This paper develops a new approach to the analysis of longitudinal paired comparison data, where comparisons of the same objects by the same judges are made on more than one occasion. As an alternative to other recent approaches to such data, which are based on Kalman filter- ing, our approach treats the problem as one of multivariate multinomial data, allowing dependence terms between comparisons over time to be incorporated. The resulting model can be fitted as a Poisson log-linear model and has parallels with the quadratic binary exponential distribution of Cox. An example from the British Household Panel Survey illustrates the approach. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Convex cycles play a role e.g. in the context of product graphs. We introduce convex cycle bases and describe a polynomial-time algorithm that recognizes whether a given graph has a convex cycle basis and provides an explicit construction in the positive case. Relations between convex cycles bases and other types of cycles bases are discussed. In particular we show that if G has a unique minimal cycle bases, this basis is convex. Furthermore, we characterize a class of graphs with convex cycles bases that includes partial cubes and hence median graphs. (authors' abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Measuring the performance of Freight Villages (FVs) has important implications for logistics companies and other related companies as well as governments. In this paper we apply Data Envelopment Analysis (DEA) to measure the performance of European FVs in a purely data-driven way incorporating the nature of FVs as complex operations that use multiple inputs and produce several outputs. We employ several DEA models and perform a complete sensitivity analysis of the appropriateness of the chosen input and output variables, and an assessment of the robustness of the efficiency score. It turns out that about half of the 20 FVs analyzed are inefficient, with utilization of the intermodal area and warehouse capacity and level of goods handed the being the most important areas of improvement. While we find no significant differences in efficiency between FVs of different sizes and in different countries, it turns out that the FVs Eurocentre Toulouse, Interporto Quadrante Europa and GVZ Nürnberg constitute more than 90% of the benchmark share. / Series: Working Papers on Information Systems, Information Business and Operations

Diese Dissertation beschäftigt sich mit EDP-Konvergenz. Dabei handelt es sich um einen Konvergenzbegriff auf dem Gebiet der verallgemeinerten Gradientensysteme und metrischen Gradientensysteme, der geeignet ist für Gradientenflüsse, die von einem kleinen Parameter abhängen. EDP-Konvergenz liefert einen Algorithmus, der es erlaubt in der Energie und dem Dissipationspotenzial zum Grenzwert überzugehen. Es ist die fundamentale Frage evolutionärer Γ-Konvergenz, wie das Limes-Dissipationspotenzial berechnet werden kann. Das Ziel dieser Arbeit ist es aufzuzeigen, dass EDP-Konvergenz das mikro- und das makroskopische Dissipationspotenzial in einer sinnvollen und eindeutigen Art und Weise in Beziehung setzt. Anhand von drei Beispielen wird der Konvergenzbegriff untersucht: die Diffusionsgleichung auf einem dünnen, dreischichtigen Gebiet, die Poröse-Medien-Gleichung mit einer dünnen Membran und ein Modell mit oszillierender Energie. Es wird die Definition von relaxierter EDP-Konvergenz und EDP-Konvergenz mit Kippung motiviert. EDP-Konvergenz basiert auf dem Prinzip, dass es ein Gleichgewicht zwischen Energie und Dissipation gibt – das Energie-Dissipations-Prinzip (EDP). Mittels Γ-Konvergenz wird sowohl in der Energie, als auch dem totalen Dissipationsfunktional zum Grenzwert übergegangen. Durch die zusätzliche Entkopplung von Zustand und Triebkraft wird die Dissipationslandschaft erkundet und die kinetische Beziehung des Limessystems ermittelt. Das Modell mit oszillierender Energie zeigt die Bedeutung der kinetischen Beziehung – und damit der Kippung – für die Herleitung des Limes-Dissipationspotenzials auf. Die Modelle mit Wasserstein-Dissipation zeigen, dass das Limes-Dissipationspotenzial nicht der naive Grenzwert ist. Insbesondere können klassische Gradientensysteme mit quadratischer Dissipation zu verallgemeinerten Gradientensysteme konvergieren. / In the realm of generalized gradient systems and metric gradient systems we study a notion of convergence suited for gradient flows which depend on a small parameter. This notion is called EDP-convergence. In order to understand the convergence of gradient systems we need an algorithm to derive the limiting energy as well as the limiting dissipation potential. The fundamental question of evolutionary Γ-convergence is how to compute the limit dissipation potential. The aim of this thesis is to show that EDP-convergence connects the microscopic dissipation potential with the macroscopic, i.e. limiting, dissipation potential in a meaningful and unique way. As a proof of concept 3 different examples are presented: (i) the diffusion equation on a thin sandwich-like domain, (ii) the porous medium equation with a thin interface and (iii) a wiggly energy model. We show how the gradient flow concept that is used in this thesis can be used to obtain also gradient flows with respect to the Wasserstein metric. We motivate the definition of relaxed EDP-convergence and EDP- convergence with tilting. EDP-convergence is based upon the principle that there is an energy-dissipation-balance involving the total dissipation functional and the energy difference – the energy-dissipation-principle (EDP). The limit passage, in both the energy and the total dissipation functional, is performed in terms of Γ-convergence. By perturbing the flow as well as the driving force, the dissipation-landscape is explored and a kinetic relation for the limit system can be established. The wiggly energy model demonstrates the importance of the kinetic relation for the construction of the limiting dissipation potential and thus the introduction of tilts. The models with a Wasserstein dissipation show that the limiting dissipation potential is not the naive limit. In particular, classical gradient systems with a quadratic dissipation potential converge to a generalized gradient systems.

Ziel dieser Arbeit ist theoretische Eigenschaften verschiedener Bootstrap Methoden zu untersuchen. Als Ergebnis führen wir die Konvergenzraten des Bootstrap-Verfahrens ein, die sich auf die Differenz zwischen der tatsächlichen Verteilung einer Statistik und der Resampling-Näherung beziehen. In dieser Arbeit analysieren wir die Verteilung der l2-Norm der Summe unabhängiger Vektoren, des Summen Maximums in hoher Dimension, des Wasserstein-Abstands zwischen empirischen Messungen und Wassestein-Barycenters. Um die Bootstrap-Konvergenz zu beweisen, verwenden wir die Gaussche Approximations technik. Das bedeutet dass man in der betrachteten Statistik eine Summe unabhängiger Vektoren finden muss, so dass Bootstrap eine erneute Abtastung dieser Summe ergibt. Ferner kann diese Summe durch Gaussche Verteilung angenähert und mit der Neuabtastung Verteilung als Differenz zwischen Kovarianzmatrizen verglichen werden. Im Allgemeinen scheint es sehr schwierig zu sein, eine solche Summe unabhängiger Vektoren aufzudecken, da einige Statistiken (zum Beispiel MLE) keine explizite Gleichung haben und möglicherweise unendlich dimensional sind. Um mit dieser Schwierigkeit fertig zu werden, verwenden wir einige neuartige Ergebnisse aus der statistischen Lerntheorie. Darüber hinaus wenden wir Bootstrap bei Methoden zur Erkennung von Änderungspunkten an. Im parametrischen Fall analysieren wir den statischen Likelihood Ratio Test (LRT). Seine hohen Werte zeigen Änderungen der Parameter Verteilung in der Datensequenz an. Das Maximum von LRT hat eine unbekannte Verteilung und kann mit Bootstrap kalibriert werden. Wir zeigen die Konvergenzraten zur realen maximalen LRT-Verteilung. In nicht parametrischen Fällen verwenden wir anstelle von LRT den Wasserstein-Abstand zwischen empirischen Messungen. Wir testen die Genauigkeit von Methoden zur Erkennung von Änderungspunkten anhand von synthetischen Zeitreihen und Elektrokardiographiedaten. Letzteres zeigt einige Vorteile des nicht parametrischen Ansatzes gegenüber komplexen Modellen und LRT. / The objective of this thesis is to explore theoretical properties of various bootstrap methods. We introduce the convergence rates of the bootstrap procedure which corresponds to the difference between real distribution of some statistic and its resampling approximation. In this work we analyze the distribution of Euclidean norm of independent vectors sum, maximum of sum in high dimension, Wasserstein distance between empirical measures, Wassestein barycenters. In order to prove bootstrap convergence we involve Gaussian approximation technique which means that one has to find a sum of independent vectors in the considered statistic such that bootstrap yields a resampling of this sum. Further this sum may be approximated by Gaussian distribution and compared with the resampling distribution as a difference between variance matrices. In general it appears to be very difficult to reveal such a sum of independent vectors because some statistics (for example, MLE) don't have an explicit equation and may be infinite-dimensional. In order to handle this difficulty we involve some novel results from statistical learning theory, which provide a finite sample quadratic approximation of the Likelihood and suitable MLE representation. In the last chapter we consider the MLE of Wasserstein barycenters model. The regularised barycenters model has bounded derivatives and satisfies the necessary conditions of quadratic approximation. Furthermore, we apply bootstrap in change point detection methods. In the parametric case we analyse the Likelihood Ratio Test (LRT) statistic. Its high values indicate changes of parametric distribution in the data sequence. The maximum of LRT has a complex distribution but its quantiles may be calibrated by means of bootstrap. We show the convergence rates of the bootstrap quantiles to the real quantiles of LRT distribution. In non-parametric case instead of LRT we use Wasserstein distance between empirical measures. We test the accuracy of change point detection methods on synthetic time series and electrocardiography (ECG) data. Experiments with ECG illustrate advantages of the non-parametric approach versus complex parametric models and LRT.

Wir betrachten die Detektion und Lokalisation von plötzlichen Änderungen in der Kovarianzstruktur hochdimensionaler zufälliger Daten. Diese Arbeit schlägt zwei neuartige Ansätze für dieses Problem vor. Die Vorgehensweise beinhaltet im Wesentlichen Verfahren zum Test von Hypothesen, welche ihrerseits die Wahl geeigneter kritischer Werte erfordern. Dafür werden Kalibrierungsschemata vorgeschlagen, die auf unterschiedlichen Nichtstandard-Bootstrap-Verfahren beruhen. Der eine der beiden Ansätze verwendet Techniken zum Schätzen inverser Kovarianzmatrizen und ist durch Anwendungen in der neurowissenschaftlichen Bildgebung motiviert. Eine Beschränkung dieses Ansatzes besteht in der für die Schätzung der „Precision matrix“ wesentlichen Voraussetzung ihrer schwachen Besetztheit. Diese Bedingung ist im zweiten Ansatz nicht erforderlich. Die Beschreibung beider Ansätze wird gefolgt durch ihre theoretische Untersuchung, welche unter schwachen Voraussetzungen die vorgeschlagenen Kalibrierungsschemata rechtfertigt und die Detektion von Änderungen der Kovarianzstruktur gewährleistet. Die theoretischen Resultate für den ersten Ansatz basieren auf den Eigenschaften der Verfahren zum Schätzen der Präzisionsmatrix. Wir können daher die adaptiven Schätzverfahren für die Präzisionsmatrix streng rechtfertigen. Alle Resultate beziehen sich auf eine echt hochdimensionale Situation (Dimensionalität p >> n) mit endlichem Stichprobenumfang. Die theoretischen Ergebnisse werden durch Simulationsstudien untermauert, die durch reale Daten aus den Neurowissenschaften oder dem Finanzwesen inspiriert sind. / We consider the detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The study proposes two novel approaches for this problem. The approaches are essentially hypothesis testing procedures which requires a proper choice of a critical level. In that regard calibration schemes, which are in turn different non-standard bootstrap procedures, are proposed. One of the approaches relies on techniques of inverse covariance matrix estimation, which is motivated by applications in neuroimaging. A limitation of the approach is a sparsity assumption crucial for precision matrix estimation which the second approach does not rely on. The description of the approaches are followed by a formal theoretical study justifying the proposed calibration schemes under mild assumptions and providing the guaranties for the break detection. Theoretical results for the first approach rely on the guaranties for inference of precision matrix procedures. Therefore, we rigorously justify adaptive inference procedures for precision matrices. All the results are obtained in a truly high-dimensional (dimensionality p >> n) finite-sample setting. The theoretical results are supported by simulation studies, most of which are inspired by either real-world neuroimaging or financial data.

Corticotropin releasing factor (CRF) has been implicated to act as a neurotransmitter or modulator in central nervous activation during stress. In this study, we examined the regulatory effect of CRF on the expression and function of the norepinephrine transporter (NET) in vitro. SK-N-BE (2) M17 cells were exposed to different concentrations of CRF for different periods. Results showed that exposure of cells to CRF significantly increased mRNA and protein levels of NET in a concentration- and time-dependent manner. The CRF-induced increase in NET expression was mimicked by agonists of either CRF receptor 1 or 2. Furthermore, similar CRF treatments induced a parallel increase in the uptake of [3H] norepinephrine. Both increased expression and function of NET caused by CRF were abolished by simultaneous administration of CRF receptor antagonists, indicating a mediation by CRF receptors. However, there was no additive effect for the combination of both receptor antagonists. Chromatin immunoprecipitation assays confirm an increased acetylation of histone H3 on the NET promoter following treatment with CRF. Taken together, this study demonstrates that CRF up-regulates the expression and function of NET in vitro. This regulation is mediated through CRF receptors and an epigenetic mechanism related to histone acetylation may be involved. This CRF-induced regulation on NET expression and function may play a role in development of stress-related depression and anxiety. This study demonstrated that corticotropin release factor (CRF) up-regulated the expression and function of norepinephrine transporter (NET) in a concentration- and time-dependent manner, through activation of CRF receptors and possible histone acetylation in NET promoter. The results indicate that their interaction may play an important role in stress-related physiological and pathological status. This study demonstrated that corticotropin release factor (CRF) up-regulated the expression and function of norepinephrine transporter (NET) in a concentration- and time-dependent manner, through activation of CRF receptors and possible histone acetylation in NET promoter. The results indicate that their interaction may play an important role in stress-related physiological and pathological status.

Glucocorticoids affect cellular and molecular events in brains by modulating the expression of many genes during stress. In the present study, we examined the regulatory effect of corticosterone on the expression and function of the norepinephrine transporter (NET) in vitro. The results show that exposure of SK-N-BE(2)C cells to corticosterone for 14 days significantly increased mRNA (up to 43%) and protein (up to 71%) levels of NET in the concentration- dependent manner. Longer exposure (21 days) resulted in greater increases in the levels of mRNAs (up to about 160%) and proteins (up to about 250%) of the NET. The up-regulatory effect of corticosterone on NET expression lasted a persistent period after cessation of exposure. Associated with the corticosterone-induced enhancement in NET expression, there was a parallel increase in the uptake of [3H]norepinephrine by SK-N-BE(2)C cells. Increased NET expression and function were abolished after exposure of cells to corticosterone in combination with mifepristone or spironolactone, two specific antagonists of corticosteroid receptors. This is consistent with the hypothesis that corticosterone-induced NET up-regulation is mediated by corticosteroid receptors. Nevertheless, there was no synergistic effect for a combination of both corticosteroid receptor antagonists. A similar up-regulation of NET protein levels was also observed after exposing PC12 cells to corticosterone. The present findings demonstrate that corticosterone up-regulates the expression and function of NET in vitro, indicating the action of corticosterone on the noradrenergic phenotype may play an important role in the correlation between stress and the development of depression.

Phox2a and Phox2b are two homeodomain proteins that control the differentiation of noradrenergic neurons during embryogenesis. In the present study, we examined the possible effect of Phox2a/2b on the in vitro expression of the norepinephrine transporter (NET) and dopamine β-hydroxylase (DBH), two important markers of the noradrenergic system. SK-N-BE(2)C cells were transfected with cDNAs or short hairpin RNAs specific to the human Phox2a and Phox2b genes. Transfection of 0.1 to 5 μg of cDNAs of Phox2a or Phox2b significantly increased mRNA and protein levels of NET and DBH in a concentration-dependent manner. As a consequence of the enhanced expression of NET after transfection, there was a parallel increase in the uptake of [ 3H]norepinephrine. Co-transfection of Phox2a and Phox2b did not further increase the expression of noradrenergic markers when compared with transfection of either Phox2a or Phox2b alone. Transfection of shRNAs specific to Phox2a or Phox2b genes significantly reduced mRNA and protein levels of NET and DBH after shutdown of endogenous Phox2, which was accompanied by a decreased [3H]norepinephrine uptake. Furthermore, there was an additive effect after cotransfection with both shRNAs specific to Phox2a or Phox2b genes on NET mRNA levels. Finally, the reduced DBH expression caused by the shRNA specific to Phox2a could be reversed by transfection with Phox2b cDNA and vice versa. The present findings verify the determinant role of Phox2a and Phox2b on the expression and function of NET and DBH in vitro. Further clarifying the regulatory role of these two transcription factors on key proteins of the noradrenergic system may open a new avenue for therapeutics of aging-caused dysfunction of the noradrenergic system.

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