Brain networks (Chair: EMMA TOWLSON)

It is well known that synchronization patterns and coherence play a major role in the functioning of brain networks,both in pathological and in healthy states [1]. In particular, in the perception of sound, one can observe an increase incoherence between the global dynamics in the network and the auditory input [2]. Here we show that synchronizationscenarios are determined by a fi ne interplay between network topology, the location of the input, and frequencies of thesecortical input signals [3]. To this end, we analyze the infl uence of an external stimulation in a network of FitzHugh-Nagumo oscillators with empirically measured structural connectivities, and discuss diff erent areas of cortical stimulation, including the auditory cortex.[1] Schöll, E., Partial synchronization patterns in brain networks. Europhys. Lett. 136, 18001 (2021), invited perspective article.[2] Sawicki, J., Hartmann, L., Bader, R. and Schöll, E, Modelling the perception of music in brain network dynamics. Front. Netw.Physiol. 2, 910920 (2022).[3] Sawicki, J. and Schöll, E., Interplay of synchronization and cortical input in models of brain networks, Europhys. Lett. 146,41001 (2024), invited perspective article.

Understanding the brain's complex network structure requires innovative mathematical frameworks that can capture its multiscale nature. Higher-order mathematical representations, particularly topological data analysis (TDA), have already demonstrated value in revealing organizational principles of brain function that remain hidden in traditional network approaches [1]. While these approaches and traditional network science have provided valuable insights, the integration of higher-order approaches with modern machine learning frameworks presents new opportunities for understanding brain organization. We propose representing brain networks as combinatorial complexes (CCs) [2], a novel mathematical structure developed within topological deep learning (TDL) that can simultaneously encode hierarchical and set-type relationships in neural systems (Figure 1).As neuroscience transitions into the era of big data and machine learning, we propose a computational framework for mapping brain network data to higher-order domains. Our CC-based framework aims to enrich traditional connectivity information by capturing the synchronic interplay between multiple brain regions and their dependencies. Our preliminary experiments with topological lifting methods for preserving network structure show promising results [3]. And by incorporating explainable AI techniques, our framework ensures that the derived insights remain interpretable and meaningful to neuroscientists.Using fMRI data, we examine how CC representations capture neural organization patterns compared to traditional graph-based analyses. This mathematical representation works seamlessly with combinatorial complex neural networks (CCNNs), providing a natural bridge between TDL and neuroscience. Our approach extends beyond traditional graph neural networks (GNNs) while maintaining interpretability, offering a foundation for understanding how higher-order brain structures give rise to cognition and behavior.

Studying structural brain networks has witnessed significant advancement in recent decades. Findings revealed a geometric principle, the exponential distance rule (EDR) showing that the number of neurons decreases exponentially with the length of their axons. This neuron-level information was used to build a region-level EDR network model that was able to explain various characteristics of inter-areal cortical networks in macaques, mice, and rats.The complete connectome of the Drosophila has recently been mapped providing information also about the network of neuropils (projectome). A recent study demonstrated the presence of the EDR in Drosophila, which we revisit in our study by precisely measuring the characteristic decay rate. This parameter is needed for testing the validity of the EDR random network model. Next, we demonstrate that the EDR model effectively accounts for numerous binary and weighted properties of the projectome. We also analyze the modularity of the projectome with a hierarchical clustering method that provides a realistic modular structure, with symmetric organization and clusters localized in space.Our study illustrates that the EDR model is a suitable null model for analyzing networks of brain regions, as it captures properties of region-level networks in very different species. The importance of the null model lies in its ability to facilitate the identification of functionally significant features not caused by inevitable geometric constraints, as we illustrate with the pronounced asymmetry of connection weights important for functional hierarchy. We also provide a first attempt to build this hierarchy of brain regions using the introduced asymmetry measure.

Anatomical connectivity between different brain regions can be mapped to a network representation, the connectome, where the intensities of the links, the weights, influence resilience and functional processes. Yet, many features associated with these weights are not fully understood, particularly their multiscale organization. In this paper, we elucidate the architecture of weights, including weak ties, in multiscale human brain connectomes reconstructed from empirical data. Our findings reveal multiscale self-similarity, including the ordering of weak ties, in every individual connectome and group representative. This phenomenon is captured by a renormalization technique, based on a geometric model that replicates weak and strong ties across all length scales. The observed symmetry represents a signature of criticality in the weighted connectivity of the human brain and raises important questions for future research, such as the existence of symmetry breaking at some scale or whether it is preserved in cases of neurodegeneration or psychiatric disorder.

Communication pathways in the brain are represented by a network of structural connectivity between regions. This representation, referred to as a connectome, also quantifies the strength of edges and contains important information to understand signal propagation in the brain. Some edges of a connectome may be redundant for communication. Removing redundancy reveals a subgraph of the connectome, called the metric backbone (MB), containing all of its original nodes and the subset of edges that obey the triangle inequality. Identifying the MB quantifies the robustness of communication via an algebraically principled and exact network sparsification method. We investigate human connectomes from the NKI study for 567 subjects from about 6 to 85 years old. Nodes correspond to brain regions, and edge distance weights are inversely proportional to the density of white matter streamlines. For each connectome, we compute the MB as described in [3] and implemented in the distanceclosure package [8]. The relative backbone size, τ, gives the fraction of edges contributing to shortest-path communication. Our analysis reveals very small MBs: τ ∈ (0.13, 0.19) with τavg ≈ 0.15, which are smaller than previously known for the connectome of a single subject (τ ≈ 0.18), and for c-elegans (τ ≈ 0.47). We also find a significant and robust decrease in τ with age in the initial 30 years, which remains stable for the next 20 years, while a slight increase is observed for older age groups, albeit with much greater variation. Finally, we observe that backbones contain similar proportions of edges from each brain hemisphere until 50 years. Afterwards, the fraction of intra-hemisphere edges has a significant increase with age. Biologically, they suggest that brain communication becomes more robust in the initial 3 decades of life, but it also becomes a little more entrenched in each hemisphere with age.

The prevalent fully connected architecture of neural network models is computationally inefficient, exceeding the energy expenditure of the human brain by over 100-fold. In contrast, the brain's connectivity is sparse and efficient, learning with just a few watts. Brain-inspired network science research can play a relevant role in designing low-consumption and efficient deep learning. Sparse training (ST) aims to ameliorate deep learning by replacing fully connected artificial neural networks (ANNs) with sparse or ultra-sparse ones, such as brain networks are.We introduce epitopological learning and Cannistraci-Hebb sparse training (CHT), a brain-inspired network science methodology that is gradient free and adopt the mere network topology for predicting the sparse connectivity in dynamic sparse training of neural networks. Epitopological learning is a field of network science and complex network intelligence that studies how to implement learning on complex networks by changing the shape of their connectivity structure (epitopological plasticity). One way to implement Epitopological (epi- means new) Learning is via link prediction: predicting the likelihood of non-observed links to appear in the network. Cannistraci-Hebb learning theory inspired the CH3-L3 network automata rule effective for general-purpose link prediction. Results show that CHT can surpass the performance of fully connected networks with MLP architecture by using only 1% of the connections (99% sparsity) and significantly reducing the active neuron network size to 20% of the original nodes on three basic datasets, demonstrating improved generalization while decreasing model size. Remarkable results are achieved also with 0.1% of the connections (99.9% sparsity). We present evidence in Transformers and LLMs across different sparsity levels, where CHT outperforms other prevalent dynamic sparse training methods in tasks such as Machine Translation, Arithmetic Reasoning, and Language Modelling.

Neuromorphic technologies often employ a point-neuron model, neglecting the spatiotemporal nature of neuronal computation. Dendritic morphology and synaptic organization are structurally tailored for spatiotemporal information processing, enabling various computations such as visual perception. Here, we introduce a neuromorphic computational model termed ‘dendristor’, which integrates synaptic organization with dendritic tree-like morphology. The dendristor presents bioplausible nonlinear integration of excitatory/inhibitory synaptic inputs and silent synapses with diverse spatial distribution dependency, emulating direction selectivity, which is the feature to react to signal direction on the dendrite. Silent synapses turn to be crucial in dendritic computation, enhancing direction selectivity. Finally, we develop a neuromorphic dendritic neural circuit which we adopt as a building-block to design a multi-layer network system that emulates 3D spatial motion perception in the retina. The proposed dendritic computation demonstrates unique capabilities compared to the current paradigms in electronic device engineering for neuromorphic computation, providing solutions to explore new frontiers in network-based artificial intelligence, neurocomputation and brain-inspired computing.

Deep brain stimulation (DBS) is a successful symptom-relieving treatment for Parkinson’s disease (PD). However, the introduction of advanced directional DBS electrodes significantly expands the programming parameter space, rendering the traditional trial-and-error approach for DBS optimization impractical and demonstrating the need for computational tools. Our recently developed DBS model using The Virtual Brain simulation tool, i.e. whole-brain simulations based on dynamic neural mass models coupled via the connectome, was able to reproduce multiple biologically plausible effects of DBS in PD (Meier et al., 2022). In the current work, we extend our virtual DBS model towards higher resolution for the stimulus input, now sensitive to the exact 3D location of the activated contact, incorporating streamline activations and the electric field.We simulate DBS of N=14 PD patients with available empirical data on contact activations of N=392 different electrode settings with corresponding motor task outcome. A linear model based on the principal component involvement of the simulated network dynamics demonstrated a correlation between predicted and empirically observed motor task improvements due to DBS of r=0.386 (p<10-4) in a leave-one-out cross-validation. Benchmarking revealed a trend towards better predictions with our “sweet dynamics” than imaging-based static models such as the sweet spot (r=0.16, p<0.05) and sweet streamline (r=0.26, p<10-4) models (Hollunder et al., 2024). Furthermore, our model outperforms the traditional trial-and-error method in predicting optimal clinical settings for individual patients, e.g. achieving over a 60% likelihood of identifying the optimal contact within the first two suggested contacts.In the future, the identified sweet dynamics can be used to optimize the electrode placement and settings in silico in individual patients, showcasing the potential benefit of network-based simulations for improving clinical routine.