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，摘出一片聽懂的寫篇部落格紀念一下吧。

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

Time	Speaker	No.	Title
14:30-15:00	Wei Lin	ST-07	Dynamical time series analytics: From networks construction to dynamics prediction

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） $M_X\in R^n$ based on delay coordinate embedding: $X(t) = [x(t),x(t − \delta t), . . . ,x(t − (n − 1)\delta t)]$, where $n$ is the embedding dimension and $\delta$

t\delta t is a proper time lag.

CME method (detect time delay): Say we are given time series $x(t)$ and $y(t)$ as well as a set of possible time delays: KaTeX parse error: Unexpected character: '' at position 7: \Gamma̲ = {\tau_1,\tau…. For each candidate time delay $\tau_i$, we let $z$

(t)=x(t−τi)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

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

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）。

RESULTS

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

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

$Y_{t+1}=Y_t(\gamma_y-\gamma_yY_t-K_2X_{t-\tau_2})$

where $\gamma_x=3.78, \gamma_y = 3.77$, $K_1$ and $K_2$ are the coupling parameters, and $\tau_1$ and $\tau_2$ are the intrinsic time delays that we aim to determine from time series. 後面也舉了幾個微分方程的例子。 疑問：他所舉例都是兩個節點的連線，並沒有把方法運用到網路中。