/explore
|
You are here 
|
fabricebaudoin.blog | ||
| | | | |
pfzhang.wordpress.com
Consider a smooth one-parameter family $latex {f_t}$ of diffeomorphisms on a manifold $latex M$. It is a flow if $latex f_0(x)=x$ and $latex f_{t}\circ f_{s}(x) = f_{s+t}(x)$ for every $latex x\in M$, , $latex t ,s \in \mathbb{R}$. Set $latex X(x)=\lim\limits_{h\to 0} \frac{1}{h}(f_h(x) - x)$. This generates a vector field $latex X: M \to TM$.... |
|
| | | | | ||
| | | | |
wildtopology.com
Let $latex C_n$ be the circle of radius $latex 1/n$ centered at $latex (1/n,0)$ with basepoint $latex b_0=(0,0)$. Let $latex \mathbb{E}_o=\bigcup_{k\in\mathbb{N}}C_{2k-1}$ be the odd circles of the earring space and $latex \mathbb{E}_e=\bigcup_{k\in\mathbb{N}}C_{2k}$ be the even circles so that the union $latex \mathbb{E}=\mathbb{E}_o\cup \mathbb{E}_e$ is the usual earring space and $latex \mathbb{E}_o\cap \mathbb{E}_e=\{b_0\}$. Embed $latex \mathbb{E}\subseteq... |
|
| | | | | ||
| | | | |
mikespivey.wordpress.com
The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... |
|
| | | | | ||
| | | | |
aria42.com
Numerical optimization is at the core of much of machine learning. In this post, we derive the L-BFGS algorithm, commonly used in batch machine learning applications. |
|
| | | |||
