A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Kingship by Descent or Kingship by Election? The Contested Title of James VI and I

Throughout the reign of Elizabeth I, a steady stream of tracts appeared in English print to vindicate the succession of the most prominent contenders, Mary and James Stuart of Scotland. This article offers a comprehensive account of the polemical battle between the supporters and opponents of the Stuarts, and further identifies various theories of English kingship, most notably the theory of corporate kingship, developed by the Stuart polemicists to defend the Scottish succession. James's accession to the English throne in March 1603 marked the protracted end of the debate over the succession. The article concludes by suggesting that, while powerfully renouncing the opposition to his succession, over the course of his attempt to unify his two kingdoms, James and his supporters ultimately departed from the polemic of corporate kingship, for a more assertive language of kingship by natural and divine law.

Interactions of dietary whole-grain intake with fasting glucose- and insulin-related genetic loci in individuals of European descent: a meta-analysis of 14 cohort studies.

Whole-grain foods are touted for multiple health benefits, including enhancing insulin sensitivity and reducing type 2 diabetes risk. Recent genome-wide association studies (GWAS) have identified several single nucleotide polymorphisms (SNPs) associated with fasting glucose and insulin concentrations in individuals free of diabetes. We tested the hypothesis that whole-grain food intake and genetic variation interact to influence concentrations of fasting glucose and insulin. Via meta-analysis of data from 14 cohorts comprising ∼ 48,000 participants of European descent, we studied interactions of whole-grain intake with loci previously associated in GWAS with fasting glucose (16 loci) and/or insulin (2 loci) concentrations. For tests of interaction, we considered a P value <0.0028 (0.05 of 18 tests) as statistically significant. Greater whole-grain food intake was associated with lower fasting glucose and insulin concentrations independent of demographics, other dietary and lifestyle factors, and BMI (β [95% CI] per 1-serving-greater whole-grain intake: -0.009 mmol/l glucose [-0.013 to -0.005], P < 0.0001 and -0.011 pmol/l [ln] insulin [-0.015 to -0.007], P = 0.0003). No interactions met our multiple testing-adjusted statistical significance threshold. The strongest SNP interaction with whole-grain intake was rs780094 (GCKR) for fasting insulin (P = 0.006), where greater whole-grain intake was associated with a smaller reduction in fasting insulin concentrations in those with the insulin-raising allele. Our results support the favorable association of whole-grain intake with fasting glucose and insulin and suggest a potential interaction between variation in GCKR and whole-grain intake in influencing fasting insulin concentrations.

"Racism in a Melting Pot...?" Trinidadian mid-life transnational migrants' views on race and colour-class on return to their homes of descent

This paper deals with second-generation, one-and-a-half generation and ‘‘prolonged sojourner” Trinidadian transnational migrants, who have decided to ‘return’ to the birthplace of their parents. Based on 40 in-depth interviews, the paper considers both the positive and critical things that these youthful transnational migrants report about returning to, and living in, this multi-ethnic plural society and the salience of racial and colour-class stratification as part of their return migration experiences. Our qualitative analysis is based on the narratives provided by these youthful returnees, as relayed ‘‘in their own words”, presenting critical reflections on racism, racial identities and experiences as transnational Trinidadians. It is clear that it is contexts such as contemporary working environments, family and community that act as the reference points for the adaptation ‘‘back home” of this strongly middle-class cohort. We accordingly encounter a diverse, sometimes contesting set of racial issues that emerge as salient concerns for these returnees. The consensus is that matters racial remain as formidable legacies in the hierarchical stratification of Trinidadian society for a sizeable number. Many of our respondents reported the positive aspects of racial affirmation on return. But for another sub-set, the fact that multi-ethnic and multi-cultural mixing are proudly embraced in Trinidad meant that it was felt that return experiences were not overly hindered, or blighted by obstacles of race and colour-class. For these returnees, Trinidad and Tobago is seen as representing a 21st century ‘‘Melting Pot”. But for others the continued existence of racial divisions within society – between ethnic groups and among those of different skin shades – was lamented. In the views of these respondents, too much racial power is still ascribed to ‘near-whiteness’. But for the most part, the returnees felt that where race played a part in their new lives, this generally served to advantage them. However, although the situation in Trinidad appears to have been moderated by assumptions that it remains a racial ‘Melting Pot’, the analysis strongly suggests that the colour-class system of stratification is still playing an essential role, along with racial stereotyping in society at large.

The persistence of solar activity indicators and the descent of the sun into Maunder Minimum conditions

The recent low and prolonged minimum of the solar cycle, along with the slow growth in activity of the new cycle, has led to suggestions that the Sun is entering a Grand Solar Minimum (GSMi), potentially as deep as the Maunder Minimum (MM). This raises questions about the persistence and predictability of solar activity. We study the autocorrelation functions and predictability R^2_L(t) of solar indices, particularly group sunspot number R_G and heliospheric modulation potential phi for which we have data during the descent into the MM. For R_G and phi, R^2_L (t) > 0.5 for times into the future of t = 4 and 3 solar cycles, respectively: sufficient to allow prediction of a GSMi onset. The lower predictability of sunspot number R_Z is discussed. The current declines in peak and mean R_G are the largest since the onset of the MM and exceed those around 1800 which failed to initiate a GSMi.

Sparse model construction using coordinate descent optimization

We propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1- penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Medial contact and smaller plantar loads characterize individuals with Patellofemoral Pain Syndrome during stair descent

Objectives: To investigate plantar pressure distribution in individuals with and without Patellofemoral Pain Syndrome during the Support phase of stair descent. Design: Observational case-control study. Participants: 30 Young adults With Patellofemoral Pain Syndrome and 44 matched controls. Main outcome measures: Contact area, peak pressure and pressure-time integral (Novel Pedar-X system) were evaluated in six plantar areas (medial, central and lateral rearfoot: midfoot; medial and lateral forefoot) during stair descent. Results: Contact area was greater in the Patellofemoral Pain Syndrome Group at medial rearfoot (p = 0.019) and midfoot (p < 0.001). Subjects with Patellofemoral pain Syndrome presented smaller peak pressures (p < 0.001). Conclusion: The pattern of plantar pressure distribution during stair descent in Patellofemoral Pain Syndrome Subjects was different from controls. This seems to be related to greater medial rearfoot and midfoot Support. Smaller plantar loads found in Patellofemoral Pain Syndrome subjects during stair descent reveal a more Cautious motor pattern in a challenging task. (C) 2009 Elsevier Ltd. All rights reserved.