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Category: mathematics – Page 53

In today’s column, I am going to identify and explain the momentous pairing of both generative AI and data science. These two realms are each monumental in their own respective ways, thus they are worthy of rapt attention on a standalone basis individually. On top of that, when you connect the dots and bring them together as a working partnership, you have to admire and anticipate big changes that will arise, especially as the two fields collaboratively reinvent data strategies all told.

This is entirely tangible and real-world, not merely something abstract or obtuse.

I will first do a quick overview of generative AI. If you are already versed in generative AI, perhaps do a fast skim on this portion.

Foundations Of Generative AI

Continue reading “Generative AI And Data Science Have Mightily Paired Up To Reinvent Data Strategies, Exemplified Via Release Of OpenAI’s ChatGPT Code Interpreter” | >

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.”

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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.

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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.

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“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.

Zachary has an MA in Nonproliferation and Terrorism Studies from Middlebury Institute of International Studies, and a BS in Mathematics and International Relations from the University of Puget Sound.

His work has been featured in numerous international media outlets including the New York Times, Slate, NPR, Forbes, New Scientist, WIRED, Foreign Policy, the BBC, and many others.

Continue reading “Zachary Kallenborn — Existential Terrorism” | >

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.

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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, claude.ai. 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.

As we work to improve both the performance and safety of our models, we have increased the length of Claude’s input and output. Users can input up to 100K tokens in each prompt, which means that Claude can work over hundreds of pages of technical documentation or even a book. Claude can now also write longer documents — from memos to letters to stories up to a few thousand tokens — all in one go.

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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. – claude.ai – 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.

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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.

In a world where researchers are racing to make a quantum computer that can do complex math, building a new rubber block might not seem like much. But physicist Lennard Kwakernaak finds the “complexity of simple things” intriguing, and it is a tough ask to make an inanimate object count.

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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.

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