Uncertain causal knowledge is stored in fuzzy cognitive maps (FCMs). FCMs are fuzzy signed digraphs with feedback. The sign (+ or-) of FCM edges indicates causal increase or causal decrease. The fuzzy degree of causality is indicated by a number in [- 1, 1]. FCMs learn by modifying their causal connections in sign and magnitude, structurally analogous to the way in which neural networks learn. An appropriate causal learning law for inductively inferring FCMs from time-series data is the differential Hebbian law, which modifies causal connections by correlating time derivatives of FCM node outputs. The differential Hebbian law contrasts with Hebbian output-correlation learning laws of adaptive neural networks. FCM nodes represent variable phenomena or fuzzy sets. An FCM node nonlinearly transforms weighted summed inputs into numerical output, again in analogy to a model neuron. Unlike expert systems, which are feedforward search trees, FCMs are nonlinear dynamical systems. FCM resonant states are limit cycles, or time-varying patterns. An FCM limit cycle or hidden pattern is an FCM inference. Experts construct FCMs by drawing causal pictures or digraphs. The corresponding connection matrices are used for inferencing. By additively combining augmented connection matrices, any number of FCMs can be naturally combined into a single knowledge network. The credibility wi in [0, 1] of the ith expert is included in this learning process by multiplying the ith expert's augmented FCM connection matrix by w i. Combining connection matrices is a simple type of adaptive inference. In general, connection matrices are modified by an unsupervised learning law, such as the

RNA profiling analysis and new techniques such as proteomics are yielding vast amounts of data on gene expression and protein levels. This points to the need to develop new methodologies to identify and analyze complex biological networks. This chapter describes the development of a Java-based tool that helps dynamically find and visualize metabolic networks. The tool consists of three parts. The first part is a text-mining tool that pulls out potential metabolic relationships from the PubMed database. These relationships are then reviewed by a domain expert and added to an existing network model. The result is visualized using an interactive graph display module. The basic metabolic or regulatory flow in the network is modeled using fuzzy cognitive maps. Causal connections are pulled out from sequence data using a genetic algorithm-based logical proposition generator that searches for temporal patterns in microarray data. Examples from the regulatory and...

This paper presents a new method to create and tune joint fuzzy sets. Multidimensional fuzzy sets define the if-part fuzzy sets of rules in feedforward fuzzy function approximators. These joint set functions do not factor into a product of scalar fuzzy sets (such as triangles or bell curves) and so they do not ignore the correlation structure among the input components. The joint set functions transform a scalar distance measure that preserves the correlation structure. Supervised learning tunes the metrical joint set functions and tunes the scalar set functions that make up factorable joint set functions. Factorable joint set functions tend to collapse to spikes in high dimensions. This holds for all joint set functions that combine factors with product or minimum or other t-norms. Simulations suggest that some metrical joint set functions may offer a practical tool for fuzzy function approximation in higher dimensions and in L p function spaces. 1 Another Curse of Dimensionality: F...

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, analytic reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogatebased optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers.

This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources.