Parameterized Differential Equations over k((t))(x)

In this article, we consider the inverse Galois problem for parameterized differential equations over k((t))(x) with k any field of characteristic zero and use the method of patching over fields due to Harbater and Hartmann. As an application, we prove that every connected semisimple k((t))-split linear algebraic group is a parameterized Galois group over k((t))(x).Comment: 13 page

Embedding problems of division algebras

A finite group G is called admissible over a given field if there exists a central division algebra that contains a G-Galois field extension as a maximal subfield. We give a definition of embedding problems of division algebras that extends both the notion of embedding problems of fields as in classical Galois theory, and the question which finite groups are admissible over a field. In a recent work by Harbater, Hartmann and Krashen, all admissible groups over function fields of curves over complete discretely valued fields with algebraically closed residue field of characteristic zero have been characterized. We show that also certain embedding problems of division algebras over such a field can be solved for admissible groups.Comment: 19 page

Tenfold your photons -- a physically-sound approach to filtering-based variance reduction of Monte-Carlo-simulated dose distributions

X-ray dose constantly gains interest in the interventional suite. With dose being generally difficult to monitor reliably, fast computational methods are desirable. A major drawback of the gold standard based on Monte Carlo (MC) methods is its computational complexity. Besides common variance reduction techniques, filter approaches are often applied to achieve conclusive results within a fraction of time. Inspired by these methods, we propose a novel approach. We down-sample the target volume based on the fraction of mass, simulate the imaging situation, and then revert the down-sampling. To this end, the dose is weighted by the mass energy absorption, up-sampled, and distributed using a guided filter. Eventually, the weighting is inverted resulting in accurate high resolution dose distributions. The approach has the potential to considerably speed-up MC simulations since less photons and boundary checks are necessary. First experiments substantiate these assumptions. We achieve a median accuracy of 96.7 % to 97.4 % of the dose estimation with the proposed method and a down-sampling factor of 8 and 4, respectively. While maintaining a high accuracy, the proposed method provides for a tenfold speed-up. The overall findings suggest the conclusion that the proposed method has the potential to allow for further efficiency.Comment: 6 pages, 3 figures, Bildverarbeitung f\"ur die Medizin 202

An RDoC-inspired examination of pharmacological, sex-specific, and hormonal modulators of Positive Valence Systems

The Positive Valence Systems (PVS) are a major domain of the Research Domain Criteria framework (RDoC), which aims at promoting precision medicine for psychiatry, based on a profound understanding of the psychological and biological basis of shared behavioral symptoms. The PVS domain describes basic processes of reward processing, which can be disrupted in several mental disorders, such as schizophrenia, substance use disorders, and major depressive disorder. Investigating basic mechanisms of PVS constructs is important to understand central aspects which contribute to these transdiagnostic motivational syndromes. In my doctoral thesis, I investigated pharmacological, sex-specific, and hormonal modulators of PVS constructs. I focused on the constructs reward responsiveness and reward valuation in the context of motivational behavior in healthy humans. In study 1, I examined the neurotransmitter serotonin, and in particular a selective serotonin reuptake inhibitor (SSRI) as modulator of reward responsiveness on a neural level, using functional magnetic resonance imaging (fMRI). In studies 2 and 3, I inquired into sex-specific and hormonal modulators of reward valuation to elucidate sex-specific integration of benefits and costs on a behavioral level. In study 1, I found that an acute SSRI dose modulated the processing of punishment cues in caudate and thalamus brain regions, which have been identified as transdiagnostic neural markers of disrupted reward responsiveness. In study 2, I identified sex differences in reward valuation, which depended on different encoding of benefits, not costs. Study 3 did not yield substantial differences in reward valuation depending on different hormonal states in women. The RDoC initiative aims at understanding core features and modulators of shared behavioral symptoms, ranging from normal to abnormal behavior. Understanding basic mechanisms is an important first step towards transdiagnostic clinical translation. Within this scope, my work has implications for testing clinical translation of pharmacological and behavioral treatments specifically targeted to PVS constructs, which take sex-specific behavioral variability into account

Correlates of depressive symptoms among Latino and Non-Latino White adolescents: Findings from the 2003 California Health Interview Survey

BACKGROUND: The prevalence of depression is increasing not only among adults, but also among adolescents. Several risk factors for depression in youth have been identified, including female gender, increasing age, lower socio-economic status, and Latino ethnic background. The literature is divided regarding the role of acculturation as risk factor among Latino youth. We analyzed the correlates of depressive symptoms among Latino and Non-Latino White adolescents residing in California with a special focus on acculturation. METHODS: We performed an analysis of the adolescent sample of the 2003 California Health Interview Survey, which included 3,196 telephone-interviews with Latino and Non-Latino White adolescents between the ages of 12 and 17. Depressive symptomatology was measured with a reduced version of the Center for Epidemiologic Studies Depression Scale. Acculturation was measured by a score based on language in which the interview was conducted, language(s) spoken at home, place of birth, number of years lived in the United States, and citizenship status of the adolescent and both of his/her parents, using canonical principal component analysis. Other variables used in the analysis were: support provided by adults at school and at home, age of the adolescent, gender, socio-economic status, and household type (two parent or one parent household). RESULTS: Unadjusted analysis suggested that the risk of depressive symptoms was twice as high among Latinos as compared to Non-Latino Whites (10.5% versus 5.5 %, p < 0.001). The risk was slightly higher in the low acculturation group than in the high acculturation group (13.1% versus 9.7%, p = 0.12). Similarly, low acculturation was associated with an increased risk of depressive symptoms in multivariate analysis within the Latino subsample (OR 1.54, CI 0.97–2.44, p = 0.07). Latino ethnicity emerged as risk factor for depressive symptoms among the strata with higher income and high support at home and at school. In the disadvantaged subgroups (higher poverty, low support at home and at school) Non-Latino Whites and Latinos had a similar risk of depressive symptoms. CONCLUSION: Our findings suggest that the differences in depressive symptoms between Non-Latino Whites and Latino adolescents disappear at least in some strata after adjusting for socio-demographic and social support variables

Effects of Tissue Material Properties on X-Ray Image, Scatter and Patient Dose Determined using Monte Carlo Simulations

With increasing patient and staff X-ray radiation awareness, many efforts have been made to develop accurate patient dose estimation methods. To date, Monte Carlo (MC) simulations are considered golden standard to simulate the interaction of X-ray radiation with matter. However, sensitivity of MC simulation results to variations in the experimental or clinical setup of image guided interventional procedures are only limited studied. In particular, the impact of patient material compositions is poorly investigated. This is mainly due to the fact, that these methods are commonly validated in phantom studies utilizing a single anthropomorphic phantom. In this study, we therefore investigate the impact of patient material parameters mapping on the outcome of MC X-ray dose simulations. A computation phantom geometry is constructed and three different commonly used material composition mappings are applied. We used the MC toolkit Geant4 to simulate X-ray radiation in an interventional setup and compared the differences in dose deposition, scatter distributions and resulting X-ray images. The evaluation shows a discrepancy between different material composition mapping up to 20 % concerning directly irradiated organs. These results highlight the need for standardization of material composition mapping for MC simulations in a clinical setup.Comment: 6 pages, 4 figures, Bildverarbeitung f\"ur die Medizin 201