© XY 2020 ... You are unauthorized to view this page. Username Password Remember Me Forgot Password


Can you solve this puzzle? #8
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #7
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #6
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #5
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #4
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #3
© XY 2020 ... You are unauthorized to view this page.

Can you solve this puzzle? #2
© XY 2020 ... You are unauthorized to view this page.

Strictly Monotone Weight Functions on Directed Graphs
OUTLINE Introduction General Definitions When can any weight function be turned into a strictly monotone weight function? Weighted Directed Graphs in Applications Autonomous Driving Quantum Walks Artificial Neural Networks SUMMARY: We define a directed graph as a space with any binary relation, and we define a strictly monotone weight function on any directed graph. We prove when no weight function on a directed graph can be turned into a strictly monotone weight function, and we give a characterization of any strictly monotone weight function. Finally, we mention the use of weighted directed graphs in autonomous driving research, quantum information, and deep learning. Introduction Here is an example…

Topological Manifolds
OUTLINE Introduction A generalization to infinite dimension Is there any relationship between an infinitedimensional manifold and a finitedimensional manifold? Manifolds in applications Infection dynamics Topological data analysis Riemannian manifold optimization software library SUMMARY: We define a manifold of an infinite dimension, which is an extension of a finitedimensional manifold, and we show in what sense an infinitedimensional manifold is related to any finitedimensional manifold. We then mention the use of manifolds in applications. Introduction Given any point $x$ on the surface of a sphere and any circle drawn around $x$, the region inside the circle approaches the shape of a 2dimensional ``flat'' disk as the circle gets smaller. The…