Equivalence and Reduction of Hidden Markov Models

This report studies when and why two Hidden Markov Models (HMMs) may represent the same stochastic process. HMMs are characterized in terms of equivalence classes whose elements represent identical stochastic processes. This characterization yields polynomial time algorithms to detect equivalent HMMs. We also find fast algorithms to reduce HMMs to essentially unique and minimal canonical representations. The reduction to a canonical form leads to the definition of 'Generalized Markov Models' which are essentially HMMs without the positivity constraint on their parameters. We discuss how this generalization can yield more parsimonious representations of stochastic processes at the cost of the probabilistic interpretation of the model parameters.

Speeding up the learning of equivalence classes of Bayesian network structures

R. Daly, Q. Shen and S. Aitken. Speeding up the learning of equivalence classes of Bayesian network structures. Proceedings of the 10th International Conference on Artificial Intelligence and Soft Computing, pages 34-39.

Using ant colony optimisation in learning Bayesian network equivalence classes

R. Daly, Q. Shen and S. Aitken. Using ant colony optimisation in learning Bayesian network equivalence classes. Proceedings of the 2006 UK Workshop on Computational Intelligence, pages 111-118.

A Framework for the Scoring of Operators on the Search Space of Equivalence Classes of Bayesian Network Structures

R. Daly and Q. Shen. A Framework for the Scoring of Operators on the Search Space of Equivalence Classes of Bayesian Network Structures. Proceedings of the 2005 UK Workshop on Computational Intelligence, pages 67-74.

What's 'Novel' About It? Substantial Equivalence, Precaution and Consumer Protection 1997-2004

Salmon, Naomi, 'What's 'Novel' About It? Substantial Equivalence, Precaution and Consumer Protection 1997-2004', Environmental Law Review, (2005), 7(2) pp.138-149 RAE2008

A Self-Organizing Neural Network Model for Redundant Sensory-Motor Control, Motor Equivalence, and Tool Use

A neural network is introduced which provides a solution of the classical motor equivalence problem, whereby many different joint configurations of a redundant manipulator can all be used to realize a desired trajectory in 3-D space. To do this, the network self-organizes a mapping from motion directions in 3-D space to velocity commands in joint space. Computer simulations demonstrate that, without any additional learning, the network can generate accurate movement commands that compensate for variable tool lengths, clamping of joints, distortions of visual input by a prism, and unexpected limb perturbations. Blind reaches have also been simulated.

Development and psychometric evaluation of the spirituality instrument (SpI-27) in a sample of people with chronic illness

Background: Spirituality is fundamental to all human beings, existing within a person, and developing until death. This research sought to operationalise spirituality in a sample of individuals with chronic illness. A review of the conceptual literature identified three dimensions of spirituality: connectedness, transcendence, and meaning in life. A review of the empirical literature identified one instrument that measures the three dimensions together. Yet, recent appraisals of this instrument highlighted issues with item formulation and limited evidence of reliability and validity. Aim: The aim of this research was to develop a theoretically-grounded instrument to measure spirituality – the Spirituality Instrument-27 (SpI-27). A secondary aim was to psychometrically evaluate this instrument in a sample of individuals with chronic illness (n=249). Methods: A two-phase design was adopted. Phase one consisted of the development of the SpI-27 based on item generation from a concept analysis, a literature review, and an instrument appraisal. The second phase established the psychometric properties of the instrument and included: a qualitative descriptive design to establish content validity; a pilot study to evaluate the mode of administration; and a descriptive correlational design to assess the instrument’s reliability and validity. Data were analysed using SPSS (Version 18). Results: Results of exploratory factor analysis concluded a final five-factor solution with 27 items. These five factors were labelled: Connectedness with Others, Self-Transcendence, Self-Cognisance, Conservationism, and Connectedness with a Higher Power. Cronbach’s alpha coefficients ranged from 0.823 to 0.911 for the five factors, and 0.904 for the overall scale, indicating high internal consistency. Paired-sample t-tests, intra-class correlations, and weighted kappa values supported the temporal stability of the instrument over 2 weeks. A significant positive correlation was found between the SpI-27 and the Spirituality Index of Well-Being, providing evidence for convergent validity. Conclusion: This research addresses a call for a theoretically-grounded instrument to measure spirituality.

The development and psychometric properties of the HIV and Abuse Related Shame Inventory (HARSI).

Shame has been shown to predict sexual HIV transmission risk behavior, medication non-adherence, symptomatic HIV or AIDS, and symptoms of depression and PTSD. However, there remains a dearth of tools to measure the specific constructs of HIV-related and sexual abuse-related shame. To ameliorate this gap, we present a 31-item measure that assesses HIV and sexual abuse-related shame, and the impact of shame on HIV-related health behaviors. A diverse sample of 271 HIV-positive men and women who were sexually abused as children completed the HIV and Abuse Related Shame Inventory (HARSI) among other measures. An exploratory factor analysis supported the retention of three-factors, explaining 56.7% of the sample variance. These internally consistent factors showed good test-retest reliability, and sound convergent and divergent validity using eight well-established HIV specific and general psychosocial criterion measures. Unlike stigma or discrimination, shame is potentially alterable through individually-focused interventions, making the measurement of shame clinically meaningful.

Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Computing regular equivalence: practical and theoretical issues

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which group actors are playing equivalent roles. They term these methods positional analysis techniques. The most general definition is regular equivalence which captures the idea that equivalent actors are related in a similar way to equivalent alters. Regular equivalence gives rise to a whole class of partitions on a network. Given a network we have two different computational problems. The first is how to find a particular regular equivalence. An algorithm exists to find the largest regular partition but there are not efficient algorithms to test whether there is a regular k-partition. That is a partition in k groups that is regular. In addition, when dealing with real data, it is unlikely that any regular partitions exist. To overcome this problem relaxations of regular equivalence have been proposed along with optimisation techniques to find nearly regular partitions. In this paper we review the algorithms that have developed to find particular regular equivalences and look at some of the recent theoretical results which give an insight into the complexity of finding regular partitions.

Predicting toxic gas concentrations resulting from enclosure fires using local equivalence ratio concept linked to fire field models

A practical CFD method is presented in this study to predict the generation of toxic gases in enclosure fires. The model makes use of local combustion conditions to determine the yield of carbon monoxide, carbon dioxide, hydrocarbon, soot and oxygen. The local conditions used in the determination of these species are the local equivalence ratio (LER) and the local temperature. The heat released from combustion is calculated using the volumetric heat source model or the eddy dissipation model (EDM). The model is then used to simulate a range of reduced-scale and full-scale fire experiments. The model predictions for most of the predicted species are then shown to be in good agreement with the test results