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Machine Learning algorithm can predict evolution of chaotic models without knowing the equations

Machine Learning algorithm can predict evolution of chaotic models without knowing the equations | Amazing Science | Scoop.it

Half a century ago, the pioneers of chaos theory discovered that the “butterfly effect” makes long-term prediction impossible. Even the smallest perturbation to a complex system (like the weather, the economy or just about anything else) can touch off a concatenation of events that leads to a dramatically divergent future. Unable to pin down the state of these systems precisely enough to predict how they’ll play out, we live under a veil of uncertainty.

 

But now artificial intelligence is here to help. In a series of results reported in the journals Physical Review Letters and Chaos, scientists have used machine learning — the same computational technique behind recent successes in artificial intelligence — to predict the future evolution of chaotic systems out to stunningly distant horizons. The approach is being lauded by outside experts as groundbreaking and likely to find wide application.

 

“I find it really amazing how far into the future they predict” a system’s chaotic evolution, said Herbert Jaeger, a professor of computational science at Jacobs University in Bremen, Germany. The findings come from veteran chaos theorist Edward Ott and four collaborators at the University of Maryland. They employed a machine-learning algorithm called reservoir computing to “learn” the dynamics of an archetypal chaotic system called the Kuramoto-Sivashinsky equation. The evolving solution to this equation behaves like a flame front, flickering as it advances through a combustible medium. The equation also describes drift waves in plasmas and other phenomena, and serves as “a test bed for studying turbulence and spatiotemporal chaos,” said Jaideep Pathak, Ott’s graduate student and the lead author of the new papers.

 

The algorithm knows nothing about the Kuramoto-Sivashinsky equation itself; it only sees data recorded about the evolving solution to the equation. This makes the machine-learning approach powerful; in many cases, the equations describing a chaotic system aren’t known, crippling dynamicists’ efforts to model and predict them. Ott and company’s results suggest you don’t need the equations — only data. “This paper suggests that one day we might be able perhaps to predict weather by machine-learning algorithms and not by sophisticated models of the atmosphere,” Kantz said.

 

Besides weather forecasting, experts say the machine-learning technique could help with monitoring cardiac arrhythmias for signs of impending heart attacks and monitoring neuronal firing patterns in the brain for signs of neuron spikes. More speculatively, it might also help with predicting rogue waves, which endanger ships, and possibly even earthquakes.

 

Ott particularly hopes the new tools will prove useful for giving advance warning of solar storms, like the one that erupted across 35,000 miles of the sun’s surface in 1859. That magnetic outburst created aurora borealis visible all around the Earth and blew out some telegraph systems, while generating enough voltage to allow other lines to operate with their power switched off. If such a solar storm lashed the planet unexpectedly today, experts say it would severely damage Earth’s electronic infrastructure. “If you knew the storm was coming, you could just turn off the power and turn it back on later,” Ott said.

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Math music: Herman Haverkort presents sonifications of two-dimensional Hilbert curves

Math music: Herman Haverkort presents sonifications of two-dimensional Hilbert curves | Amazing Science | Scoop.it

 Herman Haverkort performs sound experiments with a mathematical construct called a Hilbert curve and links them through turning-function mapping (mapping directions of line segments in the sketch to pitch, and different levels of refinement to different voices). This  can be extended to the sonification of a four-dimensional curve using the same technique. A variation on this scheme yields to sound renderings of the Harmonious Hilbert curves in up to six dimensions.

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Using physics, math and models to fight cancer drug resistance

Using physics, math and models to fight cancer drug resistance | Amazing Science | Scoop.it

Despite the increasing effectiveness of breast cancer treatments over the last 50 years, tumors often become resistent to the drugs used. While drug combinations could be part of the solution to this problem, their development is very challenging. In this blog post Jorge Zanudo explains how it is possible to combine physical and mathemathical models with clinical and biological data to determine which drug combinations would be most effective in breast cancer therapy.


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Conway's Game of life is a programmable computer which can calculate the Fibonacci number series

This is Nicolas Loizeau's programmable computer implemented in Conway's game of life computing Fibonacci sequence. Soon artificial self-encoding life forms are possible.

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Scientists create first mathematical model that predicts immunotherapy success

Scientists create first mathematical model that predicts immunotherapy success | Amazing Science | Scoop.it
Researchers at the Icahn School of Medicine at Mount Sinai have created the first mathematical model that can predict how a cancer patient will benefit from certain immunotherapies, according to a study published in Nature.

 

Scientists have long sought a way to discover whether patients will respond to new checkpoint inhibitor immunotherapies and to better understand the characteristics that indicate a tumor can be successfully treated with them. The proposed mathematical model, which captures aspects of the tumor's evolution and the underlying interactions of the tumor with the immune system, is more accurate than previous genomic biomarkers in predicting how the tumor will respond to immunotherapy.

 

"We present an interdisciplinary approach to studying immunotherapy andimmune surveillance of tumors," said Benjamin Greenbaum, PhD, the senior author, who is affiliated with the departments of Medicine, Hematology and Medical Oncology, Pathology, and Oncological Sciences at The Tisch Cancer Institute at the Icahn School of Medicine at Mount Sinai. "This approach will hopefully lead to better mechanistic predictive modeling of response and future design of therapies that further take advantage of how the immune system recognizes tumors." This novel model also has the potential to help find new therapeutic targets within the immune system and to help design vaccines for patients who do not typically respond to immunotherapy.

 

To create this model, researchers used data from melanoma and lung cancer patients being treated with immune checkpoint inhibitors. The model tracked many properties within the immune response to the drugs, particularly neoantigens, which are specific to mutating and growing tumors.

 

Neoantigens have the potential to be prime immunotherapy targets, and the proposed framework will likely be useful in studies of acquired resistance to immunotherapy and may be crucial for understanding the circumstances in which immunotherapy causes autoimmune-like side effects.


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Scientists discover more than 600 new periodic orbits of the famous three body problem

Scientists discover more than 600 new periodic orbits of the famous three body problem | Amazing Science | Scoop.it

The famous three-body problem can be traced back to Isaac Newton in 1680s, thereafter Lagrange, Euler, Poincare and so on. Studies on the three-body problem leaded to the discovery of the so-called sensitivity dependence of initial condition (SDIC) of chaotic dynamic system. Nowadays, the chaotic dynamics is widely regarded as the third great scientific revolution in physics in 20th century, comparable to the relativity and the quantum mechanics. Thus, the studies on three-body problem have very important scientific meanings.

 

Poincaré in 1890 revealed that trajectories of three-body systems are commonly non-periodic, i.e. not repeating. This can explain why it is so hard to gain periodic orbits of three-body system. In the 300 years since three-body problem was first recognized, only three families of periodic orbits had been found, until 2013 when Suvakov and Dmitrasinovic [Phys. Rev. Lett. 110, 114301 (2013)] made a breakthrough to numerically find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum (see http://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem).

 

Currently, two scientists, XiaoMing Li and ShiJun Liao at Shanghai Jiaotong University, China, successfully gained 695 families of periodic orbits of the above-mentioned Newtonian planar three-body system by means of national supercomputer TH-2 at Guangzhou, China, which are published online via SCIENCE CHINA-Physics Mechanics Astronomy, 2017, Vol. 60, No. 12: 129511. The movies of these orbits are given on the website http://numericaltank.sjtu.edu.cn/three-body/three-body.htm

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A trick to visualizing higher dimensions

How do you think about a sphere in four dimensions? What about ten dimensions? Problem driven learning on at https://brilliant.org/3b1b

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Buddhabrot fractal method - an alternative method of displaying Mandelbrot sets

Buddhabrot fractal method - an alternative method of displaying Mandelbrot sets | Amazing Science | Scoop.it
An alternative method of displaying the Mandelbrot set yields a lifelike image of a seated buddha.

 

In 1993, Melinda Green discovered a novel approach to visualizing the Mandelbrot set that yielded the now iconic Buddhabrot. In the course of my apeirographic explorations, I have found other luminous figures hidden within the complex plane. I call them anthropobrots. A recent mathematical article, “The Multitude behind the Buddhabrot” defines anthropobrots and related concepts mathematically via the definitional framework that led to their discovery.

 

James Travers did his own experimentation with the Buddhabrot algorithm which led him down a path to those that have resulted in anthropobrots. In fact, he has discovered a variety of Buddhabrot-related fractal forms generated through altered equations, and calls the results Buddhabrot Mutants.

 

Some other links:

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Researchers analyze flocking behavior on curved surfaces

Researchers analyze flocking behavior on curved surfaces | Amazing Science | Scoop.it

A murmuration of starlings. The phrase reads like something from literature or the title of an arthouse film. In fact, it is meant to describe the phenomenon that results when hundreds, sometimes thousands, of these birds fly in swooping, intricately coordinated patterns through the sky.

Or in more technical terms, flocking. But birds are not the only creatures that flock. Such behavior also takes place on a microscopic scale, such as when bacteria roam the folds of the gut. Yet bird or bacteria, all flocking has one prerequisite: The form of the entity must be elongated with a "head" and "tail" to align and move with neighbors in an ordered state.

 

Physicists study flocking to better understand dynamic organization at various scales, often as a way to expand their knowledge of the rapidly developing field of active matter. Case in point is a new analysis by a group of theoretical physicists, including Mark Bowick, deputy director of UC Santa Barbara's Kavli Institute for Theoretical Physics (KITP).

 

Generalizing the standard model of flocking motion to the curved surface of a sphere rather than the usual linear plane or flat three-dimensional space, Bowick's team found that instead of spreading out uniformly over the whole sphere, arrowlike agents spontaneously order into circular bands centered on the equator.

 

The team's findings appear in the journal Physical Review X.


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Algebraic Numbers

Algebraic Numbers | Amazing Science | Scoop.it

This is a picture of the algebraic numbers in the complex plane, made by David Moore based on earlier work by Stephen J. Brooks, and available along with other neat stuff at Moore’s site Math and Code.

 

Algebraic numbers are roots of polynomials with integer coefficients. The integers 0 and 1 are the big dots near the bottom, while ii is near the top. In this picture, the color of a point indicates the degree of the polynomial of which it’s a root:

• red = roots of linear polynomials, i.e. rational numbers,

• green = roots of quadratic polynomials,

• blue = roots of cubic polynomials,

• yellow = roots of quartic polynomials, and so on.

 

The size of a point decreases exponentially with the ‘complexity’ of the simplest polynomial with integer coefficient of which it’s a root. Here the complexity is the sum of the absolute values of the coefficients of that polynomial.

 

There are many patterns in this picture that call for explanation! For example, look near the point ii. Can you describe some of these patterns, formulate some conjectures about them, and prove some theorems? Maybe you can dream up a stronger version of Roth’s theorem, which says roughly that algebraic numbers tend to ‘repel’ rational numbers of low complexity.

 

David Moore made this image using software created by Stephen J. Brooks on Wikipedia

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New Number Systems Seek Their Lost Primes

New Number Systems Seek Their Lost Primes | Amazing Science | Scoop.it
For centuries mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering
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Hypercomplex Fractals

Hypercomplex Fractals | Amazing Science | Scoop.it
Hypercomplex numbers are similar to the usual 2D complex numbers, except they can be extended to 3 dimensions or more. When you use hypercomplex numbers to generate fractals, you can create some interesting looking 3D fractals.
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Retired man solves one of hardest maths problems and no one notices

Retired man solves one of hardest maths problems and no one notices | Amazing Science | Scoop.it

A retired German man has found the proof to a complex geometry and probability problem that experts have tried to solve for decades, only for his achievement to go largely unnoticed.  Thomas Royen was reportedly brushing his teeth when he struck upon an idea in July 2014.  Then 67 years old, the former statistician for a pharmaceutical company, from Schwalbach am Taunus, a town on the edge of Frankfurt, found the solution to the conjecture, known as the Gaussian correlation inequality (GCI). 


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A New Kind of Science: A 15-Year View

A New Kind of Science: A 15-Year View | Amazing Science | Scoop.it
Stephen Wolfram looks back at his bold take on the computational universe.
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The Kepler Problem and the 600-Cell in 4 Dimensional Space

The Kepler Problem and the 600-Cell in 4 Dimensional Space | Amazing Science | Scoop.it

Studying the exact radii of the planets’ orbits led Johannes Kepler to discover that these orbits aren’t circular but rather elliptical. By 1619 this led him to what we call now Kepler’s laws of planetary motion. And those, in turn, helped Newton to verify Hooke’s hunch that the force of gravity goes as the inverse square of the distance between bodies!

 

In honor of this, the problem of a particle orbiting in an inverse square force law is now called the Kepler problem. John Carlos Baez, Greg Egan, and Layra Idarani have come across a solid mathematical connection between the Platonic solids and the Kepler problem. And it involves a detour into the 4th dimension! It’s a remarkable fact that the Kepler problem has not just the expected conserved quantities—energy and the 3 components of angular momentum—but also 3 more: the components of the Runge–Lenz vector. To understand those extra conserved quantities, go here:

• Greg Egan, The ellipse and the atom.

 

Noether proved that conserved quantities come from symmetries. Energy comes from time translation symmetry. Angular momentum comes from rotation symmetry. Since the group of rotations in 3 dimensions, called SO(3), is itself 3-dimensional, it gives 3 conserved quantities, which are the 3 components of angular momentum.

 

None of this is really surprising. But if we take the angular momentum together with the Runge–Lenz vector, we get 6 conserved quantities—and these turn out to come from the group of rotations in 4 dimensions, SO(4), which is itself 6-dimensional. The obvious symmetries in this group just rotate a planet’s elliptical orbit, while the non-obvious ones can also squash or stretch it, changing the eccentricity of the orbit. To be precise, all this is true only for the ‘bound states’ of the Kepler problem: the circular and elliptical orbits, not the parabolic or hyperbolic ones, which work in a somewhat different way.

 

Why should the Kepler problem have symmetries coming from rotations in 4 dimensions? This is a fascinating puzzle—we know a lot about it, but I doubt the last word has been spoken. For an overview, go here:

• John Baez, Mysteries of the gravitational 2-body problem.

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Mathematicians crack 44-year-old problem

Mathematicians crack 44-year-old problem | Amazing Science | Scoop.it

Zilin Jiang from Technion — Israel Institute of Technology and Alexandr Polyanskii from the Moscow Institute of Physics and Technology (MIPT) have proved László Fejes Tóth’s zone conjecture. Formulated in 1973, it says that if a unit sphere is completely covered by several zones, their combined width is at least π. The proof, published in the journal Geometric and Functional Analysis, is important for discrete geometry and enables new problems to be formulated.

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Leech lattice and sphere packing in higher dimensional space explained

Leech lattice and sphere packing in higher dimensional space explained | Amazing Science | Scoop.it

What is a leech lattice? It turns out that it’s the only even integral unimodular lattice with no roots in fewer than 32 dimensions. Each of these terms will take some explaining:

  • A lattice, as mentioned at the beginning of this article, is a set of vectors in Euclidean space which is closed under addition.
  • A lattice is integral if the dot product of any two vectors is an integer.
  • An integral lattice is described as even if the squared norm of any vectors is an even integer. Otherwise, it is an odd integral lattice.
  • A lattice is unimodular if the fundamental parallelotope has unit volume, or the determinant of the generating matrix is ±1. Equivalently, the lattice has a density of one point per unit volume. Even integral unimodular lattices only occur in dimensions divisible by 8, with the unique example in 8 dimensions being the E8 lattice.
  • For an even unimodular lattice, a root is a vector of squared norm 2. The Leech lattice has none of these, so the shortest nonzero vectors have a squared norm of 4 (or, equivalently, a length of 2).

 

Because the shortest distance between two lattice points is equal to 2, that means that we can place a ball of unit radius centred on each lattice point. Each sphere touches precisely 196560 others, which is the maximum for 24 dimensions. The kissing number problemhas also been solved in 1, 2, 3, 4 and 8 dimensions, with values of 2, 6, 12, 24 and 240, respectively, attained by the integer lattice, hexagonal lattice, FCC lattice, D4 lattice and E8 lattice, respectively.

 

If we enlarge the spheres to a radius of √2, they will overlap and cover all space. Establishing that the covering radius is equal to √2 is non-trivial, and involves analysing all 23 types of deep hole (points maximally distant from lattice points) encountered in the Leech lattice. Each type of deep hole corresponds to one of the 23 other even unimodular 24-dimensional lattices, known as Niemeier lattices.

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What are Fractals and why do we care?

What are Fractals and why do we care? | Amazing Science | Scoop.it

Fractal geometry is a field of maths born in the 1970’s and mainly developed by Benoit Mandelbrot. The geometry that is taught in school is about how to make shapes; fractal geometry is no different. While the shapes in classical geometry are ‘smooth’, such as a circle or a triangle, the shapes that come out of fractal geometry are ‘rough’ and infinitely complex. However fractal geometry is still about making shapes, measuring shapes and defining shapes, just like classical geomety.

 

There are two reasons why people should care about fractal geometry:

 

  1. The process by which shapes are made in fractal geometry is amazingly simple yet completely different to classical geometry. While classical geometry uses formulas to define a shape, fractal geometry uses iteration. It therefore breaks away from giants such as Pythagoras, Plato and Euclid and heads in another direction. Classical geometry has enjoyed over 2,000 years of scrutinization. Fractal geometry has enjoyed only 40.
  2. The shapes that come out of fractal geometry look like nature derived. This is an amazing fact that is hard to ignore. As we all know, there are no perfect circles in nature and no perfect squares. Not only that, but when you look at trees or mountains or river systems, they don’t resemble any shapes one is used to in math. However with simple formulas iterated multiple times, fractal geometry can model these natural phenomena with alarming accuracy. If you can use simple mathematics to make things look like the world around us, you know you’re onto a winner. Fractal geometry does this with ease.

 

This article shall give a quick overview of how to make fractal shapes and show how these shapes can resemble nature. It shall then go on to talk about dimensionality, which is a good way to measure fractals. It ends by discussing how fractal geometry is also beneficial because randomness can be introduced into the structure of a fractal shape.

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A Breakthrough in Packing Higher Dimensional Spheres

How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres in the first episode of Infinite Series, a show that tackles the mysteries and the joy of mathematics. From Logic to Calculus, from Probability to Projective Geometry, Infinite Series both entertains and challenges its viewers to take their math game to the next level.

 

Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don't even understand in 4 dimensions.

Sphere Packing in Higher Dimensions - Quanta Magazine
https://www.quantamagazine.org/201603...

Why You Should Care about High-Dimensional Sphere Packing - Scientific American
https://blogs.scientificamerican.com/...

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Understanding Complex Numbers and Quaternions

Understanding Complex Numbers and Quaternions | Amazing Science | Scoop.it

In this article the author explains the concept of Quaternions in an easy to understand way. Complex Numbers and Quaternions are explained in detail as well as all the different operations that can be applied to them. The author also compares applications of matrices, Euler angles, and tries to explain when you would want to use Quaternions instead of Euler angles or matrices and when you would not.

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Mathematics predicts a sixth mass extinction by 2100

Mathematics predicts a sixth mass extinction by 2100 | Amazing Science | Scoop.it
By 2100, oceans may hold enough carbon to launch mass extermination of species in future millennia.

 

In the past 540 million years, the Earth has endured five mass extinction events, each involving processes that upended the normal cycling of carbon through the atmosphere and oceans. These globally fatal perturbations in carbon each unfolded over thousands to millions of years, and are coincident with the widespread extermination of marine species around the world.

 

The question for many scientists is whether the carbon cycle is now experiencing a significant jolt that could tip the planet toward a sixth mass extinction. In the modern era, carbon dioxide emissions have risen steadily since the 19th century, but deciphering whether this recent spike in carbon could lead to mass extinction has been challenging. That's mainly because it's difficult to relate ancient carbon anomalies, occurring over thousands to millions of years, to today's disruptions, which have taken place over just a little more than a century.

 

Now Daniel Rothman, professor of geophysics in the MIT Department of Earth, Atmospheric and Planetary Sciences and co-director of MIT's Lorenz Center, has analyzed significant changes in the carbon cycle over the last 540 million years, including the five mass extinction events. He has identified "thresholds of catastrophe" in the carbon cycle that, if exceeded, would lead to an unstable environment, and ultimately, mass extinction.

 

In a paper published in Science Advances, he proposes that mass extinction occurs if one of two thresholds are crossed: For changes in the carbon cycle that occur over long timescales, extinctions will follow if those changes occur at rates faster than global ecosystems can adapt. For carbon perturbations that take place over shorter timescales, the pace of carbon-cycle changes will not matter; instead, the size or magnitude of the change will determine the likelihood of an extinction event.

 

Taking this reasoning forward in time, Rothman predicts that, given the recent rise in carbon dioxide emissions over a relatively short timescale, a sixth extinction will depend on whether a critical amount of carbon is added to the oceans. That amount, he calculates, is about 310 gigatons, which he estimates to be roughly equivalent to the amount of carbon that human activities will have added to the world's oceans by the year 2100.

 

Does this mean that mass extinction will soon follow at the turn of the century? Rothman says it would take some time -- about 10,000 years -- for such ecological disasters to play out. However, he says that by 2100 the world may have tipped into "unknown territory."

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Theorem of the Day

Theorem of the Day | Amazing Science | Scoop.it

250+ math theorems. Can you solve some of them?

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Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics

Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics | Amazing Science | Scoop.it

Datasets which are identical over a number of statistical properties, yet produce dissimilar graphs, are frequently used to illustrate the importance of graphical representations when exploring data. A recent paper presents a novel method for generating such datasets, along with several examples. This technique varies from previous approaches in that new datasets are iteratively generated from a seed dataset through random perturbations of individual data points, and can be directed towards a desired outcome through a simulated annealing optimization strategy.

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Arturo Pereira's curator insight, August 12, 2017 9:25 AM
Reality is more complex than just numbers. Mistrust those who see the world only through the lenses of Excel sheets.
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New Shapes Solve Infinite Pool-Table Problem

New Shapes Solve Infinite Pool-Table Problem | Amazing Science | Scoop.it

Two “rare jewels” have illuminated a mysterious object that’s at the center of many mathematical questions.

 

Strike a billiard ball on a frictionless table with no pockets so that it never stops bouncing off the table walls. If you returned years later, what would you find? Would the ball have settled into some repeating orbit, like a planet circling the sun, or would it be continually tracing new paths in a ceaseless exploration of its felt-covered plane?

 

These kinds of questions occurred to mathematical minds centuries ago, in relation to the long-term trajectories of real objects in outer space, and for nearly that long they’ve seemed impossible to determine exactly. What will a bouncing ball be up to a billion years from now? It’s as hard to answer as it sounds.

 

More recently, though, mathematicians have achieved a succession of stunning breakthroughs. One of the latest results, yet to be published, describes a new category of what are known as “optimal” billiard tables — shapes whose particular angles make it possible to understand every billiard path that could occur within them. The newfound shapes are among a handful of optimal billiard tables ever discovered, and part of an even more select group of quadrilaterals with that property.

 

“They are like these rare jewels,” said Curt McMullen, a mathematician at Harvard University and a co-author of the work along with Alex Wright of Stanford University, Ronen Mukamel of Rice University and Alex Eskin of the University of Chicago.

To find these jewels, these four mathematicians used an elegant set of methods that allow mathematicians to reimagine the claustrophobic, rebounding world of a billiard table as an elegant universe of smooth curves arcing unimpeded through space.

 

There, the far-out future of the billiard path can be apprehended at a glance — while at the same time, perfect billiard tables end up serving as clues about the nature of the exotic higher-dimensional space in which they appear.

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New algorithm generates folding patterns to produce any 3-D origami structure

New algorithm generates folding patterns to produce any 3-D origami structure | Amazing Science | Scoop.it

In a 1999 paper, Erik Demaine—now an MIT professor of electrical engineering and computer science, but then an 18-year-old PhD student at the University of Waterloo, in Canada—described an algorithm that could determine how to fold a piece of paper into any conceivable 3-D shape.

 

 

It was a milestone paper in the field of computational origami, but the algorithm didn't yield very practical folding patterns. Essentially, it took a very long strip of paper and wound it into the desired shape. The resulting structures tended to have lots of seams where the strip doubled back on itself, so they weren't very sturdy.

 

At the Symposium on Computational Geometry in July, Demaine and Tomohiro Tachi of the University of Tokyo will announce the completion of a quest that began with that 1999 paper: a universal algorithm for folding origami shapes that guarantees a minimum number of seams.

 

"In 1999, we proved that you could fold any polyhedron, but the way that we showed how to do it was very inefficient," Demaine says. "It's efficient if your initial piece of paper is super-long and skinny. But if you were going to start with a square piece of paper, then that old method would basically fold the square paper down to a thin strip, wasting almost all the material. The new result promises to be much more efficient. It's a totally different strategy for thinking about how to make a polyhedron."

 

Demaine and Tachi are also working to implement the algorithm in a new version of Origamizer, the free software for generating origami crease patterns whose first version Tachi released in 2008.

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