Distributionally Robust Markov Decision Processes and their Connection to Risk Measures

We consider robust Markov Decision Processes with Borel state and action spaces, unbounded cost and finite time horizon. Our formulation leads to a Stackelberg game against nature. Under integrability, continuity and compactness assumptions we derive a robust cost iteration for a fixed policy of the decision maker and a value iteration for the robust optimization problem. Moreover, we show the existence of deterministic optimal policies for both players. This is in contrast to classical zero-sum games. In case the state space is the real line we show under some convexity assumptions that the interchange of supremum and infimum is possible with the help of Sion's minimax Theorem. Further, we consider the problem with special ambiguity sets. In particular we are able to derive some cases where the robust optimization problem coincides with the minimization of a coherent risk measure. In the final section we discuss two applications: A robust LQ problem and a robust problem for managing regenerative energy

Minimizing Spectral Risk Measures Applied to Markov Decision Processes

We study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in B\"auerle and Ott (2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital

Measuring Electronic Health Literacy: Development, Validation, and Test of Measurement Invariance of a Revised German Version of the eHealth Literacy Scale

Background: The World Wide Web has become an essential source of health information. Nevertheless, the amount and quality of information provided may lead to information overload. Therefore, people need certain skills to search for, identify, and evaluate information from the internet. In the context of health information, these competencies are summarized as the construct of eHealth literacy. Previous research has highlighted the relevance of eHealth literacy in terms of health-related outcomes. However, the existing instrument assessing eHealth literacy in the German language reveals methodological limitations regarding test development and validation. The development and validation of a revised scale for this important construct is highly relevant. Objective: The objective of this study was the development and validation of a revised German eHealth literacy scale. In particular, this study aimed to focus on high methodological and psychometric standards to provide a valid and reliable instrument for measuring eHealth literacy in the German language. Methods: Two internationally validated instruments were merged to cover a wide scope of the construct of eHealth literacy and create a revised eHealth literacy scale. Translation into the German language followed scientific guidelines and recommendations to ensure content validity. Data from German-speaking people (n=470) were collected in a convenience sample from October to November 2020. Validation was performed by factor analyses. Further, correlations were performed to examine convergent, discriminant, and criterion validity. Additionally, analyses of measurement invariance of gender, age, and educational level were conducted. Results: Analyses revealed a 2-factorial model of eHealth literacy. By item-reduction, the 2 factors information seeking and information appraisal were measured with 8 items reaching acceptable-to-good model fits (comparative fit index [CFI]: 0.942, Tucker Lewis index [TLI]: 0.915, root mean square error of approximation [RMSEA]: 0.127, and standardized root mean square residual [SRMR]: 0.055). Convergent validity was comprehensively confirmed by significant correlations of information seeking and information appraisal with health literacy, internet confidence, and internet anxiety. Discriminant and criterion validity were examined by correlation analyses with various scales and could partly be confirmed. Scalar level of measurement invariance for gender (CFI: 0.932, TLI: 0.923, RMSEA: 0.122, and SRMR: 0.068) and educational level (CFI: 0.937, TLI: 0.934, RMSEA: 0.112, and SRMR: 0.063) were confirmed. Measurement invariance of age was rejected. Conclusions: Following scientific guidelines for translation and test validation, we developed a revised German eHealth Literacy Scale (GR-eHEALS). Our factor analyses confirmed an acceptable-to-good model fit. Construct validation in terms of convergent, discriminant, and criterion validity could mainly be confirmed. Our findings provide evidence for measurement invariance of the instrument regarding gender and educational level. The newly revised GR-eHEALS questionnaire represents a valid instrument to measure the important health-related construct eHealth literacy

Psychometric properties of the German revised version of the eHealth literacy scale in individuals with cardiac diseases: Validation and test of measurement invariance

Background: The internet is most people's primary source of (health) information. However, no validated instrument exists to assess eHealth literacy in the group of patient with cardiac diseases. Objective: The objective of this study was the evaluation of the psychometric properties of the German revised version of the eHealth literacy scale (GR-eHEALS) in individuals with coronary artery disease (CAD) and congestive heart failure (CHF). Methods: A cross-sectional study was conducted. N = 455 were included in the statistical analyses. The assessment compromised the GR-eHEALS, medical history, sociodemographic data, and technology-related data. Confirmatory factor analyses, correlational analyses, and tests of measurement invariance were performed. Results: The two-factorial model reached a good model fit. The sub-scales information seeking and information appraisal, as well as the eHealth literacy total score, reached high reliability coefficients. Construct and criterion validity was fully confirmed For the two-factorial model, measurement invariance up to the scalar level could be confirmed regarding the sociodemographic characteristics sex, age, and educational level. Conclusions: This study confirmed the two-factor structure, construct, and criterion validity as well as measurement invariance at the scalar level for sex, age, and educational level of the GR-eHEALS scale in a sample of individuals with CAD and CHF

Low temperature dephasing in irradiated metallic wires

We present phase coherence time measurements in quasi-one-dimensional Ag wires implanted with Ag$^{+}$ ions with an energy of $100 keV$. The measurements have been carried out in the temperature range from $100 mK$ up to $10 K$; this has to be compared with the Kondo temperature of iron in silver, i.e. $T_{K}^{Ag/Fe} \approx 4 K$, used in recent experiments on dephasing in Kondo systems\cite{mallet_prl_06,birge_prl_06}. We show that the phase coherence time is not affected by the implantation procedure, clearly proving that ion implantation process by itself \emph{does not lead to any extra dephasing} at low temperature.Comment: 4 pages, 4figure

Mindfulness and skills-based eHealth intervention to reduce distress in cancer-affected patients in the Reduct trial: Intervention protocol of the make it training optimized.

Introduction Cancer-affected patients experience high distress due to various burdens. One way to expand psycho-oncological support is through digital interventions. This protocol describes the development and structure of a web-based psycho-oncological intervention, the Make It Training optimized. This intervention is currently evaluated in the Reduct trial, a multicenter randomized controlled trial. Methods The Make It Training optimized was developed in six steps: A patient need and demand assessment, development and acceptability analysis of a prototype, the formation of a patient advisory council, the revision of the training, implementation into a web app, and the development of a motivation and evaluation plan. Results Through a process of establishing cancer-affected patients' needs, prototype testing, and patient involvement, the Make It Training optimized was developed by a multidisciplinary team and implemented in a web app. It consists of 16 interactive self-guided modules which can be completed within 16 weeks. Discussion Intervention protocols can increase transparency and increase the likelihood of developing effective web-based interventions. This protocol describes the process and results of developing a patient-oriented intervention. Future research should focus on the further personalization of web-based psycho-oncological interventions and the potential benefits of combining multiple psychotherapeutic approaches

Mental health symptoms in German elite athletes: a network analysis

IntroductionElite athletes are exposed to a variety of sport-specific stressors that may put them at particular risk for mental health symptoms and disorders. The aim of the present study was to assess data on mental health of elite athletes and investigate associations and interconnections among different variables using network analysis.MethodsA cross-sectional study was conducted from December 2021 to December 2022. The sample consisted of 275 German elite athletes (167 females) aged ≥18 years. Next to sociodemographic, medical and sport-related data, psychometric data such as psychological distress, symptoms of generalized anxiety, depression, and somatic symptom disorder have been gathered through questionnaires and analyzed by means of network analysis.ResultsOver 95.0% of the athletes showed elevated distress and 28.6% reported symptoms of depression. Results of the network analysis show, among other findings, that symptoms of somatic symptom disorder were associated with severe injuries and substance use. Moreover, elite athletes who reported a better financial situation reported fewer symptoms of depression, generalized anxiety, and somatic symptom disorder. They also reported a lower incidence of mild to moderate injuries and severe injuries, fewer years spent in elite sports, less substance use, and fewer training sessions per week. Conversely, these athletes reported a higher level of distress. Furthermore, sex, financial situation and number of training units per week emerged as significant predictors for mental health symptoms.DiscussionElite athletes showed increased numbers regarding mental health symptoms. Providing appropriate mental health interventions for elite athletes and further analysis of factors that influence the mental health of elite athletes and their interplay seem to be of central importance for the general well-being of elite athletes

Dynamics of defect formation

A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as a function of the rate of increase of the critical parameter. The procedure is valid in both the overdamped and underdamped limits. In one space dimension, we perform quantitative comparison with numerical simulations of the nonlinear nonautonomous stochastic partial differential equation and report on signatures of underdamped dynamics.Comment: 4 pages, LaTeX, 4 figures. Submitted to Physical Revie