You know the routine. You come across a topological space X and you need to find its fundamental group. Unfortunately, X is an unfamiliar space and it's too difficult to look at explicit loops and relations. So what do you do? You look for another space Y that is homotopy equivalent to X and whose fundamental group is much easier to compute. And voila! Since X and Y are homotopy equivalent, you know that the fundamental group of X is isomorphic to the fundamental group of Y. Mission accomplished. Below is a list of some homotopy equivalences which I think are pretty clever and useful to keep in your back pocket for, say, a qualifying exam or some other pressing topological occasion.
The joyous lion of theoretical computer science Boaz Barak is reporting on Avi Wigderson's book Mathematics and Computation which is on Avi's homepage. I read through an earlier version and it is highly recommended! Let me also recommend Avi's earlier survey on interaction between CS and math.
It’s easy to miss the forest for the trees without a comprehensive view of what the proverbial forest looks like. As a result, here's a compiled a list of..
Several weeks ago a friend and I were discussing C++ logging frameworks. He had some issues with his company’s home-made logger, mainly regarding call latenc...
I co-founded PrepMe in 2001. We were one of the first education companies online and the first purely online, personalized platform. We were acquired in 2011 by Providence Equity-backed Ascend Learning. In the last month, I've had 3 VC firms bring me in to chat with their partnership about education and 6 independent entrepreneurs reach out to…
Quite a few people have asked me recently about choosing a GPU for Machine Learning. As it stands, success with Deep Learning heavily dependents on having the right hardware to work with. When I was…
We introduce AlphaGo Zero, the latest evolution of AlphaGo, the first computer program to defeat a world champion at the ancient Chinese game of Go. Zero is even more powerful and is arguably the strongest Go player in history. Previous versions of AlphaGo initially trained on thousands of human amateur and professional games to learn how to play Go. AlphaGo Zero skips this step and learns to play simply by playing games against itself, starting from completely random play. In doing so, it quickly surpassed human level of play and defeated the previously published champion-defeating version of AlphaGo by 100 games to 0.
This expands the range of procedures surgical robots can be involved in, and thus the size of the market. Da Vinci itself has four arms, three of which...
The codebase contains a replica of the AlphaZero methodology, built in Python and Keras. Gain a deeper understanding of how AlphaZero works and adapt the code to plug in new games.
Lately I’ve been writing a game engine in C++. I’m using it to make a little mobile game called Hop Out. Here’s a clip captured from my iPhone 6. (Unmute for …
Applications are open for the ACT Applied Category Theory Research School 2018! And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the method is full…
Precise control of thedistribution of specific proteins is essential for many biological processes. An LMU team has now described a new model for intracellular pattern formation. Here, the shape of the cell itself plays a ...
A simple open-source scene manager, and WavefrontOBJ file loader in C# and OpenGL (OpenTK). Runs on MacOS, Windows, and Linux.; Author: David Jeske; Updated: 27 Dec 2014; Section: OpenGL; Chapter: Multimedia; Updated: 27 Dec 2014
OpenGL 4 with OpenTK in C# Part 1: Initialize the GameWindow; Author: Eowind; Updated: 27 Jan 2017; Section: OpenGL; Chapter: Multimedia; Updated: 27 Jan 2017
Learning how to grow up and be more mature starts with knowing what you truly value. Being an adult means sticking to your values, even when it's not popular or doesn't benefit you.