Comparing connectomes across subjects and populations at different scales.

Brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals. In the literature, two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects: 1) the global comparison where a single measure that summarizes the information of each brain is used in a statistical test; 2) the local analysis where a single test is performed either for each node/connection which implies a multiplicity correction, or for each group of nodes/connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction. We comment on the different levels of analysis and present some methods that have been proposed at each scale. We highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis.

Models that include supercoiling of topological domains reproduce several known features of interphase chromosomes.

Understanding the structure of interphase chromosomes is essential to elucidate regulatory mechanisms of gene expression. During recent years, high-throughput DNA sequencing expanded the power of chromosome conformation capture (3C) methods that provide information about reciprocal spatial proximity of chromosomal loci. Since 2012, it is known that entire chromatin in interphase chromosomes is organized into regions with strongly increased frequency of internal contacts. These regions, with the average size of ∼1 Mb, were named topological domains. More recent studies demonstrated presence of unconstrained supercoiling in interphase chromosomes. Using Brownian dynamics simulations, we show here that by including supercoiling into models of topological domains one can reproduce and thus provide possible explanations of several experimentally observed characteristics of interphase chromosomes, such as their complex contact maps.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.