From e09bde2cbd8f3bd8de9efe60ce89c5de63366653 Mon Sep 17 00:00:00 2001
From: Gaspard Jankowiak <gaspard.jankowiak@uni-graz.at>
Date: Wed, 24 Apr 2024 11:17:52 +0200
Subject: [PATCH] [numerics] markdownify a bit

---
 en/numerics/FJMT.2024/index.md | 47 +++++++++++++++++++++++-----------
 1 file changed, 32 insertions(+), 15 deletions(-)

diff --git a/en/numerics/FJMT.2024/index.md b/en/numerics/FJMT.2024/index.md
index 29d67f1..102c72e 100644
--- a/en/numerics/FJMT.2024/index.md
+++ b/en/numerics/FJMT.2024/index.md
@@ -9,38 +9,55 @@ math: true
 {% assign sigma_array = "0.001, 0.002, 0.004, 0.012" | split: ", " %}
 {% assign mu_array = "0.001, 0.005, 0.01, 0.05, 0.20833333333333334, 0.36666666666666664, 0.525, 0.6833333333333333, 0.8416666666666667, 1.0" | split: ", " %}
 {% assign prefix = "/s/numerics/FJMT.2024/plots_23_04_2024/results/LFR_separated/N_micro=1000,N_mfl=301" %}
+{% assign prefix = "https://gaspard.janko.fr/s/numerics/FJMT.2024/plots_23_04_2024/results/LFR_separated/N_micro=1000,N_mfl=301" %}
 {% for sigma in sigma_array %}
 
-<style>.manual_center_1500 { margin-left: -367px; }</style>
+<style>
+.manual_center_1500 { margin-left: -367px; margin-top: 1em; width: 1500px; height: 750px; }
+h3 { margin-top: 1em; margin-bottom: 0.5em; font-size: 110%; }
+p { margin-top: 1em; }
+</style>
 
 <h2>$β$ distribution with $σ² = {{sigma}}$</h2>
-<h4 id="LFR301_var=0.001_movies">Movies (ensemble averages)</h4>
-{% for mu in mu_array -%}
-<a href="{{ prefix }}/σ²={{ sigma }}/μ={{ mu }}/movie_without_g.mp4">μ={{ mu | round: 4 }}</a>{% unless forloop.last %} · {% endunless -%}
+<h3 id="LFR301_var=0.001_movies">Movies (ensemble averages)</h3>
+
+|----------|
+| R1 {% for mu in mu_array -%}
+| [μ={{ mu | round: 4 }}]({{ prefix }}/σ²={{ sigma }}/μ={{ mu }}/movie_without_g.mp4){% if forloop.last -%} | {% endif -%}
 {% endfor %}
 
 <h3 id="LFR301_var=0.001_graphs">Graphs</h3>
+
+|----------|
 {% for run in (1..5) -%}
-<p>
-  Run {{ run }}:
-  {% for mu in mu_array -%}
-  <a href="{{ prefix }}/σ²={{ sigma }}/μ={{ mu }}/micro-{{ run }}/graph_LFR.png">μ={{ mu | round: 4 }}</a>{% unless forloop.last %} · {% endunless -%}
+| R{{ run }} {% for mu in mu_array -%}
+| [μ={{ mu | round: 4 }}]({{ prefix }}/σ²={{ sigma }}/μ={{ mu }}/micro-{{ run }}/graph_LFR.png){% if forloop.last -%} | {% endif -%}
   {% endfor %}
-</p>
 {% endfor %}
-<h4>Dynamics</h4>
 
-<img src="{{ prefix }}/σ²={{ sigma }}/comparison.svg" height="750" width="1500"/>{:.manual_center_1500}
+<h3>Dynamics</h3>
 
-<h4>Graph properties</h4>
-<img src="{{ prefix }}/σ²={{ sigma }}/graph_analysis.svg" height="750" width="1500" />{:.manual_center_1500}
+Convergence rates are computed over the time span marked in blue in the first plot.
 
-<h4>g(t=0), 1 row per run, p increasing →</h4>
+**Parameters:**
+
+- $\mu$: LFR mixing parameter
+- $T^*$: time to consensus = $-1/\log(\vert\lambda_2\vert) \cdot \delta t$, where $\lambda_2$ is the second largest eigenvalue of the transition matrix for the associated time discrete model. See [here](https://doi.org/10.1016/j.ins.2019.02.028).
+- [assortativity](https://en.wikipedia.org/wiki/Assortativity)
+- [clustering coeff.](https://en.wikipedia.org/wiki/Clustering_coefficient)
+
+
+![convergence]({{ prefix }}/σ²={{ sigma }}/comparison.svg){:.manual_center_1500}
+
+<h3>Graph properties</h3>
+![graph metrics]({{ prefix }}/σ²={{ sigma }}/graph_analysis.svg){:.manual_center_1500}
+
+<h3>g(t=0), 1 row per run, p increasing →</h3>
 <div class="form">
   <label>Brightness: </label><input id="slider_LFR301_var={{ sigma }}" type="range" min="1"
     max="10" value="1" step="1" /><span id="brightness_LFR301_var={{ sigma }}">1</span>
 </div>
-<img id="g_init_LFR301_var={{ sigma }}" src="{{ prefix }}/σ²={{ sigma }}/g_init_montage.png" width="1500" />{:.manual_center_1500}
+<img src="{{ prefix }}/σ²={{ sigma }}/g_init_montage.png" id="g_init_LFR301_var={{ sigma }}"/>{:.manual_center_1500}
 
 {% endfor %}