Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

Tunable External Cavity Semiconductor Lasers.

In this study, we propose a new method to tune the semiconductor laser lasing frequency and reducing the laser linewidth using an external deriving field. We redeveloped Floquet S-matrix which determines the transmission probabilities and the shape and position of the induced quasibound state, which accumulated incident electrons. We explored the S-matrix numerically for various system parameters. We found that the oscillating field amplitude V1 plays a curial rule in defining the profile of electrons accumulations in the quasibound state and the field’s strength made sift the position of the quasibound state. This sift in the bound state energy due field’s strength is used to tune the lasing frequency and the output of the semiconductor laser linewidth is improved by changing the field’s amplitude the deriving field. By narrowing down the electron accumulations profile the laser linewidth would be narrower