Stimulating Cultures

June 9, 2022

As of last week, I have a new preprint on arXiv.

First of all, I want to thank the amazing team who worked on this project, especially Hideaki, Johannes and Jordi who had to endure grumpy me during countless group meetings (and a bunch of extra ones). Seriously, thanks guys!

Brains are modular and cultures should be, too!

When presenting this in talks, I start by explaining that it would be cool to have neuronal cultures that well represent the living brain. However, as most of you probably know, cultures do their own thing and tend to be bursty—where occasional, rather short and synchronous events of high activity (bursts) take turns with extended episodes of silence. In 2018, Hideaki and his lab managed to limit these bursts (which usually light up the whole system) to sub-parts of the culture. They achieved this by making the topology of the cultures modular, effectively making it harder for a local burst to propagate to other modules. Thus, the effect was strongest when modules were at the brink of being disconnected from one another. Although individual modules still show the burst-like dynamics, the dynamics of the whole system are less synchronized, getting much closer to real-brain dynamics.

Brains are busy places.

Looking for another aspect that real brains have and cultures lack, we started to consider background noise. Think of it: Brains are constantly exposed to sensory stimuli, which tend to make their way into the dynamics one way or another, leading to an omnipresent (noisy) baseline activity of all neurons. On the other hand, cultures sit around in a glass dish, and although they perceive more of their environment than we usually expect, they do not have much to do. Hence, in this work we stimulated the cultures in a random and asynchronous manner. Adding such an asynchronous input reduced synchrony further than modularity alone.

We then used simulations of LIF-Neurons (using the awesome Brian2 simulator) and developed a minimal, mean-field like model to explain the reduced synchrony under stimulation. Unexpectedly, the noisy input that makes neurons fire sporadically depletes the average synaptic resources in modules. This can best be seen when considering module-level trajectories in the Rate-Resource plane, as you can see on the right-hand side in the clip below. For long times, when no module-level burst occurs, resources recover and firing-rates are low. Once charged enough, a burst occurs and resources discharge rapidly as the modules’ neurons fire at high rate.

As you might guess from the clip, the noisy input does not only deplete the average amount of synaptic resources, it also lowers the minimum amount of resources needed to start module-level bursts (increasing their frequency). Now, due to the inhomogeneous degree distributions that are caused by the modular architecture (few axons connect across modules, but many axons connect within) the input-driven resource depletion affects the activations across modules more than within. Thus, module-level bursts persist but system-wide synchronization is reduced.

Links

• Our preprint on arXiv
• Yamamoto et al., Impact of modular organization on dynamical richness in cortical networks
• Zierenberg et al., Homeostatic Plasticity and External Input Shape Neural Network Dynamics
• Brian2, A clock-driven simulator for spiking neural networks
• All my code for simulations and analysis is already on github, check back here once we are out of peer review :)

About color

Nov 12, 2020

I was looking for suitable color maps the other day when trying to squeeze too much data into a plot. Usually I prefer to just remove some details for the sake of clarity, but even then, color matters.

Procrastinating away the afternoon, I stumbled upon this super nice article on color palettes by Samantha Zhang. She gives a comprehensive overview of aspects to consider when picking colors, such as how to make your plots accessible to colorblind readers. Best of all, she provides a long list of resources, links and tools that help with the process.

Since then, Samantha’s article became my go-to resource on color in data science, and I am currently testing out three of her color maps in a paper draft. Below you find a python snippet to mimic them in matplotlib.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap

custom_cmaps = dict()
custom_cmaps["cold"] = [
    (0, "white"),
    (0.25, "#DCEDC8"),
    (0.45, "#42B3D5"),
    (0.75, "#1A237E"),
    (1, "black"),
]
custom_cmaps["hot"] = [
    (0, "white"),
    (0.3, "#FEEB65"),
    (0.65, "#E4521B"),
    (0.85, "#4D342F"),
    (1, "black"),
]
custom_cmaps["pinks"] = [
    (0, "white"),
    (0.2, "#FFECB3"),
    (0.45, "#E85285"),
    (0.65, "#6A1B9A"),
    (1, "black"),
]

def cmap_for_mpl(colors, n_bins=512):
    return LinearSegmentedColormap.from_list("custom_cmap", colors, N=n_bins)

# for functions that use color map objects
cmap = cmap_for_mpl(custom_cmaps["pinks"])

# or to get discrete color values, call cmap() with a value between 0 and 1
num_lines = 5
for idx in range(num_lines):
    clr = cmap((idx + 1) / (num_lines + 1))
    x = np.arange(100)/np.pi
    plt.axis('off')
    plt.plot(x, np.sin(x + idx*np.pi/4) + idx, label=idx, color=clr)

Links

• Samantha’s article
• Colormaps in matplotlib
• Colormaps in seaborn
• Creating custom colormaps in matplotlib

COVID-19 Inference and Forecast

How Effective are Interventions?

May 17, 2020

Our paper about estimating the effects of governmental interventions on the spread of COVID-19 is now out in Science!

Over the past months, my colleagues and I have worked on modeling the COVID-19 spread in Germany. Our approach uses Bayesian inference and Markov-Chain Monte-Carlo sampling on an SIR-model to find epidemiological parameters. It allows us to identify change points in the spreading rate (that is, when and how much the spreading rate changes). Check the links below for all the details!

[Science] [ArXiv] [GitHub]

I want to take the opportunity to thank everyone involved for this amazing collaboration. This has been, and still is, a truly great team effort. I feel that we have made a valuable contribution, and for me personally, the project made quarantine and working from home much more enjoyable! Thanks guys!

Website Content from Markdown

May 15, 2020

Time to celebrate, this is my first content that uses the new format.

For a while I have been noticing that it feels too cumbersome to add content to this site; writing is hard and it is harder when you do it in html. Then there is markdown, which feels completely opposite. It is convenient, easy to read and easy to write in any editor. You can even write a paper with colleagues in real time, without ever leaving your browser. Seriously, if you are not familiar with markdown yet, let me recommend spending a few minutes of procrastination to check it out.

Considering the goal to get markdown files onto my custom site, the only hurdle was to render the .md files to html. First, I considered parsing only once before uploading everything so that page loads remain snappy. Then I realized that parsing an average document takes less than 10ms and ended up using Parsedown, a render in php. This allows me to simply drop the .md files into a folder on the server, php fetches them and parsedown creates the html for every file.

See this snippet of php:

foreach (glob("folder_with_markdown_files/*.md") as $file) {
    $html = Parsedown::instance()->text(file_get_contents($file));
    echo "<hr><div class='markdown'>";
    echo $html;
    echo "</div>";
}

Related things to check out

• Parsedown, fast php markdown parser
• Marked 2, great markdown previewer on macOS
• CodiMD, real-time markdown editor, in the browser
• Markdown Cheatsheet