Merge pull request #164 from marscher/nb56_review

[nb05] motivate pcca usage, destinct hmm

Author: cwehmeyer

notebooks/05-pcca-tpt.ipynb

@@ -8,7 +8,13 @@
     "\n",
     "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons Licence\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" title='This work is licensed under a Creative Commons Attribution 4.0 International License.' align=\"right\"/></a>\n",
     "\n",
-    "In this notebook, we will cover how to use PCCA++ to extract a coarse representation of the MSM. We will further investigate how to use TPT to follow the pathways of the processes.\n",
+    "In this notebook, we will cover how to use PCCA++ to extract a coarse representation of the MSM. We will further investigate how to use transition path theory (TPT) to follow the pathways of the processes.\n",
+    "When we want to analyze pathways, models with fewer states are more often desirable, since these are easier to understand. PCCA allows us to assign the microstates directly to metastable macrostates and TPT uses this group assignment to compute fluxes and pathways. \n",
+    "\n",
+    "\n",
+    "Another method to get a model with viewer states are hidden Markov state models (HMM), introduced in notebook 07 [➜ 📓](07-hidden-markov-state-models.ipynb). In contrast to computing memberships of microstates to meta stable sets as in PCCA, in HMMs we directly obtain a model with viewer states.\n",
+    "\n",
+    "\n",
     "Here you can find literature on the used methods:\n",
     "\n",
     "- <a id=\"ref-1\" href=\"#cite-pcca_plus_plus\">roeblitz-weber-14</a>\n",
@@ -45,7 +51,7 @@
    "metadata": {},
    "source": [
     "## Case 1: preprocessed, two-dimensional data (toy model)\n",
-    "We start by loading the data and the previously analyzed MSM from disk:"
+    "We start by loading the data and the previously analyzed MSM  (estimated in notebook 04 [➜ 📓](04-msm-analysis.ipynb)) from disk:"
    ]
   },
   {
@@ -67,7 +73,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We currently have an MSM with 50 discrete states which was validated for two metastable states in the previous notebook. Internally, the metastable states have been computed using the Perron Cluster Cluster Analysis (PCCA++) method <a id=\"ref-4\" href=\"#cite-pcca_plus_plus\">roeblitz-14</a>. Let's analyze this in more detail here. We can explicitly compute it by calling `msm.pcca()`:"
+    "We currently have an MSM with 50 discrete states which was validated for two metastable states in the previous notebook. Internally, the metastable states have been computed using the Perron Cluster Cluster Analysis (PCCA++) method <a id=\"ref-4\" href=\"#cite-pcca_plus_plus\">roeblitz-14</a>. Let's analyze this in more detail here. We can explicitly compute it by calling `msm.pcca()`."
    ]
   },
   {
@@ -259,6 +265,7 @@
     "bayesian_msm = pyemma.load('nb4.pyemma', model_name='ala2_bayesian_msm')\n",
     "cluster = pyemma.load('nb4.pyemma', model_name='ala2_cluster')\n",
     "\n",
+    "# not to be used in MSM estimation (artificical transitions between individual trajectories)!\n",
     "dtrajs_concatenated = np.concatenate(cluster.dtrajs)"
    ]
   },
@@ -314,7 +321,9 @@
    "source": [
     "PCCA++ nicely separates the high-density regions and we find that each of the basins was assigned a metastable set. This indicates that our projection indeed describes the slow dynamics.\n",
     "\n",
-    "We concatenate all three discrete trajectories and obtain a single trajectory of metastable states which we use to visualize the metastable state memberships of all datapoints. We further compute the state with the highest membership to a PCCA metastable state to plot a state label there:"
+    "We concatenate all three discrete trajectories and obtain a single trajectory of metastable states which we use to visualize the metastable state memberships of all datapoints. We further compute the state with the highest membership to a PCCA metastable state to plot a state label there.\n",
+    "\n",
+    "⚠️ Note that the concatenated discrete trajectories (dtrajs) are not meant to be used for MSM estimation (artificial transitions), but only for visualization and indexing purposes ⚠️"
    ]
   },
   {
@@ -938,7 +947,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.6.6"
   },
   "toc": {
    "base_numbering": 1,

notebooks/06-expectations-and-observables.ipynb

@@ -53,7 +53,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Case 1: preprocessed, two-dimensional data (toy model)"
+    "## Case 1: preprocessed, two-dimensional data (toy model)\n",
+    "\n",
+    "Again we estimate the MSM for the two-dimensional toy model to perform further analysis on."
    ]
   },
   {
@@ -898,7 +900,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.6.6"
   },
   "toc": {
    "base_numbering": 1,