A comparison of two approaches for solving unconstrained influence diagrams

AbstractInfluence diagrams and decision trees represent the two most common frameworks for specifying and solving decision problems. As modeling languages, both of these frameworks require that the decision analyst specifies all possible sequences of observations and decisions (in influence diagrams, this requirement corresponds to the constraint that the decisions should be temporarily linearly ordered). Recently, the unconstrained influence diagram was proposed to address this drawback. In this framework, we may have a partial ordering of the decisions, and a solution to the decision problem therefore consists not only of a decision policy for the various decisions, but also of a conditional specification of what to do next. Relative to the complexity of solving an influence diagram, finding a solution to an unconstrained influence diagram may be computationally very demanding w.r.t. both time and space. Hence, there is a need for efficient algorithms that can deal with (and take advantage of) the idiosyncrasies of the language. In this paper we propose two such solution algorithms. One resembles the variable elimination technique from influence diagrams, whereas the other is based on conditioning and supports any-space inference. Finally, we present an empirical comparison of the proposed methods

Sequential influence diagrams: A unified asymmetry framework

We describe a new graphical language for specifying asymmetric decision problems. The language is based on a filtered merge of several existing languages including sequential valuation networks, asymmetric influence diagrams, and unconstrained influence diagrams. Asymmetry is encoded using a structure resembling a clustered decision tree, whereas the representation of the uncertainty model is based on the (unconstrained) influence diagram framework. We illustrate the proposed language by modeling several highly asymmetric decision problems, and we describe an efficient solution procedure

Sequential Influence Diagrams: A Unified Asymmetry Framework

We describe a new graphical language for specifying asymmetric decision problems. The language is based on a filtered merge of several existing languages including sequential valuation networks, asymmetric influence diagrams, and unconstrained influence diagrams. Asymmetry is encoded using a structure resembling a clustered decision tree, whereas the representation of the uncertainty model is based on the (unconstrained) influence diagram framework. We illustrate the proposed language by modeling several highly asymmetric decision problems, and we outline an efficient solution procedure

A sensitivity analysis on the springback behavior of the Unconstrained Bending Problem

Sheet metal forming software is commonly used in the automotive and sheet metal\ud sectors to support the design stage. However, the ability of the currently available software to\ud accurately predict springback is limited. A sensitivity analysis of the springback behavior of a\ud simple product is performed to gain more knowledge into the various factors contributing to the\ud predictability of springback. The sensitivity analysis comprises both numerical and physical\ud aspects and results are reported in this article

On the D = 4, N = 2 Non-Renormalization Theorem

Using the harmonic superspace background field formulation for general D=4, N=2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N=2 non-renormalization theorem; specifically, the absence of ultraviolet divergences beyond the one-loop level. Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy effective action at two loops.Comment: 16 pages, LATEX, uses FEYMAN macros, minor change

The interplay between thermodynamics and kinetics in the solid-state synthesis of layered oxides.

In the synthesis of inorganic materials, reactions often yield non-equilibrium kinetic byproducts instead of the thermodynamic equilibrium phase. Understanding the competition between thermodynamics and kinetics is a fundamental step towards the rational synthesis of target materials. Here, we use in situ synchrotron X-ray diffraction to investigate the multistage crystallization pathways of the important two-layer (P2) sodium oxides Na0.67MO2 (M = Co, Mn). We observe a series of fast non-equilibrium phase transformations through metastable three-layer O3, O3' and P3 phases before formation of the equilibrium two-layer P2 polymorph. We present a theoretical framework to rationalize the observed phase progression, demonstrating that even though P2 is the equilibrium phase, compositionally unconstrained reactions between powder precursors favour the formation of non-equilibrium three-layered intermediates. These insights can guide the choice of precursors and parameters employed in the solid-state synthesis of ceramic materials, and constitutes a step forward in unravelling the complex interplay between thermodynamics and kinetics during materials synthesis