Maximizing the divergence from a hierarchical model of quantum states

We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.Comment: 18 pages, 1 figure, v2: improved exposition, v3: less typo

Temporal Technical and Profit Efficiency Measurement: Definitions, Duality and Aggregation Results

The shortage function, an important tool in production theory, measures potential increases in outputs and decreases in inputs for a given direction g at a given date. To develop a temporal version of technical efficiency measurement, we introduce the concept of a temporal shortage function. This temporal efficiency measure is easily computed using linear programming. We also establish a duality result stating that the temporal profit function and the temporal shortage function are dual to one another. This result has two consequences. First, one can derive a shadow price path via the shadow prices of the temporal shortage function. Second, transposing the classic Farrell inefficiency decomposition, temporal profit efficiency is decomposed into temporal technical and temporal allocative efficiency components. Finally, in line with the recent literature on aggregation over firms, this contribution treats the possibilities and limits of the aggregation of efficiency measures over time.Temporal shortage function; temporal profit function; aggregation over time

Nuclear emergency decision support : a behavioural OR perspective

Operational researchers, risk and decision analysts need consider many behavioural issues. Despite many OR applications in nuclear emergency decision support, the literature has not paid sufficient attention to behavioural matters. In working on designing decision support processes for nuclear emergency management, we have encountered many behavioural issues. In this paper we synthesise the findings in the literature with our experience and identify a number of behavioural challenges to nuclear emergency decision support. In addition to challenges in model-building and interaction, we pay attention to a behavioural issue that is often neglected: the analysis itself and the communication of its implications may have behavioural consequences. We introduce proposals to address these challenges. First, we propose the use of models relying on incomplete preference information, outlining a framework and illustrating it with data from a previous decision analysis for the Chernobyl Project. Moreover, we reflect on the responsibility that rests on the analyst in addressing behavioural issues sensitively in order to lessen the effects on public stress. In doing so we make a distinction between System 1 Societal Deliberation and System 2 Societal Deliberation and discuss how this can help structure societal deliberation in the context of nuclear emergencies

Decomposition techniques for large scale stochastic linear programs

Stochastic linear programming is an effective and often used technique for incorporating uncertainties about future events into decision making processes. Stochastic linear programs tend to be significantly larger than other types of linear programs and generally require sophisticated decomposition solution procedures. Detailed algorithms based uponDantzig-Wolfe and L-Shaped decomposition are developed and implemented. These algorithms allow for solutions to within an arbitrary tolerance on the gap between the lower and upper bounds on a problem\u27s objective function value. Special procedures and implementation strategies are presented that enable many multi-period stochastic linear programs to be solved with two-stage, instead of nested, decomposition techniques. Consequently, abroad class of large scale problems, with tens of millions of constraints and variables, can be solved on a personal computer. Myopic decomposition algorithms based upon a shortsighted view of the future are also developed. Although unable to guarantee an arbitrary solution tolerance, myopic decomposition algorithms may yield very good solutions in a fraction of the time required by Dantzig-Wolfe/L-Shaped decomposition based algorithms.In addition, derivations are given for statistics, based upon Mahalanobis squared distances,that can be used to provide measures for a random sample\u27s effectiveness in approximating a parent distribution. Results and analyses are provided for the applications of the decomposition procedures and sample effectiveness measures to a multi-period market investment model