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.

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.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

The present study focuses on single-case data analysis and specifically on two procedures for quantifying differences between baseline and treatment measurements The first technique tested is based on generalized least squares regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns (i.e., independent measurements, different serial dependence underlying processes, constant or phase-specific autocorrelation and data variability, different types of trend, and slope and level change). The results suggest that the two techniques perform adequately for a wide range of conditions and researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

Nasopalatine duct cyst: report of 22 cases and review of the literature

Objectives: Nasopalatine duct cysts (NPDCs) are the most common developmental, epithelial and non-odontogenic cysts of the maxillae. The present study describes the clinicopathological characteristics of 22 NPDCs and discusses their etiology, incidence, treatment and prognosis, with a review of the literature on the subject. Study design: A retrospective observational study was made comprising a period of 36 years (1970-2006), and yielding a series of 22 patients with histopathological confirmation of NPDC. Surgical treatment was carried out under local anesthesia and comprised the dissection and removal of the cyst adopting a usually palatine approach, with the preparation of an enveloping flap from 1.4 to 2.4. Results: No statistically significant correlation was observed between the size of the lesion and patient age, although the size of the cyst differed according to patient gender, with a mean NPDC diameter of 16 mm in males and 12 mm in females. In no case did we observe root reabsorption or loss of vitality of the upper incisors following surgery. The X-ray image was rounded in 15 cases and heart-shaped in the remaining 7 cases. In the majority of cases panoramic X-rays and periapical and occlusal X-rays sufficed to identify the lesion, though computed tomography was used in cases of doubt. Conclusions: The etiology of NPDC is unclear. Simple surgical resection is recommended, followed by clinical and radiological control to ensure correct resolution of the case.

Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] is used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current, but the frontshear modes are localized closer to the coast than are the backshear modes. Moreover, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical analysis performed on realistic current profiles confirm the behavior anticipated by the analytical model. The theory has been applied to a current profile fitted to data measured during the 1980 Nearshore Sediment Transport Studies experiment at Leadbetter Beach that has an extremum of background vorticity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory based only on backshear instability fai led to do so.

Nasopalatine duct cyst: report of 22 cases and review of the literature

Objectives: Nasopalatine duct cysts (NPDCs) are the most common developmental, epithelial and non-odontogenic cysts of the maxillae. The present study describes the clinicopathological characteristics of 22 NPDCs and discusses their etiology, incidence, treatment and prognosis, with a review of the literature on the subject. Study design: A retrospective observational study was made comprising a period of 36 years (1970-2006), and yielding a series of 22 patients with histopathological confirmation of NPDC. Surgical treatment was carried out under local anesthesia and comprised the dissection and removal of the cyst adopting a usually palatine approach, with the preparation of an enveloping flap from 1.4 to 2.4. Results: No statistically significant correlation was observed between the size of the lesion and patient age, although the size of the cyst differed according to patient gender, with a mean NPDC diameter of 16 mm in males and 12 mm in females. In no case did we observe root reabsorption or loss of vitality of the upper incisors following surgery. The X-ray image was rounded in 15 cases and heart-shaped in the remaining 7 cases. In the majority of cases panoramic X-rays and periapical and occlusal X-rays sufficed to identify the lesion, though computed tomography was used in cases of doubt. Conclusions: The etiology of NPDC is unclear. Simple surgical resection is recommended, followed by clinical and radiological control to ensure correct resolution of the case.

Treatment of oral mucocele - scalpel versus C02 laser

Objective: To compare the results obtained after oral mucocele resection with the scalpel versus the CO2 laser, based on the complications and recurrences after surgery Patients and Methods: Of the 68 patients we studied who have mucocele, 38 were resected with a scalpel and the remaining 30 with the CO2 laser (5-7 W). Patient sex and age were documented, along with location of the lesion as well as size, symptoms, duration, etiological factors, type of treatment, complications and recurrences after surgical removal. Results: The sample comprised 40 males and 28 females, aged between 6-65 years. The histological diagnosis was extravasation mucocele in 95% of the cases. The most frequent location was the lower lip (73.5%). The mean lesion diameter was 9 mm , and in most cases no evident etiological factor was recorded. The mean duration of the lesion was 4 months. Among the cases of conventional surgical removal of mucocele, recurrence was recorded in 8.8% of the cases, and 13.2% of the patients suffered postoperative complications - the most frequent being the presence of fibrous scars. There were no complications or relapses after a minimum follow-up of 12 months in the cases subjected to CO2 laser treatment. Conclusions: Oral mucocele ablation with the CO2 laser offers more predictable results and fewer complications and recurrences than conventional resection with the scalpel