Super-resolution in confocal scanning microscopy: II :The incoherent case

For pt.I see ibid. vol.3, p.195 (1987). The authors have shown that the resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data. These analyses were restricted to the case of coherent illumination. They investigate, along similar lines, the incoherent case, which applies to fluorescence microscopy. They investigate the one-dimensional and two-dimensional square-pupil problems and they prove, by means of numerical computations of the singular value spectrum and of the impulse response function, that for a signal-to-noise ratio of, say 10%, it is possible to obtain an improvement of approximately 60% in resolution with respect to the conventional incoherent light confocal microscope. This represents a working bandwidth of 3.5 times the Rayleigh limit.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability, and the possible processes associated with compositional data sets from many disciplines. In this paper we concentrate on geochemical data sets. First we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of subcompositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained together with the necessary tools for a staying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland. Finally we point out a number of unresolved problems in the statistical analysis of compositional processes

OTHR impulsive interference suppression in strong clutter background

External interferences can severely degrade the performance of an Over-the-horizon radar (OTHR), so suppression of external interferences in strong clutter environment is the prerequisite for the target detection. The traditional suppression solutions usually began with clutter suppression in either time or frequency domain, followed by the interference detection and suppression. Based on this traditional solution, this paper proposes a method characterized by joint clutter suppression and interference detection: by analyzing eigenvalues in a short-time moving window centered at different time position, Clutter is suppressed by discarding the maximum three eigenvalues at every time position and meanwhile detection is achieved by analyzing the remained eigenvalues at different position. Then, restoration is achieved by forward-backward linear prediction using interference-free data surrounding the interference position. In the numeric computation, the eigenvalue decomposition (EVD) is replaced by values decomposition (SVD) based on the equivalence of these two processing. Data processing and experimental results show its efficiency of noise floor falling down about 10-20 dB.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

Variations of the FEAST Eigenvalue Algorithm

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is extended to contours and quadrature schemes that are recursively subdividable. A general complex recursive algorithm is implemented on rectangular and diamond contours. The accuracy of different quadrature schemes for various contours is investigated.

Aprehender dibujando: los dibujos de Luis Borobio

Este artículo es una contribución al entendimiento del dibujo como aprehensión de su objeto, en general, y de la arquitectura, en particular, es decir, como definición de lo tangible que luego se materializará en la obra. Para ello, tomamos como referencia algunos dibujos de Luis Borobio (1924-2005), arquitecto y catedrático de Estética, poeta y caricaturista, que ilustran sus libros y cuyo valor, como apuntes a mano alzada, es el de dar a entender, de manera sencilla y eficaz, aquello que representan. De este estudio se desprende su capacidad para la transmisión de conocimiento, el sentido del boceto como metáfora y de la caricatura como crítica, herramientas con las que la mano llega a conocer y dar a conocer su objeto. Se añade una reflexión final sobre Mi árbol, verdadero manual de expresión gráfica, idóneo para contribuir a esclarecer la dialéctica entre masa y espacio que es propia de toda arquitectura.

Caracterización del archivo de investigación : Un estudio de caso

El objetivo del artículo es describir los procesos administrativos del área de investigación en la Escuela Interamericana de Bibliotecología de la Universidad de Antioquia (Medellín-Colombia) en relación al archivo documental en sus diferentes niveles y tipologías. Para ello se realizó, en primer lugar, una identificación de la experiencia en investigación de la Escuela y, en segundo, una caracterización de los procesos de tratamiento archivístico del archivo de investigación, con el fin de proponer planteamientos conceptuales y metodológicos sobre este tipo de archivos. Por último, se plantean algunas recomendaciones y consideraciones finales sobre el archivo de investigación como un tipo especializado, de singular valor para la gestión y apropiación social del conocimiento científico y/o tecnológico.

Caracterización del archivo de investigación : Un estudio de caso

El objetivo del artículo es describir los procesos administrativos del área de investigación en la Escuela Interamericana de Bibliotecología de la Universidad de Antioquia (Medellín-Colombia) en relación al archivo documental en sus diferentes niveles y tipologías. Para ello se realizó, en primer lugar, una identificación de la experiencia en investigación de la Escuela y, en segundo, una caracterización de los procesos de tratamiento archivístico del archivo de investigación, con el fin de proponer planteamientos conceptuales y metodológicos sobre este tipo de archivos. Por último, se plantean algunas recomendaciones y consideraciones finales sobre el archivo de investigación como un tipo especializado, de singular valor para la gestión y apropiación social del conocimiento científico y/o tecnológico.

Caracterización del archivo de investigación : Un estudio de caso

El objetivo del artículo es describir los procesos administrativos del área de investigación en la Escuela Interamericana de Bibliotecología de la Universidad de Antioquia (Medellín-Colombia) en relación al archivo documental en sus diferentes niveles y tipologías. Para ello se realizó, en primer lugar, una identificación de la experiencia en investigación de la Escuela y, en segundo, una caracterización de los procesos de tratamiento archivístico del archivo de investigación, con el fin de proponer planteamientos conceptuales y metodológicos sobre este tipo de archivos. Por último, se plantean algunas recomendaciones y consideraciones finales sobre el archivo de investigación como un tipo especializado, de singular valor para la gestión y apropiación social del conocimiento científico y/o tecnológico.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.