Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Scalable In Situ Hybridization on Tissue Arrays for Validation of Novel Cancer and Tissue-Specific Biomarkers

Tissue localization of gene expression is increasingly important for accurate interpretation of large scale datasets from expression and mutational analyses. To this end, we have (1) developed a robust and scalable procedure for generation of mRNA hybridization probes, providing >95% first-pass success rate in probe generation to any human target gene and (2) adopted an automated staining procedure for analyses of formalin-fixed paraffin-embedded tissues and tissue microarrays. The in situ mRNA and protein expression patterns for genes with known as well as unknown tissue expression patterns were analyzed in normal and malignant tissues to assess procedure specificity and whether in situ hybridization can be used for validating novel antibodies. We demonstrate concordance between in situ transcript and protein expression patterns of the well-known pathology biomarkers KRT17, CHGA, MKI67, PECAM1 and VIL1, and provide independent validation for novel antibodies to the biomarkers BRD1, EZH2, JUP and SATB2. The present study provides a foundation for comprehensive in situ gene set or transcriptome analyses of human normal and tumor tissues

Young people's data governance preferences for their mental health data: MindKind Study findings from India, South Africa, and the United Kingdom

Mobile devices offer a scalable opportunity to collect longitudinal data that facilitate advances in mental health treatment to address the burden of mental health conditions in young people. Sharing these data with the research community is critical to gaining maximal value from rich data of this nature. However, the highly personal nature of the data necessitates understanding the conditions under which young people are willing to share them. To answer this question, we developed the MindKind Study, a multinational, mixed methods study that solicits young people's preferences for how their data are governed and quantifies potential participants' willingness to join under different conditions. We employed a community-based participatory approach, involving young people as stakeholders and co-researchers. At sites in India, South Africa, and the UK, we enrolled 3575 participants ages 16-24 in the mobile app-mediated quantitative study and 143 participants in the public deliberation-based qualitative study. We found that while youth participants have strong preferences for data governance, these preferences did not translate into (un)willingness to join the smartphone-based study. Participants grappled with the risks and benefits of participation as well as their desire that the "right people" access their data. Throughout the study, we recognized young people's commitment to finding solutions and co-producing research architectures to allow for more open sharing of mental health data to accelerate and derive maximal benefit from research

The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts

The impact of non-Gaussian height distribution and spectral properties on the lubrication performance of counterformal (point) contacts is quantitatively studied (film parameter, Λ, and asperity load ratio, La) by developing a mixed lubrication model. The Weibull height distribution function and power spectral density (PSD) are used to generate artificial surface topographies (non-Gaussian and Gaussian, isotropic), as these surface topographies are found in many tribological components. The set of variables needed to parametrize and their effect on mixed lubrication is discussed, including the shape parameter, the autocorrelation length, the wavelength ratio, and the Hurst coefficient. It is revealed that a rough surface with a lower shape parameter exhibits higher hydrodynamic lift. The spectral properties (the autocorrelation length and the wavelength ratio) of rough surfaces significantly affect the film parameter and the hydrodynamic and asperity pressures. The film parameter is slightly influenced by the Hurst coefficient.Validerad;2024;Nivå 2;2024-04-03 (hanlid);Full text license: CC BY 4.0</p

The Influence of Non-Gaussian Roughness and Spectral Properties on Mixed Lubrication for Heavily Loaded Counterformal Contacts

The impact of non-Gaussian height distribution and spectral properties on the lubrication performance of counterformal (point) contacts is quantitatively studied (film parameter, Λ, and asperity load ratio, La) by developing a mixed lubrication model. The Weibull height distribution function and power spectral density (PSD) are used to generate artificial surface topographies (non-Gaussian and Gaussian, isotropic), as these surface topographies are found in many tribological components. The set of variables needed to parametrize and their effect on mixed lubrication is discussed, including the shape parameter, the autocorrelation length, the wavelength ratio, and the Hurst coefficient. It is revealed that a rough surface with a lower shape parameter exhibits higher hydrodynamic lift. The spectral properties (the autocorrelation length and the wavelength ratio) of rough surfaces significantly affect the film parameter and the hydrodynamic and asperity pressures. The film parameter is slightly influenced by the Hurst coefficient.Validerad;2024;Nivå 2;2024-04-03 (hanlid);Full text license: CC BY 4.0</p