Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Visualization and validation of (Q)SAR models

Analyzing and modeling relationships between the structure of chemical compounds, their physico-chemical properties, and biological or toxic effects in chemical datasets is a challenging task for scientific researchers in the field of cheminformatics. Therefore, (Q)SAR model validation is essential to ensure future model predictivity on unseen compounds. Proper validation is also one of the requirements of regulatory authorities in order to approve its use in real-world scenarios as an alternative testing method. However, at the same time, the question of how to validate a (Q)SAR model is still under discussion. In this work, we empirically compare a k-fold cross-validation with external test set validation. The introduced workflow allows to apply the built and validated models to large amounts of unseen data, and to compare the performance of the different validation approaches. Our experimental results indicate that cross-validation produces (Q)SAR models with higher predictivity than external test set validation and reduces the variance of the results. Statistical validation is important to evaluate the performance of (Q)SAR models, but does not support the user in better understanding the properties of the model or the underlying correlations. We present the 3D molecular viewer CheS-Mapper (Chemical Space Mapper) that arranges compounds in 3D space, such that their spatial proximity reflects their similarity. The user can indirectly determine similarity, by selecting which features to employ in the process. The tool can use and calculate different kinds of features, like structural fragments as well as quantitative chemical descriptors. Comprehensive functionalities including clustering, alignment of compounds according to their 3D structure, and feature highlighting aid the chemist to better understand patterns and regularities and relate the observations to established scientific knowledge. Even though visualization tools for analyzing (Q)SAR information in small molecule datasets exist, integrated visualization methods that allows for the investigation of model validation results are still lacking. We propose visual validation, as an approach for the graphical inspection of (Q)SAR model validation results. New functionalities in CheS-Mapper 2.0 facilitate the analysis of (Q)SAR information and allow the visual validation of (Q)SAR models. The tool enables the comparison of model predictions to the actual activity in feature space. Our approach reveals if the endpoint is modeled too specific or too generic and highlights common properties of misclassified compounds. Moreover, the researcher can use CheS-Mapper to inspect how the (Q)SAR model predicts activity cliffs. The CheS-Mapper software is freely available at http://ches-mapper.org.

Predictors of sickness absence in patients with a new episode of low back pain in primary care

This study examines predictors of sickness absence in patients presenting to a health practitioner with acute/ subacute low back pain (LBP). Aims of this study were to identify baseline-variables that detect patients with a new LBP episode at risk of sickness absence and to identify prognostic models for sickness absence at different time points after initial presentation. Prospective cohort study investigating 310 patients presenting to a health practitioner with a new episode of LBP at baseline, three-, six-, twelve-week and six-month follow-up, addressing work-related, psychological and biomedical factors. Multivariate logistic regression analysis was performed to identify baseline-predictors of sickness absence at different time points. Prognostic models comprised 'job control', 'depression' and 'functional limitation' as predictive baseline-factors of sickness absence at three and six-week follow-up with 'job control' being the best single predictor (OR 0.47; 95%CI 0.26-0.87). The six-week model explained 47% of variance of sickness absence at six-week follow-up (p<0.001). The prediction of sickness absence beyond six-weeks is limited, and health practitioners should re-assess patients at six weeks, especially if they have previously been identified as at risk of sickness absence. This would allow timely intervention with measures designed to reduce the likelihood of prolonged sickness absence.

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.

Feelings of revenge, retaliation motive, and posttraumatic stress reactions in crime victims

Individuals with posttraumatic stress disorder (PTSD) are often said to experience strong feelings of revenge. However, there is a need for confirmatory empirical studies. Therefore, in a study of 174 victims of violent crimes, the relation between feelings of revenge and posttraumatic stress reactions was investigated. Feelings of revenge were correlated with intrusion and hyperarousal but not with avoidance. Feelings of revenge explained incremental variance of intrusion and hyperarousalwhen the variance explained by victimological variables was controlled. The retaliation motive implied in feelings of revenge did not account for the relation between feelings of revenge and posttraumatic stress reactions. However, the relation was moderated by the time since victimization. Therefore, feelings of revenge must presumably be regarded as a maladaptive coping reaction to experienced injustice, but not in the first period after victimization.

Concordance Probability and Discriminatory Power in Proportional Hazards Regression

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytic expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer.

Model Evaluation Based on the Distribution of Estimated Absolute Prediction Error

The construction of a reliable, practically useful prediction rule for future response is heavily dependent on the "adequacy" of the fitted regression model. In this article, we consider the absolute prediction error, the expected value of the absolute difference between the future and predicted responses, as the model evaluation criterion. This prediction error is easier to interpret than the average squared error and is equivalent to the mis-classification error for the binary outcome. We show that the distributions of the apparent error and its cross-validation counterparts are approximately normal even under a misspecified fitted model. When the prediction rule is "unsmooth", the variance of the above normal distribution can be estimated well via a perturbation-resampling method. We also show how to approximate the distribution of the difference of the estimated prediction errors from two competing models. With two real examples, we demonstrate that the resulting interval estimates for prediction errors provide much more information about model adequacy than the point estimates alone.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

The KIDSCREEN-27 quality of life measure for children and adolescents: psychometric results from a cross-cultural survey in 13 European countries

OBJECTIVE: To assess the construct and criterion validity of the KIDSCREEN-27 health-related quality of life (HRQoL) questionnaire, a shorter version of the KIDSCREEN-52. METHODS: The five-dimensional KIDSCREEN-27 was tested in a sample of 22,827. For criterion validity the correlation with and the percentage explained variance of the scores of the KIDSCREEN-52 instrument were examined. Construct validity was assessed by testing a priori expected associations with other generic HRQoL measures (YQOL-S, PedsQL, CHIP), indicators of physical and mental health, and socioeconomic status. Age and gender differences were investigated. RESULTS: Correlation with corresponding scales of the KIDSCREEN-52 ranged from r = 0.63 to r = 0.96, and r2 ranged from 0.39 to 0.92. Correlations between other HRQoL questionnaires and KIDSCREEN-27 dimensions were moderate to high for those assessing similar constructs (r = 0.36 to 0.63). Statistically significant and sizeable differences between physically and mentally healthy and ill children were found in all KIDSCREEN-27 dimensions together with strong associations with psychosomatic complaints (r = -0.52). Most of the KIDSCREEN-27 dimensions showed a gradient according to socio-economic status, age and gender. CONCLUSIONS: The KIDSCREEN-27 seems to be a valid measure of HRQoL in children and adolescents. Further research is needed to assess longitudinal validity and sensitivity to change.

Endoscopic scoring of the tracheal septum in horses and its clinical relevance for the evaluation of lower airway health in horses

REASONS FOR PERFORMING STUDY: Although endoscopic scoring of the tracheal septum thickness is used as a diagnostic tool for evaluation of lower airway disease, its clinical relevance and reliability have never been critically assessed in the horse. OBJECTIVES: To investigate if septum thickness scores (STS) are reliable and serve as a clinically useful indicator of lower airway disease status and/or inflammation. METHODS: The variance of STS attributable to the horse, observer and changes over time was determined. The distribution of STS in a population of clinically normal horses and correlations of STS with age, gender, as well as mucus accumulation and cell differentials of tracheobronchial secretions and bronchoalveolar lavage fluid were investigated. Effects of altered pulmonary ventilation, induced by different drugs, on STS were assessed. Finally, STS of horses affected with recurrent airway obstruction (RAO) were compared to those of clinically normal horses. RESULTS: Recorded STS showed excellent intra- and satisfactory interobserver agreement Established clinical, endoscopic and cytological measures of lower airway inflammation, i.e. mucus accumulation scores and airway neutrophilia, did not correlate with STS. In horses age > or = 10 years, septum scores were significantly higher (P = 0.022) than in younger horses. Septum thickness scores did not differ significantly between clinically normal and RAO-affected horses both in exacerbation and in remission. Horses with markedly increased breathing effort (i.e. with metacholine- or lobeline hydrochloride-challenge), often differed markedly (up to 1.9 scores), but the average of end-inspiratory and end-expiratory STS did not differ from baseline STS. CONCLUSIONS AND CLINICAL RELEVANCE: Endoscopic STS are a reproducible measure, but STS did not correlate with clinical, endoscopic and cytological findings indicative of RAO or inflammatory airway disease.

Modeling of electroosmotic and electrophoretic mobilization in capillary and microchip isoelectric focusing

Our dynamic capillary electrophoresis model which uses material specific input data for estimation of electroosmosis was applied to investigate fundamental aspects of isoelectric focusing (IEF) in capillaries or microchannels made from bare fused-silica (FS), FS coated with a sulfonated polymer, polymethylmethacrylate (PMMA) and poly(dimethylsiloxane) (PDMS). Input data were generated via determination of the electroosmotic flow (EOF) using buffers with varying pH and ionic strength. Two models are distinguished, one that neglects changes of ionic strength and one that includes the dependence between electroosmotic mobility and ionic strength. For each configuration, the models provide insight into the magnitude and dynamics of electroosmosis. The contribution of each electrophoretic zone to the net EOF is thereby visualized and the amount of EOF required for the detection of the zone structures at a particular location along the capillary, including at its end for MS detection, is predicted. For bare FS, PDMS and PMMA, simulations reveal that EOF is decreasing with time and that the entire IEF process is characterized by the asymptotic formation of a stationary steady-state zone configuration in which electrophoretic transport and electroosmotic zone displacement are opposite and of equal magnitude. The location of immobilization of the boundary between anolyte and most acidic carrier ampholyte is dependent on EOF, i.e. capillary material and anolyte. Overall time intervals for reaching this state in microchannels produced by PDMS and PMMA are predicted to be similar and about twice as long compared to uncoated FS. Additional mobilization for the detection of the entire pH gradient at the capillary end is required. Using concomitant electrophoretic mobilization with an acid as coanion in the catholyte is shown to provide sufficient additional cathodic transport for that purpose. FS capillaries dynamically double coated with polybrene and poly(vinylsulfonate) are predicted to provide sufficient electroosmotic pumping for detection of the entire IEF gradient at the cathodic column end.

Utilizing Gaussian-Schell model beams to mitigate atmospheric turbulence in free space optical communications / by Kyle R. Drexler.

Turbulence affects traditional free space optical communication by causing speckle to appear in the received beam profile. This occurs due to changes in the refractive index of the atmosphere that are caused by fluctuations in temperature and pressure, resulting in an inhomogeneous medium. The Gaussian-Schell model of partial coherence has been suggested as a means of mitigating these atmospheric inhomogeneities on the transmission side. This dissertation analyzed the Gaussian-Schell model of partial coherence by verifying the Gaussian-Schell model in the far-field, investigated the number of independent phase control screens necessary to approach the ideal Gaussian-Schell model, and showed experimentally that the Gaussian-Schell model of partial coherence is achievable in the far-field using a liquid crystal spatial light modulator. A method for optimizing the statistical properties of the Gaussian-Schell model was developed to maximize the coherence of the field while ensuring that it does not exhibit the same statistics as a fully coherent source. Finally a technique to estimate the minimum spatial resolution necessary in a spatial light modulator was developed to effectively propagate the Gaussian-Schell model through a range of atmospheric turbulence strengths. This work showed that regardless of turbulence strength or receiver aperture, transmitting the Gaussian-Schell model of partial coherence instead of a fully coherent source will yield a reduction in the intensity fluctuations of the received field. By measuring the variance of the intensity fluctuations and the received mean, it is shown through the scintillation index that using the Gaussian-Schell model of partial coherence is a simple and straight forward method to mitigate atmospheric turbulence instead of traditional adaptive optics in free space optical communications.

DC MICROGRID STABILIZATION THROUGH FUZZY CONTROL OF INTERLEAVED, HETEROGENEOUS STORAGE ELEMENTS

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.

Is the relation between early post-session reports and treatment outcome an epiphenomenon of intake distress and early response? A multi-predictor analysis in outpatient psychotherapy

The early phase of psychotherapy has been regarded as a sensitive period in the unfolding of psychotherapy leading to positive outcomes. However, there is disagreement about the degree to which early (especially relationship-related) session experiences predict outcome over and above initial levels of distress and early response to treatment. The goal of the present study was to simultaneously examine outcome at post treatment as a function of (a) intake symptom and interpersonal distress as well as early change in well-being and symptoms, (b) the patient's early session-experiences, (c) the therapist's early session-experiences/interventions, and (d) their interactions. The data of 430 psychotherapy completers treated by 151 therapists were analyzed using hierarchical linear models. Results indicate that early positive intra- and interpersonal session experiences as reported by patients and therapists after the sessions explained 58% of variance of a composite outcome measure, taking intake distress and early response into account. All predictors (other than problem-activating therapists' interventions) contributed to later treatment outcomes if entered as single predictors. However, the multi-predictor analyses indicated that interpersonal distress at intake as well as the early interpersonal session experiences by patients and therapists remained robust predictors of outcome. The findings underscore that early in therapy therapists (and their supervisors) need to understand and monitor multiple interconnected components simultaneously

Effects of two traits of the ecological state equation on our understanding of species coexistence and ecosystem services

Species coexistence has been a fundamental issue to understand ecosystem functioning since the beginnings of ecology as a science. The search of a reliable and all-encompassing explanation for this issue has become a complex goal with several apparently opposing trends. On the other side, seemingly unconnected with species coexistence, an ecological state equation based on the inverse correlation between an indicator of dispersal that fits gamma distribution and species diversity has been recently developed. This article explores two factors, whose effects are inconspicuous in such an equation at the first sight, that are used to develop an alternative general theoretical background in order to provide a better understanding of species coexistence. Our main outcomes are: (i) the fit of dispersal and diversity values to gamma distribution is an important factor that promotes species coexistence mainly due to the right-skewed character of gamma distribution; (ii) the opposite correlation between species diversity and dispersal implies that any increase of diversity is equivalent to a route of “ecological cooling” whose maximum limit should be constrained by the influence of the third law of thermodynamics; this is in agreement with the well-known asymptotic trend of diversity values in space and time; (iii) there are plausible empirical and theoretical ways to apply physical principles to explain important ecological processes; (iv) the gap between theoretical and empirical ecology in those cases where species diversity is paradoxically high could be narrowed by a wave model of species coexistence based on the concurrency of local equilibrium states. In such a model, competitive exclusion has a limited but indispensable role in harmonious coexistence with functional redundancy. We analyze several literature references as well as ecological and evolutionary examples that support our approach, reinforcing the meaning equivalence between important physical and ecological principles.