Archive for the ‘mathematics’ category: Page 61

Aug 27, 2022

Wickedly Fast Frontier Supercomputer Officially Ushers in the Next Era of Computing

Posted by in categories: mathematics, supercomputing

Today, Oak Ridge National Laboratory’s Frontier supercomputer was crowned fastest on the planet in the semiannual Top500 list. Frontier more than doubled the speed of the last titleholder, Japan’s Fugaku supercomputer, and is the first to officially clock speeds over a quintillion calculations a second—a milestone computing has pursued for 14 years.

That’s a big number. So before we go on, it’s worth putting into more human terms.

Imagine giving all 7.9 billion people on the planet a pencil and a list of simple arithmetic or multiplication problems. Now, ask everyone to solve one problem per second for four and half years. By marshaling the math skills of the Earth’s population for a half-decade, you’ve now solved over a quintillion problems.

Aug 26, 2022

From bits to p-bits: One step closer to probabilistic computing

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

Tohoku University scientists in Japan have developed a mathematical description of what happens within tiny magnets as they fluctuate between states when an electric current and magnetic field are applied. Their findings, published in the journal Nature Communications, could act as the foundation for engineering more advanced computers that can quantify uncertainty while interpreting complex data.

Classical computers have gotten us this far, but there are some problems that they cannot address efficiently. Scientists have been working on addressing this by engineering computers that can utilize the laws of quantum physics to recognize patterns in . But these so-called quantum computers are still in their early stages of development and are extremely sensitive to their surroundings, requiring extremely low temperatures to function.

Now, scientists are looking at something different: a concept called probabilistic computing. This type of computer, which could function at , would be able to infer potential answers from complex input. A simplistic example of this type of problem would be to infer information about a person by looking at their purchasing behavior. Instead of the computer providing a single, discrete result, it picks out patterns and delivers a good guess of what the result might be.

Aug 26, 2022

Existential Hope Special with Morgan Levine | On the Future of Aging

Posted by in categories: biotech/medical, genetics, life extension, mathematics, robotics/AI

Foresight Existential Hope Group.
Program & apply to join: https://foresight.org/existential-hope/

In the Existential Hope-podcast (https://www.existentialhope.com), we invite scientists to speak about long-termism. Each month, we drop a podcast episode where we interview a visionary scientist to discuss the science and technology that can accelerate humanity towards desirable outcomes.

Continue reading “Existential Hope Special with Morgan Levine | On the Future of Aging” »

Aug 25, 2022

Physicists entangle more than a dozen photons efficiently

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

Physicists at the Max Planck Institute of Quantum Optics have managed to entangle more than a dozen photons efficiently and in a defined way. They are thus creating a basis for a new type of quantum computer. Their study is published in Nature.

The phenomena of the quantum world, which often seem bizarre from the perspective of the common everyday world, have long since found their way into technology. For example, entanglement: a quantum-physical connection between particles that links them in a strange way over arbitrarily long distances. It can be used, for example, in a quantum computer—a computing machine that, unlike a conventional computer, can perform numerous mathematical operations simultaneously. However, in order to use a quantum computer profitably, a large number of entangled particles must work together. They are the for calculations, so-called qubits.

“Photons, the particles of light, are particularly well suited for this because they are robust by nature and easy to manipulate,” says Philip Thomas, a doctoral student at the Max Planck Institute of Quantum Optics (MPQ) in Garching near Munich. Together with colleagues from the Quantum Dynamics Division led by Prof. Gerhard Rempe, he has now succeeded in taking an important step towards making usable for technological applications such as quantum computing: For the first time, the team generated up to 14 entangled photons in a defined way and with high efficiency.

Aug 25, 2022

GAMEOPT: An algorithm to optimize the flow of vehicles through dynamic unsignalized intersections

Posted by in categories: energy, information science, mathematics, transportation

Managing road intersections in crowded and dynamic environments, such as urban areas, can be highly challenging. The poor management of traffic at these can lead to road accidents, wastage of fuel, and environmental pollution.

Researchers at the University of Maryland have recently developed GAMEOPT, a that could help manage unsignalized road intersections with high traffic more efficiently. The research team with members, Nilesh Suriyarachchi, Rohan Chandra, John S. Baras and Dinesh Manocha introduced their method in a recent paper to be published in the proceedings of the 25th IEEE International Conference on Intelligent Transportation Systems (IEEE ITSC 2022). This method combines optimization techniques with ideas from game theory, a mathematical construct that represents situations in which different agents are competing with one another.

Forty percent of all crashes, 50% of serious collisions, and 20% of fatalities occur at unsignalized intersections,” Chandra, a member of the research team, told TechXplore. “Our primary objective is to improve traffic flow and in poorly regulated or unregulated traffic intersections. To achieve this objective, we propose an algorithm that combines ideas from optimization and game theory to understand how different traffic agents cooperate and negotiate with each other at traffic intersections.”

Aug 22, 2022

How Mathematicians Make Sense of Chaos

Posted by in categories: mathematics, space

In 1,885, King Oscar II of Sweden announced a public challenge consisting of four mathematical problems. The French polymath Henri Poincaré focused on one related to the motion of celestial bodies, the so-called n-body problem. Will our solar system continue its clocklike motion indefinitely, will the planets fly off into the void, or will they collapse into a fiery solar death?

Poincaré’s solution — which indicated that at least some systems, like the sun, Earth and moon, were stable — won the prestigious prize, and an accompanying article was printed for distribution in 1889. Unfortunately, his solution was incorrect.

Poincaré admitted his error and paid to have the copies of his solution destroyed (which cost more than the prize money). A month later, he submitted a corrected version. He now saw that even a system with only three bodies could behave too unpredictably — too chaotically — to be modeled. So began the field of dynamical systems.

Aug 22, 2022

Mathematicians suggest liquid crystals could be used to create building blocks for a new kind of computer

Posted by in categories: computing, mathematics

A pair of researchers at MIT have found evidence suggesting that a new kind of computer could be built based on liquid crystals rather than silicon. In their paper published in the journal Science Advances, Žiga Kos and Jörn Dunkel outline a possible design for a computer that takes advantage of slight differences in the orientation of the molecules that make up liquid crystals and the advantages such a system would have over those currently in use.

Most modern screens are made using (LCDs). Such displays are made by growing crystals in a flat plane. These crystals are made up of rod-shaped that line up in a parallel fashion (those that line up the wrong way are removed). The orientation of the molecules in LCDs are not all perfect alignments, of course, but they are close enough to allow for sharp imagery.

In this new effort, Kos and Dunkel, suggest it should be possible to take advantage of those slight misalignments to create a new way to hold and manipulate computer data. They note that such a computer could encode a unique value to each type of misalignment to hold a bit of data. Thus, a computer using this approach would not be constrained to conventional binary bits—it could have a whole host of options, perhaps making it much faster than machines used today (depending on how quickly the orientations could be changed).

Aug 21, 2022

New Proof Reveals the Hidden Structure of Common Equations

Posted by in categories: information science, mathematics

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

Aug 19, 2022

Theorem of everything: The secret that links numbers and shapes

Posted by in category: mathematics

Circa 2018 face_with_colon_three

For millennia mathematicians have struggled to unify arithmetic and geometry. Now one young genius could have brought them in sight of the ultimate prize.

Aug 19, 2022

Journal of Applied and Industrial Mathematics

Posted by in category: mathematics

Circa 2016 face_with_colon_three

A subset C of infinite-dimensional binary cube is called a perfect binary code with distance 3 if all balls of radius 1 (in the Hamming metric) with centers in C are pairwise disjoint and their union cover this binary cube. Similarly, we can define a perfect binary code in zero layer, consisting of all vectors of infinite-dimensional binary cube having finite supports. In this article we prove that the cardinality of all cosets of perfect binary codes in zero layer is the cardinality of the continuum. Moreover, the cardinality of all cosets of perfect binary codes in the whole binary cube is equal to the cardinality of the hypercontinuum.

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