Statistical shape modeling of pathological scoliotic vertebrae: A comparative analysis

Statistical shape models (SSMs) have been used widely as a basis for segmenting and interpreting complex anatomical structures. The robustness of these models are sensitive to the registration procedures, i.e., establishment of a dense correspondence across a training data set. In this work, two SSMs based on the same training data set of scoliotic vertebrae, and registration procedures were compared. The first model was constructed based on the original binary masks without applying any image pre- and post-processing, and the second was obtained by means of a feature preserving smoothing method applied to the original training data set, followed by a standard rasterization algorithm. The accuracies of the correspondences were assessed quantitatively by means of the maximum of the mean minimum distance (MMMD) and Hausdorf distance (H(D)). Anatomical validity of the models were quantified by means of three different criteria, i.e., compactness, specificity, and model generalization ability. The objective of this study was to compare quasi-identical models based on standard metrics. Preliminary results suggest that the MMMD distance and eigenvalues are not sensitive metrics for evaluating the performance and robustness of SSMs.

Genuine cross-correlations: Which surrogate based measure reproduces analytical results best?

The analysis of short segments of noise-contaminated, multivariate real world data constitutes a challenge. In this paper we compare several techniques of analysis, which are supposed to correctly extract the amount of genuine cross-correlations from a multivariate data set. In order to test for the quality of their performance we derive time series from a linear test model, which allows the analytical derivation of genuine correlations. We compare the numerical estimates of the four measures with the analytical results for different correlation pattern. In the bivariate case all but one measure performs similarly well. However, in the multivariate case measures based on the eigenvalues of the equal-time cross-correlation matrix do not extract exclusively information about the amount of genuine correlations, but they rather reflect the spatial organization of the correlation pattern. This may lead to failures when interpreting the numerical results as illustrated by an application to three electroencephalographic recordings of three patients suffering from pharmacoresistent epilepsy.

Theta burst transcranial magnetic stimulation is associated with increased EEG synchronization in the stimulated relative to unstimulated cerebral hemisphere

Theta burst transcranial magnetic stimulation (TBS) may induce behavioural changes that outlast the stimulation period. The neurophysiological basis of these behavioural changes are currently under investigation. Given the evidence that cortical information processing relies on transient synchronization and desynchronization of neuronal assemblies, we set out to test whether TBS is associated with changes of neuronal synchronization as assessed by surface EEG. In four healthy subjects one TBS train of 600 pulses (200 bursts, each burst consisting of 3 pulses at 30 Hz, repeated at intervals of 100 ms) was applied over the right frontal eye field and EEG synchronization was assessed in a time-resolved manner over 60 min by using a non-overlapping moving window. For each time step the linear cross-correlation matrix for six EEG channels of the right and for the six homotopic EEG channels of the left hemisphere were computed and their largest eigenvalues used to assess changes of synchronization. Synchronization was computed for broadband EEG and for the delta, theta, alpha, beta and gamma frequency bands. In all subjects EEG synchronization of the stimulated hemisphere was significantly and persistently increased relative to EEG synchronization of the unstimulated hemisphere. This effect occurred immediately after TBS for the theta, alpha, beta and gamma frequency bands and 10-20 min after TBS for broadband and delta frequency band EEG. Our results demonstrate that TBS is associated with increased neuronal synchronization of the cerebral hemisphere ipsilateral to the stimulation site relative to the unstimulated hemisphere. We speculate that enhanced synchronization interferes with cortical information processing and thus may be a neurophysiological correlate of the impaired behavioural performance detected previously.

Development of the Davos Assessment of Cognitive Biases Scale (DACOBS)

Objective: Cognitive problems and biases play an important role in the development and continuation of psychosis. A self-report measure of these deficits and processes was developed (Davos Assessment of Cognitive Biases Scale: DACOBS) and is evaluated in this study. Methods: An item pool made by international experts was used to develop a self-report scale on a sample of 138 schizophrenia spectrum patients. Another sample of 71 patients was recruited to validate the subscales. A group of 186 normal control subjects was recruited to establish norms and examine discriminative validity. Results: Factor analyses resulted in seven factors, each with six items (jumping to conclusions, belief inflexibility bias, attention for threat bias, external attribution bias, social cognition problems, subjective cognitive problems and safety behavior). All factors independently explained the variance (eigenvalues > 2) and total explained variance was 45%. Reliability was good (Cronbach's alpha = .90; split-half reliability = .92; test–retest reliability = .86). The DACOBS discriminates between schizophrenia spectrum patients and normal control subjects. Validity was affirmed for five of seven subscales. The scale ‘Subjective Cognitive problems’ was not associated with objective cognitive functioning and ‘Social cognition problems’ was not associated with the Hinting task, but with the scale measuring ideas of social reference. Conclusions: The DACOBS scale, with seven independent subscales, is reliable and valid for use in clinical practice and research.

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Grain yield variation and association of major traits in brown-seeded genotypes of tef [Eragrostis tef (Zucc.)Trotter]

Background Tef [Eragrostis tef (Zucc.) Trotter] is the major cereal crop of Ethiopia where it is annually cultivated on more than three million hectares of land by over six million small-scale farmers. It is broadly grouped into white and brown-seeded type depending on grain color, although some intermediate color grains also exist. Earlier breeding experiments focused on white-seeded tef, and a number of improved varieties were released to the farming community. Thirty-six brown-seeded tef genotypes were evaluated using a 6 × 6 simple lattice design at three locations in the central highlands of Ethiopia to assess the productivity, heritability, and association among major pheno-morphic traits. Results The mean square due to genotypes, locations, and genotype by locations were significant (P < 0.01) for all traits studied. Genotypic and phenotypic coefficients of variations ranged from 2.5 to 20.3 % and from 4.3 to 21.7 %, respectively. Grain yield showed significant (P < 0.01) genotypic correlation with shoot biomass and harvest index, while it had highly significant (P < 0.01) phenotypic correlation with all the traits evaluated. Besides, association of lodging index with biomass and grain yield was negative and significant at phenotypic level while it was not significant at genotypic level. Cluster analysis grouped the 36 test genotypes into seven distinct classes. Furthermore, the first three principal components with eigenvalues greater than unity extracted 78.3 % of the total variation. Conclusion The current study, generally, revealed the identification of genotypes with superior grain yield and other desirable traits for further evaluation and eventual release to the farming community.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Signature, positive Hopf plumbing and the Coxeter transformation

By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations are positive real or lie on the unit circle. By optimally bounding the signature of tree-like positive Hopf plumbings from below by the genus, we prove that at least two thirds of them lie on the unit circle. In contrast, we show that for divide links, the signature cannot be linearly bounded from below by the genus.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.