeming puzzle that has bedeviled hapless mathematicians for decades.

Dec 14, 2019

Ask Ethan: Could Octonions Unlock How Reality Really Works?

Posted by in categories: education, mathematics, physics

The octonions themselves will never be “the answer” to how reality works, but they do provide a powerful, generalized mathematical structure that has its own unique properties. It includes real, complex, and quaternion mathematics, but also introduces fundamentally unique mathematical properties that can be applied to physics to make novel — but speculative and hitherto unsupported — predictions.

Octonions can give us and idea of which possibilities might be compelling to look at in terms of extensions to known physics and which ones might be less interesting, but there are no concrete observables predicted by the octonions themselves. Pierre Ramond, my former professor who taught me about octonions and Lie groups in physics, was fond of saying, “octonions are to physics what the Sirens were to Ulysses.” They definitely have an allure, but if you dive in, they may drag you to a hypnotic, inescapable doom.

Their mathematical structure holds an incredible richness, but nobody knows whether that richness means anything for our Universe or not.

Dec 7, 2019

Mathematician Finds Easier Way to Solve Quadratic Equations

Posted by in categories: energy, information science, mathematics

Quadratic equations are polynomials, meaning strings of math terms. An expression like “x + 4” is a polynomial. They can have one or many variables in any combination, and the magnitude of them is decided by what power the variables are taken to. So x + 4 is an expression describing a straight line, but (x + 4)² is a curve. Since a line crosses just once through any particular latitude or longitude, its solution is just one value. If you have x², that means two root values, in a shape like a circle or arc that makes two crossings.

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