前幾天去廈門開會（DDAP10），全英文演講加之大家口音都略重，說實話聽演講主要靠看ppt，摘出一篇聽懂的寫篇部落格紀念一下吧。

11.2 Session-A 13:30-18:00 WICC G201

主要講了他的兩個工作，一個是重構的工作，一個是預測的工作，分別發表在PRE和PNAS上。

第一篇工作

Detection of time delays and directional interactions based on time series from complex dynamical systems

ABSTRACT

Data-based and model-free accurate identification of intrinsic（固有） time delays and directional interactions.

METHOD

Given a time series $x(t)$, one forms a manifold（流形） $M_{}$

CME method:

Say we are given time series $x(t)$ and $y(t)$ as well as a set of possible time delays: $\Gamma = \{\tau_1,\tau_2, … ,\tau_m\}$. For each candidate time delay $\tau_i$, we let $z(t) = x(t − \tau_i)$ and form the manifolds $M_Y$ and $M_Z$ with $n_y$ and $n_z$ being the respective embedding dimensions. For each point $Y(\hat{t}) \in M_Y$ , we find $K$ nearest neighbors $Y(t_j)(j = 1,2, …,K)$, which are mapped to the mutual neighbors $Z(t_j) \in M_Z(j = 1,2, …,K)$ by the cross map. We then estimate $Z(t)$ by averaging these mutual neighbors through $\hat{Z}(\hat{t})|M_Y=(1/K)\sum^K_{j=1}Z(t_j)$. Finally, we define the CME score as

$s(\tau)=(n_Z)^{-1}trace(\Sigma_{\hat{Z}}^{-1}cov(\hat{Z},Z)\Sigma_Z^{-1})$

It is straightforward to show $0\leq s\leq 1$. The larger the value of $s$, the stronger the driving force from $x(t−\tau)$ to $y(t)$. In a plot of $s(\tau)$, if there is a peak at $\tau_k\in \Gamma$, the time delay from $X$ to $Y$ can be identified as $\tau_k$.
可以理解為如果 $x$是以延遲 $\tau_k$作用於 $y$，那麼當 $y$的情況（ $Y$）類似時， $\tau_k$之前的 $x$（也就是 $z$）的情況( $Z$)也應該類似（協方差大，相關性強），形式上和pearson相關係數一樣。

RESULTS

To validate our CME method, we begin with a discrete-time logistic model of two non-identical species:

$X_{t+1}=X_t(\gamma_x-\gamma_xX_t-K_1Y_{t-\tau_1})$