Percolation in an ultrametric space

Percolation in an ultrametric space

We study percolation in the hierarchical lattice of order N where the probability of connection between two points separated by distance k is of the form ck/N , δ > −1. Since the distance is an ultrametric, there are significant differences with percolation in the Euclidean lattice. We consider three regimes: δ < 1, where percolation occurs, δ > 1, where it does not occur, and δ = 1 which is th...

Diffusion in an ultrametric space : a simple case

Percolation in protein sequence space

The currently known protein sequences are not distributed equally in sequence space, but cluster into families. Analyzing the cluster size distribution gives a glimpse of the large and unknown extant protein sequence space, which has been explored during evolution. For six protein superfamilies with different fold and function, the cluster size distributions followed a power law with slopes bet...

A model for modified electrode with carbon nanotube composites using percolation theory in fractal space

We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

An Ultrametric Model of Reactive Programming

We describe a denotational model of higher-order functional reactive programming using ultrametric spaces, which provide a natural Cartesian closed generalization of causal stream functions. We define a domain-specific language corresponding to the model. We then show how reactive programs written in this language may be implemented efficiently using an imperatively updated dataflow graph and g...