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--- attic:dynstat [2019/08/30 14:57] – chunchung
+++ attic:dynstat [2022/05/21 16:00] (current) – [2018-07-02] chunchung
@@ Line 1: / Line 1: @@
-====== Statistical Modeling for Dynamics of Biological Systems ======
+====== Statistical Approaches to Structure and Activities of Dynamic Systems ======
-Multi-channel dynamical data is segmented into binary state configurations $\left\{\sigma_i\right\}$. The occurrence of the states is assumed to follow Boltzmann distribution \[P\left(\left\{\sigma_i\right\}\right) \propto e^{-E\left(\left\{\sigma_i\right\}\right)}.\] With unlimited amount of data, this distribution can be used to define the energy for each state.
+We will use a [[dynstat:glass|spin-glass model]] to understand the relationship between structure and dynamics. The major goal is to establish a formal approach for inferring the internal structure of a system given its observed dynamics.
+===== Short term questions and tasks =====
+==== 2018-05-24 ====
+  - Given $\langle J\rangle$ and $\Delta J$, characterize resultant dynamics with eigenvalues $\lambda_n$ of covariance or correlation matrix $C$.
+  - How much are the eigenvalues influenced by the realized coupling configuration? (With an ensemble created with different seeds of random number generator, do the eigenvalues change significantly? What are their variances?)
+  - Fit the eigenvalues with $$\lambda_n\sim n^{-\alpha}.$$ Perform systematic calculations to find the relationship between $\alpha$ and $\langle J\rangle$, $\Delta J$.
+  - Are there other ways to characterize the activity data beside $\alpha$?
+  - Fixing $\langle J\rangle$ and $\Delta J$, does forms of the distribution $P(J)$ influence $\alpha$? For example, does having a long tail matters?
+==== 2018-05-30 ====
+Showing results in [[[[playground:results-2018-05-25|results-2018-05-25]].
+==== 2018-07-02 ====
+[[[[jy:results|results]]