Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

The Web KnowARR Framework: Orchestrating Computational Intelligence with Graph Databases

This chapter presents fuzzy cognitive maps (FCM) as a vehicle for Web knowledge aggregation, representation, and reasoning. The corresponding Web KnowARR framework incorporates findings from fuzzy logic. To this end, a first emphasis is particularly on the Web KnowARR framework along with a stakeholder management use case to illustrate the framework’s usefulness as a second focal point. This management form is to help projects to acceptance and assertiveness where claims for company decisions are actively involved in the management process. Stakeholder maps visually (re-) present these claims. On one hand, they resort to non-public content and on the other they resort to content that is available to the public (mostly on the Web). The Semantic Web offers opportunities not only to present public content descriptively but also to show relationships. The proposed framework can serve as the basis for the public content of stakeholder maps.

ADDPLOT: Stata module to add twoway plot objects to an existing twoway graph

addplot adds twoway plot objects to an existing twoway graph. This is useful if you want to add additional objects such as titles or extra data points to a twoway graph after it has been created. Most of what addplot can do, can also be done by rerunning the original graph command including additional options or plot statements. addplot, however, might be useful if you have to modify a graph for which you cannot rerun the original command, for example, because you only have the graph file but not the data that were used to create the graph. Furthermore, addplot can do certain things that would be difficult to achieve in a single graph command (e.g. customizing individual subgraphs within a by-graph). addplot also provides a substitute for some of the functionality of the graph editor.

A note on adding objects to an existing twoway graph

In Stata, graphs are usually generated by one call to the graph command. Sometimes, however, it would be convenient to be able to add objects to a graph after the graph has been created. In this article, I provide a command called addplot that offers such functionality for twoway graphs, capitalizing on an undocumented feature of Stata's graphics system.

MASCG: Multi-Atlas Segmentation Constrained Graph method for accurate segmentation of hip CT images

This paper addresses the issue of fully automatic segmentation of a hip CT image with the goal to preserve the joint structure for clinical applications in hip disease diagnosis and treatment. For this purpose, we propose a Multi-Atlas Segmentation Constrained Graph (MASCG) method. The MASCG method uses multi-atlas based mesh fusion results to initialize a bone sheetness based multi-label graph cut for an accurate hip CT segmentation which has the inherent advantage of automatic separation of the pelvic region from the bilateral proximal femoral regions. We then introduce a graph cut constrained graph search algorithm to further improve the segmentation accuracy around the bilateral hip joint regions. Taking manual segmentation as the ground truth, we evaluated the present approach on 30 hip CT images (60 hips) with a 15-fold cross validation. When the present approach was compared to manual segmentation, an average surface distance error of 0.30 mm, 0.29 mm, and 0.30 mm was found for the pelvis, the left proximal femur, and the right proximal femur, respectively. A further look at the bilateral hip joint regions demonstrated an average surface distance error of 0.16 mm, 0.21 mm and 0.20 mm for the acetabulum, the left femoral head, and the right femoral head, respectively.

PSHARE: Stata module to compute and graph percentile shares

-pshare- computes and graphs percentile shares from individual level data. Percentile shares are often used in inequality research to study the distribution of income or wealth. They are defined as differences between Lorenz ordinates of the outcome variable. Technically, the observations are sorted in increasing order of the outcome variable and the specified percentiles are computed from the running sum of the outcomes. Percentile shares are then computed as differences between percentiles, divided by total outcome. pshare requires moremata to be installed on the system; see ssc describe moremata.

Building the View Graph of a Category by Exploiting Image Realism

We propose a weakly supervised method to arrange images of a given category based on the relative pose between the camera and the object in the scene. Relative poses are points on a sphere centered at the object in a given canonical pose, which we call object viewpoints. Our method builds a graph on this sphere by assigning images with similar viewpoint to the same node and by connecting nodes if they are related by a small rotation. The key idea is to exploit a large unlabeled dataset to validate the likelihood of dominant 3D planes of the object geometry. A number of 3D plane hypotheses are evaluated by applying small 3D rotations to each hypothesis and by measuring how well the deformed images match other images in the dataset. Correct hypotheses will result in deformed images that correspond to plausible views of the object, and thus will likely match well other images in the same category. The identified 3D planes are then used to compute affinities between images related by a change of viewpoint. We then use the affinities to build a view graph via a greedy method and the maximum spanning tree.

LOGITCPRPLOT: Stata module to graph component-plus-residual plot for logistic regression

logitcprplot can be used after logistic regression for graphing a component-plus-residual plot (a.k.a. partial residual plot) for a given predictor, including a lowess, local polynomial, restricted cubic spline, fractional polynomial, penalized spline, regression spline, running line, or adaptive variable span running line smooth

CPRPLOT2: Stata module to graph component-plus-residual plots for transformed regressors

cprplot2 is a variation of official Stata's cprplot and is used for graphing component-plus-residual plots (a.k.a. partial residual plots). Additional features (compared to cprplot): (1) cprplot2 can handle variables that enter the model repeatedly via different transformations (for example, polynomials). (2) cprplot2 can display component-plus-residual plots using the original units for transformed variables in the model. (3) A wrapper is provided to quickly display several component-plus-residual plots in a single image.