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 asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

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.

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.

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.

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.