Showing papers by "Paris Dauphine University published in 1993"

Axioms and fundamental equations of image processing

Abstract: Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: “architectural requirements” like locality, recursivity and causality in the scale space, “stability requirements” like the comparison principle and “morphological requirements”, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.

Representation and Control of Infinite Dimensional Systems

Abstract: Preface to the Second Edition Preface to Volume I of the First Edition Preface to Volume II of the First Edition List of Figures Introduction Part I. Finite Dimensional Linear Control of Dynamical Systems Control of Linear Finite Dimensional Differential Systems Linear Quadratic Two-Person Zero-Sum Differential Games Part II. Representation of Infinite Dimensional Linear Control Dynamical Systems Semi-groups of Operators and Interpolation Variational Theory of Parabolic Systems Semi-group Methods for Systems with Unbounded Control and Observation Operators Differential Systems with Delays Part III. Qualitative Properties of Linear Control Dynamical Systems Controllability and Observability for a Class of Infinite Dimensional Systems Part IV. Quadratic Optimal Control: Finite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Part V. Quadratic Optimal Control: Infinite Time Horizon Systems with Bounded Control Operators: Control Inside the Domain Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary Appendix A. An Isomorphism Result References Index

Looking for the Bernoulli shift

Abstract: We prove a result on the topological entropy of a large class of Hamiltonian systems. This result is obtained variationally by constructing “multibump” homoclinic solutions.

Economic evaluation of pharmaceuticals: a European perspective.

Abstract: In recent years there has been a large increase in the number of economic evaluations of pharmaceuticals. Many of these studies have been commissioned by individual pharmaceutical companies, in support of new or existing products. In 2 countries, Australia and Canada (in the province of Ontario), draft guidelines issued by the government have outlined the requirements for economic evaluations to be submitted in support of requests for reimbursement (government subsidy) of particular products. One consequence of the guidelines is that they clarify what is required, and in specifying the procedure for submission of dossiers, identify a clear audience for the economic evaluation. In contrast, the situation in Europe is diverse. A wide range of healthcare systems exist, including national health services and more liberal systems, involving a wide range of insurers and providers. European countries also differ widely in their approach to the pricing and reimbursement of pharmaceuticals. Because of this diversity, the nature, conduct and impact of economic evaluation in Europe is not clear. It is therefore difficult for pharmaceutical companies to develop appropriate strategies for economic evaluation and for analysts to decide on appropriate study methodology. This article reviews the nature of any official guidance or requirements for economic evaluation, the potential for use of economic evaluation, the range of studies carried out and the identifiable impacts. There is currently no official guidance in any country, although some countries are considering issuing guidelines. In some countries there is official encouragement to pharmaceutical companies to undertake studies, and where economic data have been presented they have been considered by the relevant committees. The potential uses of economic evaluation vary widely from country to country. These can be classified in terms of a potential role in undertaking national price negotiations, deciding on reimbursement status or copayment level, deciding on inclusion in local formularies or in treatment guidelines, or in improving prescribing decisions. Approximately 80 economic evaluations of pharmaceutical products have been conducted to date in Europe, covering a wide range of clinical areas. There are relatively few examples of identifiable effects of such studies. In part this is because it is often difficult to assess the part played by various items of data. Nevertheless, the overriding conclusion is that economic evaluation of medicines is likely to be more relevant in Europe in the future. The problem for the pharmaceutical industry is in determining when and how.

Query languages for relational multidatabases

Abstract: With the existence of many autonomous databases widely accessible through computer networks, users will require the capability to jointly manipulate data in different databases. A multidatabase system provides such a capability through a multidatabase manipulation language, such as MSQL. We propose a theoretical foundation for such languages by presenting a multirelational algebra and calculus based on the relational algebra and calculus. The proposal is illustrated by various queries on an example multidatabase. It is shown that properties of the multirelational algebra may be used for optimization and that every multirelational algebra query can be expressed as a multirelational calculus query. The connection between the multirelational languages and MSQL, the multidatabase version of SQL, is also investigated.

Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 2 : Stability is equivalent to the binding of neutral subsystems

Abstract: This paper is the sequel of a previous work where we showed a general necessary and sufficient condition for the stability of an arbitrary molecular system (possibly ionized) in the framework of Hartree or Thomas-Fermi type theories. This condition, roughly speaking, meant that certain particular subsystems have to be bound. We show here in particular that this condition reduces for general molecular system with nonnegative excess charge to the binding of all subsystems with the same property. For neutral inolecular systems, this reduces to the binding of all neutral subsystems. In both cases, all other subsystems can be bound. We also show that, for the Hartree-Fock and Hartree models, this condition involves only “physical” sulxystems We use these reduced conditions to conclude allout the stability or the binding in some particular cases. This work 1s also the second of a series devoted to these equations and we shall come back on the binding of neutral systems in Part 3.

A General Two-Stage Approach to Inducing Rules from Examples

Abstract: A two-stage approach for inducing rules from examples is presented. The first stage consists in a breadth-first exploration which generates all ‘relevant’ rules. The second stage consists in selecting a subset of these rules so as to produce a ‘satisfactory’ description. Rough sets concepts may be used in cases of incomplete or inconsistent examples.

A mountain pass method for the numerical solution of semilinear wave equations

Abstract: It is well-known that periodic solutions of semilinear wave equations can be obtained as critical points of related functionals. In the situation that we studied, there is usually an obvious solution obtained as a solution of linear problem. We formulate a dual variational problem in such a way that the obvious solution is a local minimum. We then find additional non-obvious solutions via a numerical mountain pass algorithm, based on the theorems of Ambrosetti, Rabinowitz and Ekeland. Numerical results are presented.

Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.: Part 3 : Binding of neutral subsystems.

Abstract: This paper is the third of a series devoted to the study of the binding of atoms, molecules and ions and of the stability of general molecular systems including molecular ions, in the context of Hartree and Thomas-Fermi type theories. For Thomas-Fermi-von WeizsOcker or Thomas-Fermi-Dirac-von Weizsacker models, we prove here that neutral systems can be bound and in view of the results shown in the preceding parts this yields the stability of arbitrary molecules (general neutral molecular systems). For the Hartree and Hartree-Fock models, we prove that neutral planar systems can be bound and this yields the stability of arbitrary tetraatomic molecules for instance. Various variants and extensions are also considered.

2. Borrowing Constraints and International Comovements

Abstract: It is now well understood how the presence of borrowing constraints can affect the time series properties of aggregate economic data In particular the results in Scheinkman and Weiss [9] show that borrowing constraints may cause the appearance of economic fluctuations in an economy where, if the perfect risk sharing implied by a full set of contingent claims markets was available, no aggregate fluctuations would be observed Departures from perfect risk-sharing across countries would also have several implications for the behavior ofthe international comovements ofeconomic time series Scheinkman [8] suggested that correlation of consumption series across countries could be used to test for the presence of a full set of contingent claims markets Also, as it is shown formally below, if the output of different countries are Pareto substitutes in consumption, in a complete markets setting, the correlation of output series should be smaller (algebraically) than that of the corresponding productivity series In this paper we construct a formal model of a two country economy that allows us to derive implications of the presence of borrowing constraints on the behavior of economic time series Simulations of the model reveal that it is capable of generating significant positive correlation across output series even in the presence of uncorrelated productivity shocks This result suggests that borrowing constraints can be used to explain the substantial positive correlation of output growth across countries in the presence of almost no correlation of productivity growth series (cf Costello [5]) Further the model can generate a much lower consumption correlation than

Filippov and invariance theorems for mutational inclusions of tubes

Abstract: The framework of transitions and mutational calculus inspired by shape optimization allows the notions of derivative, tangent cone, and differential equation to be extended to a metric space and especially to the family of all nonempty compact subsets of a given domainE. It gives tools to study the evolution of tubes and fundamental theorems such as those of Cauchy-Lipschitz, Nagumo, or Lyapunov, well known in vector spaces, can be adapted to mutational equations. The present paper deals with mutational inclusions of tubes which include many tube control problems and an adaptation of the Filippov theorem is proved. As a consequence, an invariance theorem is stated.

Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. Part 4: Binding of neutral systems for the Hartree model

Abstract: This paper is the fourth of a series devoted to the study of the stability of general molecular systems in Thomas-Fermi or Hartree type models. In the preceding part, the authors proved the binding of arbitrary neutral systems for Thomas-Fermi type theories and of planar neutral systems for the Hartree model. In this part, they manage to get rid of this restriction and thus prove the binding and the stability of arbitrary neutral systems for the Hartree model. 23 refs.

The cut cone III: On the role of triangle facets

Abstract: The cut polytopeP n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP n arises from the triangle inequalities:x ij +x ik +x jk ≤ 2 andx ij -x ik -x jk ≤ 0 for 1 ≤i,j, k ≤n. Hence, the metric polytope Mn, defined as the solution set of the triangle inequalities, is a relaxation ofP n . We consider several properties of geometric type for Pn, in particular, concerning its position withinM n . Strengthening the known fact ([3]) thatP n has diameter 1, we show that any set ofk cuts,k ≤ log2 n, satisfying some additional assumption, determines a simplicial face ofM n and thus, also, ofP n . In particular, the collection of low dimension faces ofP n is contained in that ofM n . Among a large subclass of the facets ofP n , the triangle facets are the closest ones to the barycentrum of Pn and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP n and its triangle facets are mentioned.

La recherche d'information par le consommateur : Proposition d'une échelle de mesure:

Abstract: Cet article retrace la procedure adoptee pour la creation d'une echelle multi-items destinee a mesurer l'activite de recherche d'information engagee par le consommateur prealablement a l'achat. Dans un premier temps, les difficultes relatives a la mesure de l'activite de recherche d'information, et en particulier de sa composante interne, sont presentees et discutees. La multidimensionalite de la recherche d'information est ensuite demontree a travers l'evaluation de la structure factorielle, de la fiabilite et de la validite de l'echelle proposee. L'article conclut sur l'opportunite de cerner la recherche d'information du consommateur a travers ses facettes sous-jacentes, ce qui presente des avantages, tant au niveau theorique que pratique, par rapport aux approches globales proposees dans la litterature.

A geometric theory for L 2 -stability of the inverse problem in a one-dimensional elliptic equation from an H 1 -observation

Abstract: This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.

Convergence of cascade algorithms introduced by I. Daubechies

Abstract: Orthonormal wavelets are often constructed by an iteration procedure commonly referred to as thecascade algorithm. We obtain an asymptotic expansion and deduce necessary and sufficient conditions for convergence in Sobolev norms.

Differential inclusions for mathematical morphology

Abstract: In mathematical morphology, we are led to study the evolution of morphological tubes. By using some appropriate notions of set- valued analysis, viability theory and non-smooth analysis, this paper provides differential inclusions which govern these tubes.

Efficient algorithm for computing the antigranulometry

Abstract: The principle of shape recognition by using granulometries, is to transform a binary planar shape into a curve which is translation, rotation and scale invariant by a family of morphological transformations depending on the size of the structuring element. This paper presents a fast algorithm for the computation of the anti-granulometry by closings which avoids boundary effects. This algorithm is based on a simple geometric transformation called the `Steiner Inverse Transform', on which original theoretical results are given.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

An introduction to the hilbert uniqueness method

Abstract: We give in this paper a short presentation of the Hilbert Uniqueness Method, introduced by J.L. Lions, in 1988 [7] [8]. This method has aroused a lot of interest among scientists, from both origins, partial differential equations and general dynamic systems. The paper of J.E. Lagnese [3] gives an excellent survey of the method and its connection with other approaches, including earlier results of D.L. Russell [9] and works of I. Lasiecka, tL Trigglani [6] ... and others.

Do Advisory Fees Contain Evidence of a Principal‐Agent Conflict?

Abstract: In a world where the objectives of managers differ from the objectives of shareholders, the analysis of management response to a tender offer must consider the possibility that management's response is a function of their equity interest in the company.

Remarks on the separation principle

Abstract: The objective of the paper is to extend the applicability of the separation principle to the case of nonsmooth feedbacks, by allowing an extension of the concept of admissible controls. Topics covered in the paper include: the Bellman equation; solution of the separated problem; and a new definition of the problem of optimal stochastic control with partial information. >

Statistical Evidence of the Endogeneity Problem: Predicting the Outcome of Tender Offers

Abstract: In the paper “Predicting the Outcome of Tender Offers: An Endogeneity Problem”, we argue that previous econometric models designed to predict the outcome of tender offers have been estimated incorrectly. We illustrate that the source of the estimation error comes from variables which are posited to explain the outcome of tender offers and treated as exogenous when in fact they are endogenous. We discuss the possibility, using the Nelson‐Olson simultaneous equation model, to solve the endogeneity problem. Although correct at the theoretical level we did not actually estimate the model using the Nelson‐ Olson technique. The complexity of applying the Nelson‐ Olson technique motivated us to search for an alternative solution to the endogeneity problem.