Plane waves and response matrices

The relative ease with which high-throughput data can be collected on the same sampling units has raised interest in relating high-dimensional data sets. This problem can be framed as a multivariate regression model with one data set treated as a response matrix and the other as a covariate matrix. The high-dimensionality of both the response and covariate matrices along with the complex correlation structures within each raises statistical challenges. Here, we review a stochastic partitioning method that addresses this problem by fitting a mixture of regression models with variable selection, thereby uncovering in a unified manner group structures and key relationships between the data sets. The problem of variable selection in this context poses added difficulties compared to standard regression settings, as the membership of objects into different components has to be learned simultaneously with the search of component-specific predictors. We emphasize the practical applicability of the method using real data and illustrate features of the associated R package SPaVS.

In this novel forecasting algorithm to calculate the unit‐impulse response matrix of an unbounded medium to analyse dynamic medium‐structure interaction in the time domain based on the substructure method, a finite‐element region adjacent to the structure–medium interface consisting of two or three rows only is introduced. Its exterior boundary is chosen to be similar to the interior boundary which coincides with the structure–medium interface. At similar boundaries of the unbounded medium the unit‐impulse response matrices are a function of the dimensionless time. The unit‐impulse response matrix at the exterior boundary can be forecasted from that at the interior boundary via this dimensionless time by taking advantage of the time delay of waves propagating between these two boundaries. The forecasting algorithm based solely on the finite‐element method is exact in the finite‐element sense in modelling the unbounded medium.

Numerical methods based on transformation of variables are developed to improve the computational efficiency of the variational nodal method (VNM). Reordering and orthogonal transformations of the nodal unknowns are found to reduce the coefficient matrices of VNM into block-diagonal forms. These forms make it possible to reduce greatly the number of floating-point operations in matrix manipulations and hence to reduce the computational times. The red-black response matrix acceleration by transformation of interface partial-current variables has been extended to three-dimensional geometries and higher orders of spatial and angular approximations. These combined methods are incorporated within the algorithms currently used in the variational nodal code VARIANT at Argonne National Laboratory. All primary algorithms ranging from the generation of response matrices to the iterative solution method for the response matrix equations are modified to implement the new formulation. The efficiency of the new methods is tested on eigenvalue problems by comparing the computation times of the new and existing methods. Three-dimensional calculations are performed in hexagonal and Cartesian geometry for various spatial and angular approximations. The test results show that very significant gains can be obtained especially for the coupling coefficient calculations in higher angular approximations. More than an order of magnitude reduction of the total computing time is achieved in the best case.

Our aim is to characterize those matrices that are the response matrix of a semi-positive definite Schr?dinger operator on a circular planar network. Our findings generalize the known results and allow us to consider both nonsingular and non diagonally dominant matrices as response matrices. To this end, we define the Dirichlet-to-Robin map associated with a Schr?dinger operator on general networks, and we prove that it satisfies the alternating property which is essential to characterize the response matrices.

Development and validation of the three-dimensional dynamic code—KIKO3D

The eigenmodes of the time reversal operator are studied for a single rigid cylinder with elliptical cross-section leading to an asymmetric inter-element response matrix in reflection measurement mode. The elliptical cylinder is of considerable interest in scattering problems and it encompasses within the limit both the circular cross-section case and the strip. Variable cylinder properties will include cross-sectional area, eccentricity and angle of inclination of the semi-major axis with respect to the axis of symmetry of a probing transducer array. Approximations of the exact solutions determining the far-field response using a modal expansion with scattering coefficients computed via Mathieu functions will be discussed. Analysis of simulated results will indicate that for scatterers near the Rayleigh limit it is possible to characterize the aspect ratio of the target using subarray methods.

Image fusion serves as the basis for automatic target recognition; it maps images of teh same scene received from different sensors into a common reference system. A novel fusion method is described that employs image local response and the hybrid evolutionary algorithm (HEA). Given geometric transformation A(V) under parameter vector V (e.g. affine image transformation) of the images subjected to fusion, image local response is defined as image transform components of the parameter vector V are applied to the image, and the corresponding variations of the least squared differences of the gray levels of the two images (i.e. before and after parameter variation) form the image response matrix. The transform R(V) extracts only the dynamic contents of the image, i.e. the salient features that are most sensitive to geometric transformation A(V). Since R(V) maps the image onto itself, the result of the mapping is largely invariant to the type of the sensor that was used to obtain the image. Once the response matrices are built for all images subjected to fusion, HEA is used to map the images into the common reference system.

A Study of Certified Diabetes Educators: A Descriptive Exploration of the Delivery of Diabetes Self-Management Support in Community-based Settings in Ontario

We present a direct slope-based correction algorithm to simultaneously control two deformable mirrors (DMs) in a woofer-tweeter adaptive optics system. A global response matrix was derived from the response matrices of each deformable mirror and the voltages for both deformable mirrors were calculated simultaneously. This control algorithm was tested and compared with a 2-step sequential control method in five normal human eyes using an adaptive optics scanning laser ophthalmoscope. The mean residual total root-mean-square (RMS) wavefront errors across subjects after adaptive optics (AO) correction were 0.128 ± 0.025 μm and 0.107 ± 0.033 μm for simultaneous and 2-step control, respectively (7.75-mm pupil). The mean intensity of reflectance images acquired after AO convergence was slightly higher for 2-step control. Radially-averaged power spectra calculated from registered reflectance images were nearly identical for all subjects using simultaneous or 2-step control. The correction performance of our new simultaneous dual DM control algorithm is comparable to 2-step control, but is more efficient. This method can be applied to any woofer-tweeter AO system.

The authors describe a two-dimensional (vector) regressional model for examining the anisotropic response of ice drift and ocean current velocity (“drift velocity”) to surface wind forcing. Illustration of the method is limited to sea ice response. The principal mathematical and physical properties of the model are outlined, together with estimates of the “response matrices” and the corresponding “response ellipses” (drift velocity response to a unity wind velocity forcing). For each direction, φ, of the wind vector the method describes a corresponding “wind factor” α(φ) (relative drift speed) and “turning angle” θ(φ) (the angle between the drift velocity and wind vector). The major ellipse axis corresponds to the direction of the “effective wind” (φ = φmax) and the minor axis to the direction of the “noneffective” wind. The eigenvectors of the response matrix define wind directions that are the same as the wind-induced drift velocity directions. Depending on the water depth and offshore distance, six analytical cases are possible, ranging from rectilinear response ellipses near the coast to purely circular response ellipses in the open ocean. The model is used to examine ice drift along the western shelf of Sakhalin Island (Sea of Okhotsk). Responses derived from the vector regression (four parameter) method are less constrained and therefore more representative of wind-induced surface motions than those derived using the traditional complex transfer function (two parameter) approach.

A numerical procedure for assessing the performance of an active noise and vibration control system for a harmonically excited weakly coupled multimodal vibroacoustic system is presented. The structure and the contiguous acoustic space have been modeled separately with a commercially available finite element analysis package (ANSYS) and then combined using a modal coupling theory for weakly coupled systems. Numerical results are compared against experimental measurements for a finite longitudinally stiffened cylinder with an integral floor. Experimental based response matrices were measured and used to predict the system response. Modal analysis was applied in order to reduce the required effort in determining the response matrix. A design methodology for optimizing the physical control system is reviewed and several trends presented.

Spatial homogenization method based on the inverse problem

Methods for reconstruction of the density distribution of nuclear power

Finite difference applied to the reconstruction method of the nuclear power density distribution

A new method termed Directive Line Source Model (DLSM) is presented for predicting the diffracted field produced by a sound wave incident on a rigid or pressure release half plane. In the new method the edge of the half plane is modeled as an infinite set of directive point sources continuously distributed along the edge. Because DLSM is fast, simple and intuitive, it is a promising tool for the study of diffraction. It can be applied for several types of incident radiation: omnidirectional cylindrical and spherical waves, plane waves, as well as waves from directional sources. Wedges may also be treated. Finally, DLSM can handle diffraction by an arbitrarily shaped edge profile, for example, a half plane having an edge that is jagged instead of straight. Results for plane, cylindrical and spherical incident waves, as well as for arrays of line and point sources, are presented and their agreement with known analytical solutions is demonstrated. Predictions based on DLSM compare favorably with experimental data.