The transient fluctuation of the prosperity of firms in a network economy is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the fixed cost expense to the firms to produce those...

To shed light on the understanding of the angiogenesis process, we study a simplified lattice model for the capillary network formation between an existing blood vessel and an initially hypoxic tissue. We consider that the cells of the tissue surface can release growth factors that will diffuse,...

In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for...

The suprachiasmatic nucleus (SCN) of the hypothalamus is the mammalian circadian pacemaker that plays a dominant role in the generation and control of daily physiological and behavioral rhythms. The coupling of the SCN neuronal activity with the solar day–night cycle and the intercellular...

We consider a new and extended spatial neuron model in which the neuronal electrical depolarization from resting level satisfies a cable partial differential equation. The synaptic input current is also a function of space and time and satisfies a first order linear partial differential equation...

Lagrangian stochastic models are recognized as being powerful tools for pollutant dispersion at different scales in complex terrain and at different stability conditions. One of the still unresolved problems is the difficulty of including chemical reactions when, for example, NO2 or O3...

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression...

We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual market shows the power-law tail of the distribution of returns with the exponent outside the Levy...

In many real-world networks, the number of links increases non-linearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic accelerated growth in a network where links are...

The appearance of cancer in a tissue is thought to be the result of two or more successive mutations. We propose a stochastic model that allows for an exact computation of the distribution of the waiting time for a second mutation. This models the time of appearance of the first cancerous cell...