Fully discrete finite element data assimilation method for the heat equation

We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty of the $H^1$-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen, Data assimilation for the heat equation using stabilized finite element methods, arXiv, 2016, combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from $t=0$, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the $L^2$-norm at the final time

Non-parametric machine learning for biological sequence data

In the past decade there has been a massive increase in the volume of biological sequence data, driven by massively parallel sequencing technologies. This has enabled data-driven statistical analyses using non-parametric predictive models (including those from machine learning) to complement more traditional, hypothesis-driven approaches. This thesis addresses several challenges that arise when applying non-parametric predictive models to biological sequence data. Some of these challenges arise due to the nature of the biological system of interest. For example, in the study of the human microbiome the phylogenetic relationships between microorganisms are often ignored in statistical analyses. This thesis outlines a novel approach to modelling phylogenetic similarity using string kernels and demonstrates its utility in the two-sample test and host-trait prediction. Other challenges arise from limitations in our understanding of the models themselves. For example, calculating variable importance (a key task in biomedical applications) is not possible for many models. This thesis describes a novel extension of an existing approach to compute importance scores for grouped variables in a Bayesian neural network. It also explores the behaviour of random forest classifiers when applied to microbial datasets, with a focus on the robustness of the biological findings under different modelling assumptions.Open Acces

Modelling phylogeny in 16S rRNA gene sequencing datasets using string kernels

Bacterial community composition is measured using 16S rRNA (ribosomal ribonucleic acid) gene sequencing, for which one of the defining characteristics is the phylogenetic relationships that exist between variables. Here, we demonstrate the utility of modelling these relationships in two statistical tasks (the two sample test and host trait prediction) by employing string kernels originally proposed in natural language processing. We show via simulation studies that a kernel two-sample test using the proposed kernels, which explicitly model phylogenetic relationships, is powerful while also being sensitive to the phylogenetic scale of the difference between the two populations. We also demonstrate how the proposed kernels can be used with Gaussian processes to improve predictive performance in host trait prediction. Our method is implemented in the Python package StringPhylo (available at github.com/jonathanishhorowicz/stringphylo)

Syncrip/hnRNP Q is required for activity-induced Msp300/Nesprin-1 expression and new synapse formation.

Memory and learning involve activity-driven expression of proteins and cytoskeletal reorganization at new synapses, requiring posttranscriptional regulation of localized mRNA a long distance from corresponding nuclei. A key factor expressed early in synapse formation is Msp300/Nesprin-1, which organizes actin filaments around the new synapse. How Msp300 expression is regulated during synaptic plasticity is poorly understood. Here, we show that activity-dependent accumulation of Msp300 in the postsynaptic compartment of the Drosophila larval neuromuscular junction is regulated by the conserved RNA binding protein Syncrip/hnRNP Q. Syncrip (Syp) binds to msp300 transcripts and is essential for plasticity. Single-molecule imaging shows that msp300 is associated with Syp in vivo and forms ribosome-rich granules that contain the translation factor eIF4E. Elevated neural activity alters the dynamics of Syp and the number of msp300:Syp:eIF4E RNP granules at the synapse, suggesting that these particles facilitate translation. These results introduce Syp as an important early acting activity-dependent regulator of a plasticity gene that is strongly associated with human ataxias