Archive for the ‘mathematics’ category

Aug 17, 2019

Physicists solve 2,000-year-old optical problem

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

A trio of physicists from the National Autonomous University of Mexico and Tec de Monterrey has solved a 2,000-year-old optical problem—the Wasserman-Wolf problem. In their paper published in the journal Applied Optics, Rafael González-Acuña, Héctor Chaparro-Romo, and Julio Gutiérrez-Vega outline the math involved in solving the puzzle, give some examples of possible applications, and describe the efficiency of the results when tested.

Over 2,000 years ago, Greek scientist Diocles recognized a problem with —when looking through devices equipped with them, the edges appeared fuzzier than the center. In his writings, he proposed that the effect occurs because the lenses were spherical—light striking at an angle could not be focused because of differences in refraction. Isaac Newton was reportedly stumped in his efforts to solve the problem (which became known as ), as was Gottfried Leibniz.

In 1949, Wasserman and Wolf devised an analytical means for describing the problem, and gave it an official name—the Wasserman-Wolf problem. They suggested that the to solving the problem would be to use two aspheric adjacent surfaces to correct aberrations. Since that time, researchers and engineers have come up with a variety of ways to fix the problem in specific applications—most particularly cameras and telescopes. Most such efforts have involved creating aspherical lenses to counteract refraction problems. And while they have resulted in improvement, the solutions have generally been expensive and inadequate for some applications.

Aug 15, 2019

Generative Design: Alien Parts from Natural Evolution

Posted by in categories: 3D printing, energy, evolution, mathematics

We’re only a handful of months away from the year 2020, and with the way parts look and tech acts, it finally feels like we’re entering the future. It’s a future crafted by sophisticated 3D printers and machining centers, using materials provided by global-reaching supply chains and connected to an exponential rate of new superpowered gadgets. Nowadays, there’s really no reason to think any manufacturing feat is impossible. If something doesn’t exist, it’s just that we haven’t figured it out yet.

And this futuristic techtopia brimming with potential wouldn’t be possible if not for engineers—those dedicated, uber-creative folks plotting such a course, continuously improving the world around through the super power of… math.

Mathematics has been the indispensable fuel to make the impossible possible since at least the ancient Egyptians more than four thousand years ago. The Great Pyramid of Giza is the world’s oldest monument to its power. Amazingly, its geometrical elegance was calculated on papyrus scrolls, most of which have turned to dust long ago. Yet the universal language of math still speaks through its dimensions. And it will continue to do so for time immemorial.

Aug 15, 2019

AI validates evolution’s oldest mathematical model

Posted by in categories: mathematics, robotics/AI

Butterfly co-mimic pairs from the species Heliconius erato (odd columns) and Heliconius melpomene (even columns) sorted by greatest similarity (along rows, top left to bottom right) using machine learning.

J Hoyal Cuthill

Aug 13, 2019

Researchers discover that the rate of telomere shortening predicts species lifespan

Posted by in categories: biotech/medical, information science, life extension, mathematics

A flamingo lives 40 years and a human being lives 90 years; a mouse lives two years and an elephant lives 60. Why? What determines the lifespan of a species? After analyzing nine species of mammals and birds, researchers at the Spanish National Cancer Research Center (CNIO) found a very clear relationship between the lifespan of these species and the shortening rate of their telomeres, the structures that protect the chromosomes and the genes they contain. The relationship is expressed as a mathematical equation, a formula that can accurately predict the longevity of the species. The study was done in collaboration with the Madrid Zoo Aquarium and the University of Barcelona.

“The telomere shortening rate is a powerful predictor of ,” the authors write in the prestigious journal Proceedings of the National Academy of Sciences (PNAS).

The study compares the telomeres of mice, goats, dolphins, gulls, reindeer, vultures, flamingos, elephants and humans, and reveals that species whose telomeres shorten faster have shorter lives.

Aug 4, 2019

A Decades-Old Computer Science Puzzle Was Solved in Two Pages

Posted by in categories: computing, mathematics, science

A paper posted online this month has settled a nearly 30-year-old conjecture about the structure of the fundamental building blocks of computer circuits. This “sensitivity” conjecture has stumped many of the most prominent computer scientists over the years, yet the new proof is so simple that one researcher summed it up in a single tweet.

“This conjecture has stood as one of the most frustrating and embarrassing open problems in all of combinatorics and theoretical computer science,” wrote Scott Aaronson of the University of Texas, Austin, in a blog post. “The list of people who tried to solve it and failed is like a who’s who of discrete math and theoretical computer science,” he added in an email.

The conjecture concerns Boolean functions, rules for transforming a string of input bits (0s and 1s) into a single output bit. One such rule is to output a 1 provided any of the input bits is 1, and a 0 otherwise; another rule is to output a 0 if the string has an even number of 1s, and a 1 otherwise. Every computer circuit is some combination of Boolean functions, making them “the bricks and mortar of whatever you’re doing in computer science,” said Rocco Servedio of Columbia University.

Jul 26, 2019

Could a black hole be used as portable gravity device?

Posted by in categories: cosmology, mathematics, physics

I don’t use the term artificial gravity because, the gravity from a black hole is real.

If you have harnessed and are able to control a black hole would you be able to use it as portable gravity device?

I don’t really have the physics and the math to to figure it out. But it would seem that if you are in a low gravity environment, you could place a black hole under the floor, and have gravity. Presumably by changing the distance between the floor and the black hole you could adjust to 1 gravity or partial gravity.

Jul 15, 2019

Researchers’ deep learning algorithm solves Rubik’s Cube faster than any human

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

Since its invention by a Hungarian architect in 1974, the Rubik’s Cube has furrowed the brows of many who have tried to solve it, but the 3D logic puzzle is no match for an artificial intelligence system created by researchers at the University of California, Irvine.

DeepCubeA, a learning algorithm programmed by UCI scientists and mathematicians, can find the solution in a fraction of a second, without any specific domain knowledge or in-game coaching from humans. This is no simple task considering that the cube has completion paths numbering in the billions but only one goal state—each of six sides displaying a solid color—which apparently can’t be found through random moves.

For a study published today in Nature Machine Intelligence, the researchers demonstrated that DeepCubeA solved 100 percent of all test configurations, finding the to the goal state about 60 percent of the time. The algorithm also works on other combinatorial games such as the sliding tile , Lights Out and Sokoban.

Jul 15, 2019

Physicists Reverse Time for Tiny Particles Inside a Quantum Computer

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

Time goes in one direction: forward. Little boys become old men but not vice versa; teacups shatter but never spontaneously reassemble. This cruel and immutable property of the universe, called the “arrow of time,” is fundamentally a consequence of the second law of thermodynamics, which dictates that systems will always tend to become more disordered over time. But recently, researchers from the U.S. and Russia have bent that arrow just a bit — at least for subatomic particles.

In the new study, published Tuesday (Mar. 12) in the journal Scientific Reports, researchers manipulated the arrow of time using a very tiny quantum computer made of two quantum particles, known as qubits, that performed calculations. [Twisted Physics: 7 Mind-Blowing Findings]

At the subatomic scale, where the odd rules of quantum mechanics hold sway, physicists describe the state of systems through a mathematical construct called a wave function. This function is an expression of all the possible states the system could be in — even, in the case of a particle, all the possible locations it could be in — and the probability of the system being in any of those states at any given time. Generally, as time passes, wave functions spread out; a particle’s possible location can be farther away if you wait an hour than if you wait 5 minutes.

Jul 13, 2019

The biological computer is an implantable device that is mainly used for tasks like monitoring the body’s activities or inducing therapeutic effects

Posted by in categories: biotech/medical, chemistry, computing, mathematics

The biological computer is an implantable device that is mainly used for tasks like monitoring the body’s activities or inducing therapeutic effects, all at the molecular or cellular level. This is made up of RNA, DNA and proteins and can also perform simple mathematical calculations.

DNA computing is a branch of computing which uses DNA, biochemistry, and molecular biology hardware, instead of the traditional silicon-based computer technologies. Research and development in this area concerns theory, experiments, and applications of DNA computing.…/finally-a-dna-computer-that-can-ac…/

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Jul 12, 2019

Strange warping geometry helps to push scientific boundaries

Posted by in categories: computing, mathematics, particle physics, space, transportation

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond the capabilities of modern computers, so scientists at Princeton University have turned to an unusual branch of geometry instead.

Researchers led by Andrew Houck, a professor of electrical engineering, have built an electronic array on a microchip that simulates in a hyperbolic plane, a geometric surface in which space curves away from itself at every point. A hyperbolic plane is difficult to envision—the artist M.C. Escher used in many of his mind-bending pieces—but is perfect for answering questions about particle interactions and other challenging mathematical questions.

The research team used superconducting circuits to create a lattice that functions as a hyperbolic space. When the researchers introduce photons into the lattice, they can answer a wide range of difficult questions by observing the photons’ interactions in simulated hyperbolic space.

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