Non-Standard Errors

peer reviewe

Limit theorems for pp-domain functionals of stationary Gaussian fields

Fix an integer $p\geq 1$ and refer to it as the number of growing domains. For each $i\in\{1,\ldots,p\}$, fix a compact subset $D_i\subseteq\mathbb R^{d_i}$ where $d_1,\ldots,d_p\ge 1$. Let $d= d_1+\dots+d_{p}$ be the total underlying dimension. Consider a continuous, stationary, centered Gaussian field $B=(B_x)_{x\in \mathbb R^d}$ with unit variance. Finally, let $\varphi:\mathbb R \rightarrow \mathbb R$ be a measurable function such that $\mathrm E[\varphi(N)^2]<\infty$ for $N\sim N(0,1)$. In this paper, we investigate central and non-central limit theorems as $t_1,\ldots,t_p\to\infty$ for functionals of the form $$Y(t_1,\dots,t_p):=\int_{t_1D_1\times\dots \times t_pD_p}\varphi(B_{x})dx.$$ Firstly, we assume that the covariance function $C$ of $B$ is {\it separable} (that is, $C=C_1\otimes\ldots\otimes C_{p}$ with $C_i:\mathbb R^{d_i}\to\mathbb R$), and thoroughly investigate under what condition $Y(t_1,\dots,t_p)$ satisfies a central or non-central limit theorem when the same holds for $\int_{t_iD_i}\varphi(B^{(i)}_{x_i})dx_i$ for at least one (resp. for all) $i\in \{1,\ldots,p\}$, where $B^{(i)}$ stands for a stationary, centered, Gaussian field on $\mathbb R^{d_i}$ admitting $C_i$ for covariance function. When $\varphi$ is an Hermite polynomial, we also provide a quantitative version of the previous result, which improves some bounds from A. Reveillac, M. Stauch, and C. A. Tudor, Hermite variations of the fractional brownian sheet, Stochastics and Dynamics 12 (2012). Secondly, we extend our study beyond the separable case, examining what can be inferred when the covariance function is either in the Gneiting class or is additively separable

Un master en sciences infirmières en Belgique francophone : un pas supplémentaire vers la pratique infirmière avancée

peer reviewed4. Quality educatio

Interpreting Omics Data in Parkinson’s Disease: A Statistical, Machine Learning, and Graph Representation Learning Approach

Parkinson’s disease (PD) is characterized by the heterogeneity and complexity of both its clinical symptoms and molecular mechanisms, which hinders the development of reliable diagnostic and prognostic biomarkers. This thesis presents an integrated approach to identify cross-sectional and longitudinal molecular signatures associated with PD diagnosis and motor symptoms by incorporating domain-specific knowledge into the analysis and modeling of blood transcriptomics and metabolomics. Statistical analyses and machine learning algorithms were applied to identify, compare, and interpret relevant factors for predicting PD diagnosis and motor dysfunction severity using molecular measurements at baseline and over time. Both individual molecules and aggregated, higher-level functional representations of global activity changes in cellular pathways, compartments, and protein complex signatures were examined. In addition, two modelling pipelines exploiting graph representation learning on sample similarity networks and molecular interaction networks were implemented for PD case-control classification. Although the resulting machine learning models still have limitations in terms of predictive performance, they highlight a number of robust and pronounced PD-specific changes at baseline and over time, including changes in mitochondrial β-oxidation of fatty acids and purine/xanthine metabolism. These changes remain significant when the analyses are adjusted for relevant confounders, such as the effects of dopaminergic medications on plasma metabolomics. In addition to different machine learning methods, different feature selection approaches were evaluated, highlighting the Lasso approach with unsupervised filters as a favorable strategy. Furthermore, the investigation of longitudinal data showed that even with a limited number of available time points, identified candidate dynamic biomarkers hold promise for further validation studies in larger cohorts with multiple follow-up examinations. Finally, the study of omics data using graph representation learning on molecular interaction networks provided mechanistic insights, confirming changes in known PD-associated genes and metabolites, and uncovering promising new candidate markers. While the use of molecular interaction networks is limited by experimental biases and the incompleteness of known interactions, networks built upon sample similarity among omics profiles can provide an unbiased graph structure, although interpretation of the results may be more challenging. Overall, the comprehensive study of statistical, machine learning, and graph representation learning models presented in this thesis highlights the benefits of using prior domain knowledge for omics data analysis and reveals robust disease associations at the level of single molecules and higher-level representations. The work illustrates the potential of higherlevel functional and network representations, together with dynamic biomarker analysis of longitudinal data, for building predictive models to study a complex and heterogeneous disease such as PD. In addition to these methodological findings, the biological results provide new insights into relevant disease mechanisms in PD and lay the groundwork for validation studies in larger, independent cohorts

Hierarchical Bipartite Graph Convolutional Network for Recommendation

peer reviewe

None

Disciplinary terminology can be very challenging for students to master at the required pace. To this end, I use a multi-pronged pedagogical approach based on a flipped classroom model which personalises learning while optimising the use of classroom time. Some time ahead of class, students prepare the chapter by reading it and completing a Moodle quiz on its content. In this 'preparatory task' they also specify what chapter content they would particularly like to be explained in class. By using these preparatory task outputs, I am therefore able to tailor teaching to students’ needs. The foundational learning from these tasks and classes is next applied and consolidated in more advanced seminar tasks. As part of their completion, students work in ‘learning teams’, which enables peer learning. Visual study sheets and quizlets further facilitate independent learning. The approach has been used with several Bachelor cohorts and has received very positive student evaluations

Performing the Finite Energy Airy-Hermite-Hollow Gaussian Beam in a turbulent atmosphere

peer reviewe

Collective Bargaining about Corporate Social Responsibility

If a profit-maximising firm credibly commits to an employment-enhancing Corporate Social Responsibility (CSR) objective in negotiations with a trade union, the union can reduce its wage demands. Lower wages, ceteris paribus, raise profits, while the increase in employment enhances the payoff of a wage-setting trade union. Therefore, both the firm and the trade union can be better off in the presence of a collectively bargained CSR-objective than in its absence. Accordingly, establishing a CSR-objective can give rise to a Pareto-improvement and can mitigate the inefficiency resulting from collective wage negotiations

Assessing symptoms of long/post COVID and chronic fatigue syndrome using the DePaul symptom questionnaire-2: a validation in a German-speaking population

peer reviewedObjective: A subset of Covid-19 survivors will develop persisting health sequelae (i.e. Long Covid/LC or Post Covid/PC) similar to Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS). In the absence of a reliable biomarker to diagnose LC/PC and ME/CFS, their classification based on symptoms becomes indispensable. Hence, we translated and validated the DePaul Symptom Questionnaire−2 (DSQ-2), to offer a screening tool for the German-speaking population. Methods: A sample of healthy adults, and adults with ME/CFS and LC/PC (N = 502) completed a reduced-item version of the DSQ-2 and SF-36 questionnaire online. We performed an exploratory factor analysis, assessed construct validity, diagnostic accuracy and compared the symptom profiles of individuals with ME/CFS versus LC/PC versus healthy adults. Results: Exploratory factor analysis revealed a 10-factor solution with excellent internal consistencies. The sensitivity of the DSQ-2 was excellent. The specificity was moderate with moderate inter-rater reliability. Construct validity of the DSQ-2 was supported by strong negative correlations with physical health subscales of the SF-36. A visual comparison of the symptom profiles of individuals with ME/CFS versus LC/PC revealed a comparable pattern. Conclusion: Despite lower symptom severity, individuals with LC/PC reported significantly stronger limitations in general health and physical functioning and were more likely to meet ME/CFS diagnostic criteria with ongoing sickness duration, suggesting that ME/CFS can be considered a long-term sequela of LC/PC. This study offers a translated and validated version of the reduced-item DSQ-2 that can guide medical evaluation and aid physicians in identifying a ME/CFS-like subtype of LC/PC