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Optimal non-Markovian composite search algorithms for spatially correlated targets
No full textAbstract
We study the efficiency of a wide class of stochastic non-Markovian search strategies for spatially correlated target distributions. For an uninformed searcher that performs a non-composite random search, a ballistically moving search is optimal for destructible targets, even when the targets are correlated. For an informed searcher that can measure the time elapsed since the last target encounter and performs a composite search consisting of alternating extensive ballistic trajectories and intensive non-Markovian search trajectories, the efficiency can be more than three times higher compared to a ballistic searcher. We optimize the memory function that describes the intensive non-Markovian search motion and find a single-exponential memory function to be optimal. In our extended search model the intensive search mode is activated when the distance between two consecutively found targets in the extensive search mode is smaller than a threshold length called the memory distance dm. We find that a finite value of dm quite generally leads to optimal search efficiency for correlated target distributions
A one-step blended soundproof-compressible model with balanced data assimilation: theory and idealised tests
No full textA challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Acoustic fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended numerical model with seamless access to the compressible and the soundproof pseudo-incompressible dynamics. Here, the blended modelling strategy by Benacchio et al., MWR, vol. 142 (2014) is upgraded in an advanced numerical framework and extended with a Bayesian local ensemble data assimilation method. Upon assimilation of data, the model configuration is switched to the pseudo-incompressible regime for one time-step. After that, the model configuration is switched back to the compressible model for the duration of the assimilation window. The switching between model regimes is repeated for each subsequent assimilation window. An improved blending strategy for the numerical model ensures that a single time-step in the pseudo-incompressible regime is sufficient to suppress imbalances coming from the initialisation and data assimilation. This improvement is based on three innovations: (i) the association of pressure fields computed at different stages of the numerical integration with actual time levels; (ii) a conversion of pressure-related variables between the model regimes derived from low Mach number asymptotics; and (iii) a judicious selection of the pressure variables used in converting numerical model states when a switch of models occurs. Idealised two-dimensional travelling vortex and buoyancy-driven bubble convection experiments show that acoustic imbalances arising from data assimilation can be eliminated by using this blended model, thereby achieving balanced analysis fields
Definition, detection and trackingof persistent structures in atmospheric flows
No full textLong-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.
Johannes von Lindheim, Abhishek Harikrishnan, Tom Dörffel, Rupert Klein, Peter Koltai, Natalia Mikula, Annette Müller, Peter Névir, George Pacey, Robert Polzin, Nikki Vercautere
Contributions to the detection of non-reference sequences in population-scale NGS data
No full textNon-reference sequence (NRS) variants are a less frequently investigated class of genomic structural variants (SV). Here, DNA sequences are found within an individual that are novel with respect to a given reference. NRS occur predominantly due to the fact that a linear reference genome lacks biological diversity and ancestral sequence if it was primarily derived from a single or few individuals. Therefore, newly sequenced individuals can yield genomic sequences which are absent from a reference genome. With the increasing throughput of sequencing technologies, SV detection has become possible across tens of thousands of individuals. When using short-read data, the detection of NRS variants inevitably involves a de novo assembly which is a complex computational problem and requires high-quality sequence data at high coverage. Previous studies have demonstrated how sequence data of multiple genomes can be combined for the reliable detection of NRS variants. However, the algorithms proposed in these studies have a limited capability to process large sets of genomes. This thesis introduces novel contributions for the discovery of NRS variants in many genomes, which scale to considerably larger numbers of genomes than previous methods. A practical software tool, PopIns2, that was developed to apply the presented methods is elucidated in greater detail. The highlight among the new contributions is a procedure to merge contig assemblies of unaligned reads from many individuals into a single set of NRS by heuristically generating a weighted minimum path cover for a colored de Bruijn graph. Tests on simulated data show that PopIns2 ranks among the best approaches in terms of quality and reliability and that its approach yields the best precision for a growing number of genomes processed. Results on the Polaris Diversity Cohort and a set of 1000 Icelandic human genomes demonstrate unmatched scalability for the application on population-scale datasets
Stable Isotopomers of myo-Inositol Uncover a Complex MINPP1-Dependent Inositol Phosphate Network
No full textThe water-soluble inositol phosphates (InsPs) represent a functionally diverse group of small-molecule messengers involved in a myriad of cellular processes. Despite their centrality, our understanding of human InsP metabolism is incomplete because the available analytical toolset to characterize and quantify InsPs in complex samples is limited. Here, we have synthesized and applied symmetrically and unsymmetrically 13C-labeled myo-inositol and inositol phosphates. These probes were utilized in combination with nuclear magnetic resonance spectroscopy (NMR) and capillary electrophoresis mass spectrometry (CE-MS) to investigate InsP metabolism in human cells. The labeling strategy provided detailed structural information via NMR─down to individual enantiomers─which overcomes a crucial blind spot in the analysis of InsPs. We uncovered a novel branch of InsP dephosphorylation in human cells which is dependent on MINPP1, a phytase-like enzyme contributing to cellular homeostasis. Detailed characterization of MINPP1 activity in vitro and in cells showcased the unique reactivity of this phosphatase. Our results demonstrate that metabolic labeling with stable isotopomers in conjunction with NMR spectroscopy and CE-MS constitutes a powerful tool to annotate InsP networks in a variety of biological contexts
Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics
No full textNeurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the synaptic vesicle to the calcium channels determines the release probability and consequently the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal
The impact of membrane protein diffusion on GPCR signaling
No full textSpatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of Gs-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor–G protein complex’s relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling
Numerical homogenization of fractal interface problems
Get PDFWe consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal geometry. Our main results concern the construction of projection operators with suitable stability and approximation properties. The existence of such projections then allows for the application of existing concepts from localized orthogonal decomposition (LOD) and successive subspace correction to construct first multiscale discretizations and iterative algebraic solvers with scale-independent convergence behavior for this class of problems.
Volume 56, Number 4, July-August
Page(s
Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects
No full textWhen described by a one-dimensional reaction
coordinate, pair-reaction rates in a solvent depend, in addition to
the potential barrier height and the friction coefficient, on the
potential shape, the effective mass, and the friction relaxation
spectrum, but a rate theory that accurately accounts for all of these
effects does not exist. After a review of classical reaction-rate
theories, we show how to extract all parameters of the generalized
Langevin equation (GLE) and, in particular, the friction memory
function from molecular dynamics (MD) simulations of two
prototypical pair reactions in water, the dissociation of NaCl and of
two methane molecules. The memory exhibits multiple time scales
and, for NaCl, pronounced oscillatory components. Simulations of
the GLE by Markovian embedding techniques accurately
reproduce the pair-reaction kinetics from MD simulations without any fitting parameters, which confirms the accuracy of the
approximative form of the GLE and of the parameter extraction techniques. By modification of the GLE parameters, we investigate
the relative importance of memory, mass, and potential shape effects. Neglect of memory slows down NaCl and methane
dissociation by roughly a factor of 2; neglect of mass accelerates reactions by a similar factor, and the harmonic approximation of the
potential shape gives rise to slight acceleration. This partial error cancellation explains why Kramers’ theory, which neglects memory
effects and treats the potential shape in harmonic approximation, describes reaction rates better than more sophisticated theories. In
essence, all three effects, friction memory, inertia, and the potential shape nonharmonicity, are important to quantitatively describe
pair-reaction kinetics in water
Simulation of a particle domain in a continuum/fluctuating hydrodynamics reservoir
No full textIn molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this Letter, we show a novel approach where the latest version of the adaptive resolution scheme (AdResS), with noninteracting tracers as particles’ reservoir, is combined with a fluctuating hydrodynamics (FHD) solver. The resulting algorithm, supported by a solid mathematical model, allows for a physically consistent exchange of matter and energy between the particle domain and its fluctuating continuum reservoir. Numerical tests are performed to show the validity of the algorithm. Differently from previous algorithms of the same kind, the current approach allows for simulations where, in addition to density fluctuations, also thermal fluctuations can be accounted for, thus large complex molecular systems, as, for example, hydrated biological membranes in a thermal field, can now be efficiently treated