Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

The permanence of the client under uncertain estimations

Marketing has studied the permanence of a client within an enterprise because it is a key element in the study of the value (economic) of the client (CLV). The research that they have developed is based in deterministic or random models, which allowed estimating the permanence of the client, and the CLV. However, when it is not possible to apply these schemes for not having the panel data that this model requires, the period of time of a client with the enterprise is uncertain data. We consider that the value of the current work is to have an alternative way to estimate the period of time with subjective information proper of the theory of uncertainty.

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified.

Anàlisi de les claus criptogràfiques utilitzades en bitcoin

El present projecte realitza una anàlisi de les claus criptogràfiques utilitzades en bitcoin. El projecte introdueix les nocions bàsiques necessàries de les corbes el·líptiques, la criptografia de corbes el·líptiques i els bitcoins per a realitzar l’anàlisi. Aquesta anàlisi consisteix en explorar el codi de diferents wallets bitcoin i realitzar un estudi empíric de l’aleatorietat de les claus. Per últim, el projecte introdueix el concepte de wallet determinista, el seu funcionament i alguns dels problemes que presenta.

Propagation through fractal media: The Sierpinski gasket and the Koch curve

We present new analytical tools able to predict the averaged behavior of fronts spreading through self-similar spatial systems starting from reaction-diffusion equations. The averaged speed for these fronts is predicted and compared with the predictions from a more general equation (proposed in a previous work of ours) and simulations. We focus here on two fractals, the Sierpinski gasket (SG) and the Koch curve (KC), for two reasons, i.e. i) they are widely known structures and ii) they are deterministic fractals, so the analytical study of them turns out to be more intuitive. These structures, despite their simplicity, let us observe several characteristics of fractal fronts. Finally, we discuss the usefulness and limitations of our approa