8️⃣ And if you want more, we also have a connectome-based reservoir computing toolbox (conn2res) and mini-review:

www.nature.com/articles/s41...

7️⃣ Altogether, across multiple benchmarks, we show that hierarchical modularity endows networks with computationally advantageous properties, providing insight into the relationship between neural network structure and function.

Code: github.com/netneurolab/...

6️⃣ So far, we considered considered synthetic graphs, but what about real brains?

We implement dMRI brain networks as reservoirs. Again, hierarchical modularity positively contributes to computational performance.

Amazingly, reservoir timescales correlate with empirical timescales derived from MEG.

5️⃣ How well do these networks perform multiple tasks simultaneously? We assign memory tasks to half the modules, and non-linear transformation tasks to the other half.

Again, we find that higher-order hierarchical modular networks consistently outperform their lower-order counterparts.

4️⃣ To uncover the topological underpinnings of these differences in dynamics, we consider the motif composition of the reservoir.

More complex motifs containing at least three edges are all enriched in higher-order hierarchical modular networks, supporting more complex computations.

3️⃣ How does hierarchical modularity shape dynamics to improve memory? We compute timescales from nodal time series at criticality.

Higher-order hierarchical modular reservoirs show more variability in timescales, yielding a bigger pool of timescales and richer temporal expansion of input signals.

2️⃣ We start by evaluating the reservoir’s ability to preserve representations of past stimuli with the widely used memory capacity task.

Higher-order hierarchical modular networks consistently perform best, particularly at criticality.

1️⃣ We use stochastic block models to generate synthetic multi-level hierarchical modular networks.

We then implement them as reservoirs to evaluate their cognitive capacity.

5️⃣

Huge thanks to Sanjay Kalra and the CALSNIC team, J Hansen, @vincebaz.bsky.social @goliashf.bsky.social L Collins @dadarmahsa.bsky.social @alaindagher.bsky.social !!

code: github.com/netneurolab/...

8️⃣ Finally, we consider spinal- and bulbar-onset subtypes. Epicenters in spinal-onset are mainly in primary motor cortex and paracentral lobule. In bulbar-onset, epicenters are prominent in lower paracentral gyrus and inferior frontal gyrus, aligning with the clinical presentation of the subtypes.

7️⃣ If cortical epicenters reflect the spatial focus of ALS pathology, do they also correlate with the clinical manifestation? Indeed: epicenter maps are correlated with poor motor function, including abnormal index finger and foot tapping scores, daily physical function, and muscle tone.

6️⃣ We next ask whether the network epicenters of ALS atrophy are enriched for specific biological processes, cellular components, and cell types.

5️⃣ We next investigate whether spreading is more likely between regions that share biological features, including (1) gene expression, (2) neurotransmitter receptors, (3) laminar differentiation, (4) metabolism, and (5) hemodynamics.

4️⃣ We apply two methods to back-reconstruct the spreading trajectory and infer the most likely cortical location of the epicenter: (1) a network-based node ranking method, and (2) a susceptible-infected-removed (SIR) dynamical model.

Epicenter rankings are consistent with ALS pathological staging.

3️⃣ We next assess the extent to which the spatial patterning of atrophy is related to structural connectivity.

Regional atrophy is correlated with the mean atrophy of its structurally connected neighbours, consistent with the notion of network spread of pathology.