Given a set of distinct integers, S, return all possible subsets.
Note:
For example, If S = [1,2], a solution is:
| List | |
| -------------- | |
| * Statistics - MCMC | |
| * Statistics - One long run vs Many short runs | |
| * CS - Non-backtracking | |
| * CS - Tree Sampling vs Graph Sampling | |
| * Other things | |
| Non-backtracking RW | |
| ===================== | |
| Preview URL: | |
| http://bit.ly/16U4JHf | |
| Basic Idea | |
| ------------- | |
| 1. Push $P'(e_{ij}, e_{jk}) \geq P(j,k) $ |
| Knockout Client for Meteor | |
| ============== | |
| [**Knockout**](http://knockoutjs.com/) is a JavaScript MVVM (a modern variant of MVC) library that makes it easier to create rich, desktop-like user interfaces with JavaScript and HTML. It uses observers to make your UI automatically stay in sync with an underlying data model, along with a powerful and extensible set of declarative bindings to enable productive development. | |
| ### Install | |
| ```bash | |
| mrt add knockout-client |
| knockout-client-pager | |
| ============== | |
| pager.js is a JavaScript library based on KnockoutJS and jQuery that provides the possibility of creating single page applications in a declarative fashion - nesting subpages inside subpages where each subpage can be developed standalone but still communicate between each other. | |
| Combined with Meteor, pager.js provide us with a complete and robust client side routing framework. For more details, see pager.js official [demo](http://pagerjs.com/demo/). | |
| ### Install | |
| ```bash |
| ## Using random initial nodes | |
| #### Divide the groups into two arbitrary groups | |
| as733: | |
|  |
| ## Using random groups without memorized | |
| as733: | |
|  |
| ## Groups divided by degree | |
| #### Procedure | |
| 1. Sort neighbors according to their degree | |
| 2. Divide these neighbors into first half and last half (i.e. a group of lower degree nodes and a group of higher degree nodes) | |
| 3. Jump from one group to another if possible |
| ## Experimental results 8.31 | |
| #### Graph explanation | |
| Each point in the graph is the average of 5000 runs. It took about two days to generate one graph. Former results are only 500 runs. | |
| #### Observation: |
| # Note | |
| ### Preliminaries | |
| * Definition of asymptotic variance of the estimator $\hat{\mu_n}=\frac{1}{n}\sum_{t=1}^nf(X_t)$ is | |
| $$V_{\infty}(\hat{\mu}) = \lim_{n\rightarrow\infty}nV(\hat{\mu_n}) $$ | |
| ### 1) Peskun's theorem on modifying a reversible chain to avoid staying in the same state | |
| _**Theorem 1 (Peskun 1973):** Let $X_1, X_2, \dots$ and $X'_1, X'_2, \dots$ be two irreducible Markov Chain on the finite state space $\mathcal{X}$, both of which are reversible with respect to the distribution $\pi$, and hence have $\pi$ as their unique invariant distribution. Let the transition probabilities for these chains be_ |