A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.

On the Baker-Akhiezer function in the AKNS scheme

Expressions for the Baker-Akhiezer function and their logarithmic space and time derivatives are derived in terms of the matrix elements of U - V matrices and 'squared basis functions'. These expressions generalize the well known formulas for the KdV equation case and establish links between different forms of the Whitham averaging procedure.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Spectroscopic studies of the Eu3+ and Er3+ ions in the fluorozirconate LaZr2F11 matrix

An investigation by optical spectroscopy of the Eu3 + and Er3 + active ions in the crystallized fluorozirconate matrix LaZr2F11 is presented. The D-5(1) --> F-7(0-5) emission lines of Eu3 + are used to extract the F-7(0-5) energy scheme and the observed extinctions permit the deduction of irreducible representations (IRREPS) associated with corresponding sub-levels in the D-2 symmetry. The crystal field analysis was carried out on a 387 x 387 basis set, comprising the F-7, D-5(1,2,3) F-5(1,2), (5)G(1,2,3) and P-3(1,2,3,4,5,6) terms of the Eu-3 (+) 4f(6) configuration. The deviation and rms are 6.8 and 7.9 cm (-1), respectively for 38 levels and ten parameters. The experimental crystal field parameters are in good agreement with the ab-initio ones. Moreover, the relative intensities of the D-5(0) --> F-7(2,3,4) emissions are well reproduced by an 'ab-initio' calculation, except for three lines. The Er3 + ions introduced in LaZr2F11, microcrystals also lie in an unique crystallographic site. A total of 31 energy levels were recorded and the crystal field analysis led to 6.6 and 7.8 cm (-1) for the deviation and rms, respectively, for nine variable parameters taken into account. The experimental CF parameters for Er3 + and Eu3 + are very similar, which seems to show that the host lattice contracts around the smaller Er3 + ion. The informations given by both Eu3 + and Eu3 + optical probes in LaZr2F11 are very consistent with the structure previously determined for the isotypic PrZr2F11 fluoride. (C) 2000 Elsevier B.V. B.V. All rights reserved.

A W-matrix methodology for solving sparse network equations on multiprocessor computers

This paper describes a methodology for solving efficiently the sparse network equations on multiprocessor computers. The methodology is based on the matrix inverse factors (W-matrix) approach to the direct solution phase of A(x) = b systems. A partitioning scheme of W-matrix , based on the leaf-nodes of the factorization path tree, is proposed. The methodology allows the performance of all the updating operations on vector b in parallel, within each partition, using a row-oriented processing. The approach takes advantage of the processing power of the individual processors. Performance results are presented and discussed.

Magnetic and optical investigation of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29-x) B2O3 center dot xFe(2)O(3) glass matrix

Samples of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29 - x)B2O3 center dot xFe(2)O(3) (mol%), with 0.0 <= x <= 17.5, were prepared by the fusion method and investigated by electron paramagnetic resonance (EPR), optical absorption (OA) and Mossbauer spectroscopy (MS). The EPR spectra of the as-synthesized samples exhibit two well-defined EPR signals around g = 4.27 and g = 2.01 and a visible EPR shoulder around g = 6.4, assigned to isolated Fe3+ ion complexes (g = 4.27 and g = 6.4) and Fe3+-based clusters (g = 2.01). Analyses of both EPR line intensity and line width support the model picture of Fe3+-based clusters built in from two sources of isolated ions, namely Fe2+ and Fe3+; the ferrous ion being used to build in iron-based clusters at lower x-content (below about x = 2.5%) whereas the ferric ion is used to build in iron-based clusters at higher x-content (above about x = 2.5%). The presence of Fe2+ ions incorporated within the glass template is supported by OA data with a strong band around 1100 nm due to the spin-allowed E-5(g)-T-5(2g) transition in an octahedral coordination with oxygen. Additionally, Mossbauer data (isomer shift and quadrupole splitting) confirm incorporation of both Fe2+ and Fe3+ ions within the template, more likely in tetrahedral-like environments. We hypothesize that ferrous ions are incorporated within the glass template as FeO4 complex resulting from replacing silicon in non-bridging oxygen (SiO3O-) sites whereas ferric ions are incorporated as FeO4 complex resulting from replacing silicon in bridging-like oxygen silicate groups (SiO4). (C) 2012 Elsevier Masson SAS. All rights reserved.

Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

The S-1/S-2 exciton interaction in 2-pyridone center dot 6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S-1 and S-2 electronic states of the doubly hydrogen-bonded dimer 2-pyridone center dot 6-methyl-2-pyridone (2PY center dot 6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C-2h symmetric (2-pyridone) 2 homodimer, in which the S-1 <- S-0 transition is symmetry-forbidden but the S-2 <- S-0 transition is allowed, the symmetry-breaking by the additional methyl group in 2PY center dot 6M2PY leads to the appearance of both the S-1 and S-2 origins, which are separated by Delta(exp) = 154 cm(-1). When combined with the separation of the S-1 <- S-0 excitations of 6M2PY and 2PY, which is delta = 102 cm(-1), one obtains an S-1/S-2 exciton coupling matrix element of V-AB, el = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S-1/S-2 <- S-0 spectrum of 2PY center dot 6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a' vibration and to the intermolecular sigma' stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a') = 0.15 and C(sigma') = 0.05, which places this dimer in the weak-coupling limit. However, the S-1/S-2 state exciton splittings Delta(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra-and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY center dot 6M2PY the electronic splitting is quenched by a factor of similar to 30 (i.e., the vibronic quenching factor is Gamma(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine center dot 6-methyl-2-pyridone (2HP center dot 6M2PY) are also observed and assigned. (C) 2011 American Institute of Physics.

Differential gene and protein expression in abluminal sprouting and intraluminal splitting forms of angiogenesis

In adult skeletal muscle, abluminal sprouting or longitudinal splitting of capillaries can be initiated separately by muscle overload and elevated microcirculation shear stress respectively. In the present study, gene and protein expression patterns associated with the different forms of angiogenesis were examined using a targeted gene array (Superarray), validated by quantitative RT (reverse transcription)-PCR and immunoblots. Sprouting angiogenesis induced large changes in expression levels in genes associated with extracellular matrix remodelling, such as MMP-2 (matrix metalloproteinase-2), TIMP (tissue inhibitor of metalloproteinases), SPARC (secreted protein, acidic and rich in cysteine) and thrombospondin. Changes in neuropilin, midkine and restin levels, which may underpin changes in endothelial morphology, were seen during splitting angiogenesis. Up-regulation of VEGF (vascular endothelial growth factor), Flk-1, angiopoietin-2 and PECAM-1 (platelet/endothelial cell adhesion molecule-1) was seen in both forms of angiogenesis, representing a common angiogenic response of endothelial cells. In conclusion, the present study demonstrates that general angiogenic signals from growth factors can be influenced by the local microenvironment resulting in differing forms of capillary growth to produce a co-ordinated expansion of the vascular bed.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Order 10 4 speedup in global linear instability analysis using matrix formation

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

Adaptive protection scheme for MVC-encoded stereoscopic video streaming in IP-based networks

We present an adaptive unequal error protection (UEP) strategy built on the 1-D interleaved parity Application Layer Forward Error Correction (AL-FEC) code for protecting the transmission of stereoscopic 3D video content encoded with Multiview Video Coding (MVC) through IP-based networks. Our scheme targets the minimization of quality degradation produced by packet losses during video transmission in time-sensitive application scenarios. To that end, based on a novel packet-level distortion model, it selects in real time the most suitable packets within each Group of Pictures (GOP) to be protected and the most convenient FEC technique parameters, i.e., the size of the FEC generator matrix. In order to make these decisions, it considers the relevance of the packet, the behavior of the channel, and the available bitrate for protection purposes. Simulation results validate both the distortion model introduced to estimate the importance of packets and the optimization of the FEC technique parameter values.

Investigations into an optimal transmission scheme for a MIMO system operating in a ricain fading environment

This paper describes investigations into an optimal transmission scheme for a multiple input multiple output (MIMO) system operating in a Rician fading environment. The considerations are reduced to determining a covariance matrix of transmitted signals which maximizes the MIMO capacity under the condition that the receiver has perfect knowledge of the channel while the transmitter has the information about selected statistical quantities which are measured at the receiver. An optimal covariance matrix, which requires information of the Rice factor and the signal to noise ratio, is determined. The transmission scheme relying on the choice of the proposed covariance matrix outperforms the other transmission schemes which were reported earlier in the literature. The proposed scheme realizes an upper bound limit for the MIMO capacity under arbitrary Rician fading conditions. ©2005 IEEE

Student input in the development of a marking scheme for improved engineering logbooks

Engineers logbooks are an important part of the CDIO process, as a prequel to the logooks they will be expected to keep when in industry. Previously however, students logbooks were insufficient and students did not appear to appreciate the importance of the logbooks or how they would be assessed. In an attempt to improve the students understanding and quality of logbooks, a group of ~100 1st year CDIO students were asked to collaboratively develop a marking matrix with the tutors. The anticipated outcome was that students would have more ownership in, and a deeper understanding of, the logbook and what is expected from the student during assessment. A revised marking matrix was developed in class and a short questionnaire was implemented on delivery of the adapted matrix to gauge the students response to the process. Marks from the logbooks were collected twice during teaching period one and two and compared to marks from previous years. This poster will deliver the methodology and outcomes for this venture.