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Category: mathematics

The equations of physics are things that we humans created to understand the Universe, and it can be hard to disentangle them from the Universe’s innate properties. It turns out that one of the weirdest things scientists have come up with, what Albert Einstein derisively called “spooky action at a distance,” is more than just math: It’s a fact of reality.

That concept is also known as entanglement, and it’s what allows particles that have once interacted to share a connection regardless of the separation between them. A team of physicists in the United Kingdom used some dense mathematics to come to their Einstein-angering conclusion, taking an important step towards proving whether quantum mechanics’ weirdness is just the math talking, or whether it speaks to innate physical requirements. Their mathematical proof’s main assumption is that any new physics theory should be backward-compatible with the physics you learned in high school.

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As moviemaking becomes as much a science as an art, the moviemakers need ever-better ways to gauge audience reactions. Did they enjoy it? How much… exactly? At minute 42? A system from Caltech and Disney Research uses a facial expression tracking neural network to learn and predict how members of the audience react, perhaps setting the stage for a new generation of Nielsen ratings.

The research project, just presented at IEEE’s Computer Vision and Pattern Recognition conference in Hawaii, demonstrates a new method by which facial expressions in a theater can be reliably and relatively simply tracked in real time.

It uses what’s called a factorized variational autoencoder — the math of it I am not even going to try to explain, but it’s better than existing methods at capturing the essence of complex things like faces in motion.

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But if there is some kind of unifying computational principle governing our grey matter, what is it? Dr. Tsien has studied this for over a decade, and he believes he’s found the answer in something called the Theory of Connectivity.

“Many people have long speculated that there has to be a basic design principle from which intelligence originates and the brain evolves, like how the double helix of DNA and genetic codes are universal for every organism,” Tsien said. “We present evidence that the brain may operate on an amazingly simple mathematical logic.”

The Theory of Connectivity holds that a simple algorithm, called a power-of-two-based permutation taking the form of n=2i-1 can be used to explain the circuitry of the brain. To unpack the formula, let’s define a few key concepts from the theory of connectivity, specifically the idea of a neuronal clique. A neuronal clique is a group of neurons which “fire together” and cluster into functional connectivity motifs, or FCMs, which the brain uses to recognize specific patterns or ideas. One can liken it to branches on a tree, with the neuronal clique being the smallest unit of connectivity, a mere twig, which when combined with other cliques, link up to form an FCM. The more complex the idea being represented in the brain, the more convoluted the FCM. The n in n=2i-1 specifies the number of neuronal cliques that will fire in response to a given input, i.

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The grand theory of almost everything actually represents a collection of several mathematical models that proved to be timeless interpretations of the laws of physics.

Here is a brief tour of the topics covered in this gargantuan equation.

This version of the Standard Model is written in the Lagrangian form. The Lagrangian is a fancy way of writing an equation to determine the state of a changing system and explain the maximum possible energy the system can maintain.

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(Phys.org)—In the late 1800s when scientists were still trying to figure out what exactly atoms are, one of the leading theories, proposed by Lord Kelvin, was that atoms are knots of swirling vortices in the aether. Although this idea turned out to be completely wrong, it ushered in modern knot theory, which today is used in various areas of science such as fluid dynamics, the structure of DNA, and the concept of chirality.

Now in a new paper published in Physical Review Letters, mathematical physicist Paul Sutcliffe at Durham University in the UK has theoretically shown that nanoparticles called magnetic skyrmions can be tied into various types of knots with different magnetic properties. He explains that, in a sense, these nanoknots represent a “nanoscale resurrection of Kelvin’s dream of knotted fields.”

Skyrmions are the name of a general class of particles that are made by twisting a field. When this field is a magnetic field, the skyrmions are called magnetic skyrmions. Magnetic skyrmions have attracted a lot of attention recently due to their potential applications in spintronics, where electron spins (which are related to the electron’s magnetic properties) are exploited in the design of transistors, storage media, and related devices.

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According to a mind-bending new theory, a black hole could actually be a tunnel between universes, meaning our universe may be nested inside a black hole that is part of a larger universe. The theory explains that the matter doesn’t collapse into a single point, but rather gushes out a “white hole” at the other end of the black one.

The theory was published in the journal Physics Letters B, by Indiana University physicist Nikodem Poplawski. In his article, he presents new mathematical models of the spiraling motion of matter falling into the black hole. His equations suggest that wormholes are probable alternatives to the “space-time singularities” originally predicted by Albert Einstein.

Einstein’s equations for general relativity suggest singularities are created whenever matter in a given region gets too dense as would happen at the center of a black hole. Singularities are infinitely dense and hot, and take up no space. This idea has been supported by indirect evidence but has never been fully accepted into the scientific community.

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Individuals who mine Bitcoins needn’t be miners. We call them ‘miners’ because they are awarded BTC as they solve mathematical computations. The competition to unearth these reserve coins also serves a vital purpose. They validate the transactions of Bitcoin users all over the world: buyers, loans & debt settlement, exchange transactions, inter-bank transfers, etc. They are not really miners. They are more accurately engaged in transaction validation or ‘bookkeeping’.

There are numerous proposals for how to incentivize miners once all 21 million coins have been mined/awarded in May 2140. Depending upon the network load and the value of each coin, we may need to agree on an alternate incentive earlier than 2140. At the opening of the 2015 MIT Bitcoin Expo, Andreas Antonopolous proposed some validator incentive alternatives. One very novel suggestion was based on game theory and involved competition and status rather than cash payments.

I envision an alternative approach—one that also addresses the problem of miners and users having different goals. In an ideal world the locus of users should intersect more fully with the overseers…

To achieve this, I have proposed that every wallet be capable of also mining, even if the wallet is simply a smartphone app or part of a cloud account at an exchange service. To get uses participating in validating the transactions of peers, any transaction fee could be waived for anyone who completes 1 validation for each n transactions. (Say one validation for every five or ten transactions). In this manner, everyone pitches in a small amount of resources to maintain a robust network.

A small transaction fee would accrue to anyone who does not participate in ‘mining’ at all. That cost will float with supply and demand. Users can duck the fee by simply participating in the validation process, which continues to be based on either proof-of-work, proof-of-stake — or one of the more exotic proof theories that are being proposed now.

Philip Raymond co-chairs Cryptocurrency Standards Association. He produces
The Bitcoin Event, edits A Wild Duck and is a frequent contributor to Quora

Physicists have come up with what they claim is a mathematical model of a theoretical “time machine” — a box that can move backwards and forwards through time and space.

The trick, they say, is to use the curvature of space-time in the Universe to bend time into a circle for hypothetical passengers sitting in the box, and that circle allows them to skip into the future and the past.

“People think of time travel as something as fiction. And we tend to think it’s not possible because we don’t actually do it,” says theoretical physicist and mathematician, Ben Tippett, from the University of British Columbia in Canada.

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2017 begins on Monday in Vancouver, Canada, and will explore the theme “The Future You.” If the future you is anything like the future us, you are likely curled up in a big cushy chair right now, devouring the contents of a book that flips your thinking. Below, some reading suggestions from the speaker program. Read, enjoy and stay tuned to the TED Blog for beat-by-beat coverage of the conference.

TED2017 begins on Monday in Vancouver, Canada, and will explore the theme “The Future You.” If the future you is anything like the future us, you are likely curled up in a big cushy chair right now, devouring the contents of a book that flips your thinking. Below, some reading suggestions from the speaker program. Read, enjoy and stay tuned to the TED Blog for beat-by-beat coverage of the conference.

Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy by Cathy O’Neil. The decisions that affect our lives are no longer made by humans — they’re made by algorithms. This might sound like a great way around bias and discrimination, but these things are often built right into our mathematical models. When it comes to college admissions, decisions on parole, applications to jobs and the affects of a bad credit score, O’Neil explores the unintended consequences of algorithms. (Read an excerpt.)

The Telomere Effect: A Revolutionary Approach to Living Younger, Healthier, Longer by Elizabeth Blackburn and Elissa Epel. Molecular biologist Elizabeth Blackburn received the Nobel Prize in Medicine for her discovery of telomeres, the ends of chromosomes that — like shoelace tips — keep our genetic information from fraying. Both telomeres and telomerase, an enzyme that restores worn-down telomeres, appear central to the aging process. This book looks at the research — then turns its attention to how our thoughts, bodies and social worlds affect us on the cellular level.

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