Archive for the ‘mathematics’ category: Page 5

Mar 22, 2023

An expanding universe is simulated in a quantum droplet

Posted by in categories: cosmology, mathematics, quantum physics

Unfortunately for the field of cosmology, there is only one universe. This makes performing experiments in the same way as other scientific fields quite a challenge. But it turns out that the universe and the quantum fields that permeate it are highly analogous to quantum fluids like Bose-Einstein condensates (BECs), at least from a mathematical point of view. These fluids can be the subject of experiments, allowing cosmology to be studied in the lab.

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In a paper published in Nature, researchers at Heidelberg University in Germany have for the first time used a BEC to simulate an expanding universe and certain quantum fields within it. This allows for the study of important cosmological scenarios. Not only is the universe currently expanding, but it is believed that in the first fractions of a second after the Big Bang it underwent a period of extremely rapid expansion known as “inflation.” This process would have expanded the microscopic fluctuations of quantum fields in the early universe to the size of galaxy clusters, seeding the large-scale structure of our universe today.

Mar 21, 2023

Fourier Transformations Reveal How AI Learns Complex Physics

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

One of the oldest tools in computational physics — a 200-year-old mathematical technique known as Fourier analysis — can reveal crucial information about how a form of artificial intelligence called a deep neural network learns to perform tasks involving complex physics like climate and turbulence modeling, according to a new study.

The discovery by mechanical engineering researchers at Rice University is described in an open-access study published in the journal PNAS Nexus, a sister publication of the Proceedings of the National Academy of Sciences.

“This is the first rigorous framework to explain and guide the use of deep neural networks for complex dynamical systems such as climate,” said study corresponding author Pedram Hassanzadeh. “It could substantially accelerate the use of scientific deep learning in climate science, and lead to much more reliable climate change projections.”

Mar 20, 2023

GPT-4 Beats 90% Of Lawyers Trying To Pass The Bar

Posted by in categories: biological, law, mathematics, robotics/AI


In 1997, IBM’s Deep Blue defeated the reigning world champion chess player, Garry Kasparov. In 2016, Google’s AlphaGo defeated one of the worlds top Go players in a five-game match. Today, OpenAI released GPT-4, which it claims beats 90% of humans who take the bar to become a lawyer, and 99% of students who compete in the Biology Olympiad, an international competition that tests the knowledge and skills of high school students in the field of biology.

In fact, it scores in the top ranks for at least 34 different tests of ability in fields as diverse as macroeconomics, writing, math, and — yes — vinology.

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Mar 18, 2023

Fine Tuned Universe: the critics strike back

Posted by in categories: cosmology, mathematics, quantum physics

At the end of of 2022, we released a film offering a reply to the fine tuning argument for God from leading physicists and philosophers of physics. This included both those that doubt there is any fine tuning and those that think there is but it can be solved by naturalistic means.
Subsequently astrophysicist Luke Barnes and philosopher Philip Goff offered their criticism of our criticism. Here we have assembled some of our original talking heads to review their criticism and offer a reply, defending the original position that fine tuning argument for God does not work.
Our original film can be found here:

Luke Barnes and Philip Goff’s reply is here: and we also recommend this video on Bayes theorem on the Majesty of Reason Channel:

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Mar 16, 2023

Quantum Light Could Probe Chemical Reactions in Real Time

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

For their new study, the researchers aimed to understand how quantum correlations inside a source material, be it a gas or a mineral, would impact the quantum properties of the light bursts coming out, if at all. “High harmonic generation is a very important area. And still, until recently, it was described by a classical picture of light,” Kaminer says.

In quantum mechanics, figuring out what’s going on with more than a few particles at the same time is notoriously difficult. Kaminer and Alexey Gorlach, a graduate student in his lab, used their COVID-imposed isolation to try to make progress on a fully quantum description of light emitted in high harmonics. “It’s really crazy; Alexey built a super complex mathematical description on a scale that we’ve never had before,” Kaminer says.

Next, to fully incorporate the quantum properties of the material used to generate this light, Kaminer and Gorlach teamed up with Andrea Pizzi, then a graduate student at the University of Cambridge and now a postdoctoral fellow at Harvard University.

Mar 16, 2023

The Hidden Mathematics of Crowds: How Pedestrians Inadvertently Self-Organize

Posted by in category: mathematics

Mathematical research from the University of Bath in the United Kingdom has shed new light on the formation and behavior of crowds.

Have you ever pondered how people, without having a discussion or even giving it a second thought, instinctively form lanes when walking through a crowded area?

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Mar 16, 2023

Sinister Algorithms: The dark side of our future

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

Algorithms are complex mathematical formulas used to perform tasks in our digital world. They are programmed to process information, make decisions, and take actions. Algorithms are used in various applications, such as search engines, social media, autonomous vehicles, and digital assistants.

But not all algorithms are innocent. Some algorithms have a sinister #scary side that poses a threat to our privacy, our freedom, and our humanity… #aiscarystories #aihorrorstories #scarystories #scarystory #horrorstories #horrorstory #realstories #realhorrorstories #realscarystories #truestories #truestory #creapystories #AIScarystory #AIHorror #artificialintelligence #scaryai #scaryartificialintelligence #trueaiscarystories #truescarystories.

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Mar 15, 2023

OpenAI Releases ChatGPT-4 And Performs Impressive Demonstration

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

OpenAI has released a new version of ChatGPT, claiming that the new language learning model is capable of passing – and even excelling in – a variety of academic exams.

ChatGPT-4, which will be available on Bing as well as the OpenAI website, is more reliable and more creative than its predecessor, according to OpenAI. The team tested the model on a number of exams designed for humans, from the bar exam to biology, using publicly available papers. While no additional training was given to the model ahead of the tests, it was able to perform well on most subjects, performing in the estimated 90th percentile for the bar exam and the 86th-100th in art history.

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Mar 15, 2023

Transiting mini-Neptune exoplanet characterized as having either gaseous atmosphere, an ocean or both

Posted by in categories: mathematics, space

An international team of planetary scientists has characterized some of the features of an exoplanet named HD-207496-b, located approximately 138 light years from Earth. In their paper accepted for publication in the journal Astronomy & Astrophysics, and currently posted on the arXiv preprint server, the group describes their study of the exoplanet and the two theories regarding its likely makeup.

The HD-207496-b was discovered as part of a larger effort to characterize naked core planets. As such, the team was analyzing HARPS of HD-207496—a bright k dwarf. By adding TESS photometry data, the group was able to measure the stars’ brightness and wavelength, and by studying the exoplanet’s transit characteristics, the team was able to calculate its period, mass, radius and density. That led them to a bit of a conundrum—was the exoplanet gaseous or watery?

The researchers calculated that the exoplanet had a radius 2.25 times that of Earth, with an orbit of 6.44 days. And it had a mass that was approximately 6.1 times Earth’s. Simple math showed that the exoplanet had a density of 3.27 grams per cubic centimeter, which is less than that of Earth.

Mar 15, 2023

Karl Friston — World Renowned Researcher — Joins Verses Technologies as Chief Scientist

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

He was ranked the number 1 most influential neuroscientist in the world by Semantic Scholar in 2016, and has received numerous awards and accolades for his work. His appointment as chief scientist of Verses not only validates their platform’s framework for advancing AI implementations but also highlights the company’s commitment to expanding the frontier of AI research and development.

Friston is short listed for a Nobel Prize, is one of the most cited scientists in human history with over 260,000 academic citations, and invented all of the mathematics behind the fMRI scan. As one pundit put it, “what Einstein was to physics, Friston is to Intelligence.”

Indeed Friston’s expertise will be invaluable in helping the company execute its vision of deploying a plethora of technologies working toward a smarter world through AI.

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