Entwined Planar Spirals for Artificial Surfaces

Entwined engrams

The nematode Caenorhabditis elegans displays a surprisingly sophisticated behavioral repertoire that includes the utilization of both associative and non-associative forms of learning. Elucidating the molecular basis of learning remains a fundamental, yet daunting, challenge of modern neuroscience. In Pereira and van der Kooy (ref. 2), we described the use of a two input-two output stimuli syst...

Target Patterns and Spirals in Planar Reaction-Diffusion Systems

Solutions of reaction-diffusion equations on a circular domain are considered. With Robin boundary conditions, the primary instability may be a Hopf bifurcation with eigenfunctions exhibiting prominent spiral features. These eigenfunctions, defined by Bessel functions of complex argument, peak near the boundary and are called wall modes. In contrast, if the boundary conditions are Neumann or Di...

Representation of Adsorption Data for the Case of Energetically Heterogeneous Solid Surfaces Using Artificial Neural Network

Dispersion Corrections at Planar Surfaces

When simulating a molecular system, a cutoff distance for interactions is often used to speed up the simulations. This is made at the cost of neglecting some interactions which will lead to inaccurate results for energy, pressure components and surface tension (for systems with surfaces). To compensate for the neglected long-range interactions, continuum corrections can be added to the surface ...

Planar Graphs on Nonplanar Surfaces

It is shown that embeddings of planar graphs in arbitrary surfaces other than the 2-sphere have a special structure. It turns out that these embeddings can be described in terms of noncontractible curves in the surface, meeting the graph in at most two points (which may taken to be vertices of the graph). The close connection between the homology group of the surface and the planar graph embedd...