Archive for the ‘mathematics’ category: Page 16

Jul 16, 2023

We can’t predict the future, but appreciating its uncertainties will make us happier

Posted by in categories: biological, evolution, mathematics, neuroscience

In it, he explores how we can make better, scientifically informed predictions about the world around us, using maths. “Mathematics can provide us with the objective tools to bypass the foibles of our own biology – the limitations imposed by our own thought processes, the compulsions that ultimately make us human, but let us down when it comes to making inferences about the world around us,” he writes. “They are humanity’s shortcuts: the preconceptions and cognitive biases, refined over millennia of evolution, that all too often lead us astray when we try to apply our brain’s old rules to our society’s new environments.”

No matter how tempting it is to think, “Ooh, that’s a bit spooky” when faced with a completely random coincidence or chance occurrence, we should all be expecting unusual things to happen all the time, he says.

Yates describes a person who, when browsing in a secondhand bookshop far from where they grew up, opens a copy of their favourite children’s book, only to find their own name inscribed inside. Yet, he says, “the law of truly large numbers” dictates that, just as someone wins the lottery almost every week, with enough opportunities, such extraordinary coincidences are far more likely to happen than you might think. “There are so many different types of coincidences that make us say: ‘Well, that’s extraordinary.’ But it’s not unlikely that some of them happen to us every so often.”

Jul 14, 2023

New center merges math, AI to push frontiers of science

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

With artificial intelligence poised to assist in profound scientific discoveries that will change the world, Cornell is leading a new $11.3 million center focused on human-AI collaboration that uses mathematics as a common language.

The Scientific Artificial Intelligence Center, or SciAI Center, is being launched with a grant from the Office of Naval Research and is led by Christopher J. Earls, professor of civil and environmental engineering at Cornell Engineering. Co-investigators include Nikolaos Bouklas, assistant professor of mechanical and aerospace engineering at Cornell Engineering; Anil Damle, assistant professor of computer science in the Cornell Ann S. Bowers College of Computing and Information Science; and Alex Townsend, associate professor of mathematics in the College of Arts and Sciences. All of the investigators are field faculty members of the Center for Applied Mathematics.

With the advance of AI systems – built with tangled webs of algorithms and trained on increasingly large sets of data – researchers fear AI’s inner workings will provide little insight into its uncanny ability to recognize patterns in data and make scientific predictions. Earls described it as a situation at odds with true scientific discovery.

Jul 13, 2023

Children Do Much Better in Math When Music is Added to the Lesson: New Study

Posted by in categories: mathematics, media & arts

A new study explored the causal role that music engagement has on student achievement in mathematics—and they found a significant benefit.

Researchers believe that music can make math more enjoyable, keep students engaged, and help ease their fear or anxiety about topics like fractions. The addition of music may even motivate kids to appreciate math and want to learn more.

A typical technique for integrating music into math lessons for young children involves clapping to songs with different rhythms learning numbers, and equating fractions to musical notes.

Jul 13, 2023

Zachary Kallenborn — Existential Terrorism

Posted by in categories: existential risks, mathematics, policy, security, terrorism

“Some men just want to watch the world burn.” Zachary Kallenborn discusses acts of existential terrorism, such as the Tokyo subway sarin attack by Aum Shinrikyo in 1995, which killed or injured over 1,000 people.

Zachary kallenborn is a policy fellow in the center for security policy studies at george mason university, research affiliate in unconventional weapons and technology at START, and senior risk management consultant at the ABS group.

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Jul 13, 2023

The wizardly owl brain uses “Bayesian inference” to find prey

Posted by in categories: biotech/medical, mathematics, neuroscience

This was a surprise. Animals have brain maps for vision and touch, but these are built from visual images and touch receptors that map onto the brain through direct point‑to‑point projections. With ears, it’s entirely different. The brain compares information received from each ear about the timing and intensity of a sound and then translates the differences into a unified perception of a single sound issuing from a specific region of space. The resulting auditory map allows owls to “see” the world in two dimensions with their ears.

This proved to be a big leap toward understanding how the brain of any animal, including humans, learns to grasp its environment through sound. Think of it. Standing in a forest, you hear the crack of a falling branch or the rustle of a deer’s step in the dry leaves. Your brain calculates the time and intensity of sound to determine where it’s coming from. Owls do this task with incredible speed and accuracy. Each cochlea in the owl provides the brain with the precise timing of the sound reaching that ear within 20 microseconds. This determines how accurately the brain can calculate the interaural time difference, which in turn determines the accuracy of the localization of a sound in the azimuth. “The precision in microseconds provided by the owl cochlea is better than in any other animal that has been tested,” says Köppl. “We have big heads, so the interaural time differences are larger, making the task for cochlea and brain easier. In a nutshell, it is the combination of a small head and very precise localization that makes the owl unique.”

And here’s a finding to drop the jaw. José Luis Peña, a neuroscientist at the Albert Einstein College of Medicine, and his collaborators have discovered that the sound localization system in a barn owl’s brain performs sophisticated mathematical computations to execute this pinpointing of prey. The space‑specific neurons in the owl’s specialized auditory brain do advanced math when they transmit their information, not just adding and multiplying incoming signals but averaging them and using a statistical method called “Bayesian inference,” which involves updating as more information becomes available.

Jul 12, 2023

Claude 2: We are pleased to announce Claude 2, our new model

Posted by in categories: business, education, mathematics

We are pleased to announce Claude 2, our new model. Claude 2 has improved performance, longer responses, and can be accessed via API as well as a new public-facing beta website, We have heard from our users that Claude is easy to converse with, clearly explains its thinking, is less likely to produce harmful outputs, and has a longer memory. We have made improvements from our previous models on coding, math, and reasoning. For example, our latest model scored 76.5% on the multiple choice section of the Bar exam, up from 73.0% with Claude 1.3. When compared to college students applying to graduate school, Claude 2 scores above the 90th percentile on the GRE reading and writing exams, and similarly to the median applicant on quantitative reasoning.

Think of Claude as a friendly, enthusiastic colleague or personal assistant who can be instructed in natural language to help you with many tasks. The Claude 2 API for businesses is being offered for the same price as Claude 1.3. Additionally, anyone in the US and UK can start using our beta chat experience today.

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Jul 11, 2023

Claude 2.0, Anthropic’s Latest ChatGPT Rival, Is Here — And This Time, You Can Try It

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

AI startup Anthropic has released its next major model – and this time, you can see for yourself how it compares to other AI standouts such as OpenAI’s ChatGPT or Inflection’s Pi. Anthropic announced on Tuesday that it’s released Claude 2, a large-language model that the company said showed improvement across several key benchmarks that include coding, math and reasoning skills, while producing fewer harmful answers.

Claude 2 is more widely available in its second major iteration. Anthropic launched a new beta-test website for general users to register in the U.S. and U.K. – – while opening up the new model to businesses by API at the same price they paid for Anthropic’s previous,… More.

New model Claude 2.0 is better at coding, math and reasoning, CEO Dario Amodei said. Unlike its predecessor, it’s available for general consumer use.

Continue reading “Claude 2.0, Anthropic’s Latest ChatGPT Rival, Is Here — And This Time, You Can Try It” »

Jul 6, 2023

European researchers design a rubber block that can count to ten

Posted by in categories: computing, mathematics, quantum physics

Physicist Lennard Kwakernaak finds the “complexity of simple things” intriguing, and it is a tough ask to make an inanimate object count.

A collaboration between researchers at Leiden University and AMOLF in Amsterdam has yielded a new metamaterial, a rubber block that can count. The researchers are calling it a Beam Counter and it is pretty nifty.

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Jul 6, 2023

Elusive Ninth Dedekind Number Discovered: Unlocking a Decades-Old Mystery of Mathematics

Posted by in categories: mathematics, supercomputing

Scientists from the Universities of Paderborn and Leuven solve long-known problem in mathematics.

Making history with 42 digits: Scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number. Experts worldwide have been searching for the value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there. The results will be presented in September at the International Workshop on Boolean Functions and their Applications (BFA) in Norway.

What started as a master’s thesis project by Lennart Van Hirtum, then a computer science student at KU Leuven and now a research associate at the University of Paderborn, has become a huge success. The scientists join an illustrious group with their work: Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1,897, and later by greats of early computer science such as Randolph Church and Morgan Ward. “For 32 years, the calculation of D was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all,” Van Hirtum says.

Jul 5, 2023

From Atoms to Materials: Algorithmic breakthrough unlocks path to sustainable technologies

Posted by in categories: chemistry, computing, information science, mathematics, particle physics, sustainability

New research by the University of Liverpool could signal a step change in the quest to design the new materials that are needed to meet the challenge of net zero and a sustainable future.

Published in the journal Nature, Liverpool researchers have shown that a mathematical algorithm can guarantee to predict the structure of any material just based on knowledge of the atoms that make it up.

Developed by an interdisciplinary team of researchers from the University of Liverpool’s Departments of Chemistry and Computer Science, the algorithm systematically evaluates entire sets of possible structures at once, rather than considering them one at a time, to accelerate identification of the correct solution.

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