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We have designed a cubic spline wavelet-like decomposition for the Sobolev space H (I) where I is a bounded interval. Based on a special point value vanishing property of the wavelet basis functions, a fast discrete wavelet transform (DWT) is constructed. This DWT will map discrete samples of a function to its wavelet expansion coefficients in at most 7N log N operations. Using this transform, we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations (PDEs). Then, we test the efficiency of the DWT and apply the collocation method to solve linear and nonlinear PDEs.

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In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed.

In this paper, a Spectral Stochastic Collocation Method(SSCM) is proposed for the capacitance extraction of interconnects with stochastic geometric variations for nanometer process technology. The proposed SSCM has several advantages over the existing methods. Firstly, compared with the PFA (Principal Factor Analysis) modeling of geometric variations, the K-L (Karhunen-Loeve) expansion involved in SSCM can be independent of the discretization of conductors, thus significantly reduces the computation cost. Secondly, compared with the perturbation method, the stochastic spectral method based on Homogeneous Chaos expansion has optimal (exponential) convergence rate, which makes SSCM applicable to most geometric variation cases. Furthermore, Sparse Grid combined with a MST (Minimum Spanning Tree) representation is proposed to reduce the number of sampling points and the computation time for capacitance extraction at each sampling point. Numerical experiments have demonstrated that SSCM can achieve higher accuracy and faster convergence rate compared with the perturbation method.

OBJECTIVES: This study examined the trend in cesarean section deliveries and the factors associated with it in the Minhang District of Shanghai, China. METHODS: A representative sample of the members of 2716 households in the district were interviewed in the fall of 1993. This study analyzed the data from 1959 married women of reproductive age with at least one live birth. RESULTS: During the past 3 decades, the proportion of infants born by cesarean section increased from 4.7% to 22.5%. Logistic regression analysis revealed that the highest cesarean section rate, which occurred in the most recent period of 1988 through 1993, was associated with form of medical payment, self-reported complications during pregnancy, higher birthweight, and maternal age. Government insurance pays all costs of cesarean sections and accounted for the highest proportion of the cesarean section rate. CONCLUSIONS: The high rates of cesarean sections in China are surprising given the lack of the factors that usually lead to cesarean sections. The increasing cesarean section rates may be an early indication that emerging forms of health insurance and fee-for-service payments to physicians will lead to an excessive emphasis on costly, high-technology medical care in China.

A new adaptive cell average spectral element method (SEM) is proposed to solve the time-dependent Wigner equation for transport in quantum devices. The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for the numerical solutions. The key feature of the proposed method is an analytical relation between the cell averages of the Wigner function in the k-space (local electron density for finite range velocity) and the point values of the distribution, resulting in fast transforms between the local electron density and local fluxes of the discretized Wigner equation via the fast sine and cosine transforms. Numerical results with the proposed method are provided to demonstrate its high accuracy, conservation, convergence and a reduction of the cost using adaptive meshes.