Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Perturbative corrections for staggered four-fermion operators

We present results for one-loop matching coefficients between continuum four-fermion operators, defined in the Naive Dimensional Regularization scheme, and staggered fermion operators of various types. We calculate diagrams involving gluon exchange between quark fines, and ''penguin'' diagrams containing quark loops. For the former we use Landau-gauge operators, with and without O(a) improvement, and including the tadpole improvement suggested by Lepage and Mackenzie. For the latter we use gauge-invariant operators. Combined with existing results for two-loop anomalous dimension matrices and one-loop matching coefficients, our results allow a lattice calculation of the amplitudes for KKBAR mixing and K --> pipi decays with all corrections of O(g2) included. We also discuss the mixing of DELTAS = 1 operators with lower dimension operators, and show that, with staggered fermions, only a single lower dimension operator need be removed by non-perturbative subtraction.

Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography

Purpose: To optimize the data-collection strategy for diffuse optical tomography and to obtain a set of independent measurements among the total measurements using the model based data-resolution matrix characteristics. Methods: The data-resolution matrix is computed based on the sensitivity matrix and the regularization scheme used in the reconstruction procedure by matching the predicted data with the actual one. The diagonal values of data-resolution matrix show the importance of a particular measurement and the magnitude of off-diagonal entries shows the dependence among measurements. Based on the closeness of diagonal value magnitude to off-diagonal entries, the independent measurements choice is made. The reconstruction results obtained using all measurements were compared to the ones obtained using only independent measurements in both numerical and experimental phantom cases. The traditional singular value analysis was also performed to compare the results obtained using the proposed method. Results: The results indicate that choosing only independent measurements based on data-resolution matrix characteristics for the image reconstruction does not compromise the reconstructed image quality significantly, in turn reduces the data-collection time associated with the procedure. When the same number of measurements (equivalent to independent ones) are chosen at random, the reconstruction results were having poor quality with major boundary artifacts. The number of independent measurements obtained using data-resolution matrix analysis is much higher compared to that obtained using the singular value analysis. Conclusions: The data-resolution matrix analysis is able to provide the high level of optimization needed for effective data-collection in diffuse optical imaging. The analysis itself is independent of noise characteristics in the data, resulting in an universal framework to characterize and optimize a given data-collection strategy. (C) 2012 American Association of Physicists in Medicine. http://dx.doi.org/10.1118/1.4736820]

Basis pursuit deconvolution for improving model-based reconstructed images in photoacoustic tomography

The model-based image reconstruction approaches in photoacoustic tomography have a distinct advantage compared to traditional analytical methods for cases where limited data is available. These methods typically deploy Tikhonov based regularization scheme to reconstruct the initial pressure from the boundary acoustic data. The model-resolution for these cases represents the blur induced by the regularization scheme. A method that utilizes this blurring model and performs the basis pursuit deconvolution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods via three numerical experiments. Moreover, this deconvolution including the building of an approximate blur matrix is achieved via the Lanczos bidagonalization (least-squares QR) making this approach attractive in real-time. (C) 2014 Optical Society of America

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

An Explicit Guidance Scheme For A Low-Thrust Terminal Rendezvous

An explicit near-optimal guidance scheme is developed for a terminal rendezvous of a spacecraft with a passive target in circular orbit around the earth. The thrust angle versus time profile for the continuous-thrust, constant-acceleration maneuver is derived, based on the assumption that the components of inertial acceleration due to relative position and velocity are negligible on account of the close proximity between the two spacecraft. The control law is obtained as a ''bilinear tangent law'' and an analytic solution to the state differential equations is obtained by expanding a portion of the integrand as an infinite series in time. A differential corrector method is proposed, to obtain real-time updates to the guidance parameters at regular time intervals. Simulation of the guidance scheme is carried out using the Clohessy-Wiltshire equations of relative motion as well as the inverse-square two-body equations of motion. Results for typical examples are presented.

A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Scheme of squares: Part II. Systems formalism for sinusoidal perturbations

We extend here the formalism developed in Part I (for the potentiostatic response) to the admittance analysis of the scheme of squares. The results are applicable, as before, to several configurations of the electrode such as the rotating disk or the planar. All that one has to do is “to plug in” the appropriate matrices relating the interfacial concentrations to the fluxes.

A Fuzzy Approximation Scheme for Sequential Learning in Pattern Recognition

An adaptive learning scheme, based on a fuzzy approximation to the gradient descent method for training a pattern classifier using unlabeled samples, is described. The objective function defined for the fuzzy ISODATA clustering procedure is used as the loss function for computing the gradient. Learning is based on simultaneous fuzzy decisionmaking and estimation. It uses conditional fuzzy measures on unlabeled samples. An exponential membership function is assumed for each class, and the parameters constituting these membership functions are estimated, using the gradient, in a recursive fashion. The induced possibility of occurrence of each class is useful for estimation and is computed using 1) the membership of the new sample in that class and 2) the previously computed average possibility of occurrence of the same class. An inductive entropy measure is defined in terms of induced possibility distribution to measure the extent of learning. The method is illustrated with relevant examples.

Simple Coding Scheme For Modular Arithmetic

A dual representation scheme for performing arithmetic modulo an arbitrary integer M is presented. The coding scheme maps each integer N in the range 0 <= N < M into one of two representations, each being identified by its most significant bit. The encoding of numbers is straightforward and the problem of checking for unused combinations is eliminated.

An Adaptive Scheme for Learning the Probability Threshold in Pattern Recognition

The statistical minimum risk pattern recognition problem, when the classification costs are random variables of unknown statistics, is considered. Using medical diagnosis as a possible application, the problem of learning the optimal decision scheme is studied for a two-class twoaction case, as a first step. This reduces to the problem of learning the optimum threshold (for taking appropriate action) on the a posteriori probability of one class. A recursive procedure for updating an estimate of the threshold is proposed. The estimation procedure does not require the knowledge of actual class labels of the sample patterns in the design set. The adaptive scheme of using the present threshold estimate for taking action on the next sample is shown to converge, in probability, to the optimum. The results of a computer simulation study of three learning schemes demonstrate the theoretically predictable salient features of the adaptive scheme.