Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.

Symmetric inverse consistent nonlinear registration driven by mutual information.

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

Negative determinant of Hessian features

Local image feature extractors that select local maxima of the determinant of Hessian function have been shown to perform well and are widely used. This paper introduces the negative local minima of the determinant of Hessian function for local feature extraction. The properties and scale-space behaviour of these features are examined and found to be desirable for feature extraction. It is shown how this new feature type can be implemented along with the existing local maxima approach at negligible extra processing cost. Applications to affine covariant feature extraction and sub-pixel precise corner extraction are demonstrated. Experimental results indicate that the new corner detector is more robust to image blur and noise than existing methods. It is also accurate for a broader range of corner geometries. An affine covariant feature extractor is implemented by combining the minima of the determinant of Hessian with existing scale and shape adaptation methods. This extractor can be implemented along side the existing Hessian maxima extractor simply by finding both minima and maxima during the initial extraction stage. The minima features increase the number of correspondences by two to four fold. The additional minima features are very distinct from the maxima features in descriptor space and do not make the matching process more ambiguous.

Work motivation as a determinant of organizational and professional commitment in case of temporary organizations : theoretical perspectives

The purpose of this paper is to present a theoretical framework to investigate the relationship between work motivation, organizational commitment, and professional commitment in temporary organizations. Through a review of theory, we contend that work motivation has two major patterns- internal motivation (that includes intrinsic, need-based, and self-deterministic theories), and external motivation (that includes cognitive or process-based theories of motivation) through which it has been investigated. We also subsume the nature of employee commitment to be of three types- affective, continuance, and normative. This commitment may either be towards organization or profession. A literature review reveals that the characteristics of the temporary organization - specifically tenure, and task - regulate the relationship between work motivation, and organizational commitment, and professional commitment. Relevant propositions are presented.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Work motivation as a determinant of organisational and professional commitment in temporary organisations : theoretical lenses and propositions

The purpose of this paper is to present a theoretical framework to investigate the relationship between work motivation, organisational commitment and professional commitment in temporary organisations. Through a review of theory, we contend that work motivation has two major patterns — internal motivation (which includes intrinsic, need-based and self-deterministic theories), and external motivation (which includes cognitive or process-based theories of motivation) through which it has been investigated. We also hold the nature of employee commitment to be of three types — affective, continuance and normative. This commitment may be towards either the organisation or the profession. A literature review revealed that the characteristics of the temporary organisation — specifically tenure and task — regulate the relationship between work motivation, organisational commitment and professional commitment. Testable propositions are presented.

People living in hilly residential areas in metropolitan Perth have less diabetes : spurious association or important environmental determinant?

BACKGROUND: Variations in 'slope' (how steep or flat the ground is) may be good for health. As walking up hills is a physiologically vigorous physical activity and can contribute to weight control, greater neighbourhood slopes may provide a protective barrier to weight gain, and help prevent Type 2 diabetes onset. We explored whether living in 'hilly' neighbourhoods was associated with diabetes prevalence among the Australian adult population. METHODS: Participants ([greater than or equal to]25years; n=11,406) who completed the Western Australian Health and Wellbeing Surveillance System Survey (2003-2009) were asked whether or not they had medically-diagnosed diabetes. Geographic Information Systems (GIS) software was used to calculate a neighbourhood mean slope score, and other built environment measures at 1600m around each participant's home. Logistic regression models were used to predict the odds of self-reported diabetes after progressive adjustment for individual measures (i.e., age, sex), socioeconomic status (i.e., education, income), built environment, destinations, nutrition, and amount of walking. RESULTS: After full adjustment, the odds of self-reported diabetes was 0.72 (95% CI 0.55-0.95) and 0.52 (95% CI 0.39-0.69) for adults living in neighbourhoods with moderate and higher levels of slope, respectively, compared with adults living in neighbourhoods with the lowest levels of slope. The odds of having diabetes was 13% lower (odds ratio 0.87; 95% CI 0.80-0.94) for each increase of one percent in mean slope. CONCLUSIONS: Living in a hilly neighbourhood may be protective of diabetes onset or this finding is spurious. Nevertheless, the results are promising and have implications for future research and the practice of flattening land in new housing developments.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

The Wzy O-antigen polymerase of Yersinia pseudotuberculosis O:2a has a dependence on the Wzz chain-length determinant for efficient polymerization

Lipopolysaccharide is a major immunogenic structure for the pathogen Yersinia pseudotuberculosis, which contains the O-specific polysaccharide (OPS) that is presented on the cell surface. The OPS contains many repeats of the oligosaccharide O-unit and exhibits a preferred modal chain length that has been shown to be crucial for cell protection in Yersinia. It is well established that the Wzz protein determines the preferred chain length of the OPS, and in its absence, the polymerization of O units by the Wzy polymerase is uncontrolled. However, for Y. pseudotuberculosis, a wzz mutation has never been described. In this study, we examine the effect of Wzz loss in Y. pseudotuberculosis serotype O:2a and compare the lipopolysaccharide chain-length profile to that of Escherichia coli serotype O111. In the absence of Wzz, the lipopolysaccharides of the two species showed significant differences in Wzy polymerization. Yersinia pseudotuberculosis O:2a exhibited only OPS with very short chain lengths, which is atypical of wzz-mutant phenotypes that have been observed for other species. We hypothesise that the Wzy polymerase of Y. pseudotuberculosis O:2a has a unique default activity in the absence of the Wzz, revealing the requirement of Wzz to drive O-unit polymerization to greater lengths.

Best individual template selection from deformation tensor minimization

We study the influence of the choice of template in tensor-based morphometry. Using 3D brain MR images from 10 monozygotic twin pairs, we defined a tensor-based distance in the log-Euclidean framework [1] between each image pair in the study. Relative to this metric, twin pairs were found to be closer to each other on average than random pairings, consistent with evidence that brain structure is under strong genetic control. We also computed the intraclass correlation and associated permutation p-value at each voxel for the determinant of the Jacobian matrix of the transformation. The cumulative distribution function (cdf) of the p-values was found at each voxel for each of the templates and compared to the null distribution. Surprisingly, there was very little difference between CDFs of statistics computed from analyses using different templates. As the brain with least log-Euclidean deformation cost, the mean template defined here avoids the blurring caused by creating a synthetic image from a population, and when selected from a large population, avoids bias by being geometrically centered, in a metric that is sensitive enough to anatomical similarity that it can even detect genetic affinity among anatomies.

A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Mapping of assembled epitopic regions of human chorionic gonadotropin reveals proximity of CTP alpha to the determinant loop beta 93-100

Three overlapping assembled epitopes of beta hCG have been mapped using MAb probes and a single step solid phase radioimmunoassay. These epitopes have been shown to be at receptor binding region comprising of the loop region beta Cys93-Cys100. Importance of disulphide bonds in maintaining integrity of these epitopes is assessed. Two MAbs (INN 58 and INN 22) interact with the beta region as well as the alpha C-terminal peptide, while the other MAb INN 24 interacts with only the beta region. Cross-reactivity pattern with beta hCG and hLH as web as the reported crystal structure of hCG substantiates the epitope identification. The results demonstrate utility of MAbs as probes in investigations on three-dimensional structure of gonadatropins.