Risk-informed decision-making in the presence of epistemic uncertainty

An important issue in risk analysis is the distinction between epistemic and aleatory uncertainties. In this paper, the use of distinct representation formats for aleatory and epistemic uncertainties is advocated, the latter being modelled by sets of possible values. Modern uncertainty theories based on convex sets of probabilities are known to be instrumental for hybrid representations where aleatory and epistemic components of uncertainty remain distinct. Simple uncertainty representation techniques based on fuzzy intervals and p-boxes are used in practice. This paper outlines a risk analysis methodology from elicitation of knowledge about parameters to decision. It proposes an elicitation methodology where the chosen representation format depends on the nature and the amount of available information. Uncertainty propagation methods then blend Monte Carlo simulation and interval analysis techniques. Nevertheless, results provided by these techniques, often in terms of probability intervals, may be too complex to interpret for a decision-maker and we, therefore, propose to compute a unique indicator of the likelihood of risk, called confidence index. It explicitly accounts for the decisionmaker’s attitude in the face of ambiguity. This step takes place at the end of the risk analysis process, when no further collection of evidence is possible that might reduce the ambiguity due to epistemic uncertainty. This last feature stands in contrast with the Bayesian methodology, where epistemic uncertainties on input parameters are modelled by single subjective probabilities at the beginning of the risk analysis process.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

Adaptive Measurement-Based Policy-Driven QoS Management with Fuzzy-Rule-based Resource Allocation

Fixed and wireless networks are increasingly converging towards common connectivity with IP-based core networks. Providing effective end-to-end resource and QoS management in such complex heterogeneous converged network scenarios requires unified, adaptive and scalable solutions to integrate and co-ordinate diverse QoS mechanisms of different access technologies with IP-based QoS. Policy-Based Network Management (PBNM) is one approach that could be employed to address this challenge. Hence, a policy-based framework for end-to-end QoS management in converged networks, CNQF (Converged Networks QoS Management Framework) has been proposed within our project. In this paper, the CNQF architecture, a Java implementation of its prototype and experimental validation of key elements are discussed. We then present a fuzzy-based CNQF resource management approach and study the performance of our implementation with real traffic flows on an experimental testbed. The results demonstrate the efficacy of our resource-adaptive approach for practical PBNM systems

Genome-wide scans of three independent sets of 90 Irish multiplex schizophrenia families and follow-up of selected regions in all families provides evidence for multiple susceptibility genes

From our linkage study of Irish families with a high density of schizophrenia, we have previously reported evidence for susceptibility genes in regions 5q21-31, 6p24-21, 8p22-21, and 10p15-p11. In this report, we describe the cumulative results from independent genome scans of three a priori random subsets of 90 families each, and from multipoint analysis of all 270 families in ten regions. Of these ten regions, three (13q32, 18p11-q11, and 18q22-23) did not generate scores above the empirical baseline pairwise scan results, and one (6q13-26) generated a weak signal. Six other regions produced more positive pairwise and multipoint results. They showed the following maximum multipoint H-LOD (heterogeneity LOD) and NPL scores: 2p14-13: 0.89 (P = 0.06) and 2.08 (P = 0.02), 4q24-32: 1.84 (P = 0.007) and 1.67 (P = 0.03), 5q21-31: 2.88 (P= 0.0007), and 2.65 (P = 0.002), 6p25-24: 2.13 (P = 0.005) and 3.59 (P = 0.0005), 6p23: 2.42 (P = 0.001) and 3.07 (P = 0.001), 8p22-21: 1.57 (P = 0.01) and 2.56 (P = 0.005), 10p15-11: 2.04 (P = 0.005) and 1.78 (P = 0.03). The degree of 'internal replication' across subsets differed, with 5q, 6p, and 8p being most consistent and 2p and 10p being least consistent. On 6p, the data suggested the presence of two susceptibility genes, in 6p25-24 and 6p23-22. Very few families were positive on more than one region, and little correlation between regions was evident, suggesting substantial locus heterogeneity. The levels of statistical significance were modest, as expected from loci contributing to complex traits. However, our internal replications, when considered along with the positive results obtained in multiple other samples, suggests that most of these six regions are likely to contain genes that influence liability to schizophrenia.

Gene Sets Net Correlations Analysis (GSNCA): a multivariate differential coexpression test for gene sets

Motivation: To date, Gene Set Analysis (GSA) approaches primarily focus on identifying differentially expressed gene sets (pathways). Methods for identifying differentially coexpressed pathways also exist but are mostly based on aggregated pairwise correlations, or other pairwise measures of coexpression. Instead, we propose Gene Sets Net Correlations Analysis (GSNCA), a multivariate differential coexpression test that accounts for the complete correlation structure between genes.

Results: In GSNCA, weight factors are assigned to genes in proportion to the genes' cross-correlations (intergene correlations). The problem of finding the weight vectors is formulated as an eigenvector problem with a unique solution. GSNCA tests the null hypothesis that for a gene set there is no difference in the weight vectors of the genes between two conditions. In simulation studies and the analyses of experimental data, we demonstrate that GSNCA, indeed, captures changes in the structure of genes' cross-correlations rather than differences in the averaged pairwise correlations. Thus, GSNCA infers differences in coexpression networks, however, bypassing method-dependent steps of network inference. As an additional result from GSNCA, we define hub genes as genes with the largest weights and show that these genes correspond frequently to major and specific pathway regulators, as well as to genes that are most affected by the biological difference between two conditions. In summary, GSNCA is a new approach for the analysis of differentially coexpressed pathways that also evaluates the importance of the genes in the pathways, thus providing unique information that may result in the generation of novel biological hypotheses.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Progress on core outcomes sets for critical care research

Purpose of review: Appropriate selection and definition of outcome measures are essential for clinical trials to be maximally informative. Core outcome sets (an agreed, standardized collection of outcomes measured and reported in all trials for a specific clinical area) were developed due to established inconsistencies in trial outcome selection. This review discusses the rationale for, and methods of, core outcome set development, as well as current initiatives in critical care.

Recent findings: Recent systematic reviews of reported outcomes and measurement instruments relevant to the critically ill highlight inconsistencies in outcome selection, definition, and measurement, thus establishing the need for core outcome sets. Current critical care initiatives include development of core outcome sets for trials aimed at reducing mechanical ventilation duration; rehabilitation following critical illness; long-term outcomes in acute respiratory failure; and epidemic and pandemic studies of severe acute respiratory infection.

Summary: Development and utilization of core outcome sets for studies relevant to the critically ill is in its infancy compared to other specialties. Notwithstanding, core outcome set development frameworks and guidelines are available, several sets are in various stages of development, and there is strong support from international investigator-led collaborations including the International Forum for Acute Care Trialists.

An Efficient LS-SVM-Based Method for Fuzzy System Construction

This paper proposes an efficient learning mechanism to build fuzzy rule-based systems through the construction of sparse least-squares support vector machines (LS-SVMs). In addition to the significantly reduced computational complexity in model training, the resultant LS-SVM-based fuzzy system is sparser while offers satisfactory generalization capability over unseen data. It is well known that the LS-SVMs have their computational advantage over conventional SVMs in the model training process; however, the model sparseness is lost, which is the main drawback of LS-SVMs. This is an open problem for the LS-SVMs. To tackle the nonsparseness issue, a new regression alternative to the Lagrangian solution for the LS-SVM is first presented. A novel efficient learning mechanism is then proposed in this paper to extract a sparse set of support vectors for generating fuzzy IF-THEN rules. This novel mechanism works in a stepwise subset selection manner, including a forward expansion phase and a backward exclusion phase in each selection step. The implementation of the algorithm is computationally very efficient due to the introduction of a few key techniques to avoid the matrix inverse operations to accelerate the training process. The computational efficiency is also confirmed by detailed computational complexity analysis. As a result, the proposed approach is not only able to achieve the sparseness of the resultant LS-SVM-based fuzzy systems but significantly reduces the amount of computational effort in model training as well. Three experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed learning mechanism and the sparseness of the obtained LS-SVM-based fuzzy systems, in comparison with other SVM-based learning techniques.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.