An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro

In order to reduce infant mortality in the municipality of Rio de Janeiro it is desired to encourage all mothers-to-be to attend the appropriate health care facilities. A 3-level hierarchical prenatal–neonatal health care system is described together with a basic model for optimising accessibility to facilities. A genetic algorithm to solve the basic model is developed and some numerical experience reported. Extensions to the basic model and planned future research are briefly indicated.     

Load balancing and capacity constraints in a hierarchical location model

Recent work on the location of perinatal facilities in the municipality of Rio de Janeiro resulted in the development of an uncapacitated, three-level hierarchical model. An important issue that arose during the course of the research was the need to include some form of capacity constraints into the model, especially in the higher, resource intensive level of the hierarchy. This need was felt from technical discussions related to the research work and from contacts with municipality health officials.A capacitated model is presented and solved using a Lagrangean heuristic. For smaller problems optimal solutions are found using CPLEX; it is found that the heuristic usually gives high quality solutions. Next a bi-criterion model is formulated in which the additional objective measure is the imbalance in facility loading. This is solved exactly for a small problem and approximately for the 152-vertex Rio de Janeiro data.     

Foliations invariant under Lie group transverse actions

In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups. Authors’ address: Alexandre Behague and Bruno Scárdua, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil     

On the convergence properties of Hildreth's quadratic programming algorithm

We prove the linear convergence rate of Hildreth's method for quadratic programming, in both its sequential and simulateneous versions. We give bounds on the asymptotic error constant and compare these bounds to those given by Mandel for the cyclic relaxation method for solving linear inequalities.Research of this author was partially supported by CNPq grant No. 301280/86.On leave from the Universidade Federal do Rio de Janeiro, Instituto de Matemática, Rio de Janeiro, R.J. 21.910, Brazil. Research of this author was partially supported by NIH grant HL28438.     

Practical aspects associated with location planning for maternal and perinatal assistance in Brazil

A study has been carried out aimed at reducing perinatal mortality in the municipality of Rio de Janeiro through a better distribution of health care facilities. The algorithmic aspects are detailed elsewhere and here the emphasis is on practical issues and difficulties encountered. A 3-level hierarchical model was developed. Both uncapacitated and capacitated versions are briefly described together with some results based on actual data. The project brought to light many contradictions between OR theory and practice in developing countries and, unfortunately, the models developed were not implemented by the municipality health authorities. Possible reasons for this outcome are analysed.     

Penalty computations for the set partitioning problem

The computation of penalties associated with the continuous relaxation of integer programming problems can be useful to derive conditional and relational tests which allow to fix some variables at their optimal value or to generate new constraints (cuts). We study in this paper the computation and the use of penalties as a tool to improve the efficiency of algorithms for solving set partitioning problems. This leads to a preprocessing scheme which can be embedded within any exact or approximate algorithm. The strength of these penalties is illustrated through computational results on some real-world set partitioning problems.This work was sponsored by FINEP (research contract number 4.3.86.0689-00), CNPq (research contract numbers 11.1592-84, 30.2281-85 and 40.2002-86.5), IBM Brazil and NSERC (grant # GP0036426).On leave from the Catholic University of Rio de Janeiro, Department of Electrical Engineering, Caixa Postal 38063, Gávea, Rio de Janeiro 22452, Brazil.     

On unconditional bases in spaces of holomorphic functions in infinite dimensions

This paper was written during the first author's stay at the Department of Mathematics of the Universidade Federal do Rio de Janeiro. He wants to thank the Department for the kind invitation and the CAPES/DAAD for its financial support.     

Hyperbolic 0–1 programming and query optimization in information retrieval

Unconstrained hyperbolic 0–1 programming can be solved in linear time when the numerator and the denominator are linear and the latter is always positive. It is NP-hard, and finding an approximate solution with a value equal to a positive multiple of the optimal one is also NP-hard, if this last hypothesis does not hold. Determining the optimal logical form of a query in information retrieval, given the attributes to be used, can be expressed as a parametric hyperbolic 0–1 program and solved in O(n logn) time, wheren is the number of elementary logical conjunctions of the attributes. This allows to characterize the optimal queries for the Van Rijsbergen synthetic criterion.This research was done in part during a visit of the first author to the Pontifical Catholic University of Rio de Janeiro in July and August 1987, sponsored by CNPq. It was also supported in part by grants 0271 and 0066 of the AFOSR to Rutgers University. The second author was with Centro de Análise de Sistemas Navais, Rio de Janeiro.     

Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model

In this study we analyse the ambulance deployment of an emergency medical system on a Brazilian highway connecting the cities of São Paulo and Rio de Janeiro. Our focus is on the mean response time of the system to an emergency call, viewed as an important component of the user service. To evaluate the system performance we applied the hypercube model, a well-known tool for planning server-to-customer systems, which is based on spatially distributed queuing theory. The results showed that the model can be effective in supporting design and operational decisions, in particular to reduce the workload unbalancing among the ambulances.     

Conical projection algorithms for linear programming

The Linear Programming Problem is manipulated to be stated as a Non-Linear Programming Problem in which Karmarkar's logarithmic potential function is minimized in the positive cone generated by the original feasible set. The resulting problem is then solved by a master algorithm that iteratively rescales the problem and calls an internal unconstrained non-linear programming algorithm. Several different procedures for the internal algorithm are proposed, giving priority either to the reduction of the potential function or of the actual cost. We show that Karmarkar's algorithm is equivalent to this method in the special case in which the internal algorithm is reduced to a single steepest descent iteration. All variants of the new algorithm have the same complexity as Karmarkar's method, but the amount of computation is reduced by the fact that only one projection matrix must be calculated for each call of the internal algorithm.Research partly sponsored by CNPq-Brazilian National Council for Scientific and Technological Development, by National Science Foundation grant ECS-857362, Office of Naval Research contract N00014-86-K-0295, and AFOSR grant 86-0116.On leave from COPPE-Federal University of Rio de Janeiro, Cx. Postal 68511, 21941 Rio de Janeiro, RJ, Brasil.     

Building the Additive Utility Functions for CAD-UFRJ Evaluation Staff Criteria

This paper presents an application of the UTA method for building utility functions for the evaluation criteria defined by the Staff Evaluation Commission (CAD) of the Rio de Janeiro Federal University (UFRJ). Every year, the CAD-UFRJ gives the staff evaluation results for each Postgraduate Engineering Programme. However, the method used to generate the staff evaluation is assumed unknown. Trying to find the CAD-UFRJ preference structure, the evaluation results supplied by CAD-UFRJ are used to apply the UTA method. Some additional information obtained from the CAD-UFRJ data is incorporated in the optimal solutions analysis.     

Exact penalty function algorithm with simple updating of the penalty parameter

A new globally convergent algorithm for minimizing an objective function subject to equality and inequality constraints is presented. The algorithm determines a search direction by solving a quadratic programming subproblem, which always has an optimal solution, and uses an exact penalty function to compute the steplength along this direction through an Armijo-type scheme. The special structure of the quadratic subproblem is exploited to construct a new and simple method for updating the penalty parameter. This method may increase or reduce the value of the penalty parameter depending on some easily performed tests. A new method for updating the Hessian of the Lagrangian is presented, and a Q-superlinear rate of convergence is established.This work was supported in part by the British Council and the Conselho Nacional de Desenvolvimento Cientifico & Tecnologico/CNPq, Rio de Janeiro, Brazil.The authors are very grateful to Mr. Lam Yeung for his invaluable assistance in computing the results and to a reviewer for constructive advice.     

Existence of periodic solutions in a model of respiratory syncytial virus RSV

In this paper we study the existence of a positive periodic solutions for nested models of respiratory syncytial virus RSV, by using a continuation theorem based on coincidence degree theory. Conditions for the existence of periodic solutions in the model are given. Numerical simulations related to the transmission of respiratory syncytial virus in Madrid and Rio Janeiro are included.     

An acceleration scheme for cyclic subgradient projections method

An algorithm for solving convex feasibility problem for a finite family of convex sets is considered. The acceleration scheme of De Pierro (em Methodos de projeção para a resolução de sistemas gerais de equações algébricas lineares. Thesis (tese de Doutoramento), Instituto de Matemática da UFRJ, Cidade Universitária, Rio de Janeiro, Brasil, 1981), which is designed for simultaneous algorithms, is used in the algorithm to speed up the fully sequential cyclic subgradient projections method. A convergence proof is presented. The advantage of using this strategy is demonstrated with some examples.     

Spatiotemporal Models for Gaussian Areal Data

We introduce a class of spatiotemporal models for Gaussian areal data. These models assume a latent random field process that evolves through time with random field convolutions; the convolving fields follow proper Gaussian Markov random field (PGMRF) processes. At each time, the latent random field process is linearly related to observations through an observational equation with errors that also follow a PGMRF. The use of PGMRF errors brings modeling and computational advantages. With respect to modeling, it allows more flexible model structures such as different but interacting temporal trends for each region, as well as distinct temporal gradients for each region. Computationally, building upon the fact that PGMRF errors have proper density functions, we have developed an efficient Bayesian estimation procedure based on Markov chain Monte Carlo with an embedded forward information filter backward sampler (FIFBS) algorithm. We show that, when compared with the traditional one-at-a-time Gibbs sampler, our novel FIFBS-based algorithm explores the posterior distribution much more efficiently. Finally, we have developed a simulation-based conditional Bayes factor suitable for the comparison of nonnested spatiotemporal models. An analysis of the number of homicides in Rio de Janeiro State illustrates the power of the proposed spatiotemporal framework.

Supplemental materials for this article are available online in the journal’s webpage.     

Integrating Geographical Information Systems and Multi-Criteria Methods: A Case Study

This paper presents an application of the integration between Geographical Information Systems (GIS) and Multi-Criteria Decision Analysis (MCDA) to aid spatial decisions. We present a hypothetical case study to illustrate the GIS–MCDA integration: the selection of the best municipal district of Rio de Janeiro State, Brazil, in relation to the quality of urban life. The best municipal district is the one that presents the closest characteristics to those considered ideal by the decision-maker. The approach adopted is the Multi-Objective Linear Programming (MOLP) and the chosen method is the Pareto Race.     

The expected number of extreme points of a random linear program

There has been increasing attention recently on average case algorithmic performance measures since worst case measures can be qualitatively quite different. An important characteristic of a linear program, relating to Simplex Method performance, is the number of vertices of the feasible region. We show 2 ⁿ to be an upper bound on the mean number of extreme points of a randomly generated feasible region with arbitrary probability distributions on the constraint matrix and right hand side vector. The only assumption made is that inequality directions are chosen independently in accordance with a series of independent fair coin tosses.We would like to thank the Institute of Pure and Applied Mathematics in Rio de Janeiro for supporting the authors' collaboration that led to this paper.     

Entire functions of exponential type bounded on the real axis and fourier transforms of distributions with bounded supports

On the complexification of the dual spaceE′ of a real Banach spaceE′ of infinite dimension, there is an entire complex valued function of exponential type, bounded onE′, hence slowly increasing onE′, which is not the Fourier transform of any distribution with bounded support onE. Partially supported by the Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, GB, Brasil and by the National Science Foundation, Washington, DC, USA. Attendance at the International Symposium on Partial Differential Equations and the Geometry of Normed Spaces was possible in part thanks to a grant from CAPES, Brasil.     

An index theory for paths that are solutions of a class of strongly indefinite variational problems

We generalize the Morse index theorem of [12,15] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distribution for . In particular we obtain Morse relations for stationary semi-Riemannian manifolds (see [7]) and for the G?del-type manifolds (see [3]). Received: 4 April 2001 / Accepted: 27 September 2001 / Published online: 23 May 2002 The authors are partially sponsored by CNPq (Brazil) Proc. N. 301410/95 and N. 300254/01-6. Parts of this work were done during the visit of the two authors to the IMPA, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, in January and February 2001. The authors wish to express their gratitude to all Faculty and Staff of the IMPA for their kind hospitality.     

Solution of polyhedra

The paper is an exposition of the authors talk on the Seminar on Differential Geometry in IMPA in Rio de Janeiro. It presents a short survey of some recent results in the metric theory of polyhedra in 3-space. Namely we emphasize on some applicatons of the theorem which is a vast generalization of the Herons formule for the area of a triangle to volumes of polyhedra.*The author is partially supported by grants of RFBR No. 02-01-00101 and Russian Ministry of Education E02-1.0-43.