Evaluation of Spatial Scan Statistics for Irregularly Shaped Clusters

Spatial scan statistics are commonly used for geographic disease cluster detection and evaluation. We propose and implement a modified version of the simulated annealing spatial scan statistic that incorporates the concept of “non-compactness” in order to penalize clusters that are very irregular in shape. We evaluate its power for the simulated annealing scan and compare it with the circular and elliptic spatial scan statistics. We observe that, with the non-compactness penalty, the simulated annealing method is competitive with the circular and elliptic scan statistic, and both have good power performance. The elliptic scan statistic is computationally faster and is well suited for mildly irregular clusters, but the simulated annealing method deals better with highly irregular cluster shapes. The new method is applied to breast cancer mortality data from northeastern United States.     

A Sparse Structured Shrinkage Estimator for Nonparametric Varying-Coefficient Model With an Application in Genomics

Many problems in genomics are related to variable selection where high-dimensional genomic data are treated as covariates. Such genomic covariates often have certain structures and can be represented as vertices of an undirected graph. Biological processes also vary as functions depending upon some biological state, such as time. High-dimensional variable selection where covariates are graph-structured and underlying model is nonparametric presents an important but largely unaddressed statistical challenge. Motivated by the problem of regression-based motif discovery, we consider the problem of variable selection for high-dimensional nonparametric varying-coefficient models and introduce a sparse structured shrinkage (SSS) estimator based on basis function expansions and a novel smoothed penalty function. We present an efficient algorithm for computing the SSS estimator. Results on model selection consistency and estimation bounds are derived. Moreover, finite-sample performances are studied via simulations, and the effects of high-dimensionality and structural information of the covariates are especially highlighted. We apply our method to motif finding problem using a yeast cell-cycle gene expression dataset and word counts in genes’ promoter sequences. Our results demonstrate that the proposed method can result in better variable selection and prediction for high-dimensional regression when the underlying model is nonparametric and covariates are structured. Supplemental materials for the article are available online.     

Homogenization of spatially dispersive metamaterial arrays in terms of generalized electric and magnetic polarizations

An anisotropic homogenization theory for spatially dispersive periodic arrays is developed, based on the microscopic Maxwell equations, that yields causal, macroscopic permittivities, and inverse permeabilities for the fundamental Floquet modes of the arrays. (Macroscopic magnetoelectric coefficients are not required.) Reality conditions, reciprocity relations, passivity conditions, and causality relations are derived for these spatially dispersive macroscopic constitutive parameters. A significant feature of the formulation is that the macroscopic permittivities and permeabilities reduce to their anisotropic-continuum definitions in terms of ordinary macroscopic averages at the low spatial and temporal frequencies. In addition, diamagnetic metamaterial arrays require no special considerations or modifications to accommodate their unusual characteristics. A numerical example of a 2D array comprised of circular–cylinder inclusions is given that confirms the theoretical results for the computed electric and magnetic or diamagnetic macroscopic polarizations.     

White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability

White noise-induced pattern formation is studied in a network composed of Morris–Lecar neuronal models with type I excitability and with initial values higher than that of the resting potential. The appearance and disappearance of spiral waves, as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function, enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks, as can be clearly seen in the signal to noise ratio curves, as the noise intensity is adjusted from small to large in a wide range. A possible physical mechanism of the multiple resonances based on the dynamics of type I excitability and initial values is provided. The potential biological significance of the noise-induced spiral waves is discussed.     

Estimation in the presence of many nuisance parameters: Composite likelihood and plug-in likelihood

We consider the incidental parameters problem in this paper, i.e. the estimation for a small number of parameters of interest in the presence of a large number of nuisance parameters. By assuming that the observations are taken from a multiple strictly stationary process, the two estimation methods, namely the maximum composite quasi-likelihood estimation (MCQLE) and the maximum plug-in quasi-likelihood estimation (MPQLE) are considered. For the MCQLE, we profile out nuisance parameters based on lower-dimensional marginal likelihoods, while the MPQLE is based on some initial estimators for nuisance parameters. The asymptotic normality for both the MCQLE and the MPQLE is established under the assumption that the number of nuisance parameters and the number of observations go to infinity together, and both the estimators for the parameters of interest enjoy the standard root-n$n$ convergence rate. Simulation with a spatial–temporal model illustrates the finite sample properties of the two estimation methods.     

Scaling reduction of the contrast of fractal speckles detected with a finite aperture

It is known that speckle patterns with fractal properties, called fractal speckles, are produced by illuminating a diffuser with the coherent light having the intensity distribution obeying a negative power law. One of key properties of fractal speckles is the spatial correlation function obeying a negative power law, which implies that such speckles have scaling properties. In detecting fractal speckles, the effect of the spatial integration is inevitable in most cases since they have speckle grains of various scales including very fine ones. To evaluate this effect, in this paper, the contrast of spatially integrated intensity distributions is investigated theoretically and experimentally for fractal speckles. The results show that the contrast reduction with the size of the detector aperture obeys a negative power function related with the exponent of the intensity correlation coefficient of fractal speckles.     

Narrow band optical filter in fluorescein doped boric acid glass saturable absorber thin films

We demonstrate narrow band optical filter like frequency response with full width half maximum (FWHM) of nearly (1.75 ± 0.25) Hz in fluorescein doped boric acid glass films [10⁻⁴ M], using modulated optical phase conjugation and a nearly non-degenerate four wave mixing technique. Modulated optical phase conjugation signals are described in the limit of a weak probe and relatively strong pump beams. Both pump beams are of nearly equal intensity at a wavelength of 514.5 nm from a continuous-wave Ar⁺ laser. The probe beam frequency has been detuned with a ramp signal using a piezo electric mirror.     

Simplification of formulas for compression wave and oscillating flow in circular pipe

We had already obtained the analytical solutions for the compression wave and steady-state oscillating flow in a pipe with a circular cross section [Sato Y, Kanki H. Formulas for compression wave and oscillating flow in circular pipe. To be published in Appl Acoust [accepted 11 Sept. 2006]]. This work contains three key-components. The first key is to simplify the formulas using the unique mathematic technique without losing the accuracy. Simplifying the formulas is the one of the most important factors for formulas used in engineering use. The results will enable us to greatly reduce the work and computation costs. The second is to verify the flow distribution calculated by our formulas. The third is to study the possibility of application of our method to the analysis in turbulent flow region. Kawata et al. have represented the validity of one-dimensional quasi-analysis in turbulent flow region, using the method of D’Souza et al. and the shear viscosity. Therefore, in this paper the validity of the analysis in a turbulence region was verified by proving theoretically that the methods of D’Souza et al. and ours are intrinsically equivalent. The proof of equivalence was accomplished using the formulas simplified in this paper.     

A comparison of spatial discretization schemes for differential solution methods of the radiative transfer equation

A comparison of discretization schemes required to evaluate the radiation intensity at the cell faces of a control volume in differential solution methods of the radiative transfer equation is presented. Several schemes developed using the normalized variable diagram and the total variation diminishing formalisms are compared along with essentially non-oscillatory schemes and genuinely multidimensional schemes. The calculations were carried out using the discrete ordinates method, but the analysis is equally valid for the finite-volume method. It is shown that the S schemes of the genuinely multidimensional family perform quite well, particularly in problems with discontinuous radiation intensity fields. However, they are time consuming, and so they do not always become more attractive regarding the trade-off between accuracy and computational requirements, in comparison with other high-order schemes that, although being less accurate, are also more economical.