The Index Bundle for a Family of Dirac-Ramond Operators

We study the index bundle of the Dirac-Ramond operator associated with a family $\pi: Z \to X$ of compact spin manifolds. We view this operator as the formal twisted Dirac operator \dd \otimes \bigotimes_{n=1}^{\infty}S_{q^n}TM_{\C} so that its index bundle is an element of $K(X)[[q]]$. When $p_1 (Z) = 0$, we derive some explicit formulas for the Chern character of this index bundle using its modular properties. We also use the modularity to identify our index bundle with an $L(E_8)$ bundle in a special case.Comment: 27 page

Appendix to Harris, Mason and Ryan LAC Isle of Wight realist evaluation

Using an Agent Based Model to estimate the avoided costs of the LAC Coordination schem

NARX-based nonlinear system identification using orthogonal least squares basis hunting

An orthogonal least squares technique for basis hunting (OLS-BH) is proposed to construct sparse radial basis function (RBF) models for NARX-type nonlinear systems. Unlike most of the existing RBF or kernel modelling methods, whichplaces the RBF or kernel centers at the training input data points and use a fixed common variance for all the regressors, the proposed OLS-BH technique tunes the RBF center and diagonal covariance matrix of individual regressor by minimizing the training mean square error. An efficient optimization method isadopted for this basis hunting to select regressors in an orthogonal forward selection procedure. Experimental results obtained using this OLS-BH technique demonstrate that it offers a state-of-the-art method for constructing parsimonious RBF models with excellent generalization performance

Elastic net prefiltering for two class classification

A two-stage linear-in-the-parameter model construction algorithm is proposed aimed at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage which constructs a sparse linear-in-the-parameter classifier. The prefiltering stage is a two-level process aimed at maximizing a model’s generalization capability, in which a new elastic-net model identification algorithm using singular value decomposition is employed at the lower level, and then, two regularization parameters are optimized using a particle-swarm-optimization algorithm at the upper level by minimizing the leave-one-out (LOO) misclassification rate. It is shown that the LOO misclassification rate based on the resultant prefiltered signal can be analytically computed without splitting the data set, and the associated computational cost is minimal due to orthogonality. The second stage of sparse classifier construction is based on orthogonal forward regression with the D-optimality algorithm. Extensive simulations of this approach for noisy data sets illustrate the competitiveness of this approach to classification of noisy data problems

Probability density estimation with tunable kernels using orthogonal forward regression

A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately

Social Change and the Family

This paper explores the social change of the past 40 years through reporting the results of a restudy. It argues that social change can be understood, culturally, as involving a process of de-institutionalisation and, structurally, as involving differentiation within elementary family groups as well as within extended family networks. Family change is set in the context of changes in the housing and labour markets and the demographic, industrial and occupational changes of the past 40 years. These changes are associated with increases in women\'s economic activity rates and a decrease in their \'degree of domesticity\'. They are also associated with increasing differentiation within families such that occupational heterogeneity is now found at the heart of the elementary family as well as within kinship groupings as was the case 40 years ago. Thus the trend towards increased differentiation identified in the original study (Rosser and Harris: The Family and Social Change) has continued into the 21st century. This is associated with a de-institutionalisation of family life and an increasing need for partners to negotiate participation in both productive and reproductive work.De-Institutionalisation, Social Change, Restudy, Occupational Differentiation, Extended Family

Explaining Small-Business Development: A Small-Business Development Model Combining the Maslow and the Hayes and Wheelwright Models

This paper looks at small-business management from the standpoint of Maslow’s hierarchy of needs and Hayes and Wheelwright’s four-stage model. The paper adapts Maslow’s hierarchy of needs model to small- business development and evolution. Additionally, Hayes and Wheelwright’s four-stage model is combined with the adapted Maslow small-business development model. The implications of the new model on the development of small businesses and future research are discussed

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memor

Symmetric RBF classifier for nonlinear detection in multiple-antenna aided systems

In this paper, we propose a powerful symmetric radial basis function (RBF) classifier for nonlinear detection in the so-called “overloaded” multiple-antenna-aided communication systems. By exploiting the inherent symmetry property of the optimal Bayesian detector, the proposed symmetric RBF classifier is capable of approaching the optimal classification performance using noisy training data. The classifier construction process is robust to the choice of the RBF width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio (SNR) gain in excess of 8 dB against the powerful linear minimum bit error rate (BER) benchmark, when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements. Index Terms—Classification, multiple-antenna system, orthogonal forward selection, radial basis function (RBF), symmetry

A happy Brexit? We should rather brace ourselves for a dramatic change in our democratic freedom - for the worse

As the Conservative MP and prospective scholar Chris Heaton-Harris reminds us, it is important when reflecting on Brexit within the academy to identify the potentially positive as well as the negative aspects of leaving the EU. Conor Gearty (LSE) scrutinises this notion of a happy Brexit, and outlines multiple areas in which the EU Withdrawal Bill will constitute a large transfer of power to the executive ..