96 lines
3.7 KiB
Markdown
96 lines
3.7 KiB
Markdown
---
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layout: default
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lang: en
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subtitle: FJMT.2024 / 23 April 2024
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math: true
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---
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# Lancichinetti-Fortunato-Radicchi (N_mfl = 301)
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{% assign sigma_array = "0.001, 0.004, 0.012" | split: ", " %}
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{% assign mu_array = "0.001, 0.005, 0.01, 0.05, 0.5" | split: ", " %}
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{% assign prefix = "https://gaspard.janko.fr/s/numerics/FJMT.2024/plots_23_04_2024/results/LFR_single_graph/N_micro=1000,N_mfl=301" %}
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<style>
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.manual_center_1500 { margin-left: -367px; margin-top: 1em; width: 1500px; height: 750px; }
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.manual_center_510 { margin-left: 128px; margin-top: 1em; width: 510px; height: 510px; }
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h3 { margin-top: 1em; margin-bottom: 0.5em; font-size: 110%; }
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p { margin-top: 1em; }
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.form { display: flex; align-items: center; margin-bottom: 0.5em; }
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.form input { margin-right: 1em; margin-left: 1em; }
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</style>
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This page shows the differences in the dynamics between the microscopic and the kinetic (meanfield) model for Lancichinetti-Fortunato-Radicchi (LFR) type graphs,
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depending on two parameters:
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- $\sigma^2$, which is the variance of the $\beta$ distributions making up the initial distribution $f$,
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- $\mu$, the so-called mixing parameter for the construction of the LFR graphs.
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{:width="750"}
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<h3 id="LFR_graphs">Graphs</h3>
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|----------|
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| {% for mu in mu_array -%}
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| [μ={{ mu | round: 4 }}]({{ prefix }}/reference/μ={{ mu }}/graph_LFR.png){% if forloop.last -%} | {% endif -%}
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{% endfor %}
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{% for sigma in sigma_array %}
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<h2>$β$ distribution with $σ² = {{sigma}}$</h2>
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<h3 id="LFR301_var=0.001_movies">Movies (ensemble averages)</h3>
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|----------|
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| R1 {% for mu in mu_array -%}
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| [μ={{ mu | round: 4 }}]({{ prefix }}/σ²={{ sigma }}/μ={{ mu }}/movie_without_g.mp4){% if forloop.last -%} | {% endif -%}
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{% endfor %}
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<h3>Dynamics</h3>
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Convergence rates are computed over the time span marked in blue in the first plot.
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**Parameters:**
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- $\mu$: LFR mixing parameter
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- $T^*$: 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).
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- [assortativity](https://en.wikipedia.org/wiki/Assortativity)
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- [clustering coeff.](https://en.wikipedia.org/wiki/Clustering_coefficient)
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{:.manual_center_1500}
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<h3>Graph properties</h3>
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{:.manual_center_1500}
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<h3>g(t=0), 1 row per run, p increasing →</h3>
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<div class="form">
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<label>Brightness: </label><input id="slider_LFR301_var={{ sigma }}" type="range" min="1"
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max="10" value="1" step="1" /><span id="brightness_LFR301_var={{ sigma }}">1</span>
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<input id="check_LFR301_var={{ sigma }}" type="checkbox">
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<label>Invert </label>
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</div>
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<img src="{{ prefix }}/σ²={{ sigma }}/g_init_montage.png" id="g_init_LFR301_var={{ sigma }}"/>{:.manual_center_510}
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{% endfor %}
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<script>
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const tags = [
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{% for sigma in sigma_array %}
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"LFR301_var={{ sigma }}",
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{% endfor %}
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];
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tags.forEach((tag) => {
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const slider = document.getElementById("slider_" + tag);
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const check = document.getElementById("check_" + tag);
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const img = document.getElementById("g_init_" + tag);
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const disp = document.getElementById("brightness_" + tag);
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update = () => {
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disp.textContent = slider.value;
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const i_val = check.checked ? "100%" : "0%";
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const new_value = slider.value;
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const new_filter_value = `brightness(${new_value}) invert(${i_val})`
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img.style.filter = new_filter_value;
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}
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slider.addEventListener("input", update);
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check.addEventListener("change", update);
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})
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</script>
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