## Archive for the ‘mathematics’ category: Page 44

Tailoring and manipulating electromagnetic wave propagation has been of great interest within the scientific community for many decades. In this context, wave propagation has been engineered by properly introducing spatial inhomogeneities along the path where the wave is traveling. Antennas and communications systems in general have greatly benefited from this wave-matter control. For instance, if one needs to re-direct the radiated field (information) from an antenna (transmitter) to a desired direction and reach a receiving antenna placed at a different location, one can simply place the former in a translation stage and mechanically steer the propagation of the emitted electromagnetic wave.

Such beam steering techniques have greatly contributed to the spatial aiming of targets in applications such as radars and point-to-point communication systems. Beam steering can also be achieved using metamaterials and metasurfaces by means of spatially controlling the effective electromagnetic parameters of a designed meta-lens antenna system and/or using reconfigurable meta-surfaces. The next question to ask: Could we push the limits of current beam steering applications by controlling electromagnetic properties of media not only in space but also in time (i.e., 4D metamaterials x, y,z, t)? In order words, would it be possible to achieve temporal aiming of electromagnetic waves?

In a new paper published in Light Science & Applications, Victor Pacheco-Peña from the School of Mathematics, Statistics and Physics of Newcastle University in UK and Nader Engheta from and Department of Electrical and Systems Engineering of the University of Pennsylvania, USA have answered this question by proposing the idea of temporal metamaterials that change from an isotropic to an anisotropic permittivity tensor. In this concept, the authors consider a rapid change of the permittivity of the whole medium where the wave is traveling and demonstrated both numerically and analytically the effects of such a temporal boundary caused by the rapid temporal change of permittivity. In so doing, forward and backward waves are produced with wave vector k preserved through the whole process while frequency is changed, depending on the values of the permittivity tensor before and after the temporal change of permittivity.

A video on Youtube claims a forecast of near-Earth objects (NEOs) shows one of these may hit Earth in November.

On November 2, 2020 an object labeled 2018 VP1″ is currently projected to come very close to Earth. The video is a little off on its math. Even so, Mike Murray of the Delta College Planetarium in Bay City, says don’t worry.

The snake bites its tail

Google AI can independently discover AI methods.

Then optimizes them

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.

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.

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.

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.

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