We determine analytically the condition number of the PageRank problem. Specifically, we prove the following statement: “Let P be an n × n row-stochastic matrix whose diagonal elements Pii = 0. Let c be a real number such that 0 ≤ c < 1. Let E be the n × n rank-one row-stochastic matrix E = ev , where e is the n-vector whose elements are all ei = 1, and v is an n-vector that represents a probab...

We present measurements of the fractal dimensions associated to the spin clusters for Z 4 and Z 5 spin models. We also attempted to measure similar fractal dimensions for the generalised Fortuin Kastelyn (FK) clusters in these models but we discovered that these clusters do not percolate at the critical point of the model under consideration. These results clearly mark a difference in the behav...

Experiments on the diffusion-limited corrosion of porous copper clusters in thin gap cells containing cupric chloride are reported. By carefully comparing corrosion front velocities and concentration profiles obtained by phase-shift interferometry with theoretical predictions, it is demonstrated that this process is well-described by a one-dimensional mean-field model for the generic reaction A...

conclusions: using n-butanolic c. coum extract in combination with ciprofloxacin offers a novel strategy to control biofilm-based infections caused by p. aeruginosa. results: the ability of biofilm formation by p. aeruginosa strains was quantitatively confirmed. the pcr method confirmed the existence of cup a gene (172 bp) in all studied strains. saponin content of the n-butanolic c. coum extra...

The diffraction of atoms from stepped surfaces is treated using the semiclassical S-matrix theory. Two different regimes of the behavior of the classical trajectories, regular and chaotic, are considered. For the latter case, the diffraction order function presents a fractal structure, and there is an infinite number of trajectories connecting the initial and final states. Using the scaling law...

The author reviews visual perception studies showing that fractal patterns possess an aesthetic quality based on their visual complexity. Specifically, people display an aesthetic preference for patterns with mid-range fractal dimensions, irrespective of the method used to generate them. The author builds upon these studies by presenting preliminary research indicating that mid-range fractals a...

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N=1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite num...

In this paper, a fractal photonic crystal fiber (F-PCF) based on the 1st iteration of Koch fractal configuration for optical communication systems is presented. Complex structure of fractal shape is build up through replication of a base shape. Nowadays, fractal shapes are used widely in antenna topics and its usage in PCF has not been investigated yet. The purpose of this research is to compar...

We introduce a method of hierarchically decomposing graph optimization problems to obtain approximate solutions with low computation. The method uses a partition on the graph to convert the original problem to a high level problem and several lower level problems. On each level, the resulting problems are in exactly the same form as the original one, so they can be further decomposed. In this w...

A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N = 1 the system reduces to the comb model where subdiffusion takes place with the transport exponent 1/2. We present an exact analytical evaluation of the transport exponent of anomalous diffusion for finite and infinite number of backbones. We show that for an arbitrarily large but finite n...