Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time (MET) of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a prefactor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both two-state and three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

A Comparative study of germination strategies of two species of genus Allium sect. Allium

Germination experiments were performed with seeds of two species of genus Allium section Allium, a rare and endangered species A. pyrenaicum and a common A. sphaerocephalon. Different pre-treatments and a photoperiod of 24 h darkness were applied in order to simulate different germination conditions. Both species showed a high percentage of viable seeds a part of which were dormant. An elevate percentage of dormant seeds could be caused by a later collection time. Low altitude populations had more mortality than the others, possibly caused by the hard summer conditions during flowering and fruiting time. Comparisons between dates of species coexistence localities only show inter-population variability and it could be caused by the detected dormancy. Darkness accelerates germination, possibly for elongation radicle stimulation. Heat-shock pre-treatments decreased germination time in seeds from localities where fire is a probable event. The rarity of A. Pyrenaicum not seems to be caused by restricted germination requirements but is attributable to distinct habitat preferences, related to his altitudinal range of distribution

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

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.

Fronts with continuous waiting-time distributions: Theory and application to virus infections

We generalize to arbitrary waiting-time distributions some results which were previously derived for discrete distributions. We show that for any two waiting-time distributions with the same mean delay time, that with higher dispersion will lead to a faster front. Experimental data on the speed of virus infections in a plaque are correctly explained by the theoretical predictions using a Gaussian delay-time distribution, which is more realistic for this system than the Dirac delta distribution considered previously [J. Fort and V. Méndez, Phys. Rev. Lett.89, 178101 (2002)]

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

Factores determinantes del tiempo de demora y resultados funcionales en pacientes con desprendimiento de retina rhegmatógeno primario tratado mediante vitrectomía vía pars plana

Propósito: Determinar, en los pacientes afectados de desprendimiento de retina rhegmatógeno primario que acudieron a nuestro centro, el tiempo de demora entre la aparición de los primeros síntomas y la visita con el cirujano. Los objetivos secundarios son describir los factores que han influido en este tiempo de demora, determinar la relación existente entre el tiempo de evolución del desprendimiento rhegmatógeno de retina primario, el estado de la mácula y el resultado funcional tras la cirugía, y describir la sintomatología referida por los pacientes. Material y Método: Estudio descriptivo prospectivo de 59 ojos de 59 pacientes con desprendimiento de retina rhegmatógeno primario que acudieron al servicio de oftalmología del hospital Vall d’Hebron entre marzo y junio del 2008. Se realizó una anamnesis y exploración oftalmológica detallada a su llegada, fueron sometidos a cirugía mediante vitrectomía vía pars plana y se les realizó un seguimiento mínimo de 6 meses determinando los resultados funcionales de la cirugía. Resultados: El tiempo de demora medio desde la aparición de los síntomas hasta la primera consulta con el facultativo fue de 4,10 días. La media del tiempo de evolución del desprendimiento rhegmatógeno de retina fue de 17,03 días. Un 84,1% de los pacientes con la mácula desprendida tenían un tiempo de evolución menor o igual a 15 días y un 15,9% un tiempo de evolución mayor a 15 días. La agudeza visual media postoperatoria de los pacientes con la mácula aplicada fue de 0,55 en escala decimal, en los pacientes con la mácula afectada de menos de 15 días de evolución fue de 0,41, y en los pacientes con la mácula afectada de más de 15 días de evolución fue de 0,33. El síntoma más frecuente fue la visión borrosa (98,3%), seguido de miodesopsias (28,8%). Conclusiones: El tiempo de demora entre la aparición de los primeros síntomas del DRR y la visita con el cirujano es superior desde la remisión al cirujano por parte del facultativo que desde la aparición de síntomas y consulta con el facultativo por el paciente. La subestimación de la gravedad por parte del paciente es la causa de demora referida más frecuente. Los pacientes con un mayor tiempo de evolución tienen un mayor porcentaje de afectación macular. Los pacientes con la mácula aplicada han tenido un mejor resultado funcional tras la cirugía del DRR que los pacientes con la mácula desprendida.

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.

Absorption and pharmacokinetics of grapefruit flavanones in beagles

The present study evaluated the pharmacokinetics of three different grapefruit flavanone forms in dog plasma and demonstrated their absorption after an oral intake of a grapefruit extract; pharmacokinetic parameters of these forms were also determined. Ten healthy beagles were administered 70 mg citrus flavonoids as a grapefruit extract contained in capsules, while two additional dogs were used as controls and given an excipient. The grapefruit flavanone naringin, along with its metabolites naringenin and naringenin glucuronide, was detected in dog plasma. Blood samples were collected between 0 and 24 h after administration of the extract. Naringin reached its maximun plasma concentration at around 80 min, whereas naringenin and naringenin glucuronide reached their maximun plasma concentrations at around 20 and 30 min, respectively. Maximum plasma concentrations of naringin, naringenin and naringenin glucuronide (medians and ranges) were 0·24 (0·05 2·08), 0·021 (0·001 0·3) and 0·09 (0·034 0·12) mmol/l, respectively. The areas under the curves were 23·16 l (14·04 70·62) min £ mmol/for nariningin, 1·78 (0·09 4·95) min £ mmol/l for naringenin and 22·5 (2·74 99·23) min £ mmol/l for naringenin glucuronide. The median and range values for mean residence time were 3·3 (1·5 9·3), 2·8 (0·8 11·2) and 8·0 (2·3 13·1) h for naringin, naringenin and naringenin glucuronide, respectively. The results of the present study demonstrate the absorption of grapefruit flavanones via the presence of their metabolites in plasma, thus making an important contribution to the field since the biological activities ascribed to these compounds rely on their specific forms of absorption.

Absorption and pharmacokinetics of green tea catechins in beagles

The present study evaluates for the first time in dogs, the kinetics of green tea catechins and their metabolic forms in plasma and urine. Ten beagles were administered 173 mg (12·35 mg/kg body weight) of catechins as a green tea extract, in capsules. Blood samples were collected during 24 h after intake and urine samples were collected during the following periods of time: 02, 26, 68 and 824 h. Two catechins with a galloyl moiety and three conjugated metabolites were detected in plasma. Most of the detected forms in plasma reached their maximum plasma concentration (Cmax) at around 1 h. Median Cmax for (2)-epigallocatechin-3-gallate (EGCG), (2)-epicatechin-3-gallate (ECG), (2)-epigallocatechin glucuronide (EGCglucuronide), (2)-epicatechin glucuronide (EC-glucuronide), (2)-epicatechin sulphate (EC sulphate) were 0·3 (range 0·11·9), 0·1 (range 00·4), 0·8 (range 0·23·9), 0·2 (range 0·1 1·7) and 1 (range 0·33·4) mmol/l, respectively. The areas under the plasma concentration v. time curves (AUC0!24) were 427 (range 1021185) mmol/l £ min for EGC-glucuronide, 112 (range 53919) mmol/l £ min for EC-sulphate, 71 (range 26306) mmol/l £ min for EGCG, 40 (range 12258) mmol/l £ min for EC-glucuronide and 14 (range 0·1124) mmol/l £ min for ECG. The values of mean residence time (MRT0!24) were 5 (range 216), 2 (range 111), 10 (range 213), 3 (range 216) and 2·4 (range 118) h for EGCG, ECG, EGC-glucuronide, EC-glucuronide and EC sulphate, respectively. In urine, catechins were present as conjugated forms, suggesting bile excretion of EGCG and ECG. Green tea catechins are absorbed following an oral administration and EGC-glucuronide is the metabolic form that remains in the organism for a longer period of time, suggesting that this compound could suffer an enterohepatic cycle.

Absorption and pharmacokinetics of grapefruit flavanones in beagles

The present study evaluated the pharmacokinetics of three different grapefruit flavanone forms in dog plasma and demonstrated their absorption after an oral intake of a grapefruit extract; pharmacokinetic parameters of these forms were also determined. Ten healthy beagles were administered 70 mg citrus flavonoids as a grapefruit extract contained in capsules, while two additional dogs were used as controls and given an excipient. The grapefruit flavanone naringin, along with its metabolites naringenin and naringenin glucuronide, was detected in dog plasma. Blood samples were collected between 0 and 24 h after administration of the extract. Naringin reached its maximun plasma concentration at around 80 min, whereas naringenin and naringenin glucuronide reached their maximun plasma concentrations at around 20 and 30 min, respectively. Maximum plasma concentrations of naringin, naringenin and naringenin glucuronide (medians and ranges) were 0·24 (0·05 2·08), 0·021 (0·001 0·3) and 0·09 (0·034 0·12) mmol/l, respectively. The areas under the curves were 23·16 l (14·04 70·62) min £ mmol/for nariningin, 1·78 (0·09 4·95) min £ mmol/l for naringenin and 22·5 (2·74 99·23) min £ mmol/l for naringenin glucuronide. The median and range values for mean residence time were 3·3 (1·5 9·3), 2·8 (0·8 11·2) and 8·0 (2·3 13·1) h for naringin, naringenin and naringenin glucuronide, respectively. The results of the present study demonstrate the absorption of grapefruit flavanones via the presence of their metabolites in plasma, thus making an important contribution to the field since the biological activities ascribed to these compounds rely on their specific forms of absorption.

Absorption and pharmacokinetics of green tea catechins in beagles

The present study evaluates for the first time in dogs, the kinetics of green tea catechins and their metabolic forms in plasma and urine. Ten beagles were administered 173 mg (12·35 mg/kg body weight) of catechins as a green tea extract, in capsules. Blood samples were collected during 24 h after intake and urine samples were collected during the following periods of time: 0-2, 2-6, 6-8 and 8-24 h. Two catechins with a galloyl moiety and three conjugated metabolites were detected in plasma. Most of the detected forms in plasma reached their maximum plasma concentration (Cmax) at around 1 h. Median Cmax for (2)-epigallocatechin-3-gallate (EGCG), (2)-epicatechin-3-gallate (ECG), (2)-epigallocatechin glucuronide (EGCglucuronide), (2)-epicatechin glucuronide (EC-glucuronide), (2)-epicatechin sulphate (EC sulphate) were 0·3 (range 0·1-1·9), 0·1 (range 0-0·4), 0·8 (range 0·2-3·9), 0·2 (range 0·1 1·7) and 1 (range 0·3-3·4) mmol/l, respectively. The areas under the plasma concentration v. time curves (AUC0!24) were 427 (range 102-1185) mmol/l £ min for EGC-glucuronide, 112 (range 53-919) mmol/l £ min for EC-sulphate, 71 (range 26-306) mmol/l £ min for EGCG, 40 (range 12-258) mmol/l £ min for EC-glucuronide and 14 (range 0·1-124) mmol/l £ min for ECG. The values of mean residence time (MRT0!24) were 5 (range 2-16), 2 (range 1-11), 10 (range 2-13), 3 (range 2-16) and 2·4 (range 1-18) h for EGCG, ECG, EGC-glucuronide, EC-glucuronide and EC sulphate, respectively. In urine, catechins were present as conjugated forms, suggesting bile excretion of EGCG and ECG. Green tea catechins are absorbed following an oral administration and EGC-glucuronide is the metabolic form that remains in the organism for a longer period of time, suggesting that this compound could suffer an enterohepatic cycle.