Multifractality, stickiness, and recurrence-time statistics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Propriedades de tranporte, caos e dissipação num sistema dinâmico não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Convective patterns under the Indo-Atlantic << box >>

Using fluid mechanics, we reinterpret the mantle images obtained from global and regional tomography together with geochemical, geological and paleomagnetic observations, and attempt to unravel the pattern of convection in the Indo-Atlantic "box" and its temporal evolution over the last 260 Myr. The << box >> presently contains a) a broad slow seismic anomaly at the CMB which has a shape similar to Pangea 250 Myr ago, and which divides into several branches higher in the lower mantle, b) a "superswell, centered on the western edge of South Africa, c) at least 6 "primary hotspots" with long tracks related to traps, and d) numerous smaller hotspots. In the last 260 Myr, this mantle box has undergone 10 trap events, 7 of them related to continental breakup. Several of these past events are spatially correlated with present-day seismic anomalies and/or upwellings. Laboratory experiments show that superswells, long-lived hotspot tracks and traps may represent three evolutionary stages of the same phenomenon, i.e. episodic destabilization of a hot, chemically heterogeneous thermal boundary layer, close to the bottom of the mantle. When scaled to the Earth's mantle, its recurrence time is on the order of 100-200 Myr. At any given time, the Indo-Atlantic box should contain 3 to 9 of these instabilities at different stages of their development, in agreement with observations. The return flow of the downwelling slabs, although confined to two main << boxes >> (Indo-Atlantic and Pacific) by subduction zone geometry, may therefore not be passive, but rather take the form of active thermochemical instabilities. (c) 2005 Elsevier B.V. All rights reserved.

Evaluation des modifications anatomiques et fonctionnelles de la macula après chirurgie des membranes néovasculaires rétrofovéolaires dans la dégénérescence maculaire liée à l'âge [Evaluation of functional and anatomical changes in the macula after surgery for retro-foveal neovascularization of membranes in age-related macular degeneration].

PURPOSE: The aim of this study was to evaluate the direct effect of surgical treatment of subfoveolar neovascular membranes in age related macular degeneration to macular functions. PATIENTS AND METHODS: Thirteen eyes of 13 patients were included in this study. Macular function was assayed by visual acuity and central visual field using the Octopus perimeter before surgery and in the first three post operative months. Pre and post operative fluorescein angiography frames were digitalized and the size of each lesions were compared. RESULTS: After a 3 months follow up, visual acuity remained stable or improved in 66% of the patients. However, visual acuity was better than 0.1 in 15% of the patients. Central visual field comparison disclosed a significant worsening of the retinal sensitivity in the 3 degree field surrounding the central point. On fluorescein frames, submacular scar was 141% of the size of the neovascular membrane. After a mean follow up of 6.9 months (range 3-14), one case of recurrence occurred. A cataract was observed in 85% of the phakic patients followed for more than six months. CONCLUSION: After a short term follow up, surgery can stabilise visual acuity, even though it remains poor. A worsening of the scotoma in the 3 degrees surrounding the central point is observed. However, patients noticed a subjective visual improvement in 62% of the case.

Event-free survival at 24 months is a robust end point for disease-related outcome in diffuse large B-cell lymphoma treated with immunochemotherapy.

PURPOSE: Studies of diffuse large B-cell lymphoma (DLBCL) are typically evaluated by using a time-to-event approach with relapse, re-treatment, and death commonly used as the events. We evaluated the timing and type of events in newly diagnosed DLBCL and compared patient outcome with reference population data. PATIENTS AND METHODS: Patients with newly diagnosed DLBCL treated with immunochemotherapy were prospectively enrolled onto the University of Iowa/Mayo Clinic Specialized Program of Research Excellence Molecular Epidemiology Resource (MER) and the North Central Cancer Treatment Group NCCTG-N0489 clinical trial from 2002 to 2009. Patient outcomes were evaluated at diagnosis and in the subsets of patients achieving event-free status at 12 months (EFS12) and 24 months (EFS24) from diagnosis. Overall survival was compared with age- and sex-matched population data. Results were replicated in an external validation cohort from the Groupe d'Etude des Lymphomes de l'Adulte (GELA) Lymphome Non Hodgkinien 2003 (LNH2003) program and a registry based in Lyon, France. RESULTS: In all, 767 patients with newly diagnosed DLBCL who had a median age of 63 years were enrolled onto the MER and NCCTG studies. At a median follow-up of 60 months (range, 8 to 116 months), 299 patients had an event and 210 patients had died. Patients achieving EFS24 had an overall survival equivalent to that of the age- and sex-matched general population (standardized mortality ratio [SMR], 1.18; P = .25). This result was confirmed in 820 patients from the GELA study and registry in Lyon (SMR, 1.09; P = .71). Simulation studies showed that EFS24 has comparable power to continuous EFS when evaluating clinical trials in DLBCL. CONCLUSION: Patients with DLBCL who achieve EFS24 have a subsequent overall survival equivalent to that of the age- and sex-matched general population. EFS24 will be useful in patient counseling and should be considered as an end point for future studies of newly diagnosed DLBCL.

Endoscopic subureteral collagen injection for the treatment of vesicoureteral reflux in infants and children.

Between June 1988 and September 1994, 100 girls and 32 boys 2 months to 15.5 years old (average 4.9 years) with 204 refluxing ureteral units were treated by endoscopic subureteral collagen injection. The collagen injected was of bovine origin and cross-linked with glutaraldehyde (Zyplast*). Followup ranged from 3 to 75 months (mean 33). Reflux was absent in 62.7% of cases 3 months after 1 endoscopic subureteral injection. Improvement to reflux grades I and II, generally not requiring further treatment, occurred in a further 15.2% of cases. A total of 66 ureters was injected twice. The overall cure rate after 1 or 2 injections was 79.4% 3 months after injection. There was no correlation between the risk of recurrent reflux and initial degree of reflux. Late recurrence of reflux following a reflux-free period occurred in 11.3% of the 204 units during the observation period, which varied from 3 months to 6 1/4 years. Reflux was absent after 1 or 2 injections, including late recurrence, in 70.6% of cases and in an additional 13.2% recurrent reflux was grade I or II, not necessitating any further treatment. Considering these results, subureteral collagen injection remains an adequate method of treatment for vesicoureteral reflux in children.

Role of surgery in pediatric epilepsy.

Twenty five percent of patients with intractable epilepsy have surgically remediable epilepsy syndromes. This article reviews the treatment paradigm for pediatric epilepsy and also the indications, methods, and surgical options for the subgroup of patients with surgically remediable epileptic disorders based on our experience in the management of these children. The article also discusses the rationale for offering surgery and the timing of surgery in these patients. The study of surgically remediable epilepsy can best be divided into focal, sub hemispheric, hemispheric and multifocal epileptic syndromes. These syndromes have both acquired and congenital etiologies and can be treated by resective or disconnective surgery. The surgical management of these conditions (with the exception of multifocal epilepsy) provides Engel's Class 1 outcome(complete seizure freedom) in approximately 80% of children. The consequences of seizure freedom leads to a marked improvement in the quality of life of these children. The benefits to society, of allowing a child to grow to adulthood with normal cognition to earn a livelihood and contribute actively to society, cannot be understated.

Drawback of aortoplasty for aneurysm of the ascending aorta associated with aortic valve disease.

BACKGROUND: Aortoplasty has been advocated for moderate dilatation of the ascending aorta associated with aortic valve disease. We report our results with this conservative approach. METHODS: Seventeen consecutive patients with unsupported aortoplasty were reviewed. Twelve patients had aortic valve regurgitation and 5 had stenosis. The aortic wall was analyzed histologically in 14 patients. Follow-up was complete, with a mean time of 6 years (range, 2.3 to 10.5 years). RESULTS: Two patients among the 15 hospital survivors died during follow-up of causes unrelated to aortic pathology. Survival at 7 years was 86.7% (+/- 8.8%). Recurring aortic aneurysms developed in 4 patients after a mean time of 63 months, with an event-free survival at 7 years of 41% (+/- 21%). All of these 4 patients had aortic valve regurgitation and cystic medial necrosis. CONCLUSIONS: The recurrence rate of aneurysms after unsupported aortoplasty and aortic valve replacement is high in patients with aortic regurgitation. This strongly suggests that in these patients, the aortic dilatation is related to an underlying wall deficiency, associated with the aortic valve pathology, rather than to the hemodynamic stress imposed by the aortic valve disease.

Combined radioimmunotherapy and chemotherapy of human colon carcinoma grafted in nude mice, advantages and limitations.

In order to determine if 5-fluorouracil (5FU) could potentiate the effect of radioimmunotherapy (RIT), nude mice bearing subcutaneous human colon carcinoma xenografts were treated by 1 or 2 intravenous injection(s) of subtherapeutic doses of 131I labeled F(ab')2 from anti-carcinoembryonic antigen monoclonal antibodies combined with 5 daily intraperitoneal injections of 5FU. Control mice received either 131I F(ab')2 alone, 5FU alone or no treatment. RIT alone induced significant tumor regression, while 5FU alone gave only minimal tumor growth inhibition. The combined treatment group also resulted in long-term tumor regression with tumors remaining significantly smaller than in the RIT alone group. There was however, no significant difference in tumor recurrence time between the groups treated with RIT alone or with RIT + 5FU. Myelotoxicity, the major side effect of RIT, detected by the decrease of peripheral white blood cells (WBC), was shown to be almost identical between the groups receiving only RIT or only 5FU. Surprisingly, there was no cumulative bone marrow toxicity in animals which received 5FU before RIT. Furthermore, in the latter group, the WBC levels after RIT were significantly higher than in the control group receiving only RIT. Taken together, the results demonstrate the higher therapeutic efficiency of RIT as compared to 5FU in this model. They do not show, however, that the combination of the two forms of treatment can induce longer tumor remission. Interestingly, the WBC results suggest that 5FU given before RIT can have a radioprotective effect on bone marrow, possibly by selecting radioresistant bone marrow stem cells.

Clinical and biochemical responses after Gamma Knife surgery for a dopamine-secreting paraganglioma: case report.

The efficacy of Gamma Knife surgery (GKS) in local tumor control of non-secreting paragangliomas (PGLs) has been fully described by previous studies. However, with regard to secreting PGL, only one previous case report exists advocating its efficacy at a biological level. The aims of this study were: 1) to evaluate the safety/efficacy of GKS in a dopamine-secreting PGL; 2) to investigate whether the biological concentrations of free methoxytyramine could be used as a marker of treatment efficacy during the follow-up. We describe the case of a 62-year-old man diagnosed with left PGL. He initially underwent complete surgical excision. Thirty months after, he developed recurrent biological and neuroradiological disease; the most sensitive biomarker for monitoring the disease, concentration of plasma free methoxytyramine, started to increase. GKS was performed at a maximal marginal dose of 16 Gy. During the following 30 months, concentration of free methoxytyramine gradually decreased from 0.14 nmol/l (2*URL) before GKS to 0.09 nmol/l, 6 months after GKS and 0.07 nmol/l at the last follow-up after GKS (1.1*URL), confirming the efficacy of the treatment. Additionally, at 30 months there was approximately 36.6% shrinkage from the initial target volume. The GKS treatment was safe and effective, this being confirmed clinically, neuroradiologically and biologically. The case illustrates the importance of laboratory tests taking into account methoxytyramine when analyzing biological samples to assess the biochemical activity of a PGL. In addition, the identification of methoxytyramine as a unique positive biomarker could designate it for the monitoring of tumor relapse after treatments, including Gamma Knife surgery.

The effect of the magnetic field of the secondary star in dwarf novae

We investigate the effect of a secondary star magnetic field on the accretion disc dynamics of dwarf novae. Simulations have been carried out with a particle code and a dipolar magnetic field structure. The magnetic field acts to remove angular momentum from the disc material, increasing the inward mass flow. This makes the accretion disc more centrally condensed, causing a reduction in the recurrence time for dwarf nova outbursts. We have produced Doppler tomograms and light curves which may be compared with observations. These tomograms are significantly different from those produced in the absence of a magnetic field on the secondary. We derive an upper limit to the magnetic moment of the secondary star in UGem of mu_2<2x10^32 A m^2. The magnetic truncation of the accretion disc produces resonance phenomena similar to those seen in the superoutbursts of SUUMa systems. While these have not been observed for systems like UGem, observations of the SUUMa systems provide us with a useful diagnostic of the disc-field interaction. We are able to place an upper limit on the magnetic moment of the secondary in ZCha of mu_2<1x10^30 A m^2.

Midday auroral breakup events and related energy and momentum transfer from the magnetosheath

Combined observations by meridian-scanning photometers, all-sky auroral TV camera and the EISCAT radar permitted a detailed analysis of the temporal and spatial development of the midday auroral breakup phenomenon and the related ionospheric ion flow pattern within the 71°–75° invariant latitude radar field of view. The radar data revealed dominating northward and westward ion drifts, of magnitudes close to the corresponding velocities of the discrete, transient auroral forms, during the two different events reported here, characterized by IMF |BY/BZ| < 1 and > 2, respectively (IMF BZ between −8 and −3 nT and BY > 0). The spatial scales of the discrete optical events were ∼50 km in latitude by ∼500 km in longitude, and their lifetimes were less than 10 min. Electric potential enhancements with peak values in the 30–50 kV range are inferred along the discrete arc in the IMF |BY/BZ| < 1 case from the optical data and across the latitudinal extent of the radar field of view in the |BY/BZ| > 2 case. Joule heat dissipation rates in the maximum phase of the discrete structures of ∼ 100 ergs cm−2 s−1 (0.1 W m−2) are estimated from the photometer intensities and the ion drift data. These observations combined with the additional characteristics of the events, documented here and in several recent studies (i.e., their quasi-periodic nature, their motion pattern relative to the persistent cusp or cleft auroral arc, the strong relationship with the interplanetary magnetic field and the associated ion drift/E field events and ground magnetic signatures), are considered to be strong evidence in favour of a transient, intermittent reconnection process at the dayside magnetopause and associated energy and momentum transfer to the ionosphere in the polar cusp and cleft regions. The filamentary spatial structure and the spectral characteristics of the optical signature indicate associated localized ˜1-kV potential drops between the magnetopause and the ionosphere during the most intense auroral events. The duration of the events compares well with the predicted characteristic times of momentum transfer to the ionosphere associated with the flux transfer event-related current tubes. It is suggested that, after this 2–10 min interval, the sheath particles can no longer reach the ionosphere down the open flux tube, due to the subsequent super-Alfvénic flow along the magnetopause, conductivities are lower and much less momentum is extracted from the solar wind by the ionosphere. The recurrence time (3–15 min) and the local time distribution (∼0900–1500 MLT) of the dayside auroral breakup events, combined with the above information, indicate the important roles of transient magnetopause reconnection and the polar cusp and cleft regions in the transfer of momentum and energy between the solar wind and the magnetosphere.