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Archive for the ‘mathematics’ category: Page 60

Nov 16, 2022

MIT solved a century-old differential equation to break ‘liquid’ AI’s computational bottleneck

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

Last year, MIT developed an AI/ML algorithm capable of learning and adapting to new information while on the job, not just during its initial training phase. These “liquid” neural networks (in the Bruce Lee sense) literally play 4D chess — their models requiring time-series data to operate — which makes them ideal for use in time-sensitive tasks like pacemaker monitoring, weather forecasting, investment forecasting, or autonomous vehicle navigation. But, the problem is that data throughput has become a bottleneck, and scaling these systems has become prohibitively expensive, computationally speaking.

On Tuesday, MIT researchers announced that they have devised a solution to that restriction, not by widening the data pipeline but by solving a differential equation that has stumped mathematicians since 1907. Specifically, the team solved, “the differential equation behind the interaction of two neurons through synapses… to unlock a new type of fast and efficient artificial intelligence algorithms.”

Continue reading “MIT solved a century-old differential equation to break ‘liquid’ AI’s computational bottleneck” »

Nov 15, 2022

Scientists Created a Black Hole in The Lab, And Then It Started to Glow

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

A new kind of black hole analog could tell us a thing or two about an elusive radiation theoretically emitted by the real thing.

Using a chain of atoms in single-file to simulate the event horizon of a black hole, a team of physicists has observed the equivalent of what we call Hawking radiation – particles born from disturbances in the quantum fluctuations caused by the black hole’s break in spacetime.

This, they say, could help resolve the tension between two currently irreconcilable frameworks for describing the Universe: the general theory of relativity, which describes the behavior of gravity as a continuous field known as spacetime; and quantum mechanics, which describes the behavior of discrete particles using the mathematics of probability.

Nov 15, 2022

How we travelled beyond infinity

Posted by in categories: biotech/medical, mathematics, quantum physics

Circa 2011 face_with_colon_three


By Amanda Gefter.

Frank Close tells the human story of how we solved The Infinity Puzzle – once the bane of physics

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Nov 15, 2022

The Riemann Hypothesis: A 160-Year-Old, Million-Dollar Math Problem

Posted by in category: mathematics

Nov 15, 2022

Boltzmann Brains — Why The Universe is Most Likely a Simulation

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

Start learning today with Brilliant! https://brilliant.org/upandatom.

Watch Part 2 over on Isaac Arthur’s channel.

Continue reading “Boltzmann Brains — Why The Universe is Most Likely a Simulation” »

Nov 14, 2022

Meta AI Has Built A Neural Theorem Prover That Has Solved 10 International Math Olympiad (IMO) Problems — 5x More Than Any Previous Artificial Intelligence AI System

Posted by in categories: mathematics, robotics/AI

The scientific world has long acknowledged that proving mathematical theorems is an essential first step in developing artificial intelligence. To prove the truth or falsity of a conjecture, one must use symbolic thinking and sort through an unlimited number of alternatives. These tasks are beyond the capabilities of even the most sophisticated AI systems.

The state of the art in artificial intelligence today is to create machines that can “solve at once” or come up with a whole answer to a problem in a single go. However, this is not how most individuals approach difficult situations. Mathematical reasoning is significantly more challenging to formalize and measure.

Meta AI has made an important development at the intersection of artificial intelligence and mathematics. The neural theorem prover developed by the team has completed five times as many IMO problems as any other AI system before it, totaling ten. Concerning miniF2F, a popular mathematics test, the AI model outperforms the state of art by 20% and outperforms Metamath by 10%.

Nov 14, 2022

Computer scientists succeed in solving algorithmic riddle from the 1950s

Posted by in categories: computing, information science, mapping, mathematics

For more than half a century, researchers around the world have been struggling with an algorithmic problem known as “the single source shortest path problem.” The problem is essentially about how to devise a mathematical recipe that best finds the shortest route between a node and all other nodes in a network, where there may be connections with negative weights.

Sound complicated? Possibly. But in fact, this type of calculation is already used in a wide range of the apps and technologies that we depend upon for finding our ways around—as Google Maps guides us across landscapes and through cities, for example.

Now, researchers from the University of Copenhagen’s Department of Computer Science have succeeded in solving the single source shortest problem, a riddle that has stumped researchers and experts for decades.

Nov 13, 2022

Mathematician who solved prime-number riddle claims new breakthrough

Posted by in categories: innovation, mathematics

After shocking the mathematics community with a major result in 2013, Yitang Zhang now says he has solved an analogue of the celebrated Riemann hypothesis.

Nov 11, 2022

The mathematics that makes us realize we don’t know much: Behavior of spin glasses

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

Spin glasses are alloys formed by noble metals in which a small amount of iron is dissolved. Although they do not exist in nature and have few applications, they have nevertheless been the focus of interest of statistical physicists for some 50 years. Studies of spin glasses were crucial for Giorgio Parisi’s 2021 Nobel Prize in Physics.

The scientific interest of spin glasses lies in the fact that they are an example of a complex system whose elements interact with each other in a way that is sometimes cooperative and sometimes adversarial. The mathematics developed to understand their behavior can be applied to problems arising in a variety of disciplines, from ecology to machine learning, not to mention economics.

Spin glasses are , that is, systems in which individual elements, the spins, behave like small magnets. Their peculiarity is the co-presence of ferromagnetic-type bonds, which tend to align the spins, with antiferromagnetic-type bonds, which tend to orient them in opposite directions.

Nov 9, 2022

Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work

Posted by in categories: computing, encryption, mathematics, quantum physics, security, space

In 1994, the computer scientist Peter Shor discovered that if quantum computers were ever invented, they would decimate much of the infrastructure used to protect information shared online. That frightening possibility has had researchers scrambling to produce new, “post-quantum” encryption schemes, to save as much information as they could from falling into the hands of quantum hackers.

Earlier this year, the National Institute of Standards and Technology revealed four finalists in its search for a post-quantum cryptography standard. Three of them use “lattice cryptography” — a scheme inspired by lattices, regular arrangements of dots in space.

Lattice cryptography and other post-quantum possibilities differ from current standards in crucial ways. But they all rely on mathematical asymmetry. The security of many current cryptography systems is based on multiplication and factoring: Any computer can quickly multiply two numbers, but it could take centuries to factor a cryptographically large number into its prime constituents. That asymmetry makes secrets easy to encode but hard to decode.

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