NodeTrix: a hybrid visualization of social networks

The need to visualize large social networks is growing as hardware capabilities make analyzing large networks feasible and many new data sets become available. Unfortunately, the visualizations in existing systems do not satisfactorily resolve the basic dilemma of being readable both for the global structure of the network and also for detailed analysis of local communities. To address this problem, we present NodeTrix, a hybrid representation for networks that combines the advantages of two traditional representations: node-link diagrams are used to show the global structure of a network, while arbitrary portions of the network can be shown as adjacency matrices to better support the analysis of communities. A key contribution is a set of interaction techniques. These allow analysts to create a NodeTrix visualization by dragging selections to and from node-link and matrix forms, and to flexibly manipulate the NodeTrix representation to explore the dataset and create meaningful summary visualizations of their findings. Finally, we present a case study applying NodeTrix to the analysis of the InfoVis 2004 coauthorship dataset to illustrate the capabilities of NodeTrix as both an exploration tool and an effective means of communicating results.     

Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems

Summary This paper presents a unique approach, named mathematical regularization, to remove the nearly-singular and singular integrals occurring in the boundary integral formulations for the solution of the boundary value problems with a pathologica integration boundary due to the very near or coinciding parts of the total boundary. Nonsingular boundary integral equations are derived for thin-walled structure problems. In the case of crack-like problems, we present two kinds of the nonsingular integral representations of the secondary fields and the derivative boundary integral equations.     

Explicit,optimal stability functionals and their application to cyclic discretization methods

The present paper contains a stability concept for discretization methods of a certain, very general classM, which is optimal (in the sense of yielding the best general, two-sided error bounds) without being more restrictive than any of the classical stability definitions. The optimal stability functional Ψ_h related to it depends on the linear part of the discretization operator, and has the important property that Ψ_h [δ] may be of orderq+1, i.e. Ψ_h [δ] = O(h ^q+1), even if the local error δ only has orderq, δ = O(h ^q). This result may be used for the construction of methods with maximum order. Its application to linear cyclic methods, for example, furnishes a new approach to the theory of linearM-cyclick-step methods of maximum order.     

Konvergenz von quadratischen Interpolations- und Flächenabgleichssplines

The purpose of this paper is to show that for continuous functions the related quadratic splines converge without any assumption on the spline grid. The points of the interpolatory grid can be chosen between the corresponding points of the spline grid with a division ratio from \(\frac{{\sqrt 2 }}{2}\) to \(1 - \frac{{\sqrt 2 }}{2}\) . In the case of continuously differentiable functions the division ratio can even be taken between 0 and 1; in addition, the order of convergence is increased. For twice differentiable functions the full order of convergence is obtained. Analogous results about the convergence of histo splines are proved.     

Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter

Let the space curveL be defined implicitly by the (n, n+1) nonlinear systemH(u)=0. A new direct Newton-like method for computing turning points ofL is described that requires per step only the evaluation of one Jacobian and 5 function values ofH. Moreover, a linear system of dimensionn+1 with 4 different right hand sides has to be solved per step. Under suitable conditions the method is shown to converge locally withQ-order two if a certain discretization stepsize is appropriately chosen. Two numerical examples confirm the theoretical results.     

On a lower bound theorem for the buckling load of elastic beams subjected to nonconservative,compressive follower loads

Summary For beams loaded withuniformly distributed follower forces, there exists a lower bound theorem, which allows to evaluate the actual buckling load approximately by means of the buckling load of the same beam loaded correspondingly with conservative unidirectional forces of the same magnitude. In this paper it is shown that the theorem remains valid for monotonically decreasing or at least not increasing follower forces. Moreover, a modified lower bound theorem can be formulated for follower loads which monotonically increase over a part or even over the whole length of the beam. In that case, a lower bound curve has to be constructed using the eigenvalue curve of the conservatively loaded beam. The intersection of the lower bound curve with the vertical axis yields a lower bound for the buckling load of the nonconservatively loaded beam.

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Zu einem Satz über die untere Schranke der Knicklast elastischer, durch Folgekräfte belasteter Stäbe

Zusammenfassung Ein für Stäbe untergleichförmig verteilten Folgekräften gültiger Satz für die untere Schranke der Knicklast gestattet die näherungsweise Ermittlung der tatsächlichen Knicklast aus der desselben Stabes unter richtungstreuer Belastung derselben Größe. In dieser Arbeit wird gezeigt, daß dieser Satz auch für monoton abnehmende oder zumindest nicht zunehmende Folgekräfte gilt. Weiters kann ein modifizierter Satz für über einen Teil des Stabes oder die ganze Stablänge monoton zunehemende Folgekräfte formuliert werden. In diesem Fall muß unter Verwendung der Eigenwertkurve des konservativ belasteten Stabes eine untere Grenzkurve ermittelt werden. Der Schnittpunkt dieser Kurve mit der vertikalen Achse ergibt eine untere Schranke der Knicklast des nichtkonservativ belasteten Stabes.

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With 8 Fugures     

Estimating errors of numerical approximation for periodic analytic functions

We give a simple method based on Cauchy's integral formula for estimating the errors of numerical approximation for periodic analytic functions. We then obtain error estimates for the quadrature formulas of Chawla and Ramakrishnan [1] for the numerical evaluation of the Cauchy principal value integral $$I\left( {f;a} \right) = \int\limits_0^{2\pi } {f(x)\cot \left( {\left( {x - a} \right)/2} \right)dx,} $$ and for the quadrature formula of Garrick [2] for the evaluation ofI (f;o), Based on these error estimates, we are led to conclude that for the evaluation ofI (f;o), Garrick's formula has a better error estimate than the formula of Chawla and Ramakrishnan with the same number of function evaluations. Finally, we extend Garrick's formula for the evaluation ofI (f;a) for arbitrarya∈[0,2π); the extended formula has, for alla, the same error estimate as Garrick's formula. While, for a=x_j, the extended formula is identical with the quadrature formula of Wittich [3], fora≠x _j, the extended formula is much better in that it uses only half the number of function evaluations of Wittich's formula for the same accuracy.     

Approximation der optimalen Vorhersage der Ausgabe stochastischer Quellen

This paper discusses the prediction of the output of a stochastic sourceQ having positive transition function. If the sourceQ has two output alphabets,X andY, then there exists such a stochastic automaton \(\mathfrak{A}(V_{opt} )\) with input alphabetX, output alphabetY, and a countable set of states, that realizes the optimal predictionV _opt fromX toY. Here it will be shown thatV _opt can be approximated with any precision by a predictionV which is realized by a stochastic automaton with finite set of states.     

Situative Managementunterstützungssysteme

Digital natives increasingly populate organizations?? management. These new-generation managers more naturally accept management support systems (MSS), but also have higher expectations about how they should accommodate their individual user preferences. As a result, managers question MSS that have been developed without configuration mechanisms to accommodate their working style, relevant MSS use cases, and different MSS access modes. The objective of this article is to reveal managers?? different MSS use situations and propose levers for tailoring (conceptual) MSS design to them. Use situations generalize classes of similar user-group preferences. We first apply findings from a literature review to cluster managers?? user-group preferences into 36 MSS use situations. Second, we propose that the selection of end-user devices can serve as a main lever for MSS configuration. Third, we complete the configuration with a MSS user-interface design. Finally, we demonstrate utility of our configuration model by presenting and evaluating a prototype.     

Lieferantenportfolio-Management für IT-Services unter Berücksichtigung von Diversifikationseffekten

By means of service-oriented architectures the IT support of processes can be designed as a portfolio of individual IT services provided by different suppliers. The processes are designed based on selection decisions between IT services that potentially have to be included. Many companies formulate a multitude of requirements for investments in IT services at ever shorter intervals. However, the scope of the desired investments usually exceeds the available budget. Thus, companies face the challenge of allocating the limited budget to investments in the most promising combination of IT services. This is hardly possible without methodical support. In addition, the allocation is often done intuitively and subject to the decision-makers?? affinity with IT. Therefore, this paper develops a quantitative, multi-period procedure model for the purpose of maximizing the enterprise value in accordance with value based management, which considers the dependencies of the periodical selection decisions. In the following, a decision logic for the heuristic solution to the selection problem is presented and its application is demonstrated by means of an illustrative case example.