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)

A soluble random-matrix model for relaxation in quantum systems

We study the relaxation of a degenerate two-level system interacting with a heat bath, assuming a random-matrix model for the system-bath interaction. For times larger than the duration of a collision and smaller than the Poincaré recurrence time, the survival probability of still finding the system at timet in the same state in which it was prepared att=0 is exactly calculated.

Modelagem hidrológica da bacia hidrográfica do rio Bengalas, Nova Friburgo, RJ, utilizando o potencial de geotecnologias na definição de áreas de risco de inundação.

A presente pesquisa concentra-se no estudo hidrológico utilizando o potencial das geotecnologias na modelagem do escoamento na bacia do rio Bengalas, cujo rio principal de mesmo nome, corta o município de Nova Friburgo, RJ, no sentido Sul-Norte. Esse município, um dos mais importantes da região serrana, sofre frequentemente com inundações e deslizamentos, onde, dados históricos e acontecimentos recentes mostram que a ocupação inadequada de encostas e calhas dos rios são as áreas destacada e negativamente afetadas. A metodologia tem suporte no uso de um SIG, extraindo informações, que por sua vez, serão entrada de dados na fase de modelagem, e reforçando a apresentação dos resultados das simulações através de mapas. Ela está divida basicamente em três etapas: "SIG", "Modelagem" e "Suporte à Tomada de Decisão/Simulação". Esse primeiro estudo permitiu compor um banco de dados geográfico com as características fisiográficas da bacia; a seleção criteriosa de uma modelagem matemática e encadeamento de seus parâmetros com os componentes do ciclo hidrológico; realizar a calibração do modelo de transformação chuva-vazão, Soil Conservation Service (CN); e simular a passagem dos volumes gerados pela precipitação efetiva na calha do rio Bengalas, com o objetivo de identificar e analisar as áreas suscetíveis a inundações na porção central da cidade de Nova Friburgo. Modelagem dessa natureza vem sendo empregada, principalmente, no gerenciamento de recursos hídricos, onde a tomada de decisões embasada nos resultados de simulações computacionais, contribuem para evitar prejuízos materiais e financeiros, e ainda, perdas de vidas humanas em áreas de risco, neste caso, aquelas suscetíveis a inundações. Analisando os resultados encontrados temos que a área suscetível à inundação para uma chuva com tempo de recorrência de 50 anos, o mais crítico estudado, seja de aproximadamente 1,0 km, distribuídos nos seus 8,5km na região central de Nova Friburgo-RJ, sendo está, ora delimitada, prioritariamente edificada.

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.

Long-term follow-up of topical 5-aminolaevulinic acid photodynamic therapy diode laser single session for non-melanoma skin cancer

Photodynamic therapy (PDT) is based on the association of a light source and tight sensitive agents in order to cause the selective death of tumor cells. To evaluate topical 5-aminolaevulinic acid (5-ALA) and diode laser photodynamic single session therapy single session for non-melanoma skin cancer (NMSC), a long-term follow-up was performed. Nineteen Bowen`s disease (BD) and 15 basal cell. carcinoma (BCC) lesions were submitted to 6-h topical and occlusive 20% 5-ALA plus DMSO and EDTA, and later were exposed to 630 nm diode laser, 100 or 300 J cm(-2) dose. At 3 months tumor-free rate was 91.2% (31/34) whereas at 60 months, 57.7% (15/26), slightly higher in BCC (63.6%; 7/11). The relation between the reduction of the clinical response and the increase of tumor dimension observed at 18 months was lost at 60 months. The sBCC recurrence was earlier compared to the nBCC one. ALA-PDT offered important advantages: it is minimally invasive, an option for patients under risk of surgical complications; clinical feasibility; treatment of multiple lesions in only one session or lesions in poor heating sites and superior esthetical results. However, the recurrence rate increase after ALA-PDT diode laser single session can be observed at tong-term follow-up, and the repetitive sessions, an additional. advantage of the method, is strongly recommended. The clinical response and recurrence time seem to be related to the laser light dose and NMSC types/sub-types, thickness and dimension, which must be considered for the choice of the ALA-PDT. (C) 2009 Elsevier B.V. All rights reserved.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

InSAR deformation measurements of the earthquake cycle in transcurrent tectonic domains, analytical and analog modeling

I applied the SBAS-DInSAR method to the Mattinata Fault (MF) (Southern Italy) and to the Doruneh Fault System (DFS) (Central Iran). In the first case, I observed limited internal deformation and determined the right lateral kinematic pattern with a compressional pattern in the northern sector of the fault. Using the Okada model I inverted the observed velocities defining a right lateral strike slip solution for the MF. Even if it fits the data within the uncertainties, the modeled slip rate of 13-15 mm yr-1 seems too high with respect to the geological record. Concerning the Western termination of DFS, SAR data confirms the main left lateral transcurrent kinematics of this fault segment, but reveal a compressional component. My analytical model fits successfully the observed data and quantifies the slip in ~4 mm yr-1 and ~2.5 mm yr-1 of pure horizontal and vertical displacement respectively. The horizontal velocity is compatible with geological record. I applied classic SAR interferometry to the October–December 2008 Balochistan (Central Pakistan) seismic swarm; I discerned the different contributions of the three Mw > 5.7 earthquakes determining fault positions, lengths, widths, depths and slip distributions, constraining the other source parameters using different Global CMT solutions. A well constrained solution has been obtained for the 09/12/2008 aftershock, whereas I tested two possible fault solutions for the 28-29/10/08 mainshocks. It is not possible to favor one of the solutions without independent constraints derived from geological data. Finally I approached the study of the earthquake-cycle in transcurrent tectonic domains using analog modeling, with alimentary gelatins like crust analog material. I successfully joined the study of finite deformation with the earthquake cycle study and sudden dislocation. A lot of seismic cycles were reproduced in which a characteristic earthquake is recognizable in terms of displacement, coseismic velocity and recurrence time.

Sediments of Lake Vens (SW European Alps, France) record large-magnitude earthquake events

We studied sediment cores from Lake Vens (2,327 m asl), in the Tinée Valley of the SW Alps, to test the paleoseismic archive potential of the lake sediments in this particularly earthquake-sensitive area. The historical earthquake catalogue shows that moderate to strong earthquakes, with intensities of IX–X, have impacted the Southern Alps during the last millennium. Sedimentological (X-ray images, grain size distribution) and geochemical (major elements and organic matter) analyses show that Lake Vens sediments consist of a terrigenous, silty material (minerals and organic matter) sourced from the watershed and diatom frustules. A combination of X-ray images, grain-size distribution, major elements and magnetic properties shows the presence of six homogenite-type deposits interbedded in the sedimentary background. These sedimentological features are ascribed to sediment reworking and grain sorting caused by earthquake-generated seiches. The presence of microfaults that cross-cut the sediment supports the hypothesis of seismic deposits in this system. A preliminary sediment chronology is provided by 210Pb measurement and AMS 14C ages. According to the chronology, the most recent homogenite events are attributable to damaging historic earthquakes in AD 1887 (Ligure) and 1564 (Roquebillière). Hence, the Lake Vens sediment recorded large-magnitude earthquakes in the region and permits a preliminary estimate of recurrence time for such events of ~400 years.

Reconstructing 4000 years of mass movement and tsunami history in a deep peri-Alpine lake (Lake Geneva, France-Switzerland)

The study of mass movements in lake sediments provides insights into past natural hazards at historic and prehistoric timescales. Sediments from the deep basin of Lake Geneva reveal a succession of six large-scale (volumes of 22 × 106 to 250 × 106 m3) mass-transport deposits, associated with five mass-movement events within 2600 years (4000 cal bp to 563 ad). The mass-transport deposits result from: (i) lateral slope failures (mass-transport deposit B at 3895 ± 225 cal bp and mass-transport deposits A and C at 3683 ± 128 cal bp); and (ii) Rhône delta collapses (mass-transport deposits D to G dated at 2650 ± 150 cal bp, 2185 ± 85 cal bp, 1920 ± 120 cal bp and 563 ad, respectively). Mass-transport deposits A and C were most probably triggered by an earthquake, whereas the Rhône delta collapses were likely to be due to sediment overload with a rockfall as the external trigger (mass-transport deposit G, the Tauredunum event in 563 ad known from historical records), an earthquake (mass-transport deposit E) or unknown external triggers (mass-transport deposits D and F). Independent of their origin and trigger mechanisms, numerical simulations show that all of these recorded mass-transport deposits are large enough to have generated at least metre-scale tsunamis during mass movement initiation. Since the Tauredunum event in 563 ad, two small-scale (volumes of 1 to 2 × 106 m3) mass-transport deposits (H and I) are present in the seismic record, both of which are associated with small lateral slope failures. Mass-transport deposits H and I might be related to earthquakes in Lausanne/Geneva (possibly) 1322 ad and Aigle 1584 ad, respectively. The sedimentary record of the deep basin of Lake Geneva, in combination with the historical record, show that during the past 3695 years, at least six tsunamis were generated by mass movements, indicating that the tsunami hazard in the Lake Geneva region should not be neglected, although such events are not frequent with a recurrence time of 0·0016 yr−1.

Turbiditic trench deposits at the South-Chilean active margin

The active plate margin of South America is characterized by a frequent occurrence of large and devastating subduction earthquakes. Here we focus on marine sedimentary records off Southern Chile that are archiving the regional paleoseismic history over the Holocene and Late Pleistocene. The investigated records - Ocean Drilling Program (ODP) Site 1232 and SONNE core 50SL - are located at ~40°S and ~38°S, within the Perú-Chile trench, and are characterized by frequent interbedded strata of turbiditic and hemipelagic origin. On the basis of the sedimentological characteristics and the association with the active margin of Southern Chile, we assume that the turbidites are mainly seismically triggered, and may be considered as paleo-megaearthquake indicators. However, the long-term changes in turbidite recurrence times appear to be strongly influenced by climate and sea level changes as well. During sea level highstands in the Holocene and Marine Isotope Stage (MIS) 5, recurrence times of turbiditic layers are substantially higher, primarily reflecting a climate-induced reduction of sediment availability and enhanced slope stability. In addition, segmented tectonic uplift changes and related drainage inversions likely influenced the postglacial decrease in turbidite frequencies. Glacial turbidite recurrence times (including MIS 2, MIS 3, cold substages of MIS 5, and MIS 6), on the other hand, are within the same order of magnitude as earthquake recurrence times derived from the historical record and other terrestrial paleoseismic archives of the region. Only during these cold stages sediment availability and slope instability were high enough to enable recording of the complete sequence of large earthquakes in Southern Chile. Our data thus suggest that earthquake recurrence times on the order of 100 to 200 years are a persistent feature at least during the last glacial period.