Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Synthetic polymer-based membrane for lithium Ion batteries

Efficient energy storage systems are increasingly needed due to advances in portable electronics and transport vehicles, lithium-ion batteries standing out among the most suitable energy storage systems for a large variety of applications. In lithium-ion batteries, the porous separator membrane plays a relevant role as it is placed between the electrodes and serves as a charge transfer medium and affects the cycle behavior. Typically, porous separators membranes are comprised of a synthetic polymeric matrix embedded in the electrolyte solution. The present chapter focus on recent advances in synthetic polymers for porous separation membranes, as well as on the techniques for membrane preparation and physicochemical characterization. The main challenges to improve synthetic polymer performance for battery separator membrane applications are also discussed.Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UID/FIS/04650/2019, UID/QUI/50006/2019, UID/QUI/0686/2016 and UID/EMS/00151/2019. The authors thank FEDER funds through the COMPETE 2020 Programme and National Funds through FCT under the project PTDC/FIS-MAC/28157/2017, Grants 38 SFRH/BPD/117838/2016 (JNP). and SFRH/BPD/112547/2015 (C.M.C). Financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) through the project MAT2016-76039-C4-3-R (AEI/FEDER, UE) (including the FEDER financial support) and from the Basque Government Industry and Education Departments under the ELKARTEK, HAZITEK and PIBA (PIBA-2018-06