Freie Universität Berlin
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Flux large deviations of independent and reacting particle systems, with implications for macroscopic fluctuation theory
Get PDFWe consider a system of independent particles on a finite state space, and prove a dynamic large-deviation principle for the empirical measure-empirical flux pair, taking the specific fluxes rather than net fluxes into account. We prove the large deviations under deterministic initial conditions, and under random initial conditions satisfying a large-deviation principle. We then show how to use this result to generalise a number of principles from Macroscopic Fluctuation Theory to the finite-space setting
Coherent structures in wind shear induced wave-turbulence-vegetation interaction in water bodies
No full textFlume experiments with particle imaging velocimetry (PIV) were conducted recently to study a complex flow problem where wind shear acts on the surface of a static water body in presence of flexible emergent vegetation and induces a rich dynamics of wave–turbulence–vegetation interaction inside the water body without any gravitational gradient. The experiments were aimed at mimicking realistic vegetated wetlands and the present work is targeted to improve the understanding of the coherent structures associated with this interaction by employing a combination of techniques such as quadrant analysis, proper orthogonal decomposition (POD), Shannon entropy and mutual information content (MIC). The turbulent transfer of momentum is found to be dominated by organized motions such as sweeps and ejections, while the wave component of vertical momentum transport does not show any such preference. Reducing the data using POD shows that wave energy for large flow depths and turbulent energy for all water depths is concentrated among the top few modes, which can allow development of simple reduced order models. Vegetation flexibility is found to induce several roll type structures, however if the vegetation density is increased, drag effects dominate over flexibility and organize the flow. The interaction between waves and turbulence is also found to be highest among flexible sparse vegetation. However, rapidly evolving parts of the flow such as the air–water interface reduces wave–turbulence interaction
Acceleration of a ground-state reaction by selective femtosecond-infrared-laser-pulse excitation
Get PDFInfrared (IR) excitation of vibrations that participate in the reaction coordinate of an otherwise thermally driven chemical reaction are believed to lead to its acceleration. Attempts at the practical realization of this concept have been hampered so far by competing processes leading to sample heating. Here we demonstrate, using femtosecond IR-pump IR-probe experiments, the acceleration of urethane and polyurethane formation due to vibrational excitation of the reactants for 1:1 mixtures of phenylisocyanate and cyclohexanol, and toluene-2,4-diisocyanate and 2,2,2-trichloroethane-1,1-diol, respectively. We measured reaction rate changes upon selective vibrational excitation with negligible heating of the sample and observed an increase of the reaction rate up to 24%. The observation is rationalized using reactant and transition-state structures obtained from quantum chemical calculations. We subsequently used IR-driven reaction acceleration to write a polyurethane square on sample windows using a femtosecond IR pulse
Reusable building blocks in biological systems.
No full textOne of the most widely recognized features of biological systems is their modularity. The modules that constitute biological systems are said to be redeployed and combined across several conditions, thus acting as building blocks. In this work, we analyse to what extent are these building blocks reusable as compared with those found in randomized versions of a system. We develop a notion of decompositions of systems into phenotypic building blocks, which allows them to overlap while maximizing the number of times a building block is reused across several conditions. Different biological systems present building blocks whose reusability ranges from single use (e.g. condition specific) to constitutive, although their average reusability is not always higher than random equivalents of the system. These decompositions reveal a distinct distribution of building block sizes in real biological systems. This distribution stems, in part, from the peculiar usage pattern of the elements of biological systems, and constitutes a new angle to study the evolution of modularity
Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities
Get PDFWhile multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC finite element approach based on deterministic adaptive mesh refinement for the arising “pathwise” problems and outline a convergence theory in terms of desired accuracy and required computational cost. Our theoretical and heuristic reasoning together with the efficiency of our new approach are confirmed by numerical experiments
Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory
Get PDFThe Dynamic State Index (DSI) is a scalar diagnostic field that quantifies local deviations from a steady and adiabatic wind solution and thus indicates non-stationarity aswell as diabaticity. The DSI-concept has originally been developed through the Energy-Vorticity Theory based on the full compressible flow equations without regard to the characteristic scale-dependence of many atmospheric processes. But such scaledependent information is often of importance, and particularly so in the context of precipitation modeling: Small scale convective events are often organized in storms, clusters up to “Großwetterlagen” on the synoptic scale. Therefore, a DSI index for the quasi-geostrophic model is developed using (i) the Energy-Vorticity Theory and (ii) showing that it is asymptotically consistent with the original index for the primitive equations. In the last part, using meteorological reanalysis data it is demonstrated on a case study that both indices capture systematically different scale-dependent precipitation information. A spin-off of the asymptotic analysis is a novel non-equilibrium time scale combining potential vorticity and the DSI indices
From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data
Get PDFOne way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the “best” approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases
Reference and taxonomy based methods for classification and abundance estimation of organisms in metagenomic samples
No full textMetagenomics provides the means to study the vast and still mostly unknown microbial world which comprises at least half of earth's genetic diversity. Computational metagenomics enables those discoveries via analysis of large amounts of data which are being generated in a fast pace with high-throughput technologies. Reference-based methods are commonly used to study environmental samples based on a set of previously assembled reference sequences which are often linked to a taxonomic classification. Finding the origin of each sequenced fragment and profiling an environmental sample as a whole are the main goals of binning and taxonomic profiling tools, respectively.
In this thesis I present three methods in computational metagenomics. Sets of curated reference sequences jointly with taxonomic classification are employed to characterize community samples. The main goal of those contributions is to improve the state-of-the-art of taxonomic profiling and binning, with fast, sensitive and precise methods.
First I present ganon, a sequence classification tool for metagenomics which works with a very large number of reference sequences. Ganon provides an efficient method to index sequences and to keep those indices updated in very short time. In addition, ganon performs taxonomic binning with strongly improved precision compared to the current available methods. For a general profiling of metagenomic samples and abundance estimation I introduce DUDes. Rather than predicting strains in the sample based only on relative abundances, DUDes first identifies possible candidates by comparing the strength of mapped reads in each node of the taxonomic tree in an iterative top-down manner. This technique works in an opposite direction of the lowest common ancestor approach. Lastly, I present MetaMeta, a pipeline to execute metagenome analysis tools and integrate their results. MetaMeta is a method to combine and enhance results from multiple taxonomic binning and profiling tools and at the same time a pipeline to easily execute tools and analyze environmental data. MetaMeta includes database generation, pre-processing, execution, and integration steps, allowing easy installation, visualization and parallelization of state-of-the-art tools. Using the same input data, MetaMeta provides more sensitive and reliable results with the presence of each identified organism being supported by several methods.
Those three projects introduce new methodologies and improved results over similar methods, constituting valuable contributions to characterize communities in a reference and taxonomy-based manner
Computational Methods for Integrative Structural Variant Analysis Across Species Boundaries
No full textStructural variations (SVs) are a phenomenon that have a tremendous impact on all species. SVs are the result of fundamental rearrangement mechanisms but can lead to severe human diseases like cancer. Rearrangement events also provide means that enable bacteria to adapt to environmental pressures where they can also happen across species boundaries in events called horizontal gene transfer (HGT). The incorporation of foreign genes from a donor into an acceptor genome can be investigated on the genomic level, the activity and protein expression changes, however, are better revealed on the proteomic level. This thesis contributes four computational methods for the detection of complex SVs of various types and sizes including HGT events from genomic next-generation sequencing (NGS) data and proteomic shotgun mass-spectrometry (MS) data. Concerning HGT events, our methods address the questions of what organisms are involved in the transfer, what genes are exactly transferred and to what position, and what are the implications on proteomic level. First, we present the generic SV detection tool Gustaf. Gustaf improves the size and type resolution compared to previous SV detection methods. A further specific advantage is the characterisation of translocations and dispersed duplications as a combination of simple, delocalised variants that have to be inferred from separate SV calls. With this basis for a more in-depth focus on HGT detection, we developed two mapping-based methods, Daisy and DaisyGPS. Daisy facilitates Gustaf and further SV detection strategies to precisely identify the transferred region within the donor and its insertion site in the acceptor genome. DaisyGPS uses metagenomic profiling strategies to identify suitable acceptor and donor references. In contrast to previous approaches based on sequence composition patterns or phylogenetic disagreements, our methods provide a detection based on sequence comparison and hence offer novel means of evidence. In the last project, we present a method for HGT detection, called Hortense, that is based on proteomic MS data. Hortense extends a standard database peptide search with a thorough cross-validation to ensure HGT properties, and is the first dedicated proteomics HGT detection method. Results from Hortense can also serve as supporting evidence and functional confirmation for HGT events proposed by our genomic-based methods. Taken together, the three HGT methods provide a full view of the transfer event that was not be possible before or with one of the methods alone