Topological phase transitions in functional brain networks.

Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization.

Transport Properties of Hydrogenated Cubic Boron Nitride Nanofilms with Gold Electrodes from Density Functional Theory.

The electrical transport properties of a four-layered hydrogen-terminated cubic boron nitride sub-nanometer film in contact with gold electrodes are investigated via density functional calculations. The sample exhibits asymmetric metallic surfaces, a fundamental feature that triggers the system to behave like a typical p-n junction diode for voltage bias in the interval -0.2 ≤ V ≤ 0.2, where a rectification ratio up to 62 is verified. Further, in the wider region -0.3 ≤ V ≤ 0.3, negative differential resistance with a peak-to-valley ratio of 10 is observed. The qualitative behavior of the I-V characteristics is described in terms of the hydrogenated cBN film equilibrium electronic structure. Such a film shows metallic surfaces due to surface electronic states at a fraction of eV above and below the Fermi level of the N-H terminated and B-H terminated surfaces, respectively, with a wide bulk-band gap characteristic of BN materials. Such a mechanism is supported by transmission coefficient calculations, with the Landauer-Büttiker formula governing the I-V characteristics.