3 Top Blog Entries Over the Last 7 Days

Integer to Rational Derivate

This image shows Here pushing the property to the limit (example in case n=3): Kudos to Stefano Maruelli on a very cool way make a Sum work its way into a Rational under certain conditions. The idea is to make a Sum capable to rise, for example, the Square of a Rational a=A/K. Of course n-th power representation of a Rational will follow by the same Telescoping Sum Property. Here is his example of a Step Sum capable to rise an Integer (A) and/or a Rational (A/K) Upper Limit, at the condition that Both the Upper and lower Limits are divisible by the Step (K) we choose.

John Morgan's beautiful brain on Riemannian Covariance Matrices

John W. Morgan | Lecture 1 | Introduction to Riemannian geometry, curvature and Ricci flow. Absolutely fantastic lecture by the great John Morgan. John Morgan is a professor of mathematics and founding director of the Simons Center for Geometry and Physics at Stony Brook University. His work is in the areas of geometry and topology. He has concentrated study of manifolds and smooth algebraic varieties. His most recent works include books, jointly with Gang Tian, explaining in detail the proof of the Poincaré conjecture and the geometrization conjecture, both of which concern the nature of three-dimensional spaces. See here.

Rory Lewis UCCS Bachelor of Innovation

Riemannian Covariance Matrices

Not that I am trying to draw in more than 3-Dimenions. But our hypothesis is that a manifold with n-dimenions with clustering could procure a machine learning system to learn different dimenions differently and thus become smart. Photo taken by Eli Brainard UCCS, Feb 6th, 2019. In general, one will find that Riemann distance is better for defining positive semidefinite matrices such as covariance matrices where one wants manifold to be able to retain n-dimenions, than Euclidian distance. To view equations, see larger version of photo here.





Blog Entries Over Time

Rory Lewis Political Engineering Artificial Intelligence

Political Engineering; How Trump's Artificial Intelligence Reshaped the Election Map

Fascinating article in NYT. Edray Goins frequently asked himself whether he was right to factor race into the challenges he faced: “Did it really happen that way, or am I blowing it out of proportion?” Photo. Jared Soares. Fewer than 1 percent of doctorates in math are awarded to African-Americans. Edray Goins, who earned one of them, found the upper reaches of the math world a challenging place. See full article in the New York Times here.

The Unexpected Creates Reward When Listening to Music

If you love it when a musician strikes that unexpected but perfect chord, you are not alone. New research shows the musically unexpected activates the reward centre of our brains, and makes us learn about the music as we listen. Researchers at McGill University put 20 volunteers through a musical reward learning task. Each participant chose a colour, then a direction. Continue @ Neuroscience News here or read the original paper here. Gold, Benjamin P., et al. Musical reward prediction errors engage the nucleus accumbens and motivate learning. Proceedings of the National Academy of Sciences Feb 2019.

Rory Lewis Political Engineering Artificial Intelligence

Political Engineering; How Trump's Artificial Intelligence Reshaped the Election Map

Bostok's amazing bigdata and very cool D3 award winning visualization. Specifically made to interact with artificial intelligence and graphics. This image shows the county shifts from 2012. See full article in the New York Times here.

Model Theory and Proof Theory of Coalgebraic Predicate Logic

Congrats to Tadeusz Litak et al. Generalization of first-order logic originating in a neglected work and show that an entirely general completeness result is NOT possible!

Abstract: We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for several natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, both in comparison with coalgebraic hybrid logics and with existing first-order proposals for special classes of Set-coalgebras (apart from relational structures, also neighbourhood frames and topological spaces). COninue reading here.

>Litak, Tadeusz, et al. "Model Theory and Proof Theory of Coalgebraic Predicate Logic." arXiv preprint arXiv:1701.03773 (2017).

Rory Lewis Political Engineering Artificial Intelligence

Political Engineering; How Trump's Artificial Intelligence Reshaped the Election Map

Bostok's amazing bigdata and very cool D3 award winning visualization. Specifically made to interact with artificial intelligence and graphics. This image shows the shift ijn counties Obama won in 2012.See full article in the New York Times here.

Rory Lewis Political Engineering Artificial Intelligence

Political Engineering; How Trump's Artificial Intelligence Reshaped the Election Map

Bostok's amazing bigdata and very cool D3 award winning visualization. Specifically made to interact with artificial intelligence and graphics. This image shows shifts in counties with populations of 150,000 or more. See full article in the New York Times here.

Rory Lewis Political Engineering Artificial Intelligence

Political Engineering; How Trump's Artificial Intelligence Reshaped the Election Map

Bostok's amazing bigdata and very cool D3 award winning visualization. Specifically made to interact with artificial intelligence and graphics. This image shows where more than 75% are whites with no college degree. See full article in the New York Times here.