Detailed program : 14:00 - 17:30

• Opening and kick-off of the workshop (14:00 - 14:05); 

  • Session I (14:00 - 15:30): 

    • • 14:05 - 14:40 : Albert-László Barabási - "Understanding the role of physicality in networks "; 

Abstract: I will explore the applications of the network science toolset to physical networks, like the brain or metamaterials, which are networks whose links are physical entities that cannot cross each other. Link physicality affects both the evolution and the structure of a network, in a way that is not captured by current graph-based approaches. Yet, the existence of an exact mapping between physical networks and independent sets allows us to derive the onset of physical effects and the emergence of a jamming transition,  demonstrating that physicality impacts the network structure even when the total volume of the links is negligible.

• • • • 14:40 - 15:05 : Maria Ercsey-Ravasz: "Modeling the inter-areal cortical network based on a distance rule: from the macaque to the mouse";

Abstract: Mammals show a wide range of brain sizes, reflecting adaptation to diverse habitats. Comparing inter-areal cortical networks across brains of different sizes and mammalian orders provides robust information on evolutionarily preserved features and species-specific processing modalities. However, these networks are spatially embedded, directed, and weighted, making comparisons challenging. Analysis of the large-scale connectome inferred from a consistent database of retrograde tracer experiments in the macaque cortex has shown that many of its local, global and weighted properties are well predicted by a simple network model based on an exponential distance rule (EDR): the number of axons decays exponentially with their length with rate λ, expressing wiring economy. Here we show that the large-scale connectome of the mouse and the rat cortex is also strongly determined by an EDR network but with a different decay rate λ. Comparisons reveal the existence of network invariants between the species, exemplified in graph motif profiles and connection similarity indices, but also significant differences, such as fractionally smaller and much weaker long-distance connections in the macaque than in the mouse. The latter lends credence to the prediction that long-distance cortico-cortical connections could be very weak in the much-expanded human cortex, implying an increased susceptibility to disconnection syndromes such as Alzheimer's disease and schizophrenia.

• • • • 15:05 - 15:30 : Ádám Timár: "A network-of-networks model for physical networks";

Abstract: Physical networks are networks represented in the Euclidean space with edges thought of as physical objects with some constraint, e.g. they cannot intersect. We define a model through a dynamical process: a sequence of loop-erased random walks on the grid, run until they hit the previously constructed piece of the network. The trajectory of one such walk will then be a vertex of the corresponding abstract network, with adjacencies given by how the trajectories hit. Relying on this representation, we model the growth of physical networks showing that volume exclusion induces heterogeneity in both node volume and degree, with the two becoming correlated. Calculating the Laplacian spectra of these networks, we show that these correlations strongly affect their function. This is a joint project with I. Bonamassa, G. Pete, M. Pósfai and S. Ö. Stefánsson.

• Coffee break (15:30 - 16:00);

  • Session II (16:00 - 17:30): 

    • • 16:00 - 16:25 : Sang Hoon Lee: "Scale-dependent landscape of semi-nested community structures of 3D chromosome contact networks";

Abstract: Mammalian DNA folds into 3D structures that facilitate and regulate genetic processes such as transcription, DNA repair, and epigenetics. Several insights derive from chromosome capture methods, such as Hi-C, which allow researchers to construct contact maps depicting 3D interactions among all DNA segment pairs. To better understand the organizing principles, several groups analyzed Hi-C data assuming a Russian-doll-like nested hierarchy where DNA regions of similar sizes merge into larger and larger structures. However, while successful, this model is incompatible with the two competing mechanisms that seem to shape a significant part of the chromosomes' 3D organization: loop extrusion and phase separation. The first part of our work aims to map out the chromosome's actual folding hierarchy from empirical data, by treating the measured DNA-DNA interactions by Hi-C as a weighted network. From such a network, we extract 3D communities using the generalized Louvain algorithm with an adjustable resolution parameter, which allows us to scan seamlessly through the community size spectrum, from A/B compartments to topologically associated domains (TADs). By constructing a hierarchical tree connecting these communities, we find that chromosomes are more complex than a perfect hierarchy. Analyzing how communities nest relative to a simple folding model, we find that chromosomes exhibit a significant portion of nested and non-nested community pairs alongside considerable randomness. In addition, by examining nesting and chromatin types, we discover that nested parts are often associated with actively transcribed chromatin. Another reoccurring issue that seems to reflect the fundamental limitation of community detection in the case of stochastic algorithms is the possibility of inconsistent detection results (the same community detection method may disagree with itself). If too strong, such inconsistencies may cause problems if the data interpretation relies too heavily on a specific community structure when there are others equally feasible. In the second part of our work, we investigate the inconsistency of 3D communities in Hi-C data. We utilize an inconsistency metric, map out the community spectrum at different scales of the Hi-C contact network, and quantify where the community separation is most inconsistent. As a result, we find that the nodal inconsistency or functional flexibility are also related to the local chromatin activity as in the nestedness analysis.

• • • • 16:25 - 16:50 : Andreas Neophytou: "Untangling the Mysteries of Supercooled Water";

Abstract: The origin of the anomalous thermodynamic properties of liquid water has been a topic of fierce debate over the last four decades, with a universal consensus yet to be established. One hypothesis, which has received strong support from both numerical and experimental studies, is that there is a first order liquid-liquid phase transition (LLPT) line for water in the supercooled region of its pressure-temperature phase diagram, terminating at a liquid-liquid critical point (LLCP). However, direct observation of the LLPT in experiments has proved elusive due to rapid crystallisation into ice from the deeply supercooled liquid. In order to develop a model system that is amenable to experimental investigation and displays a LLPT, here we design a colloidal analogue of liquid water. Using Monte Carlo simulations, we show that this colloidal water model -- a tetrahedral network liquid self-assembled from triblock patchy colloidal particles via tetrahedral clusters -- captures the anomalous thermodynamic behaviour of supercooled water and displays a LLCP. Then, using topological concepts, which have become central in the description of physical networks and understanding their phase transitions, we introduce a topological order-parameter for the LLPT. Remarkably, we reveal that the LLPT in colloidal water is between two topologically distinct liquid networks and show that this order-parameter is not only able to describe the LLPT for colloidal water, but also for two widely used molecular models of water, thereby establishing the generality of the topological description of LLPT in tetrahedral liquids, which should have far-reaching implications in understanding LLPTs.

• • • • 16:50 - 17:05 : Cory Glover: "Effects of Network Topology on Physical Entanglement";

Abstract: Physical networks are networks embedded in three-dimensional space where nodes and links have both position and thickness. We define the crossing matrix of a physical network and use it to measure entangledness in physical networks with the average crossing number. In general, there is a positive correlation between energy in the system and the average crossing number. We focus our study on linear physical networks and find that the system size, average degree, and degree heterogeneity affect the growth in network entanglement as system energy increases. 

• • • • 17:05 - 17:20 : Hillel Sanhedrai "On the evolution of physical networks";

Abstract: Unlike virtual connections, in physical networks, such as the brain or the vascular system, the links are physical objects. As such, they occupy volume and cannot intersect each other. This characteristic affects the connectivity pattern of evolving network.  We aim to find a theory to describe the evolution of such networks, with a specific focus on the degree and link length distributions.

• Closing remarks (17:20 - 17:30).