On the Local and Global Convergence of a Reduced Quasi-Newton Method

In optimization in R^n with m nonlinear equality constraints, we study the local convergence of reduced quasi-Newton methods, in which the updated matrix is of order n-m. In particular, we give necessary and sufficient conditions for q-superlinear convergence (in one step). We introduce a device to globalize the local algorithm which consists in determining a step on an arc in order to decrease an exact penalty function. We give conditions so that asymptotically the step will be equal to one

Maintaining the Positive Definiteness of the Matrices in Reduced Secant Methods for Equality Constrained Optimization

This paper proposes an algorithm for minimizing a function f on R^n in the presence of m equality constraints c that locally is a reduced secant method. The local method is globalized using a nondifferentiable augmented Lagrangian whose decrease is obtained by both a longitudinal search that decreases mainly f and a transversal search that decreases mainly ||c||. The main objective of the paper is to show that the longitudinal path can be designed in order to maintain the positive definiteness of the reduced matrices by means of the positivity of gamma_{k}^{T}, where gamma_{k} is the change in the reduced gradient and bk is the reduced longitudinal displacement

Crosslinking of rigid poly(vinyl chloride)

Various formulations for the crosslinking of rigid poly(vinyl chloride) have been investigated including three different thermal stabilisers: a tin maleate; an octyl thio tin stabiliser; and a tribasic lead sulphate. The possibility of using aminosilanes and peroxides as crosslinking agents was considered and the additives used in the formulations were bis(-trimethoxysilylpropyl)amine, a blend of trimethylol propane trimethacrylate and amorphous silica, and 1,1-di-t-butylperoxy-3,3,5-trimethyl cyclohexane incorporating 40% peroxide. It was shown that rigid poly(vinyl chloride) can be crosslinked using both aminosilane and peroxide systems and the optimum level of the aminosilane was found to be 2 phr while significant property improvements were achieved with only 0·5 phr peroxide. The effects of the various thermal stabilisers and crosslinking additives are presented and discussed

Le paludisme urbain à Yaoundé (Cameroun) : 2. Etude entomologique dans deux quartiers peu urbanisés

International audienceA one year entomological survey was carried out to precise the malaria vectors and the malaria transmission in Yaounde, the Cameroon capital (800,000 inhabitants). The study was done in two districts not yet fully urbanized: Nkol Bikok and Nkol Bisson. The latter is located at the periphery and has a pool. Anopheles gambiae was the only human malaria vector. Its agressivity for man depended on the urbanization of the district. Annual man biting rate was 284 in Nkol Bikok and 1,813 in Nkol Bisson. The densities were maximum in May-June and in October-November, corresponding to the end of the short and long rainy seasons. The presence of A. gambiae was permanent except in August-September in Nkol Bikok. In Nkol Bisson the density was higher in the houses near the pool. The yearly inoculation rate (h) was 14 in Nkol Bikok and 30 in Nkol Bisson. The vectorial transmission was observed in may in Nkol Bikok and during four months (June, August, January, February) in Nkol Bisson. These entomological data showed clearly that malaria transmission actually occurred in Yaounde and that the probability to receive at least one infected anopheline bite per year was very near to 1 for inhabitants unprotected against mosquito bites.Une étude longitudinale basée sur la capture des moustiques sur sujets humains s'est déroulée pendant un an dans deux quartiers de la ville de Yaoundé, l'un est situé à la périphérie de la ville (Nkol Bisson) et l'autre est plus central (Nkol Bikok). Ces deux quartiers présentent encore un caractère périurbain mais ils sont en pleine urbanisation. Le vecteur du paludisme humain identifé est Anopheles gambiae. Sa densité agressive pour l'homme (ma) est variable selon le degré d'urbanisation des quartiers : forte en Zone périphérique (ma annuel = I 813) et faible en zone centrale (ma annuel = 284). Cette densité est importante de mai à juin et d'octobre 6 novembre, c'est-à-dire à la fin de la petite et de la grande saison des pluies. Le taux d'inoculation (h) varie comme les densités agressives : h annuel = 30 en zone périphérique contre 14 en zone centrale. La transmission vectorielle est notable seulement pendant un mois (mai) à Nkol Bikok et pendant quatre mois (juin, août, janvier, février) à Nkol Bisson. Le risque quotidien d'au moins une inoculation par A. gambiae est environ deux fois plus élevé en zone périphérique qu'en zone centrale

Some Numerical Experiments with Variable Storage Quasi-Newton Algorithms

This paper relates some numerical experiments with variable storage quasi-Newton methods for the optimization of large-scale models. The basic idea of the recommended algorithm is to start bfgs updates on a diagonal matrix, itself generated by an update formula and adjusted to Rayleigh's ellipsoid of the local Hessian of the objective function in the direction of the change in the gradient. A variational derivation of some rank one and rank two updates in Hilbert spaces is also given

Anthropophilic mosquitoes and malaria transmission at Edea, Cameroon

International audienceAn entomological study was carried out during 1990 in the town of Edea in the south of Cameroon to study anthropophilic mosquitoes with special reference to malaria transmission. Man-biting mosquitoes were caught regularly during one night each month in two different districts: Bilalang which is a well planned suburb with 160 houses on a hill-top, provided with a piped water supply; and Pongo which is a densely urbanised suburb in a valley. From 188 man-nights 1030 mosquitoes were collected, comprising 700 Culex quinquefasciatus (68%), 262 Anopheles gambiae (25%) and others species (7%) belonging to the genus Anopheles, Mansonia, Culex and Aedes. The estimated annual biting rates of mosquitoes were 811 bites per man in Bilalang and 2,866 in Pongo. The estimated yearly malaria inoculation rates were 3.8 and 30.2 infective bites per man in Bilalang and Pongo, respectively. In different parts of Pongo district much variation existed; extreme values of the estimated yearly inoculation rate were zero and 86.3 in two houses 200 m apart, located on the top of a hill and in the bottom of a valley, respectively. This study is one of the first conducted on malaria transmission in a moderate sized African town; it shows that the mosquito populations are typically urban and differ greatly from rural ones

Global Production Increased by Spatial Heterogeneity in a Population Dynamics Model

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production.We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations

Hmm-based monitoring of packet channels

Abstract. Performance of real-time applications on network communication channels are strongly related to losses and temporal delays. Several studies showed that these network features may be correlated and exhibit a certain degree of memory such as bursty losses and delays. The memory and the statistical dependence between losses and temporal delays suggest that the channel may be well modelled by a Hidden Markov Model (HMM) with appropriate hidden variables that capture the current state of the network. In this paper we discuss on the effectiveness of using an HMM to model jointly loss and delay behavior of real communication channel. Excellent performance in modelling typical channel behavior in a set of real packet links are observed. The system parameters are found via a modified version of the EM algorithm. Hidden state analysis shows how the state variables characterize channel dynamics. State-sequence estimation is obtained by use of the Viterbi algorithm. Real-time modelling of the channel is the first step to implement adaptive communication strategies.