Placental Volumes Measured by 3-Dimensional Ultrasonography in Normal Pregnancies From 12 to 40 Weeks' Gestation

Objective. The purpose of this study was to construct nomograms of placental volumes according to gestational age and estimated fetal weight. Methods. From March to November 2007, placental volumes were prospectively measured by ultrasonography in 295 normal pregnancies from 12 to 40 weeks' gestation and correlated with gestational age and estimated fetal weight. Inclusion criteria were healthy women, singleton pregnancies with normal fetal morphologic characteristics on ultrasonography, and confirmed gestational age by first-trimester ultrasonography. Results. The mean placental volume ranged from 83 cm(3) at 12 weeks to 427.7 cm(3) at 40 weeks. Linear regression yielded the following formula for the expected placental volumes (ePV) according to gestational age (GA): ePV` (cm(3)) = -64.68 + 12.31 x GA (r = 0.572; P < .001). Placental volumes also varied according to estimated fetal weight (EFW), and the following mathematical equation was also obtained by linear regression: ePV = 94.19 + 0.09 x EFW (r = 0.505; P < 0.001). Conclusions. Nomograms of placental volumes according to gestational age and estimated fetal weight were constructed, generating reference values.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Recursos pesqueiros oriundos da pesca artesanal no reservatório de jurumirim, rio Paranapanema, Alto Paraná, Brasil

The aim of this paper was to evaluate the artisanal fisheries in the village of fishermen of Bairro da Ponte, Jurumirim reservoir. Data were collected using production forms which were filled daily by a data collector, in 2005 and 2006. The fishery yield was estimated at 15.7 kg ha(-1) year(-1), the average yield was 12.5 t year(-1) and catch per unit effort (CPUE) was 10.5 kg fisherman(-1) day(-1). We recorded 26 species of landed fish in this activity, being the "traira" (Hoplias malabaricus) the most landed fish in terms of biomass with 6,158.5 kg, representing 24.5%, of the total landed. Seasonally, the CPUE ranged from 14.5 kg fisherman(-1) day(-1) in summer/2005 to 9.0 kg fisherman(-1) day(-1) in spring/2006. The average CPUE by type of fish also showed a marked seasonality. In summer of 2005 and 2006, "curimbata" was the most landed fish, with CPUE kg fisherman(-1) day(-1) of 6.9 and 6.2, respectively. The "piavas" were the most landed fish in autumn with CPUE of 2.4 (year 2005) and 2.3 (year 2006) kg fisherman(-1) day(-1), and "traira" in winter with CPUE ranging from 3.0 to 4.0 kg fishrman(-1) day(-1), in 2005 and 2006, respectively. The mathematical modeling of simple linear regression indicated positive relationships between the monthly fish production and the number of boats in activity and of fishing trips. The study concluded that fishing is sustained only by native species; with marked seasonality for catching fish and that the area of fishing examined of the Jurumirim reservoir is among the most productive areas of the Upper Parana basin.

Sex ratio and dynamic behavior in populations of the exotic blowfly Chrysomya albiceps (Diptera, Calliphoridae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Artificial neural networks: A novel approach to analysing the nutritional ecology of a blowfly species, Chrysomya megacephala

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

Mathematical glimpse on the Y chromosome degeneration

The Y chromosomes are genetically degenerate and do not recombine with their matching partners X. Non-recombination of XY pairs has been pointed out as the key factor for the degeneration of the Y chromosome. The aim here is to show that there is a mathematical asymmetry in sex chromosomes which leads to the degeneration of Y chromosomes even in the absence of XX and XY recombination. A model for sex-chromosome evolution in a stationary regime is proposed. The consequences of their asymmetry are analyzed and lead us to a couple of conclusions. First, Y chromosome degeneration shows up v 2 more often than X chromosome degeneration. Second, if nature prohibits female mortalities from beeing exactly 50%, then Y chromosome degeneration is inevitable.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Mathematical modeling and control of population systems: Applications in biological pest control

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier B.V. All rights reserved.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Effectiveness-ntu computation with a mathematical model for cross-flow heat exchangers

Due to the wide range of design possibilities, simple manufactured, low maintenance and low cost, cross-flow heat exchangers are extensively used in the petroleum, petrochemical, air conditioning, food storage, and others industries. In this paper a mathematical model for cross-flow heat exchangers with complex flow arrangements for determining epsilon -NTU relations is presented. The model is based on the tube element approach, according to which the heat exchanger outlet temperatures are obtained by discretizing the coil along the tube fluid path. In each cross section of the element, tube-side fluid temperature is assumed to be constant because the heat capacity rate ratio C*=Cmin/Cmax tends toward zero in the element. Thus temperature is controlled by effectiveness of a local element corresponding to an evaporator or a condenser-type element. The model is validated through comparison with theoretical algebraic relations for single-pass cross-flow arrangements with one or more rows. Very small relative errors are obtained showing the accuracy of the present model. epsilon -NTU curves for several complex circuit arrangements are presented. The model developed represents a useful research tool for theoretical and experimental studies on heat exchangers performance.