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Category: mathematics – Page 83

“It’s a novel contribution that uses different methods compared to what most people have been doing,” said Steffen Gielen, a cosmologist at the University of Sheffield in the United Kingdom.

The provocative conclusion rests on a mathematical trick involving switching to a clock that ticks with imaginary numbers. Using the imaginary clock, as Hawking did in the ’70s, Turok and Boyle could calculate a quantity, known as entropy, that appears to correspond to our universe. But the imaginary time trick is a roundabout way of calculating entropy, and without a more rigorous method, the meaning of the quantity remains hotly debated. While physicists puzzle over the correct interpretation of the entropy calculation, many view it as a new guidepost on the road to the fundamental, quantum nature of space and time.

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This could help achieve even world peace ✌️ called equilibrium theory by John Nash.

Game theory mathematics is used to predict outcomes in conflict situations. Now it is being adapted through big data to resolve highly contentious issues between people and the environment.

Game theory is a mathematical concept that aims to predict outcomes and solutions to an issue in which parties with conflicting, overlapping or mixed interests interact.

In “theory,” the “game” will bring everyone towards an optimal solution or “equilibrium.” It promises a scientific approach to understanding how people make decisions and reach compromises in real-world situations.

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Its why we should reverse engineer lab rat brains, crow brains, pigs, and chimps, ending on fully reverse engineering the human brain. even if its a hassle. i still think could all be done by end of 2025.

Last year, MIT researchers announced that they had built “liquid” neural networks, inspired by the brains of small species: a class of flexible, robust machine learning models that learn on the job and can adapt to changing conditions, for real-world safety-critical tasks, like driving and flying. The flexibility of these “liquid” neural nets meant boosting the bloodline to our connected world, yielding better decision-making for many tasks involving time-series data, such as brain and heart monitoring, weather forecasting, and stock pricing.

But these models become computationally expensive as their number of neurons and synapses increase and require clunky computer programs to solve their underlying, complicated math. And all of this math, similar to many , becomes harder to solve with size, meaning computing lots of small steps to arrive at a solution.

Now, the same team of scientists has discovered a way to alleviate this by solving the differential equation behind the interaction of two neurons through synapses to unlock a new type of fast and efficient artificial intelligence algorithms. These modes have the same characteristics of liquid neural nets—flexible, causal, robust, and explainable—but are orders of magnitude faster, and scalable. This type of neural net could therefore be used for any task that involves getting insight into data over time, as they’re compact and adaptable even after training—while many traditional models are fixed.

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“Neutron stars apparently behave a bit like chocolate pralines”.

Neutron stars were first discovered more than 60 years ago, but very little is known about the interior of neutron stars, the incredibly compact cores of dead stars.

According to their findings, a press statement reveals, they bear a surprising resemblance to chocolate pralines.

Sakkmesterke/iStock.

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Are we soon going to be traveling enormous distances via wormholes?

A team of scientists from the University of Sofia in Bulgaria believes they have discovered a new method for detecting wormholes — though they still only exist in theory.

Wormholes are theorized shortcuts through space and time. Sci-fi depictions traditionally show a spacecraft traveling through a wormhole, or creating one, to traverse immense distances to far-off regions of the universe in a short amount of time.

The issue is that black holes and wormholes look very similar, and we have barely developed the technology required to directly observe the former. Now, a team of scientists believes its mathematical model can help to tell the two apart, a report from New Scientist reveals.

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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.”

“The new machine learning models we call ‘CfC’s’ [closed-form Continuous-time] replace the differential equation defining the computation of the neuron with a closed form approximation, preserving the beautiful properties of liquid networks without the need for numerical integration,” MIT professor and CSAIL Director Daniela Rus said in a Tuesday press statement. “CfC models are causal, compact, explainable, and efficient to train and predict. They open the way to trustworthy machine learning for safety-critical applications.”

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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.

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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

INFINITY. In mathematics, it’s a curiosity. In physics, it’s a disease. It reared its head back in the 1940s, with quantum electrodynamics (QED), the theory of electromagnetism.

Continue reading “How we travelled beyond infinity” | >