First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

First-passage times for non-Markovian processes: Shot noise

The stochastic-trajectory-analysis technique is applied to the calculation of the mean¿first-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes.

First-passage times for non-Markovian processes: Multivalued noise

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Absorbing boundary conditions for inertial processos

A recent paper by J. Heinrichs [Phys. Rev. E 48, 2397 (1993)] presents analytic expressions for the first-passage times and the survival probability for a particle moving in a field of random correlated forces. We believe that the analysis there is flawed due to an improper use of boundary conditions. We compare that result, in the white noise limit, with the known exact expression of the mean exit time.

Extreme times in financial markets.

We apply the theory of continuous time random walks (CTRWs) to study some aspects involving extreme events in financial time series. We focus our attention on the mean exit time (MET). We derive a general equation for this average and compare it with empirical results coming from high-frequency data of the U.S. dollar and Deutsche mark futures market. The empirical MET follows a quadratic law in the return length interval which is consistent with the CTRW formalism.

Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Time-related improvement of survival in resectable gastric cancer: the role of Japanese-style gastrectomy with D2 lymphadenectomy and adjuvant chemotherapy

Background: We investigated the change of prognosis in resected gastric cancer (RGC) patients and the role of radical surgery and adjuvant chemotherapy. Methods: We retrospectively analyze the outcome of 426 consecutive patients from 1975 to 2002, divided into 2 time-periods (TP) cohort: Before 1990 (TP1, n = 207) and 1990 or after (TP2; n= 219). Partial gastrectomy and D1-lymphadenetomy was predominant in TP1 and total gastrectomy with D2-lymphadenectomy it was in TP2. Adjuvant chemotherapy consisted of mitomycin C (MMC), 10¿20 mg/m2 iv 4 courses or MMC plus Tegafur 500 mg/m2 for 6 months. Results: Positive nodes were similar in TP2/TP1 patients with 56%/59% respectively. Total gastrectomy was done in 56%/45% of TP2/TP1 respectively. Two-drug adjuvant chemotherapy was administered in 65%/18% of TP2/TP1 respectively. Survival at 5 years was 66% for TP2 versus 42%for TP1 patients (p < 0.0001). Survival by stages II, IIIA y IIIB for TP2 versus TP1 patients was 70 vs. 51% (p = 0.0132); 57 vs. 22% (p = 0.0008) y 30 vs. 15% (p = 0.2315) respectively. Multivariate analysis showed that age, stage of disease and period of treatment were independent variables. Conclusion: The global prognosis and that of some stages have improved in recent years with case RGC patients treated with surgery and adjuvant chemotherapy.

Mometasone and desloratadine additive effect on eosinophil survival and cytokine secretion from epithelial cells

Although antihistamines and topical corticosteroids are used in combination to treat allergic rhinitis, their additive effect has not been yet demonstrated. The aim was investigate the antiinflammatory additive effect of mometasone and desloratadine on cytokine and sICAM-1 secretion by epithelial cells, and on eosinophil survival stimulated by human epithelial cells secretions from nasal mucosa and polyps. Methods Epithelial cells obtained from nasal mucosa or polyps were stimulated with 10% fetal bovine serum in presence of mometasone (10-11M-10-5M) with/without desloratadine (10-5M). Cytokine and sICAM-1 concentrations in supernatants were measured by ELISA. Peripheral blood eosinophils were incubated during 4 days with epithelial cell secretions with (10-11M-10-5M) and/or desloratadine (10-5M) and survival assessed by Trypan blue. Results are expressed as percentage (mean ± SEM) compared to control. Results Fetal bovine serum stimulated IL-6, IL-8, GM-CSF and sICAM-1 secretion. In mucosa and polyp epithelial cells, mometasone inhibited this induced secretion while desloratadine inhibited IL-6 and IL-8. The combination of 10-5M desloratadine and 10-9M mometasone reduced IL-6 secretion (48 ± 11%, p < 0.05) greater extent than mometasone alone (68 ± 10%) compared to control (100%). Epithelial cell secretions induced eosinophil survival from day 1 to 4, this effect being inhibited by mometasone. At day 4, the combination of mometasone (10-11M) and desloratadine (10-5M) provoked an increased inhibition of eosinophil survival induced by cell secretions (27 ± 5%, p < 0.01) than mometasone (44 ± 7%) or desloratadine (46 ± 7%) alone. Conclusions These results suggest that the combination of desloratadine and mometasone furoate have a greater antinflammatory effect in an in vitro model of eosinophil inflammation than those drugs administered alone.

TrkB signaling is required for postnatal survival of CNS neurons and protects hippocampal and motor neurons from axotomy-induced cell death

Newborn mice carrying targeted mutations in genes encoding neurotrophins or their signaling Trk receptors display severe neuronal deficits in the peripheral nervous system but not in the CNS. In this study, we show that trkB (¿/¿) mice have a significant increase in apoptotic cell death in different regions of the brain during early postnatal life. The most affected region in the brain is the dentate gyrus of the hippocampus, although elevated levels of pyknotic nuclei were also detected in cortical layers II and III and V and VI, the striatum, and the thalamus. Furthermore, axotomized hippocampal and motor neurons of trkB (¿/¿) mice have significantly lower survival rates than those of wild-type littermates. These results suggest that neurotrophin signaling through TrkB receptors plays a role in the survival of CNS neurons during postnatal development. Moreover, they indicate that TrkB receptor signaling protects subpopulations of CNS neurons from injury- and axotomy-induced cell death.