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Motivated by our recent work about pollution-free difference schemes for solving Helmholtz equation with high wave numbers, this paper presents an analysis of error estimate for the numerical solution on the annulus and hollow sphere domains. By applying the weighted-test-function method and defining two special interpolation operators, we first derive the existence, uniqueness, stability and the pollution-free error estimate for the one-dimensional problems gen-erated from a method based on separation of variables. Utilizing the spherical harmonics and approximations results, we then prove the pollution-free error estimate in L2-norm for multi-dimensional Helmholtz problems. [ABSTRACT FROM AUTHOR]

Background: Real Time Cell Analysis (RTCA) technology is used to monitor cellular changes continuously over the entire exposure period. Combining with different testing concentrations, the profiles have potential in probing the mode of action (MOA) of the testing substances. Results: In this paper, we present machine learning approaches for MOA assessment. Computational tools based on artificial neural network (ANN) and support vector machine (SVM) are developed to analyze the time-concentration response curves (TCRCs) of human cell lines responding to tested chemicals. The techniques are capable of learning data from given TCRCs with known MOA information and then making MOA classification for the unknown toxicity. A novel data processing step based on wavelet transform is introduced to extract important features from the original TCRC data. From the dose response curves, time interval leading to higher classification success rate can be selected as input to enhance the performance of the machine learning algorithm. This is particularly helpful when handling cases with limited and imbalanced data. The validation of the proposed method is demonstrated by the supervised learning algorithm applied to the exposure data of HepG2 cell line to 63 chemicals with 11 concentrations in each test case. Classification success rate in the range of 85 to 95% are obtained using SVM for MOA classification with two clusters to cases up to four clusters. Conclusions: Wavelet transform is capable of capturing important features of TCRCs for MOA classification. The proposed SVM scheme incorporated with wavelet transform has a great potential for large scale MOA classification and high-through output chemical screening. [ABSTRACT FROM AUTHOR]

This paper presents efficient numerical schemes for 3-D gravity field inversion. We propose a 2-D multilayer model to approximate a 3-D density distribution, and prove that the solution of the multilayer model will converge to the discretized 3-D solution. Differed from the conventional fast Fourier transform (FFT) based methods in which FFT is applied to the kernel, the proposed approach directly generates the Block-Toeplitz Toeplitz-Block (BTTB) structure by discretizing the multilayer model and the BTTB matrix is embedded into a Block-Circulant Circulant-Block (BCCB) matrix such that FFT can be utilized. In this approach, both regularization and optimal pre-conditioning operator can be constructed in the form of BTTB matrix. Consequently, very efficient solvers can be developed, and tremendous reduction in storage requirement and computing time can be achieved. To validate the new approach, numerical simulations using synthetic and real field data are reported, and numerical analysis is carried out for the inversion problems. Based on this study, we conclude that the proposed methods are capable of performing large-scale 3-D density inversions with amodest computing resource. [ABSTRACT FROM AUTHOR]

The re-weighted regularized conjugate gradient (RRCG) method has been a popular algorithm for magnetic inversion problems. In this work, we show that for a two-dimensional problem with uniform field data, the resulting coefficient matrix to be inverted has a symmetric Block-Toeplitz Toeplitz-Block (BTTB) structure. Taking advantage of the BTTB properties, the storage and computational complexity can be significantly reduced, so that the efficiency of the RRCG method is greatly improved and it is now capable of dealing with much larger system with a modest computing resource. This paper also investigates various numerical inversion schemes including the CG type and multigrid (MG) methods. It has been demonstrated that the MG is an efficient and robust numerical tool for magnetic field inversion. Not only the MG produces a rapid convergence rate, the performance is not sensitive when applying to noisy data. Numerical simulations using synthetic data and real field data are reported to confirm the effectiveness of the MG method. [ABSTRACT FROM AUTHOR]

In this paper, we develop pollution-free finite difference schemes for solving the non-homogeneous Helmholtz equation in one dimension. A family of high-order algorithms is derived by applying the Taylor expansion and imposing the conditions that the resulting finite difference schemes satisfied the original equation and the boundary conditions to certain degrees. The most attractive features of the proposed schemes are: first, the new difference schemes have a 2n--order of rate of convergence and are pollution-free. Hence, the error is bounded even for the equation at high wave numbers. Secondly, the resulting difference scheme is simple, namely it has the same structure as the standard three-point central differencing regardless the order of accuracy. Convergence analysis is presented, and numerical simulations are reported for the non-homogeneous Helmholtz equation with both constant and varying wave numbers. The computational results clearly confirm the superior performance of the proposed schemes. [ABSTRACT FROM AUTHOR]

We present high-order symplectic schemes for stochastic Hamiltonian systems pre- serving Hamiltonian functions. The approach is based on the generating function method, and we prove that the coefficients of the generating function are invariant under permutations for this class of systems. As a consequence, the proposed high-order symplectic weak and strong schemes are computationally efficient because they require less stochastic multiple integrals than the Taylor expansion schemes with the same order. [ABSTRACT FROM AUTHOR]

Three-dimensional wave equation prestack depth imaging is an important tool in reconstructing images of complex subsurface structures, and it has become a technique gaining wide popularity in oil and gas industry. This is a large-scale scientific computing problem and can be considered a process of data continuation downward with the surface data or the boundary data, such as the shot-gather data. In this paper, we first discuss the decomposition of a two-way wave equation and investigate four different approaches to approximate the square-root operator. Using the known shot-gather data as input, an unconditional stable hybrid method for the wavefield extrapolation is presented. The most attractive feature of the proposed method is that it has a natural parallel characteristic and can be effectively implemented using a cluster of PCs, in which each processor performs its own shot-gather imaging independently. To demonstrate the computational efficiency and the power of the parallel hybrid algorithm, we present two case studies: one is the well-known SEG/EAEG subsalt model which has been commonly used for validation of the prestack depth imaging algorithms, and the other is the application to a 3D wavefield extrapolation problem with real data provided by the China National Petroleum Corporation. The results clearly show the capability of the proposed method, and it demonstrates that the algorithm can be effectively implemented as a practical engineering tool for 3D prestack depth imaging. [ABSTRACT FROM AUTHOR]

Switching state-space models have been widely used in many applications arising from science, engineering, economic, and medical research. In this paper, we present a Monte Carlo Expectation Maximization (MCEM) algorithm for learning the parameters and classifying the states of a state-space model with a Markov switching. A stochastic implementation based on the Gibbs sampler is introduced in the expectation step of the MCEM algorithm. We study the asymptotic properties of the proposed algorithm, and we also describe how a nesting approach and the Rao-Blackwellized forms can be employed to accelerate the rate of convergence of the MCEM algorithm. Finally, the performance and the effectiveness of the proposed method are demonstrated by applications to simulated and physiological experimental data. [ABSTRACT FROM AUTHOR]