Causal probabilistic networks (CPNs) have proved to be a useful knowledge representation tool for modeling domains where causal relationsin a broad sense -are a natural way of relating domain concepts and where uncertainty is inherited in these relations. The domain is modeled in a CPN by use of a directed graph where the nodes represent concepts in the domain and the arcs represent causal relations. Furthermore, the quantitative relation between a node and its immediate causes is expressed as conditional probabilities. During the last few years, several schemes based on probability theory for incorporating and propagating new information throughout a CPN has emerged. As long as the domain can be modeled by use of a singly connected CPN (i.e., no more than one path between any pair of nodes), the schemes operate directly in the CPN and perform conceptually simple operations in this structure. When it comes to more complicated structures such as multiply connected CPNs (i.e., more than one path is allowed between pairs of nodes), the schemes operate in derived structures where the embedded domain knowledge no longer is as explicit and transparent as in the CPN. Furthermore, the simplicity in the operations is lost also. This report outlines a scheme-the algebra of Bayesian belief universesfor absorbing and propagating evidence in multiply connected CPNs. The scheme provides a secondary structure, a junction tree, and a simple set of algebraic operations between objects in this structure, CollectEvidence and DistributeEvidence. These are the basic tools for making inference in a CPN domain model and yield a calculus as simple as in the case of singly connected CPNs.*This work is supported in part by the EEC ESPRIT programme, project P599.
Strategic spatial planning practices have recently taken a neoliberal turn in many northwestern European countries. This neoliberalisation of strategic spatial planning has materialised partly in governance reforms aiming to reduce or abolish strategic spatial planning at national and regional scales, and partly through the normalisation of neoliberal discourses in strategic spatial planning processes. This article analyses the complex relationship, partly of unease and partly of coevolution, between neoliberalism and strategic spatial planning. Furthermore, this article discusses the key challenges for strategic spatial planning in the face of neoliberalism and argues for a need to strengthen strategic spatial planning's critical dimension.
With this paper I analyse how policy agendas are being shaped and reshaped in new soft spaces emerging in Danish spatial planning at subnational scales, and how policy making in these soft spaces seeks to infl uence formal planning arenas. The paper demonstrates how the new soft planning spaces in Danish spatial planning primarily are concerned with promoting policy agendas centred on economic development, whilst doing limited work in fi lling in the gaps between formal scales of planning, as envisaged in the planning literature. Instead, soft spaces seem to add to the increasing pressures on statutory spatial planning, being used as vehicles for neoliberal transformations of strategic spatial planning. I therefore argue for a need to maintain a critical stance towards the emergence of soft spaces in spatial planning.
The authors present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition (MPD) to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for LAZY propagation. We also identify a number of tasks performed on Bayesian networks that can benefit from MPD. These tasks are: divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. We compare the proposed algorithm with standard algorithms for decomposition of undirected graphs into their maximal prime subgraphs. The discussion shows that the proposed algorithm is simpler, more easy to comprehend, and it has the same complexity as the standard algorithms.
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