Lifeboat Foundation

I will post a bunch of links to things people can do at home while under lockdown. This is one of my favorite sites. Feel free to check it out and post from it as well.

Calculus is the key to fully understanding how neural networks function. Go beyond a surface understanding of this mathematics discipline with these free course materials from MIT.

A new study offers a better understanding of the hidden network of underground electrical signals being transmitted from plant to plant – a network that has previously been shown to use the Mycorrhizal fungi in soil as a sort of electrical circuit.

Through a combination of physical experiments and mathematical models based on differential equations, researchers explored how this electrical signalling works, though it’s not clear yet exactly what messages plants might want to transmit to each other.

The work builds on previous experiments by the same team looking at how this subterranean messaging service functions, using electrical stimulation as a way of testing how signals are carried even when plants aren’t in the same soil.

Continue reading “Plants Can Secretly Send Underground Electrical Signals. Here’s How They Do It” »

The best way to prevent this is by focusing on the basics. America needs a major all-of-society push to increase the number of U.S. students being trained in both the fundamentals of math and in the more advanced, rigorous, and creative mathematics. Leadership in implementing this effort will have to come from the U.S. government and leading technology companies, and through the funding of ambitious programs. A few ideas come to mind: talent-spotting schemes, the establishment of math centers, and a modern successor to the post-Sputnik National Defense Education Act, which would provide math scholarships to promising students along with guaranteed employment in either public or private enterprises.

Forget about “AI” itself: it’s all about the math, and America is failing to train enough citizens in the right kinds of mathematics to remain dominant.

By Michael Auslin

Continue reading “Why China’s Race For AI Dominance Depends On Math” »

Could a mathematical model help predict future mutations of the coronavirus and guide scientists’ research as they rush to develop an effective vaccine? This is a possibility being considered by researchers at the USC Viterbi School of Engineering—Ph. D. students Ruochen Yang and Xiongye Xiao and Paul Bogdan, an associate professor of electrical and computer engineering.

Over the past year, Yang and Bogdan have worked to develop a model that could be used to investigate the relationship between a network and its parts to find patterns and make predictions. Now, Xiao is applying that successful model to the current pandemic. He is examining the RNA sequence of SARS-CoV-2, also known as coronavirus, to determine whether accurate predictions can be made about how its genetic code might change in the future based on past mutations. This research is still in progress and no conclusions have been reached yet.

Published in Nature Scientific Reports, a sister journal of Nature, Yang and Bogdan’s work is detailed in their paper, “Controlling the Multifractal Generating Measures of Complex Networks.”

Researchers from the UK and Switzerland have found a mathematical means of helping regulators and business police Artificial Intelligence systems’ biases towards making unethical, and potentially very costly and damaging choices.

The collaborators from the University of Warwick, Imperial College London, and EPFL – Lausanne, along with the strategy firm Sciteb Ltd, believe that in an environment in which decisions are increasingly made without human intervention, there is a very strong incentive to know under what circumstances AI systems might adopt an unethical strategy—and to find and reduce that risk, or eliminate entirely, if possible.

Artificial intelligence (AI) is increasingly deployed in commercial situations. Consider for example using AI to set prices of insurance products to be sold to a particular customer. There are legitimate reasons for setting different prices for different people, but it may also be more profitable to make certain decisions that end up hurting the company.

Continue reading “New Mathematical Formula Unveiled to Prevent AI From Making Unethical Decisions” »

Researchers from the University of Warwick, Imperial College London, EPFL (Lausanne) and Sciteb Ltd have found a mathematical means of helping regulators and business manage and police Artificial Intelligence systems’ biases towards making unethical, and potentially very costly and damaging commercial choices—an ethical eye on AI.

In 1911, German mathematician Otto Toeplitz first posed the inscribed square problem, in which he predicted that “any closed curve contains four points that can be connected to form a square,” according to Quanta. For more than a century, it’s remained unsolved.

Updated mathematical techniques that can distinguish between two types of ‘non-Gaussian curve’ could make it easier for researchers to study the nature of quantum entanglement.

Quantum entanglement is perhaps one of the most intriguing phenomena known to physics. It describes how the fates of multiple particles can become entwined, even when separated by vast distances. Importantly, the probability distributions needed to define the quantum states of these particles deviate from the bell-shaped, or ‘Gaussian’ curves which underly many natural processes. Non-Gaussian curves don’t apply to quantum systems alone, however. They can also be composed of mixtures of regular Gaussian curves, producing difficulties for physicists studying quantum entanglement. In new research published in EPJ D, Shao-Hua Xiang and colleagues at Huaihua University in China propose a solution to this problem. They suggest an updated set of equations that allows physicists to easily check whether or not a non-Gaussian state is genuinely quantum.

As physicists make more discoveries about the nature of quantum entanglement, they are rapidly making progress towards advanced applications in the fields of quantum communication and computation. The approach taken in this study could prove to speed up the pace of these advances. Xiang and colleagues acknowledge that while all previous efforts to distinguish between both types of non-Gaussian curve have had some success, their choices of Gaussian curves as a starting point have so far meant that no one approach has yet proven to be completely effective. Based on the argument that there can’t be any truly reliable Gaussian reference for any genuinely quantum non-Gaussian state, the researchers present a new theoretical framework.

Continue reading “Mathematical Breakthrough Makes It Easier to Explore Quantum Entanglement” »

Researchers at Rochester Institute of Technology have developed MathDeck, an online search interface that allows anyone to easily create, edit and lookup sophisticated math formulas on the computer.

Created by an interdisciplinary team of more than a dozen faculty and students, MathDeck aims to make math notation interactive and easily shareable, rather than an obstacle to mathematical study and exploration. The math-aware search interface is free to the public and available to use at mathdeck.cs.rit.edu.

Researchers said the project stems from a growing public interest in being able to do web searches with math keywords and formulas. However, for many people, it can be difficult to accurately express sophisticated math without an understanding of the scientific markup language LaTeX.