Optimal Flood Levee Designs by Dynamic Programming

An economic optimal development of a levee system along a river is investigated and a dynamic programming (DP) approach is used to find the optima under various conditions. The system consists of a number of levee reaches or stages. A random input of flood wave is regarded at the upstream point of the system. There are two failure modes considered and, consequently, two parameters of the flood wave (state variables) to trigger failure modes in every stage. Stochastic DP is used since the state transition functions (flood routing along the stages) are random functions. Three methods are discussed. In Method I, the expected value of the objective function is taken first, then DP is used as a numerical technique. In Method II, a fixed design flood is chosen as an input under which both optimum cost and policy is determined. In Method III, the value of the expected optimum objective function is calculated. It is shown that the full power of DP cannot be used if Method I is applied. Future research involves comparing the solutions of the three methods

Catastrophe Theory and the Problem of Stellar Collapse

Recently, a new mathematical tool called "catastrophe theory" has been developed by the topologists Thom, Zeeman, Mather, and others in an attempt to mathematically explain the discontinuities of observed behavior due to smooth changes in the basic parameters of physical, social, and biological processes. It has been shown that the number of mathematically distinct ways in which such discontinuities may arise is small when compared with the dimension of the process, and a complete classification of all distinct types has been made for processes depending upon five or less parameters. The purpose of this note is two-fold: first, to serve as a very brief introduction to the subject of catastrophe theory and secondly, to illustrate the theory by applying it to the determination of equilibrium configurations for stellar matter which has reached the endpoint of thermonuclear evolution, the problem of "stellar collapse". It will be seen that catastrophe theory enables us to give a very satisfactory explanation for the observed phenomenon of unstable equilibrium configurations and the appearance of the so-called Chandrasekhar and Oppenheimer-Landau-Volkoff crushing points

Singularity Theory for Nonlinear Optimization Problems

Techniques from the theory of singularities of smooth mappings are employed to study the reduction of nonlinear optimization problems to simpler forms. It is shown how singularity theory ideas can be used to : 1) reduce decision space dimensionality; (2) transform the constraint space to simpler form for primal algorithms; (3) provide sensitivity analysis

Algorithms for Stochastic Inflow Nonlinear Objective Water Reservoir Control Problem

In earlier IIASA Working Papers, algorithms to determine the optimal control of a water reservoir network with stochastic inflows and nonlinear utilities have been proposed. Both studies utilize a dynamic programming-type approach, coupled with approximations of one type or another, in order to yield a computational algorithm in which the bulk of the calculation is carried out by efficient (and rapid) network flow algorithms. The purpose of this note is to present a synthesis of the work and to spell out the precise steps of an algorithm in sufficient detail to enable a computer program to be constructed

Polyhedral Dynamics - II: Geometrical Structure as a Basis for Decision Making in Complex Systems

The tools of polyhedral dynamics and dynamic programming are combined through the medium of cross-impact analysis to attack problems of organizational structure. It is argued that the standard cross-impact approaches to such problems are deficient in that they ignore the true multi-dimensional nature of such systems, as well as providing no systematic mechanism for rational decision making. The results of the analysis are illustrated by applications to the structuring of a large scientific organization and by the analysis of a simplified version of a problem arising in the energy field

Mythologies africaines dans la cartographie française au tournant du XIXe siècle.

L'article essaie de montrer que, par le biais de la cartographie, sont créées des mythologies à propos de l'Afrique que nous pouvons baptiser « de retour », c'est-à-dire qu'elles sont créées par les Occidentaux et transférées dans le projet de domination comme s'il s'agissait de qualités africaines. La première mythologie concerne la transmission d'une Afrique riche de ressources et de possibilités d'exploitation; la seconde considère que c'est une terre à valoriser dans une perspective colonialiste, car elle semble dépourvue de significations sociale et politique. L'analyse du langage cartographique des cartes des revues du début du colonialisme en Afrique occidentale française (AOF) montre que, à travers les mécanismes sémiotiques concernant les toponymes basiques (originels), on n'accordait pas d'importance au territoire produit par les populations locales. De cette façon, on dotait l'Afrique de valeurs occidentales, justifiant ainsi la légitimité des choix imposés sans tenir compte de sa diversité. Les mythologies « de retour » créées par la cartographie sont donc des interprétations induites, mais aussi des instruments pour exclure une identité originelle.The article tries to demonstrate that cartography can create mythologies about Africa that can be defined 'of return', that is, created by western people and transferred into the project of the colonies, as if they were African qualifies. The first mythology makes Africa a territory rich in resources and possibilities of exploitation; the second considers Africa as a land that must be developed according to a colonialist perspective, as it seems empty of social and political meaning. The analysis of the cartographic language of the maps published in the geographical reviews at the beginning of colonialism in French Western Africa (AOF) shows that, through the semiotic mechanisms concerning the basic designators, the territory produced by the local populations had no importance. The mythologies 'of return', created by cartography, are not only undeserved attributions, but also means which can exclude a reality, a basic identity, that exactly on the territory and through the territory could have been recovered

Some Recent Developments in the Theory and Computation of Linear Control Problems

Recent analysis and computational results for the solution of linear dynamics-quadratic cost control processes are presented. It is shown that, if the number of system inputs and outputs is less than the number of state variables, a substantial reduction in computing effort may be achieved by utilizing the new equations, termed "generalized X-Y" functions over the standard matrix Riccati equation solution. In addition to the basic X-Y equations, the paper also discusses the reduced algebraic equation for infin-infinite-interval problems, infinite-dimensional problems, the discrete-time case, and Kalman filtering problems. Numerical experiments are also reported

Connectivity and Stability in Ecological and Energy Systems

One of the more enduring topics of methodological interest at IIASA has been the problem of ascertaining and describing stability characteristics for large-scale systems. These points have been of particular applied interest in the ecology and energy areas where the terms "resilience" and "hypotheticality" have been used to intuitively characterize the type of stability of greatest practical interest. Our primary purpose in this note is to present some new results in stability theory which have great relevance to the aforementioned studies. These results deal with the problem of "connective" stability, in which the basic question is how large a perturbation in structure the system can withstand and still remain asymptotically stable. In many ways, these results are similar in spirit to structural stability questions in which the invariance of the topological features of the system trajectory is the central issue. However, the two theories are not the same as connective stability deals with the stability of a point under structural perturbation, while structural stability is concerned with trajectories. In addition, connective stability is a quantitative theory as precise numerical estimates can be given for the magnitude of the allowed perturbation, while structural stability is primarily qualitative. Therefore, we feel justified in presenting these results in order to provide systems analysts with another tool to probe the stability characteristics of applied systems. A secondary objective of this note is to point out the connections between the notion of connective stability and the idea of a system's connectivity pattern. All of these results will be illustrated with examples from energy and ecology