Freie Universität Berlin
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Multi-Sample Approaches and Applications for Structural Variant Detection
No full textIn recent years, advances in the field of sequencing technologies have enabled the field of population-scale sequencing studies. These studies aim to sequence and analyze a large set of individuals from one or multiple populations, with the aim of gaining insight into underlying genetic structure, similarities and differences. Collections of genetic variation and possible connections to various disease are some of the products of this area of research. The potential of population studies is widely considered to be huge and many more endeavors of this kind are expected in the near future. This opportunity comes with a big challenge because many computational tools that are used for the analysis of sequencing data were not designed for cohorts of this size and may suffer from limited scalability. It is therefore vital that the computational tools required for the analysis of population-scale data keep up with the quickly growing amounts of data.
This thesis contributes to the field of population-scale genetics in the development and application of a novel approach for structural variant detection. It has explicitly been designed with the large amounts of population-scale sequencing data in mind. The presented approach is capable of analyzing tens of thousands of whole-genome short-read sequencing samples jointly. This joint analysis is driven by a tailored joint likelihood ratio model that integrates information from many genomes. The efficient approach does not only save computational resources but also allows to combine the data across all samples to make sensitive and specific predictions about the presence and genotypes of structural variation present within the analyzed population. This thesis demonstrates that this approach and the computational tool PopDel that implements it compare favorably to current state-of-the-art structural variant callers that have been used in previous population-scale studies. Extensive benchmarks on simulated and real world sequencing data are provided to show the performance of the presented approach. Further, a first finding of medical relevance that directly stems from the application of PopDel on the genomes of almost 50,000 Icelanders is presented.
This thesis therefore provides a novel tool and new ideas to further push the boundaries of the analysis of massive amounts of next generation sequencing data and to deepen our understanding of structural variation and their implications for human health
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
No full textWe consider the problem of learning a linear operator θ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an inverse problem for θ with the undesirable feature that its forward operator is generally non-compact (even if θ is assumed to be compact or of p-Schatten class). However, we prove that, in terms of spectral properties and regularisation theory, this inverse problem is equivalent to the known compact inverse problem associated with scalar response regression. Our framework allows for the elegant derivation of dimension-free rates for generic learning algorithms under Hölder-type source conditions. The proofs rely on the combination of techniques from kernel regression with recent results on concentration of measure for sub-exponential Hilbertian random variables. The obtained rates hold for a variety of practically-relevant scenarios in functional regression as well as nonlinear regression with operator-valued kernels and match those of classical kernel regression with scalar response
Deep learning to decompose macromolecules into independent Markovian domains
No full textThe increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data
Temperature steerable flows and Boltzmann generators
No full textBoltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples in thermodynamic equilibrium. The equilibrium distribution is usually defined by an energy function and a thermodynamic state. Here, we propose temperature steerable flows (TSFs) which are able to generate a family of probability densities parametrized by a choosable temperature parameter. TSFs can be embedded in generalized ensemble sampling frameworks to sample a physical system across multiple thermodynamic states
Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis
No full textThe Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively applies the ensemble Kalman update to evolve (the approximation of the) prior into the posterior measure.
For the convergence analysis of the EKI it is common practice to derive a continuous version, replacing the iteration with a stochastic differential equation. In this paper we validate this approach by showing that the stochastic EKI iteration converges to paths of the continuous-time stochastic differential equation by considering both the nonlinear and linear setting, and we prove convergence in probability for the former, and convergence in moments for the latter. The methods employed can also be applied to the analysis of more general numerical schemes for stochastic differential equations in general
Sparse dictionary learning allows model-free pseudotime estimation of transcriptomics data
No full textBackground
Pseudotime estimation from dynamic single-cell transcriptomic data enables characterisation and understanding of the underlying processes, for example developmental processes. Various pseudotime estimation methods have been proposed during the last years. Typically, these methods start with a dimension reduction step because the low-dimensional representation is usually easier to analyse. Approaches such as PCA, ICA or t-SNE belong to the most widely used methods for dimension reduction in pseudotime estimation methods. However, these methods usually make assumptions on the derived dimensions, which can result in important dataset properties being missed. In this paper, we suggest a new dictionary learning based approach, dynDLT, for dimension reduction and pseudotime estimation of dynamic transcriptomic data. Dictionary learning is a matrix factorisation approach that does not restrict the dependence of the derived dimensions. To evaluate the performance, we conduct a large simulation study and analyse 8 real-world datasets.
Results
The simulation studies reveal that firstly, dynDLT preserves the simulated patterns in low-dimension and the pseudotimes can be derived from the low-dimensional representation. Secondly, the results show that dynDLT is suitable for the detection of genes exhibiting the simulated dynamic patterns, thereby facilitating the interpretation of the compressed representation and thus the dynamic processes. For the real-world data analysis, we select datasets with samples that are taken at different time points throughout an experiment. The pseudotimes found by dynDLT have high correlations with the experimental times. We compare the results to other approaches used in pseudotime estimation, or those that are method-wise closely connected to dictionary learning: ICA, NMF, PCA, t-SNE, and UMAP. DynDLT has the best overall performance for the simulated and real-world datasets.
Conclusions
We introduce dynDLT, a method that is suitable for pseudotime estimation. Its main advantages are: (1) It presents a model-free approach, meaning that it does not restrict the dependence of the derived dimensions; (2) Genes that are relevant in the detected dynamic processes can be identified from the dictionary matrix; (3) By a restriction of the dictionary entries to positive values, the dictionary atoms are highly interpretable
Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis
No full textWe establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the nonisothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretization and regularization techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalized solutions are used in cases where nonintegrable diffusion fluxes or reaction terms appear
Forecasting Surface Velocity Fields Associated With Laboratory Seismic Cycles Using Deep Learning
No full textAbstract It has been recently demonstrated that Machine Learning (ML) can predict laboratory earthquakes. Here we propose a prediction framework that allows forecasting future surface velocity fields from past ones for analog experiments of megathrust seismic cycles. Using data from two types of experiments, we explore the prediction performances of multiple Deep Learning (DL) and ML algorithms. In such a self-supervised regression, no feature extraction is required and the entire seismic cycle is forecasted. The onset, magnitude, and propagation of analog earthquakes can thus be predicted at different prediction horizons. From all architectures tested in this study, convolutional recurrent neural networks (CNN-LSTM and CONVLSTM) provide the best predictions although their performances depend on experiment characteristics and hyperparameters tuning. Analog earthquakes can be successfully anticipated up to a horizon of the order of their duration. This laboratory-based study may open new avenues for transfer learning applications with data from natural subduction zones
Upper plate response to a sequential elastic rebound and slab acceleration during laboratory-scale subduction megathrust earthquakes
No full textAn earthquake-induced stress drop on a megathrust instigates different responses on the upper plate and slab. We mimic homogenous and heterogeneous megathrust interfaces at the laboratory scale to monitor the strain relaxation on two elastically bi-material plates by establishing analog velocity weakening and neutral materials. A sequential elastic rebound follows the coseismic shear-stress drop in our elastoplastic-frictional models: a fast rebound of the upper plate and the delayed and smaller rebound on the elastic belt (model slab). A combination of the rebound of the slab and the rapid relaxation (i.e., elastic restoration) of the upper plate after an elastic overshooting may accelerate the relocking of the megathrust. This acceleration triggers/antedates the failure of a nearby asperity and enhances the early slip reversal in the rupture area. Hence, the trench-normal landward displacement in the upper plate may reach a significant amount of the entire interseismic slip reversal and speeds up the stress build-up on the upper plate backthrust that emerges self-consistently at the downdip end of the seismogenic zones. Moreover, the backthrust switches its kinematic mode from a normal to reverse mechanism during the coseismic and postseismic stages, reflecting the sense of shear on the interfac
Guidelines for data-driven approaches to study transitions in multiscale systems: The case of Lyapunov vectors
No full textThis study investigates the use of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in
dynamical systems, as recently discussed in several atmospheric sciences applications. In a first step, the needed underlying dynamical models
are derived from data using a non-parametric model-based clustering framework. The covariant Lyapunov vectors are then approximated
based on these data-driven models. The data-based numerical approach is tested using three well-understood example systems with increasing
dynamical complexity, identifying properties that allow for a successful application of the method: in particular, the method is identified to
require a clear multiple time scale structure with fast transitions between slow subsystems. The latter slow dynamics should be dynamically
characterized by invariant neutral directions of the linear approximation model