Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

RATE OF CONVERGENCE OF MAXIMUM LIKELIHOOD ESTIMATORS UNDER RELAXED SMOOTHNESS CONDITIONS ON THE LIKELIHOOD FUNCTION

This report reviews literature on the rate of convergence of maximum likelihood estimators and establishes a Central Limit Theorem, which yields an O(1/sqrt(n)) rate of convergence of the maximum likelihood estimator under somewhat relaxed smoothness conditions. These conditions include the existence of a one-sided derivative in θ of the pdf, compared to up to three that are classically required. A verification through simulation is included in the end of the report.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

Vegeu el resum a l'inici del document del fitxer adjunt.

Convergence Rates of Approximation by Translates

In this paper we consider the problem of approximating a function belonging to some funtion space Φ by a linear comination of n translates of a given function G. Ussing a lemma by Jones (1990) and Barron (1991) we show that it is possible to define function spaces and functions G for which the rate of convergence to zero of the erro is 0(1/n) in any number of dimensions. The apparent avoidance of the "curse of dimensionality" is due to the fact that these function spaces are more and more constrained as the dimension increases. Examples include spaces of the Sobolev tpe, in which the number of weak derivatives is required to be larger than the number of dimensions. We give results both for approximation in the L2 norm and in the Lc norm. The interesting feature of these results is that, thanks to the constructive nature of Jones" and Barron"s lemma, an iterative procedure is defined that can achieve this rate.

Strain rate of the South American lithospheric plate by SIRGAS-CON geodetic observations

A multiyear solution of the SIRGAS-CON network was used to estimate the strain rates of the earth surface from the changing directions of the velocity vectors of 140 geodetic points located in the South American plate. The strain rate was determined by the finite element method using Delaunay triangulation points that formed sub-networks; each sub-network was considered a solid and homogeneous body. The results showed that strain rates vary along the South American plate and are more significant on the western portion of the plate, as expected, since this region is close to the subduction zone of the Nazca plate beneath the South American plate. After using Euler vectors to infer Nazca plate movement and to orient the velocity vectors of the South American plate, it was possible to estimate the convergence and accommodation rates of the Nazca and South American plates, respectively. Strain rate estimates permitted determination of predominant contraction and/or extension regions and to establish that contraction regions coincide with locations with most of the high magnitude seismic events. Some areas with extension and contraction strains were found to the east within the stable South American plate, which may result from different stresses associated with different geological characteristics. These results suggest that major movements detected on the surface near the Nazca plate occur in regions with more heterogeneous geological structures and multiple rupture events. Most seismic events in the South American plate are concentrated in areas with predominant contraction strain rates oriented northeast-southwest; significant amounts of elastic strain can be accumulated on geological structures away from the plate boundary faults; and, behavior of contractions and extensions is similar to what has been found in seismological studies. © 2013 Elsevier Ltd.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Seawater carbonate chemistry and growth rate of Emiliania huxleyi in lab experiment

Predicting the impacts of environmental change on marine organisms, food webs, and biogeochemical cycles presently relies almost exclusively on short-term physiological studies, while the possibility of adaptive evolution is often ignored. Here, we assess adaptive evolution in the coccolithophore Emiliania huxleyi, a well-established model species in biological oceanography, in response to ocean acidification. We previously demonstrated that this globally important marine phytoplankton species adapts within 500 generations to elevated CO2. After 750 and 1000 generations, no further fitness increase occurred, and we observed phenotypic convergence between replicate populations. We then exposed adapted populations to two novel environments to investigate whether or not the underlying basis for high CO2-adaptation involves functional genetic divergence, assuming that different novel mutations become apparent via divergent pleiotropic effects. The novel environment "high light" did not reveal such genetic divergence whereas growth in a low-salinity environment revealed strong pleiotropic effects in high CO2 adapted populations, indicating divergent genetic bases for adaptation to high CO2. This suggests that pleiotropy plays an important role in adaptation of natural E. huxleyi populations to ocean acidification. Our study highlights the potential mutual benefits for oceanography and evolutionary biology of using ecologically important marine phytoplankton for microbial evolution experiments.

Developmental Rate Of Immatures Of Two Fly Species Of Forensic Importance: Sarcophaga (liopygia) Ruficornis And Microcerella Halli (diptera: Sarcophagidae).

Since insect species are poikilothermic organisms, they generally exhibit different growth patterns depending on the temperature at which they develop. This factor is important in forensic entomology, especially for estimating postmortem interval (PMI) when it is based on the developmental time of the insects reared in decomposing bodies. This study aimed to estimate the rates of development, viability, and survival of immatures of Sarcophaga (Liopygia) ruficornis (Fabricius 1794) and Microcerella halli (Engel 1931) (Diptera: Sarcophagidae) reared in different temperatures: 10, 15, 20, 25, 30, and 35 ± 1 °C. Bovine raw ground meat was offered as food for all experimental groups, each consisting of four replicates, in the proportion of 2 g/larva. To measure the evolution of growth, ten specimens of each group were randomly chosen and weighed every 12 h, from initial feeding larva to pupae, and then discarded. Considering the records of weight gain, survival rates, and stability of growth rates, the range of optimum temperature for the development of S. (L.) ruficornis is between 20 and 35 °C, and that of M. halli is between 20 and 25 °C. For both species, the longest times of development were in the lowest temperatures. The survival rate at extreme temperatures (10 and 35 °C) was lower in both species. Biological data such as the ones obtained in this study are of great importance to achieve a more accurate estimate of the PMI.

Efeito das sessões de familiarização sobre o pico de torque e taxa de desenvolvimento de torque : comparações entre jovens, meia idade e idosos = Effect of familiarization sessions on peak torque and rate of torque development : comparisons among young, middle age and elderly

Universidade Estadual de Campinas, Faculdade de Educação Física

Periodontal treatment during pregnancy decreases the rate of adverse pregnancy outcome: a controlled clinical trial

OBJECTIVES: The aim of this study was to evaluate the effects of non-surgical treatment of periodontal disease during the second trimester of gestation on adverse pregnancy outcomes. MATERIAL AND METHODS: Pregnant patients during the 1st and 2nd trimesters at antenatal care in a Public Health Center were divided into 2 groups: NIG - "no intervention" (n=17) or IG- "intervention" (n=16). IG patients were submitted to a non-surgical periodontal treatment performed by a single periodontist consisting of scaling and root planning (SRP), professional prophylaxis (PROPH) and oral hygiene instruction (OHI). NIG received PROPH and OHI during pregnancy and were referred for treatment after delivery. Periodontal evaluation was performed by a single trained examiner, blinded to periodontal treatment, according to probing depth (PD), clinical attachment level (CAL), plaque index (PI) and sulcular bleeding index (SBI) at baseline and 35 gestational weeks-28 days post-partum. Primary adverse pregnancy outcomes were preterm birth (<37 weeks), low birth weight (<2.5 kg), late abortion (14-24 weeks) or abortion (<14 weeks). The results obtained were statistically evaluated according to OR, unpaired t test and paired t test at 5% signifcance level. RESULTS: No signifcant differences were observed between groups at baseline examination. Periodontal treatment resulted in stabilization of CAL and PI (p>0.05) at IG and worsening of all periodontal parameters at NIG (p<0.0001), except for PI. Signifcant differences in periodontal conditions of IG and NIG were observed at 2nd examination (p<0.001). The rate of adverse pregnancy outcomes was 47.05% in NIG and 6.25% in IG. Periodontal treatment during pregnancy was associated to a decreased risk of developing adverse pregnancy outcomes [OR=13.50; CI: 1.47-123.45; p=0.02]. CONCLUSIONS: Periodontal treatment during the second trimester of gestation contributes to decrease adverse pregnancy outcomes.

Comparison of radial growth rate of the mutualistic fungus of Atta sexdens rubropilosa forel in two culture media

In vitro culture of the mutualistic fungus of leaf-cutting ants is troublesome due to its low growth rate, which leads to storage problems and contaminants accumulation. This paper aims at comparing the radial growth rate of the mutualistic fungus of Atta sexdens rubropilosa Forel in two different culture media (Pagnocca B and MEA LP). Although total MEA LP radial growth was greater all along the bioassay, no significant difference was detected between growth efficiencies of the two media. Previous evidences of low growth rate for this fungus were confirmed. Since these data cannot point greater efficiency of one culture medium over the other, MEA LP medium is indicated for in vitro studies with this mutualistic fungus due its simpler composition and translucent color, making the analysis easier.

Growth parameters and mortality rate of the Scomber japonicus peruanus (Jordán & Hubb, 1925) along the Peruvian coast, South Pacific

The growth parameters and the mortality rates of the Scomber japonicus peruanus (Chub mackerel) were studied based on monthly data of frequency of fork length classes obtained from commercial landings off the Peruvian coast from 1996 to 1998. The asymptotic body length and growth rate values obtained by the ELEFAN I (Electronic Length Frequency Analysis) ranged from 40.20 cm to 42.20 cm and from 0.38 to 0.39, respectively. The oscillation amplitude was 0.60; the Winter point values varied from 0.50 to 0.60 and the performance index from 2.79 to 2.84. The total mortality rate of the Chub mackerel obtained by the linearized catch curve oscillated between 1.68 and 3.35. The rate of fishing mortality varied from 1.16 to 2.78 and the exploitation rate from 0.68 to 0.84. The annual rate of natural mortality estimated by the Pauly's method ranged from 0.52 to 0.53. The results obtained allow us to conclude that the longevity of the Chub mackerel was slightly over seven years.

Density and survival rate of Culex quinquefasciatus at Parque Ecológico do Tietê, São Paulo, Brazil

Parity rate, gonotrophic cycle length, and density of a Culex quinquefasciatus female population was estimated at the Parque Ecológico do Tietê (PET), São Paulo, Brazil. Adult Cx. quinquefasciatus females were collected from vegetation along the edges of a polluted drainage canal with the use of a battery-powered backpack aspirator from September to November 2005 and from February to April 2006. We examined 255 Cx. quinquefasciatus ovaries to establish the parity rate of 0.22 and determined the gonotrophic cycle length under laboratory conditions to be 3 and 4 days. From these data, we calculated the Cx. quinquefasciatus survival rate to be 0.60 and 0.68 per day. Density of the Cx. quinquefasciatus female (5.71 females per m2) was estimated based on a population size of 28,810 individuals divided by the sampled area of 5,040 m2. Results of all experiments indicate medium survivorship and high density of the Cx. quinquefasciatus female population. This species is epidemiologically relevant in the PET area and should be a target of the vector control program of São Paulo municipality

Anomalous dephasing scattering rate of two-dimensional electrons in double quantum well structures

The results on the measurement of electrical conductivity and magnetoconductivity of a GaAs double quantum well between 0.5 and 1.1 K are reported. The zero magnetic-field conductivity is well described from the point of view of contributions made by both the weak localization and electron-electron interaction. At low field and low temperature, the magnetoconductivity is dominated by the weak localization effect only. Using the weak localization method, we have determined the electron dephasing times tau(phi) and tunneling times tau(t). Concerning tunneling, we concluded that tau(t) presents a minimum around the balance point; concerning dephasing, we observed an anomalous dependence on temperature and conductivity (or elastic mean free path) of tau(phi). This anomalous behavior cannot be explained in terms of the prevailing concepts for the electron-electron interaction in high-mobility two-dimensional electron systems.