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## Eigenvalues
Kinds of Eigenvalues
Terms modified by Eigenvalues
## Selected Abstracts## A taxometric study of alcohol abuse and dependence in a general population sample: evidence of dimensional latent structure and implications for DSM-V ADDICTION, Issue 5 2009Tim SladeABSTRACT Aims To explore, with the aid of taxometric analysis, whether alcohol abuse and alcohol dependence are each conceptualized most effectively as single latent dimensions or distinct latent categories. Design Data were taken from a nationally representative cross-sectional epidemiological survey of psychiatric and substance use disorders. Setting General population of Australia. Participants A subsample of all respondents who had consumed at least 12 drinks in the year prior to the survey and who had consumed at least three drinks on at least one single day (n = 4920 of a possible 10 641). Measurements DSM-IV criteria for alcohol abuse and dependence were assessed with the Composite International Diagnostic Interview, version 2.1. Two independent taxometric procedures, MAXimum EIGenvalue (MAXEIG) and mean above minus below a cut (MAMBAC), together with analysis of simulated dimensional and categorical data sets, were carried out. Findings Consistent evidence was found for a single latent dimension underlying the symptoms of alcohol dependence. Less consistent evidence of dimensionality was found for the symptoms of alcohol abuse. Conclusions These findings support the growing consensus regarding the need for continuous measures of alcohol use disorders to complement the traditional categorical representations in upcoming versions of the major psychiatric classification systems. [source] ## Stages of Change , Continuous Measure (URICA-E2): psychometrics of a Norwegian version JOURNAL OF ADVANCED NURSING, Issue 1 2009Anners LerdalAbstract Title.,Stages of Change , Continuous Measure (URICA-E2): psychometrics of a Norwegian version. Aim., This paper is a report of research to translate the English version of the Stages of Change continuous measure questionnaire (URICA-E2) into Norwegian and to test the validity of the questionnaire and its usefulness in predicting behavioural change. Background., While the psychometric properties of the Stages of Change categorical measure have been tested extensively, evaluation of the psychometric properties of the continuous questionnaire has not been described elsewhere in the literature. Method., Cross-sectional data were collected with a convenience sample of 198 undergraduate nursing students in 2005 and 2006. The English version of URICA-E2 was translated into Norwegian according to standardized procedures. Findings., Principal components analysis clearly confirmed five of the dimensions of readiness to change (Precontemplation Non-Believers, Precontemplation Believers, Contemplation, Preparation and Maintenance), while the sixth dimension, Action, showed the lowest Eigenvalue (0·93). Findings from the cluster analysis indicate distinct profiles among the respondents in terms of readiness to change their exercise behaviour. Conclusion., The URICA-E2 was for the most part replicated from Reed's original work. The result of the cluster analysis of the items associated with the factor ,Action' suggests that these do not adequately measure the factor. [source] ## Bench,shelf system dynamic characteristics and their effects on equipment and contents EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 13 2006Tara C. HutchinsonAbstract Economic losses during past earthquakes are strongly associated with damage and failure to nonstructural equipment and contents. Among the vast types of nonstructural elements, one important category, is scientific equipment in biological or chemical laboratories. These equipment are often mounted on heavy ceramic bench-tops of bench,shelf systems, which in turn may amplify the dynamic motions imposed. To investigate the seismic response of these types of systems, a series of shake table and field experiments were conducted considering different representative bench and shelf-mounted equipment and contents. Results from shake table experiments indicate that these equipment are generally sliding-dominated. In addition, the bench,shelf system is observed to be very stiff and when lightly loaded, has a fundamental frequency between 10 and 16 Hz. An approximate 50% reduction in the first and second fundamental frequencies is observed considering practical loading conditions. Insight into a broader range of system response is provided by conducting eigenvalue and time history analyses. Non-linear regression through the numerical data indicate acceleration amplification ratios , range from 2.6 to 1.4 and from 4.3 to 1.6, for fixed,fixed and pinned,pinned conditions, respectively. Both the experimental and numerical results support the importance of determining the potential dynamic amplification of motion in the context of accurately determining the maximum sliding displacement of support equipment and contents. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A simple persistence condition for structured populations ECOLOGY LETTERS, Issue 7 2006Alan HastingsAbstract The fundamental question in both basic and applied population biology of whether a species will increase in numbers is often investigated by finding the population growth rate as the largest eigenvalue of a deterministic matrix model. For a population classified only by age, and not stage or size, a simpler biologically interpretable condition can be used, namely whether R0, the mean number of offspring per newborn, is greater than one. However, for the many populations not easily described using only age classes, stage-structured models must be used for which there is currently no quantity like R0. We determine analogous quantities that must be greater than one for persistence of a general structured population model that have a similar useful biological interpretation. Our approach can be used immediately to determine the magnitude of changes and interactions that would either allow population persistence or would ensure control of an undesirable species. [source] ## Effects of intermediate load on damping of synchronous generator EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 4 2006P. AreeAbstract The transfer-function block-diagram model of a single-machine infinite-bus power system, originally developed by Heffron and Phillips, has been a popular analytical tool amongst power system engineers for explanation and assessment of synchronous generator dynamic behaviors. Since this model simply accounts for the generator field circuit with none of the damper circuits, it may not always give a realistic transient response. Moreover, the model considers only a grid-system load without local and intermediate loads. Hence, effects of these loads together with the damper circuits on electromechanical damping have not yet been completely studied. In this paper, the Heffron-Phillips's model has been advanced to incorporate an intermediate load plus one additional damper circuit in the q -axis. The upgraded model demonstrates a great influence of the intermediate load together with the q -axis damper circuit on the electromechanical damping and the dynamic interaction between the field and damper flux linkages. The study shows the key contributions of load to rise and fall of the damping. It appears that the electromechanical damping can be improved with regard to the unity power-factor load through increasing in the natural damping and decreasing in the automatic voltage regulator (AVR) negative damping torques. Nevertheless, the damping is mostly declined, when the load power factor is poor. Moreover, it is markedly changed in relation to various locations of load. The damping characteristics of synchronous generator are investigated using the eigenvalue and frequency response methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Identification of Quaternary Shape Memory Alloys with Near-Zero Thermal Hysteresis and Unprecedented Functional Stability ADVANCED FUNCTIONAL MATERIALS, Issue 12 2010Robert ZarnettaAbstract Improving the functional stability of shape memory alloys (SMAs), which undergo a reversible martensitic transformation, is critical for their applications and remains a central research theme driving advances in shape memory technology. By using a thin-film composition-spread technique and high-throughput characterization methods, the lattice parameters of quaternary Ti,Ni,Cu,Pd SMAs and the thermal hysteresis are tailored. Novel alloys with near-zero thermal hysteresis, as predicted by the geometric non-linear theory of martensite, are identified. The thin-film results are successfully transferred to bulk materials and near-zero thermal hysteresis is observed for the phase transformation in bulk alloys using the temperature-dependent alternating current potential drop method. A universal behavior of hysteresis versus the middle eigenvalue of the transformation stretch matrix is observed for different alloy systems. Furthermore, significantly improved functional stability, investigated by thermal cycling using differential scanning calorimetry, is found for the quaternary bulk alloy Ti50.2Ni34.4Cu12.3Pd3.1. [source] ## Development and Validation of the Headache Needs Assessment (HANA) Survey HEADACHE, Issue 4 2001Joyce A. Cramer BSObjective.,To develop and validate a brief survey of migraine-related quality-of-life issues. The Headache Needs Assessment (HANA) questionnaire was designed to assess two dimensions of the chronic impact of migraine (frequency and bothersomeness). Methods.,Seven issues related to living with migraine were posed as ratings of frequency and bothersomeness. Validation studies were performed in a Web-based survey, a clinical trial responsiveness population, and a retest reliability population. Headache characteristics (eg, frequency, severity, and treatment), demographic information, and the Headache Disability Inventory were used for external validation. Results.,The HANA was completed in full by 994 adults in the Web survey, with a mean total score of 77.98 ± 40.49 (range, 7 to 175). There were no floor or ceiling effects. The HANA met the standards for validity with internal consistency reliability (Cronbach , = .92, eigenvalue for the single factor = 4.8, and test-retest reliability = 0.77). External validity showed a high correlation between HANA and Headache Disability Inventory total scores (0.73, P<.0001), and high correlations with disease and treatment characteristics. Conclusions.,These data demonstrate the psychometric properties of the HANA. The brief questionnaire may be a useful screening tool to evaluate the impact of migraine on individuals. The two-dimensional approach to patient-reported quality of life allows individuals to weight the impact of both frequency and bothersomeness of chronic migraines on multiple aspects of daily life. [source] ## Bifurcation modeling in geomaterials: From the second-order work criterion to spectral analyses INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2009F. PrunierAbstract The present paper investigates bifurcation analysis based on the second-order work criterion, in the framework of rate-independent constitutive models and rate-independent boundary-value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi-static boundary-value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9:203,274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207,220) and the plasticity limit criterion are revived in order to clarify the application field of the second-order work criterion and to contrast these criteria. The first part of this paper analyses the second-order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (d, = Md,) or in the dual form (d, = Nd,), is discussed. In the second part, the analysis is extended to the boundary-value problems in quasi-static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary-value problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Block diagonalization of Laplacian matrices of symmetric graphs via group theory INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007A. KavehAbstract In this article, group theory is employed for block diagonalization of Laplacian matrices of symmetric graphs. The inter-relation between group diagonalization methods and algebraic-graph methods developed in recent years are established. Efficient methods are presented for calculating the eigenvalues and eigenvectors of matrices having canonical patterns. This is achieved by using concepts from group theory, linear algebra, and graph theory. These methods, which can be viewed as extensions to the previously developed approaches, are illustrated by applying to the eigensolution of the Laplacian matrices of symmetric graphs. The methods of this paper can be applied to combinatorial optimization problems such as nodal and element ordering and graph partitioning by calculating the second eigenvalue for the Laplacian matrices of the models and the formation of their Fiedler vectors. Considering the graphs as the topological models of skeletal structures, the present methods become applicable to the calculation of the buckling loads and the natural frequencies and natural modes of skeletal structures. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A refined semi-analytic design sensitivity based on mode decomposition and Neumann series INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005Maenghyo ChoAbstract Among various sensitivity evaluation techniques, semi-analytical method (SAM) is quite popular since this method is more advantageous than analytical method (AM) and global finite difference method (GFD). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the pseudo load vector calculated by differentiation using the finite difference scheme. In the present study, an iterative refined semi-analytical method (IRSAM) combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives. In eigenvalue problems, the tendency of eigenvalue sensitivity is similar to that of displacement sensitivity in static problems. Eigenvector is decomposed into rigid body mode and pure deformation mode. The present iterative SAM guarantees that the eigenvalue and eigenvector sensitivities converge to the reliable values for the wide range of perturbed size of the design variables. Accuracy and reliability of the shape design sensitivities in static problems and eigenvalue problems by the proposed method are assessed through the various numerical examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002J. T. ChenAbstract For a plane elasticity problem, the boundary integral equation approach has been shown to yield a non-unique solution when geometry size is equal to a degenerate scale. In this paper, the degenerate scale problem in the boundary element method (BEM) is analytically studied using the method of stress function. For the elliptic domain problem, the numerical difficulty of the degenerate scale can be solved by using the hypersingular formulation instead of using the singular formulation in the dual BEM. A simple example is shown to demonstrate the failure using the singular integral equations of dual BEM. It is found that the degenerate scale also depends on the Poisson's ratio. By employing the hypersingular formulation in the dual BEM, no degenerate scale occurs since a zero eigenvalue is not embedded in the influence matrix for any case. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Convergence properties of bias-eliminating algorithms for errors-in-variables identification INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 9 2005Torsten SöderströmAbstract This paper considers the problem of dynamic errors-in-variables identification. Convergence properties of the previously proposed bias-eliminating algorithms are investigated. An error dynamic equation for the bias-eliminating parameter estimates is derived. It is shown that the convergence of the bias-eliminating algorithms is basically determined by the eigenvalue of largest magnitude of a system matrix in the estimation error dynamic equation. When this system matrix has all its eigenvalues well inside the unit circle, the bias-eliminating algorithms can converge fast. In order to avoid possible divergence of the iteration-type bias-eliminating algorithms in the case of high noise, the bias-eliminating problem is re-formulated as a minimization problem associated with a concentrated loss function. A variable projection algorithm is proposed to efficiently solve the resulting minimization problem. A numerical simulation study is conducted to demonstrate the theoretical analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## The reaction between ethyl and molecular oxygen II: Further analysis INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 11 2001James A. MillerThe present investigation is a rather substantial extension and elaboration of our previous work on the same reaction. In this article we accomplish four primary objectives: 1.We show quantitatively how sensitive the high-temperature rate coefficient k(T) is to E02, the threshold energy of the transition state for direct molecular elimination of HO2 from ethylperoxy radical (C2H5O2), thus deducing a value of E02=,3.0 kcal/mol (measured from reactants). 2.We derive the result that k0(T) , k,,(T) in the high-temperature regime, where k0(T) is the zero-pressure rate coefficient, and k,,(T) is the infinite-pressure rate coefficient for the bimolecular channel. 3.Most importantly, we discuss the three different regimes of the reaction (low-temperature, transition, and high-temperature) in terms of the eigenvectors and eigenvalues of G, the transition matrix of the master equation. The transition regime is shown to be a region of avoided crossing between the two chemically significant eigenvalue curves in which the thermal rate coefficient k (T ,p) jumps from one eigenvalue to the other. This jump is accompanied by a "mixing" of the corresponding eigenvectors, through which both eigenvectors deplete the reactant. The onset of the high-temperature regime is triggered by reaching the "stabilization limit" of the ethylperoxy adduct, a limit that is induced by a shift in equilibrium of the stabilization reaction. Our identification of the prompt and secondary HO2 formed by the reaction with these eigenvalue/eigenvector pairs leads to good agreement between theory and the experiments of Clifford et al. (J Phys Chem A 2000, 104, 11549,11560). 4.Lastly, we describe the master equation results in terms of a set of elementary reactions and phenomenological rate coefficients. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 732,740, 2001 [source] ## An efficient approach for computing non-Gaussian ARMA model coefficients using Pisarenko's method INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2005Adnan Al-SmadiAbstract This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the system output. The observed signal may be corrupted by additive coloured Gaussian noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The input is not observed. The unknown model coefficients are obtained using eigenvalue,eigenvector decomposition. The derivation of this procedure is an extension of Pisarenko harmonic autocorrelation-based (PHA) method to third order statistics. It will be shown that the desired ARMA coefficients vector corresponds to the eigenvector associated with the minimum eigenvalue of a data covariance matrix of TOCs. The proposed method is also compared with well-known algorithms as well as with the PHA method. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Ab initio quantum-mechanical prediction of the IR and Raman spectra of Ca3Cr2Si3O12 Uvarovite garnet INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2010L. ValenzanoAbstract The IR and Raman spectra of uvarovite (Ca3Cr2Si3O12) garnet were simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The two sets of 17 F1u Transverse-Optical (TO) and Longitudinal-Optical (LO) frequencies are generated, together with their intensities. As regards the IR experimental spectrum, only five peaks are available, that are in excellent agreement with the calculated data (mean absolute difference smaller than 5.2 cm,1). The analysis of the TO-LO eigenvalue overlaps permits to establish a correspondence between LO and TO modes. The set of experimental Raman peaks is much reacher (23 out of 25) and the agreement with our calculations excellent ( smaller than 6 cm,1). Isotopic substitution is used to identify the zones of the spectrum where Cr and Ca contributions are relevant. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] ## Explicitly correlated SCF study of anharmonic vibrations in (H2O)2 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002Donald D. ShilladyAbstract Modeling solvation in high-pressure liquid chromatography (HPLC) requires calculation of anharmonic vibrational frequencies of solvent clusters for a statistical partition function. An efficient computational method that includes electron correlation is highly desirable for large clusters. A modified version of the "soft Coulomb hole" method of Chakravorty and Clementi has recently been implemented in a Gaussian-lobe-orbital (GLO) program (PCLOBE) to include explicit electron,electron correlation in molecules. The soft Coulomb hole is based on a modified form of Coulomb's law: An algorithm has been developed to obtain the parameter "w" from a polynomial in the effective scaling of each primitive Gaussian orbital relative to the best single Gaussian of the H1s orbital. This method yields over 90% of the correlation energy for molecules of low symmetry for which the original formula of Chakravorty and Clementi does not apply. In this work, all the vibrations of the water dimer are treated anharmonically. A quartic perturbation of the harmonic vibrational modes is constrained to be equal to the exact Morse potential eigenvalue based on a three-point fit. This work evaluates the usefulness of fitting a Morse potential to a hydrogen bond vibrational mode and finds it to be slightly better than using MP2 vibrational analysis for this important dimer. A three-point estimate of the depth, De, of a Morse potential leads to a correction formula for anharmonicity in terms of the perturbed harmonic frequency: When scaled by 0.9141, the harmonic Morse method leads to essentially the same results as scaling the BPW91 local density method by 0.9827. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] ## Global optimization for robust control synthesis based on the Matrix Product Eigenvalue Problem INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2001Yuji YamadaAbstract In this paper, we propose a new formulation for a class of optimization problems which occur in general robust control synthesis, called the Matrix Product Eigenvalue Problem (MPEP): Minimize the maximum eigenvalue of the product of two block-diagonal positive-definite symmetric matrices under convex constraints. This optimization class falls between methods of guaranteed low complexity such as the linear matrix inequality (LMI) optimization and methods known to be NP-hard such as the bilinear matrix inequality (BMI) formulation, while still addressing most robust control synthesis problems involving BMIs encountered in applications. The objective of this paper is to provide an algorithm to find a global solution within any specified tolerance , for the MPEP. We show that a finite number of LMI problems suffice to find the global solution and analyse its computational complexity in terms of the iteration number. We prove that the worst-case iteration number grows no faster than a polynomial of the inverse of the tolerance given a fixed size of the block-diagonal matrices in the eigenvalue condition. Copyright 2001 © John Wiley & Sons, Ltd. [source] ## A new scale to measure family members' perception of community health care services for persons with Huntington disease JOURNAL OF EVALUATION IN CLINICAL PRACTICE, Issue 3 2010Valmi D. Sousa PhD CNS-BC RNAbstract Rationale, aims, and objectives, Huntington disease (HD) is a progressive genetic brain disease leading to disruptive cognitive, behavioural and physical impairments. Persons with the condition and their caregivers need appropriate and accessible health care services to help them manage the disease adequately. The purpose of this study was to evaluate the psychometric properties of a new scale that measures family members' perception of community health care services (CHCS) for persons with HD. Methods, A methodological design was used to examine the initial reliability and dimensionality of the CHCS scale among 245 family members of persons with a diagnosis of HD. Data analysis consisted of computing Cronbach's , coefficients, calculating the 95% confidence interval for , and performing item-analysis and exploratory factor analysis. Results, Reliability of the scale based on Cronbach's , was 0.83. Factor analysis using principal component analysis and varimax rotation suggested that three interpretable factors underlie the scale. Factor 1, HD knowledge, had , = 0.82, eigenvalue of 4.67 and explained 33.42% of the variance; factor 2, HD community resources, had , = 0.62, eigenvalue of 1.68 and explained 12.02% of the variance; factor 3, individualized HD management, had , = 0.77, eigenvalue of 1.45 and explained 10.39% of the variance. Conclusions, Findings from this study provide evidence of both construct validity and internal consistency reliability of the CHCS scale. Further psychometric testing of the scale in other samples of family caregivers of persons with HD is warranted. [source] ## The kth Laplacian eigenvalue of a tree JOURNAL OF GRAPH THEORY, Issue 1 2007Ji-Ming GuoAbstract Let ,k(G) be the kth Laplacian eigenvalue of a graph G. It is shown that a tree T with n vertices has and that equality holds if and only if k < n, k|n and T is spanned by k vertex disjoint copies of , the star on vertices. © 2006 Wiley Periodicals, Inc. J Graph Theory [source] ## MRI diffusion tensor tracking of a new amygdalo-fusiform and hippocampo-fusiform pathway system in humans JOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 6 2009Charles D. Smith MDAbstract Purpose To use MRI diffusion-tensor tracking (DTT) to test for the presence of unknown neuronal fiber pathways interconnecting the mid-fusiform cortex and anteromedial temporal lobe in humans. Such pathways are hypothesized to exist because these regions coactivate in functional MRI (fMRI) studies of emotion-valued faces and words, suggesting a functional link that could be mediated by neuronal connections. Materials and Methods A total of 15 normal human subjects were studied using unbiased DTT approaches designed for probing unknown pathways, including whole-brain seeding and large pathway-selection volumes. Several quality-control steps verified the results. Results Parallel amygdalo-fusiform and hippocampo-fusiform pathways were found in all subjects. The pathways begin/end at the mid-fusiform gyrus above the lateral occipitotemporal sulcus bilaterally. The superior pathway ends/begins at the superolateral amygdala. The inferior pathway crosses medially and ends/begins at the hippocampal head. The pathways are left-lateralized, with consistently larger cross-sectional area, higher anisotropy, and lower minimum eigenvalue (D-min) on the left, where D-min assesses intrinsic cross-fiber diffusivity independent of curvature. Conclusion A previously-undescribed pathway system interconnecting the mid-fusiform region with the amygdala/hippocampus has been revealed. This pathway system may be important for recognition, memory consolidation, and emotional modulation of face, object, and lexical information, which may be disrupted in conditions such as Alzheimer's disease. J. Magn. Reson. Imaging 2009. © 2009 Wiley-Liss, Inc. [source] ## Invariant co-ordinate selection JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2009David E. TylerSummary., A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue,eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given. [source] ## Brassica oleracea var. costata: comparative study on organic acids and biomass production with other cabbage varieties JOURNAL OF THE SCIENCE OF FOOD AND AGRICULTURE, Issue 6 2009Carla SousaAbstract BACKGROUND: A study was undertaken to evaluate the effect of agronomic practices, harvesting time and leaf age on the organic acid composition and biomass production of Brassica oleracea L. var. costata DC (tronchuda cabbage). Samples were cultivated under eight different fertilisation regimes (two levels each of nitrogen, boron and sulfur, an organic fertiliser and no fertiliser) and collected at three different times. RESULTS: Principal component analysis of the data indicated significant differences. Three principal components with an eigenvalue higher than one accounted for 79.0% of the total variance of the data set. Samples obtained with conventional fertilisation were characterised by the highest values of fresh weight. External leaves showed higher total organic acid and malic acid contents than internal leaves, while the latter were characterised by higher proportions of citric acid. For consecutive harvests, total organic acid concentration decreased in both external and internal leaves. CONCLUSION: The use of a conventional fertilisation regime (nitrogen, boron or sulfur) improved the growth of B. oleracea var. costata without affecting its organic acid profile. However, for consecutive harvests, total organic acid concentration was observed to decrease independently of the agronomic practices tested. Leaf age influenced the quantitative composition of organic acids. Copyright © 2009 Society of Chemical Industry [source] ## In vivo diffusion tensor imaging of the human optic nerve: Pilot study in normal controls MAGNETIC RESONANCE IN MEDICINE, Issue 2 2006C.A.M. Wheeler-KingshottAbstract Diffusion tensor imaging (DTI) of the optic nerve (ON) was acquired in normal controls using zonally oblique multislice (ZOOM) DTI, which excites a small field of view (FOV) using a fast sequence with a shortened EPI echo train. This combines the benefit of low sensitivity to motion (due to the single-shot acquisition used), with the additional advantage of reduced sensitivity to magnetic field susceptibility artifacts. Reducing the bright signal from the fat and cerebrospinal fluid (CSF) surrounding the nerve are key requirements for the success of the presented method. Measurements of mean diffusivity (MD) and fractional anisotropy (FA) indices were made in a coronal section of the middle portion of the optic nerve (ON) in the right (rON) and left (lON) ONs. The average values across 10 healthy volunteers were FArON = 0.64 ± 0.09 and FAlON = 0.57 ± 0.10, and MDrON = (1173 ± 227) × 10,6 mm2 s,1 and MDlON = (1266 ± 170) × 10,6 mm2 s,1. Measurements of the principal eigenvalue of the DT and its orthogonal component were also in agreement with those expected from a highly directional structural organization. Magn Reson Med, 2006. © 2006 Wiley-Liss, Inc. [source] ## Shape optimization for low Neumann and Steklov eigenvalues MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010Alexandre GirouardAbstract We give an overview of results on shape optimization for low eigenvalues of the Laplacian on bounded planar domains with Neumann and Steklov boundary conditions. These results share a common feature: they are proved using methods of complex analysis. In particular, we present modernized proofs of the classical inequalities due to Szegö and Weinstock for the first nonzero Neumann and Steklov eigenvalues. We also extend the inequality for the second nonzero Neumann eigenvalue, obtained recently by Nadirashvili and the authors, to nonhomogeneous membranes with log-subharmonic densities. In the homogeneous case, we show that this inequality is strict, which implies that the maximum of the second nonzero Neumann eigenvalue is not attained in the class of simply connected membranes of a given mass. The same is true for the second nonzero Steklov eigenvalue, as follows from our results on the Hersch,Payne,Schiffer inequalities. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Resonance phenomena in compound cylindrical waveguides MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2006Günter HeinzelmannAbstract We study the large time asymptotics of the solutions u(x,t) of the Dirichlet and the Neumann initial boundary value problem for the wave equation with time-harmonic right-hand side in domains , which are composed of a finite number of disjoint half-cylinders ,1,,,,r with cross-sections ,,1,,,,,r and a bounded part (,compound cylindrical waveguides'). We show that resonances of orders t and t1/2 may occur at a finite or countable discrete set of frequencies ,, while u(x,t) is bounded as t,, for the remaining frequencies. A resonance of order t occurs at , if and only if ,2 is an eigenvalue of the Laplacian ,, in , with regard to the given boundary condition u=0 or ,u/,n=0, respectively. A resonance of order t1/2 occurs at , if and only if (i) ,2 is an eigenvalue of at least one of the Laplacians for the cross-sections ,,1,,,,r, with regard to the respective boundary condition and (ii) the respective homogeneous boundary value problem for the reduced wave equation ,U+,2U=0 in , has non-trivial solutions with suitable asymptotic properties as | x | ,, (,standing waves'). Copyright © 2006 John Wiley & Sons, Ltd. [source] ## The ice-fishing problem: the fundamental sloshing frequency versus geometry of holes MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004Vladimir KozlovAbstract We study an eignevalue problem with a spectral parameter in a boundary condition. This problem for the Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a half-space covered by a rigid dock with some apertures (an ice sheet with fishing holes). The dependence of the fundamental eigenvalue on holes' geometry is investigated. We give conditions on a plane region guaranteeing that the fundamental eigenvalue corresponding to this region is larger than the fundamental eigenvalue corresponding to a single circular hole. Examples of regions satisfying these conditions and having the same area as the unit disk are given. New results are also obtained for the problem with a single circular hole. On the other hand, we construct regions for which the fundamental eigenfrequency is larger than the similar frequency for the circular hole of the same area and even as large as one wishes. In the latter examples, the hole regions are either not connected or bounded by a rather complicated curves. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Eigenfunctions and Hardy inequalities for a magnetic Schrödinger operator in ,2 MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2003Bénédicte AlziaryAbstract The zero set {z,,2:,(z)=0} of an eigenfunction , of the Schrödinger operator ,V=(i,+A)2+V on L2(,2) with an Aharonov,Bohm-type magnetic potential is investigated. It is shown that, for the first eigenvalue ,1 (the ground state energy), the following two statements are equivalent: (I) the magnetic flux through each singular point of the magnetic potential A is a half-integer; and (II) a suitable eigenfunction , associated with ,1 (a ground state) may be chosen in such a way that the zero set of , is the union of a finite number of nodal lines (curves of class C2) which emanate from the singular points of the magnetic potential A and slit the two-dimensional plane ,2. As an auxiliary result, a Hardy-type inequality near the singular points of A is proved. The C2 differentiability of nodal lines is obtained from an asymptotic analysis combined with the implicit function theorem. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Boundary value problems with eigenvalue depending boundary conditions MATHEMATISCHE NACHRICHTEN, Issue 5 2009Jussi BehrndtAbstract We investigate some classes of eigenvalue dependent boundary value problems of the form where A , A+ is a symmetric operator or relation in a Krein space K, , is a matrix function and ,0, ,1 are abstract boundary mappings. It is assumed that A admits a self-adjoint extension in K which locally has the same spectral properties as a definitizable relation, and that , is a matrix function which locally can be represented with the resolvent of a self-adjoint definitizable relation. The strict part of , is realized as the Weyl function of a symmetric operator T in a Krein space H, a self-adjoint extension Ă of A × T in K × H with the property that the compressed resolvent PK (Ă , ,),1|Kk yields the unique solution of the boundary value problem is constructed, and the local spectral properties of this so-called linearization Ă are studied. The general results are applied to indefinite Sturm,Liouville operators with eigenvalue dependent boundary conditions (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## The first Dirichlet eigenvalue of a compact manifold and the Yang conjecture MATHEMATISCHE NACHRICHTEN, Issue 12 2007Jun LingAbstract We give a new estimate on the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature and provide a solution for a conjecture of H. C. Yang. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Validation of a method to measure resident doctors' reflections on quality improvement MEDICAL EDUCATION, Issue 3 2010Christopher M WittichMedical Education 2010:44: 248,255 Objectives, Resident reflection on the clinical learning environment is prerequisite to identifying quality improvement (QI) opportunities and demonstrating competence in practice-based learning. However, residents' abilities to reflect on QI opportunities are unknown. Therefore, we developed and determined the validity of the Mayo Evaluation of Reflection on Improvement Tool (MERIT) for assessing resident reflection on QI opportunities. Methods, The content of MERIT, which consists of 18 items structured on 4-point scales, was based on existing literature and input from national experts. Using MERIT, six faculty members rated 50 resident reflections. Factor analysis was used to examine the dimensionality of MERIT instrument scores. Inter-rater and internal consistency reliabilities were calculated. Results, Factor analysis revealed three factors (eigenvalue; number of items): Reflection on Personal Characteristics of QI (8.5; 7); Reflection on System Characteristics of QI (1.9; 6), and Problem of Merit (1.5; 5). Inter-rater reliability was very good (intraclass correlation coefficient range: 0.73,0.89). Internal consistency reliability was excellent (Cronbach's , 0.93 overall and 0.83,0.91 for factors). Item mean scores were highest for Problem of Merit (3.29) and lowest for Reflection on System Characteristics of QI (1.99). Conclusions, Validity evidence supports MERIT as a meaningful measure of resident reflection on QI opportunities. Our findings suggest that dimensions of resident reflection on QI opportunities may include personal, system and Problem of Merit factors. Additionally, residents may be more effective at reflecting on ,problems of merit' than personal and systems factors. [source] |