Hidden geometries in networks arising from cooperative self-assembly

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and compatibility of the building blocks are decisive factors in each phase of growth. Therefore, a comprehensive understanding of these processes is essential for the design of large assemblies of desired properties. Here, we introduce a computational model for cooperative self-assembly with simultaneous attachment of structured groups of particles, which can be described by simplexes (connected pairs, triangles, tetrahedrons and higher order cliques) to a growing network, starting from a small seed. The model incorporates geometric rules that provide suitable nesting spaces for the new group and the chemical affinity $\nu$ of the system to accepting an excess number of particles. For varying chemical affinity, we grow different classes of assemblies by binding the cliques of distributed sizes. Furthermore, to characterise the emergent large-scale structures, we use the metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. Our results show that higher Q-connectedness of the appearing simplicial complexes can arise due to only geometrical factors, i.e., for $\nu = 0$, and that it can be effectively modulated by changing the chemical potential and the polydispersity of the size of binding simplexes. For certain parameters in the model we obtain networks of mono-dispersed clicks, triangles and tetrahedrons, which represent the geometrical descriptors that are relevant in quantum physics and frequently occurring chemical clusters.Comment: 9 pages, 8 figure

Smooth crossover transition from the Delta-string to the Y-string three-quark potential

We comment on the assertion made by Caselle et al. [M. Caselle, G. Delfino, P. Grinza, O. Jahn, and N. Magnoli, J. Stat. Mech. (2006) P008.] that the confining (string) potential for three quarks makes a smooth crossover transition from the Delta-string to the Y-string configuration at interquark distances of around 0.8 fm. We study the functional dependence of the three-quark confining potentials due to a Y-string, and the Delta string and show that they have different symmetries, which lead to different constants of the motion (i.e. they belong to different universality classes in the parlance of the theory of phase transitions). This means that there is no smooth crossover between the two, when their string tensions are identical, except at the vanishing hyper-radius. We also comment on a certain two-body potential approximation to the Y-string potential

Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are delta-hyperbolic with delta(max) = 1 and the graph diameter D = 3 in each brain. While the emergent hyperbolicity in the two-brain networks varies satisfying delta(max)/D/2 LT = 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors ( triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neural correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listeners self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior

Analysis of somatic mutations in 131 human brains reveals aging-associated hypermutability

We analyzed 131 human brains (44 neurotypical, 19 with Tourette syndrome, 9 with schizophrenia, and 59 with autism) for somatic mutations after whole genome sequencing to a depth of more than 200×. Typically, brains had 20 to 60 detectable single-nucleotide mutations, but ~6% of brains harbored hundreds of somatic mutations. Hypermutability was associated with age and damaging mutations in genes implicated in cancers and, in some brains, reflected in vivo clonal expansions. Somatic duplications, likely arising during development, were found in ~5% of normal and diseased brains, reflecting background mutagenesis. Brains with autism were associated with mutations creating putative transcription factor binding motifs in enhancer-like regions in the developing brain. The top-ranked affected motifs corresponded to MEIS (myeloid ectopic viral integration site) transcription factors, suggesting a potential link between their involvement in gene regulation and autism