Detailed program : 09:00 - 12:30


Abstract: Following the lines of the first edition, the goal of this Satellite is to ignite discussions and share ideas about physical networks. We plan to welcome the speakers and the audience with a short introductory talk to outline a thread connecting the talks in the program and their relation to physical networks. 

Abstract: The graph representation of network systems as diagrams of unstructured nodes and edges has proven extremely useful in past studies. However, this approach often falls short of capturing the essential characteristics of complex physical systems. In such systems, the nodes and edges themselves can embody complexity. In this presentation, I will discuss networks comprising complex nodes and edges, using microfluidic and metamaterial networks as model systems.


Abstract: In this talk, I introduce a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a certain budget. As pairs of nodes are demanded and edges are removed, the macroscopic connected component of the graph disappears, i.e., the graph undergoes a percolation transition. I study such a shortest-path-percolation transition in homogeneous random graphs where pairs of demanded origin-destination nodes are randomly generated, and fully characterize it by means of finite-size scaling analysis. If budget is finite, the transition is identical to the one of ordinary percolation, where a single giant cluster shrinks as edges are removed from the graph; for infinite budget, the transition becomes more abrupt than the one of ordinary percolation, being characterized by the sudden fragmentation of the giant connected component into a multitude of clusters of similar size.

Abstract: Network visualization is increasingly gaining importance in many scientific and societal fields, technology and art. The main goal is to highlight patterns out of nodes interconnected by edges that are easy to understand and can facilitate communication as well as support decision-making processes. This is typically obtained by rearranging the nodes so as to minimize the edge crossings responsible of unintelligible and often unaesthetic trends. However, the spatial position of the nodes often conveys important information about the system’s geometrical and physical properties. If the nodes cannot be relocated, the amount of edge intersections exponentially increases as the number of links grows.The longer the edges, the higher the likelihood of traversing additional connections. Here, we indirectly address the edge crossing problem from a graph filtering perspective, asking whether there exists an optimal balance between the informative benefit of keeping numerous connections and the incurred cost due to their length. We demonstrate and confirm with extensive simulations that this problem admits analytical solutions showing that the optimal number of links solely depends on their spatial distribution. Denser networks naturally emerge when links connect spatially closer nodes, while sparser networks result when links connect farther nodes, thereby reducing the edge crossings disparity. This theoretical behavior matched human responses collected from N = 10687 individuals involved in an online interactive experiment where they arbitrarily selected the optimal number of links to visualize. By fitting the experimental data, we eventually derive an unbiased criterion to filter networks and get sparse representations of otherwise too dense real interconnected systems. Taken together, these results shed new light on the role of space in complex systems and provide an ecologically inspired tool to visualize and design spatial networks.



Abstract: Machine learning (ML) models have long overlooked innateness: how strong pressures for survival lead to the encoding of complex behaviors in the nascent wiring of a brain. In this talk, we will derive a neurodevelopmental encoding of artificial neural networks that considers the weight matrix of a neural network to be emergent from well-studied rules of neuronal compatibility. Rather than updating the network’s weights directly, we improve task fitness by updating the neurons’ wiring rules, thereby mirroring evolutionary selection on brain development. We find that our model (1) provides sufficient representational power for high accuracy on ML benchmarks while also compressing parameter count, and (2) can act as a regularizer, selecting simple circuits that provide stable and adaptive performance on metalearning tasks. Further, we find that adding spatial network models leads to an additional magnitude of parameter compression. In summary, by introducing neurodevelopmental considerations into ML frameworks, we not only model the emergence of innate behaviors, but also define a discovery process for structures that promote complex computations.


Abstract: Geometric random graph models have been shown to reproduce many of the structural properties observed in real networks, such as small-worldness, high levels of clustering and a scale free degree distribution. In these models, nodes are assumed to live in some underlying metric space that conditions their connectivity. In the past, the coupling between this geometry and the topology of the graph was assumed to be strong, as this was thought necessary for obtaining clustered graphs. Indeed, below a critical coupling strength the clustering coefficient does vanish in the thermodynamic limit. In this talk we study the statistical properties of this phase transition, specifically the behavior of the entropy as one crosses the critical point, which is shown to diverge. We also investigate the finite size scaling behavior and show that clustering vanishes very slowly in the weakly geometric regime, leading to high levels of clustering for finite systems, underlining the relevance of this region to real networks.

Abstract: Connectivity is fundamental to brain function; however, technical limitations have long hindered efforts to map neuronal wiring. Recent advances in electron microscopy and segmentation algorithms have enabled the reconstruction of synaptic connectivity and neuronal ultrastructure across species, from larval flies to humans. Applying physical network analyses to seven connectome datasets spanning a range of organisms, we find conserved features of neuronal morphology and connectivity. For instance, we observe that soma to soma distances between neuron pairs follow Weibull distributions, which are a generalization of the exponential distribution. We also see that synapse formation between neurons can be predicted by both the physical proximity of neuron pairs and by the lengths their dendritic arbors travel in parallel. Our findings provide a new perspective on the principles governing neuronal organization and function across diverse organisms.


Abstract: Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neural connectomes. To put the connectomes in context, we construct contactomes – networks of neurons in physical contact. We establish that physical constraints play a crucial role in shaping the network structure and can serve as a key ingredient in generative models of connectomes.


Abstract: Most classic network analysis techniques were designed to be applicable to arbitrary, generic graphs. However, the nodes of many real-world networks exist in physical space, with only nearby nodes being connected. This strongly constrains their possible connectivity structures, rendering many classic graph measures uninformative, and of limited use for classification. This is even more true in networks where only direct spatial neighbours are connected, and long-range connections are completely absent. Examples include various transport networks in biological organisms (such as vasculature, bile canaliculi, pancreatic ducts, etc.), networks of streets, mycorrhizal networks, slime moulds, etc. In all these cases, node locations almost completely determine the links in the network. We propose a novel approach to characterizing such networks through the concept of β- skeletons, a family of parametrized proximity graphs that naturally capture spatial neighbour relations. Despite its great potential, this concept has so far been mostly ignored within the field of spatial network analysis. We study the statistical properties of β-skeletons using both exact and numerical approaches, then building on these results, we introduce an innovative way of characterizing spatial point patterns by analysing their skeletons. Finally, we use three-dimensional biological network datasets to demonstrate that β-skeletons accurately capture the structure of most direct-neighbour spatial networks based on their node locations, and can thus be used to gain insight into their local network structure.