Fractals are shapes inwhichparts of the shape resemble thewhole shape in some way. Brownian motion, a type of random walk, is a fractal. Fractional Brownian motion, a biased random walk in which the walker favors certain directions at each step, is also a fractal. Used to model a wide range of phenomena, from river levels and landscape topography to computer network traffic and stock market ind...

The emergence of Mycobacterium tuberculosis (MTB) strains that are resistant to most or all available antibiotics has created a severe problem for treating tuberculosis and has spurred a quest for new antibiotic targets. Here, we demonstrate that trans-translation is essential for growth of MTB and is a viable target for development of antituberculosis drugs. We also show that an inhibitor of t...

Biological motion, human traffic and many other types of active motion rely on the supply of energy. In order to derive a rather general approach for active motion, we have proposed a model of active Brownian particles, which have the ability to take up energy from their environment, to store it in an internal energy depot and to convert internal energy to perform different activities, such as ...

The history of stochastic integration and the modelling of risky asset prices both begin with Brownian motion, so let us begin there too. The earliest attempts to model Brownian motion mathematically can be traced to three sources, each of which knew nothing about the others: the first was that of T. N. Thiele of Copenhagen, who effectively created a model of Brownian motion while studying time...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...