11 Interfakultäre Einrichtungen

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    Stochastic model for energy propagation in disordered granular chains
    (2021) Taghizadeh, Kianoosh; Shrivastava, Rohit; Luding, Stefan
    Energy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc.
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    On the accurate estimation of information-theoretic quantities from multi-dimensional sample data
    (2024) Álvarez Chaves, Manuel; Gupta, Hoshin V.; Ehret, Uwe; Guthke, Anneli
    Using information-theoretic quantities in practical applications with continuous data is often hindered by the fact that probability density functions need to be estimated in higher dimensions, which can become unreliable or even computationally unfeasible. To make these useful quantities more accessible, alternative approaches such as binned frequencies using histograms and k -nearest neighbors ( k -NN) have been proposed. However, a systematic comparison of the applicability of these methods has been lacking. We wish to fill this gap by comparing kernel-density-based estimation (KDE) with these two alternatives in carefully designed synthetic test cases. Specifically, we wish to estimate the information-theoretic quantities: entropy, Kullback–Leibler divergence, and mutual information, from sample data. As a reference, the results are compared to closed-form solutions or numerical integrals. We generate samples from distributions of various shapes in dimensions ranging from one to ten. We evaluate the estimators’ performance as a function of sample size, distribution characteristics, and chosen hyperparameters. We further compare the required computation time and specific implementation challenges. Notably, k -NN estimation tends to outperform other methods, considering algorithmic implementation, computational efficiency, and estimation accuracy, especially with sufficient data. This study provides valuable insights into the strengths and limitations of the different estimation methods for information-theoretic quantities. It also highlights the significance of considering the characteristics of the data, as well as the targeted information-theoretic quantity when selecting an appropriate estimation technique. These findings will assist scientists and practitioners in choosing the most suitable method, considering their specific application and available data. We have collected the compared estimation methods in a ready-to-use open-source Python 3 toolbox and, thereby, hope to promote the use of information-theoretic quantities by researchers and practitioners to evaluate the information in data and models in various disciplines.
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    An empirical study of Linespots : a novel past‐fault algorithm
    (2021) Scholz, Maximilian; Torkar, Richard
    This paper proposes the novel past‐faults fault prediction algorithm Linespots, based on the Bugspots algorithm. We analyse the predictive performance and runtime of Linespots compared with Bugspots with an empirical study using the most significant self‐built dataset as of now, including high‐quality samples for validation. As a novelty in fault prediction, we use Bayesian data analysis and Directed Acyclic Graphs to model the effects. We found consistent improvements in the predictive performance of Linespots over Bugspots for all seven evaluation metrics. We conclude that Linespots should be used over Bugspots in all cases where no real‐time performance is necessary.
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    Identification of linear time-invariant systems with dynamic mode decomposition
    (2022) Heiland, Jan; Unger, Benjamin
    Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
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    Multivariate motion patterns and applications to rainfall radar data
    (2023) Fischer, Svenja; Oesting, Marco; Schnurr, Alexander
    The classification of movement in space is one of the key tasks in environmental science. Various geospatial data such as rainfall or other weather data, data on animal movement or landslide data require a quantitative analysis of the probable movement in space to obtain information on potential risks, ecological developments or changes in future. Usually, machine-learning tools are applied for this task, as these approaches are able to classify large amounts of data. Yet, machine-learning approaches also have some drawbacks, e.g. the often required large training sets and the fact that the algorithms are often hard to interpret. We propose a classification approach for spatial data based on ordinal patterns. Ordinal patterns have the advantage that they are easily applicable, even to small data sets, are robust in the presence of certain changes in the time series and deliver interpretative results. They therefore do not only offer an alternative to machine-learning in the case of small data sets but might also be used in pre-processing for a meaningful feature selection. In this work, we introduce the basic concept of multivariate ordinal patterns and the corresponding limit theorem. A simulation study based on bootstrap demonstrates the validity of the results. The approach is then applied to two real-life data sets, namely rainfall radar data and the movement of a leopard. Both applications emphasize the meaningfulness of the approach. Clearly, certain patterns related to the atmosphere and environment occur significantly often, indicating a strong dependence of the movement on the environment.
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    Association between vitamin D status and eryptosis : results from the German National Cohort study
    (2023) Ewendt, Franz; Schmitt, Marvin; Kluttig, Alexander; Kühn, Julia; Hirche, Frank; Kraus, Frank B.; Ludwig-Kraus, Beatrice; Mikolajczyk, Rafael; Wätjen, Wim; Bürkner, Paul-Christian; Föller, Michael; Stangl, Gabriele I.
    Vitamin D, besides its classical effect on mineral homeostasis and bone remodeling, can also modulate apoptosis. A special form of apoptosis termed eryptosis appears in erythrocytes. Eryptosis is characterized by cell shrinkage, membrane blebbing, and cell membrane phospholipid disorganization and associated with diseases such as sepsis, malaria or iron deficiency, and impaired microcirculation. To our knowledge, this is the first study that linked vitamin D with eryptosis in humans. This exploratory cross-sectional trial investigated the association between the vitamin D status assessed by the concentration of plasma 25-hydroxyvitamin D (25(OH)D) and eryptosis. Plasma 25(OH)D was analyzed by LC-MS/MS, and eryptosis was estimated from annexin V-FITC-binding erythrocytes by FACS analysis in 2074 blood samples from participants of the German National Cohort Study. We observed a weak but clear correlation between low vitamin D status and increased eryptosis ( r  =  − 0.15; 95% CI [− 0.19, − 0.10]). There were no differences in plasma concentrations of 25(OH)D and eryptosis between male and female subjects. This finding raises questions of the importance of vitamin D status for eryptosis in terms of increased risk for anemia or cardiovascular events.
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    The effectiveness of cognitive behavioural therapy for social anxiety disorder in routine clinical practice
    (2022) Morina, Nexhmedin; Seidemann, Julienne; Andor, Tanja; Sondern, Lisa; Bürkner, Paul‐Christian; Drenckhan, Isabelle; Buhlmann, Ulrike
    Numerous randomized controlled trials have shown cognitive behaviour therapy (CBT) to be effective in treating social anxiety disorder (SAD). Yet, less is known about the effectiveness of CBT for SAD conducted by psychotherapists in training in routine clinical practice. In this study, 231 patients with SAD were treated with CBT under routine conditions and were examined at pre‐ and post‐treatment as well as at 6 and 12 months follow‐up. We applied self‐reports to assess symptoms of SAD (defined as primary outcome), depression and psychological distress (defined as secondary outcome). We conducted both completer and intent‐to‐treat analyses and also assessed the reliability of change with the reliable change index. Results revealed significant reductions in symptoms of SAD between pre‐ and post‐assessments, with effect sizes ranging from d = 0.9 to 1.2. Depending on the SAD specific questionnaire applied, 47.8% to 73.5% of the sample showed a reliable positive change, whereas 1.9% to 3.8% showed a reliable negative change. Depressive symptoms and psychological distress also decreased significantly from pre‐ to post‐assessment, with large effect sizes. Significant treatment gains regarding both primary and secondary outcomes were further observed at 6 and 12 months follow‐up. The current findings based on a large sample of patients suggest that psychotherapists in CBT training working under routine conditions can effectively treat symptoms of SAD, depression and psychological distress.
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    On the information obtainable from comparative judgments
    (2022) Bürkner, Paul-Christian
    Personality tests employing comparative judgments have been proposed as an alternative to Likert-type rating scales. One of the main advantages of a comparative format is that it can reduce faking of responses in high-stakes situations. However, previous research has shown that it is highly difficult to obtain trait score estimates that are both faking resistant and sufficiently accurate for individual-level diagnostic decisions. With the goal of contributing to a solution, I study the information obtainable from comparative judgments analyzed by means of Thurstonian IRT models. First, I extend the mathematical theory of ordinal comparative judgments and corresponding models. Second, I provide optimal test designs for Thurstonian IRT models that maximize the accuracy of people’s trait score estimates from both frequentist and Bayesian statistical perspectives. Third, I derive analytic upper bounds for the accuracy of these trait estimates achievable through ordinal Thurstonian IRT models. Fourth, I perform numerical experiments that complement results obtained in earlier simulation studies. The combined analytical and numerical results suggest that it is indeed possible to design personality tests using comparative judgments that yield trait scores estimates sufficiently accurate for individual-level diagnostic decisions, while reducing faking in high-stakes situations. Recommendations for the practical application of comparative judgments for the measurement of personality, specifically in high-stakes situations, are given.
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    The mediating effects of work characteristics on the relationship between transformational leadership and employee well-being : a meta-analytic investigation
    (2022) Teetzen, Friederike; Bürkner, Paul-Christian; Gregersen, Sabine; Vincent-Höper, Sylvie
    Evidence points to an indirect relationship between transformational leadership (TFL) and employee well-being, and numerous work characteristics have been identified as mediators. However, the relative mediating effect of different types of job resources and job demands on the TFL–well-being relationship remains unclear, rendering it impossible to determine which ones are the most influential. This study aims to provide a comprehensive analysis of the relative mediation potential of different work characteristics in the TFL–well-being relationship in multiple three-level meta-analytical structural equation models of 243 samples. Based on the JD–R Model, this study extends this theoretical framework by suggesting TFL as a predisposing variable that influences both job resources and job demands, leading to changes in indicators of both positive and negative employee well-being. The results show that, while all the examined job resources and demands mediated the TFL–well-being relationship, organizational resources were identified as the strongest mediators. Furthermore, job demands had a strong mediating effect on the relationship between TFL and negative well-being, while job resources more strongly mediated TFL and positive well-being. We present a differentiated picture of how transformational leaders can influence their employees’ well-being at the workplace, providing valuable knowledge for future research and practice.