Kernel classifier construction using orthogonal forward selection and boosting with Fisher ratio class separability measure

A greedy technique is proposed to construct parsimonious kernel classifiers using the orthogonal forward selection method and boosting based on Fisher ratio for class separability measure. Unlike most kernel classification methods, which restrict kernel means to the training input data and use a fixed common variance for all the kernel terms, the proposed technique can tune both the mean vector and diagonal covariance matrix of individual kernel by incrementally maximizing Fisher ratio for class separability measure. An efficient weighted optimization method is developed based on boosting to append kernels one by one in an orthogonal forward selection procedure. Experimental results obtained using this construction technique demonstrate that it offers a viable alternative to the existing state-of-the-art kernel modeling methods for constructing sparse Gaussian radial basis function network classifiers. that generalize well.

Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

A kernel-based two-class classifier for imbalanced data sets

Many kernel classifier construction algorithms adopt classification accuracy as performance metrics in model evaluation. Moreover, equal weighting is often applied to each data sample in parameter estimation. These modeling practices often become problematic if the data sets are imbalanced. We present a kernel classifier construction algorithm using orthogonal forward selection (OFS) in order to optimize the model generalization for imbalanced two-class data sets. This kernel classifier identification algorithm is based on a new regularized orthogonal weighted least squares (ROWLS) estimator and the model selection criterion of maximal leave-one-out area under curve (LOO-AUC) of the receiver operating characteristics (ROCs). It is shown that, owing to the orthogonalization procedure, the LOO-AUC can be calculated via an analytic formula based on the new regularized orthogonal weighted least squares parameter estimator, without actually splitting the estimation data set. The proposed algorithm can achieve minimal computational expense via a set of forward recursive updating formula in searching model terms with maximal incremental LOO-AUC value. Numerical examples are used to demonstrate the efficacy of the algorithm.

Global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays

In this paper, we study the periodic oscillatory behavior of a class of bidirectional associative memory (BAM) networks with finite distributed delays. A set of criteria are proposed for determining global exponential periodicity of the proposed BAM networks, which assume neither differentiability nor monotonicity of the activation function of each neuron. In addition, our criteria are easily checkable. (c) 2005 Elsevier Inc. All rights reserved.

Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Electronic voting systems in undergraduate teaching

One of the major differences undergraduates experience during the transition to university is the style of teaching. In schools and colleges most students study key stage 5 subjects in relatively small informal groups where teacher–pupil interaction is encouraged and two-way feedback occurs through question and answer type delivery. On starting in HE students are amazed by the sizes of the classes. For even a relatively small chemistry department with an intake of 60-70 students, biologists, pharmacists, and other first year undergraduates requiring chemistry can boost numbers in the lecture hall to around 200 or higher. In many universities class sizes of 400 are not unusual for first year groups where efficiency is crucial. Clearly the personalised classroom-style delivery is not practical and it is a brave student who shows his ignorance by venturing to ask a question in front of such an audience. In these environments learning can be a very passive process, the lecture acts as a vehicle for the conveyance of information and our students are expected to reinforce their understanding by ‘self-study’, a term, the meaning of which, many struggle to understand. The use of electronic voting systems (EVS) in such situations can vastly change the students’ learning experience from a passive to a highly interactive process. This principle has already been demonstrated in Physics, most notably in the work of Bates and colleagues at Edinburgh.1 These small hand-held devices, similar to those which have become familiar through programmes such as ‘Who Wants to be a Millionaire’ can be used to provide instant feedback to students and teachers alike. Advances in technology now allow them to be used in a range of more sophisticated settings and comprehensive guides on use have been developed for even the most techno-phobic staff.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

Power to the people: working-class demand for household power in 1930s Britain

The 1930s witnessed an intense struggle between gas and electricity suppliers for the working class market, where the incumbent utility—gas—was also a reasonably efficient (and cheaper) General Purpose Technology for most domestic uses. Local monopolies for each supplier boosted substitution effects between fuel types—as alternative fuels constituted the only local competition. Using newly-rediscovered returns from a major national household expenditure survey, we employ geographically-determined instrumental variables, more commonly used in the industrial organization literature, to show that gas provided a significant competitor, tempering electricity prices, while electricity demand was also responsive to marketing initiatives.

Processing system accepting exceptional numbers

A processing system comprises: input means arranged to receive at least one input group of bits representing at least one respective input number; output means arranged to output at least one output group of bits representing at least one respective output number; and processing means arranged to perform an operation on the at least one input group of bits to produce the at least one output group of bits such that the at least one output number is related to the at least one input number by a mathematical operation; and wherein each of the numbers can be any of a set of numbers which includes a series of numbers, positive infinity, negative infinity and nullity.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

A hypoplastic model of skeletal muscle development displaying reduced foetal myoblast cell numbers, increased oxidative myofibres and improved specific tension capacity

The major component of skeletal muscle is the myofibre. Genetic intervention inducing over-enlargement of myofibres beyond a certain threshold through acellular growth causes a reduction in the specific tension generating capacity of the muscle. However the physiological parameters of a genetic model that harbours reduced skeletal muscle mass have yet to be analysed. Genetic deletion of Meox2 in mice leads to reduced limb muscle size and causes some patterning defects. The loss of Meox2 is not embryonically lethal and a small percentage of animals survive to adulthood making it an excellent model with which to investigate how skeletal muscle responds to reductions in mass. In this study we have performed a detailed analysis of both late foetal and adult muscle development in the absence of Meox2. In the adult, we show that the loss of Meox2 results in smaller limb muscles that harbour reduced numbers of myofibres. However, these fibres are enlarged. These myofibres display a molecular and metabolic fibre type switch towards a more oxidative phenotype that is induced through abnormalities in foetal fibre formation. In spite of these changes, the muscle from Meox2 mutant mice is able to generate increased levels of specific tension compared to that of the wild type.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.