Stochastic Modelling Approach to the Incubation Time of Prionic Diseases

Transmissible spongiform encephalopathies like the bovine spongiform encephalopathy (BSE) and the Creutzfeldt-Jakob disease (CJD) in humans are neurodegenerative diseases for which prions are the attributed pathogenic agents. A widely accepted theory assumes that prion replication is due to a direct interaction between the pathologic (PrPsc) form and the host encoded (PrPc) conformation, in a kind of an autocatalytic process. Here we show that the overall features of the incubation time of prion diseases are readily obtained if the prion reaction is described by a simple mean-field model. An analytical expression for the incubation time distribution then follows by associating the rate constant to a stochastic variable log normally distributed. The incubation time distribution is then also shown to be log normal and fits the observed BSE data very well. The basic ideas of the theoretical model are then incorporated in a cellular automata model. The computer simulation results yield the correct BSE incubation time distribution at low densities of the host encoded protein

Spontaneous symmetry breaking in amnestically induced persistence

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.Comment: 4 pages, 2 color fig

Amnestically induced persistence in random walks

We study how the Hurst exponent $\alpha$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias.Comment: 4 pages, 3 figs, subm. to Phys. Rev. Let

Weakly anomalous diffusion with non-Gaussian propagators

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H approximate to 1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H = 1/2 but with a non-Gaussian propagator.FAPESPFAPESP [2011/13685-6, 2011/06757-0]CNPqCNP

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac

Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU

Contains fulltext : 172380.pdf (publisher's version ) (Open Access

A martingale approach for the elephant random walk

The purpose of this paper is to establish, via a martingale approach, some refinements on the asymptotic behavior of the one-dimensional elephant random walk (ERW). The asymptotic behavior of the ERW mainly depends on a memory parameter $p$ which lies between zero and one. This behavior is totally different in the diffusive regime $0 \leq p <3/4$, the critical regime $p=3/4$, and the superdiffusive regime $3/4<p \leq 1$. Notwithstanding of this trichotomy, we provide some new results on the almost sure convergence and the asymptotic normality of the ERW

Log-periodicity can appear in a non-Markovian random walk even if there is perfect memory of its history

The exactly solvable Elephant Random Walk (ERW) model introduced by Schütz and Trimper 15 years ago stimulated research that led to many new insights and advances in understanding anomalous diffusion. Such models have two distinct ingredients: i) long-range —possibly complete— memory of the past behavior and ii) a decision-making rule that makes use of the memory. These models are memory-neutral: the decision-making rule does not distinguish between short-term (or recent) memories and long-term (or old) memories. Here we relax the condition of memory neutrality, so that memory and decision-making become interconnected. We investigate the diffusive properties of random walks that evolve according to memory-biased decision processes and find remarkably rich phase diagrams, including a phase of log-periodic superdiffusion that may be associated with old memory and negative feedback regulating mechanisms. Our results overturn the conventional wisdom concerning the origin of log-periodicity in non-Markovian models. All previously known non-Markovian random walk models that exhibit log-periodicities in their behavior have incomplete (or damaged) memory of their history. Here we show that log-periodicity can appear even if the memory is complete, so long as there is a memory bias