Márton Pósfai, Balázs Szegedy, Iva Bačić, Luka Blagojević, Miklós Abért, János Kertész, László Lovász & Albert-László Barabási 

Nature Physics (2023)

The emergence of detailed maps of physical networks, such as the brain connectome, vascular networks or composite networks in metamaterials, whose nodes and links are physical entities, has demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone—the starting point of all graph-based approaches—cannot capture. Here, we introduce a meta-graph that helps us to discover an exact mapping between linear physical networks and independent sets, which is a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and to show that physicality affects the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, to understand the evolution and behaviour of real complex networks, the role of physicality must be fully quantified.

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Melanie Mitchell, Alessandro B. Palmarini, Arseny Moskvichev

We explore the abstract reasoning abilities of text-only and multimodal versions of GPT-4, using the ConceptARC benchmark [10], which is designed to evaluate robust understanding and reasoning with core-knowledge concepts. We extend the work of Moskvichev et al. [10] by evaluating GPT-4 on more detailed, one-shot prompting (rather than simple, zero-shot prompts) with text versions of ConceptARC tasks, and by evaluating GPT-4V, the multimodal version of GPT-4, on zero- and one-shot prompts using image versions of the simplest tasks. Our experimental results support the conclusion that neither version of GPT-4 has developed robust abstraction abilities at humanlike levels.

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A Focus issue celebrating the 50th anniversary of Kenneth Wilson’s work on the renormalization group.

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Zhang Zhang, Arsham Ghavasieh, Jiang Zhang, Manlio De Domenico

Information dynamics is vital for many complex systems with networked backbones, from cells to societies. Recent advances in statistical physics have enabled capturing the macroscopic network properties, like how diverse the flow pathways are and how fast the signals can transport, based on the network counterparts of entropy and free energy. However, given the computational challenge posed by the large number of components in real-world systems, there is a need for advanced network renormalization— i.e., compression— methods providing simpler-to-read representations while preserving the flow of information between functional units across scales. We use graph neural networks to identify suitable groups of components for coarse-graining a network and achieve a low computational complexity suitable for practical application. Even for large compressions, our approach is highly effective in preserving the flow in synthetic and empirical networks, as demonstrated by theoretical analysis and numerical experiments. Remarkably, we find that the model works by merging nodes of similar ecological niches— i.e., structural properties—, suggesting that they play redundant roles as senders or receivers of information. Our work offers a low-complexity renormalization method breaking the size barrier for meaningful compressions of extremely large networks, working as a multiscale topological lens in preserving the flow of information in biological, social, and technological systems better than existing alternatives mostly focused on structural properties of a network.

Read the full article at: www.researchsquare.com