We study Mandelbrot’s percolation process in dimension d ≥ 2. The process generates random fractal sets by an iterative procedure which starts by dividing the unit cube [0, 1]d in Nd subcubes, and independently retaining or discarding each subcube with probability p or 1− p respectively. This step is then repeated within the retained subcubes at all scales. As p is varied, there is a percolatio...

A model of food plant selection by a generalist herbivore was developed. The model was designed to predict the species composition of the diet of an herbivore based upon the joint probabilities of whether or not an individual of a plant species satisified two threshold values: some nutritional minimum and a size limit (both minimum and maximum), and the probability that it was encountered while...

We consider the stationary and the partially synchronous regimes in an all-to-all coupled neural network consisting of an infinite number of leaky integrate-and-fire neurons. Using analytical tools as well as simulation results, we show that two threshold values for the coupling strength may be distinguished. Below the lower threshold, no synchronization is possible; above the upper threshold, ...