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How Hot is Your Network?
In a paper published in Nature Physics, we have the answer, introducing the temperature of a physical network.
Pdf here: https://barabasi.com/f/1083.pdf
Thanks Yanchen Liu and @nimatabari for the collaboration. And @AliceGrishchenko for the visuals! 1/9
In a paper published in Nature Physics, we have the answer, introducing the temperature of a physical network.
Pdf here: https://barabasi.com/f/1083.pdf
Thanks Yanchen Liu and @nimatabari for the collaboration. And @AliceGrishchenko for the visuals! 1/9
In physical networks links are physical objects that cannot cross each other, like neurons in the brain or the vessels of vascular system. Such networks are not fully described by their adjacency matrix — the three dimensional layout also affect the system’s structure. 2/9
But how do we distinguish two physical networks with identical wiring but different geometrical layouts? The answer is *network isotopy*, representing different network layouts that can be transformed into each other without link-crossings. 3/9
We also introduce the graph linking number (GLN), that captures the entangledness of a layout, allowing us to define distinct isotopy classes: embeddings with different GLN cannot be isotopic to each other. 4/9
A network’s elastic energy depends linearly on the graph linking number, indicating that each tangle offers an independent contribution to the total energy. This finding allows us to analytically calculate the relationship between entaglendess and energy, predicting GLN. 5/9
We find that each isotopy class corresponds to a different energy well, separated by other isotopy classes by infinite energy barriers, establishing a direct link between isotopy and energy structure. 6/9
The formalism naturally leads to the notion of *network temperature*. The higher the temperature, the larger is the deviation of the links from the straight link trajectories, and the more entangled is the network. 7/9
We apply our formalism to brain wiring, finding that the mouse connectome is more entangled than expected based on the optimal wiring hypothesis widely used in brain science. 8/9
We could not resists, and 3D printed some of the 'hot lattices'. Come to the Ludwig Museum in Budapest, if you want to see the original!
Thanks @peterpuklus for the photo! 9/9
Thanks @peterpuklus for the photo! 9/9
