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- Mathematisch-Naturwissenschaftliche Fakultät (24) (remove)
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
In the field of disk-based parallel database management systems exists a great variety of solutions based on a shared-storage or a shared-nothing architecture. In contrast, main memory-based parallel database management systems are dominated solely by the shared-nothing approach as it preserves the in-memory performance advantage by processing data locally on each server. We argue that this unilateral development is going to cease due to the combination of the following three trends: a) Nowadays network technology features remote direct memory access (RDMA) and narrows the performance gap between accessing main memory inside a server and of a remote server to and even below a single order of magnitude. b) Modern storage systems scale gracefully, are elastic, and provide high-availability. c) A modern storage system such as Stanford's RAMCloud even keeps all data resident in main memory. Exploiting these characteristics in the context of a main-memory parallel database management system is desirable. The advent of RDMA-enabled network technology makes the creation of a parallel main memory DBMS based on a shared-storage approach feasible.
This thesis describes building a columnar database on shared main memory-based storage. The thesis discusses the resulting architecture (Part I), the implications on query processing (Part II), and presents an evaluation of the resulting solution in terms of performance, high-availability, and elasticity (Part III).
In our architecture, we use Stanford's RAMCloud as shared-storage, and the self-designed and developed in-memory AnalyticsDB as relational query processor on top. AnalyticsDB encapsulates data access and operator execution via an interface which allows seamless switching between local and remote main memory, while RAMCloud provides not only storage capacity, but also processing power. Combining both aspects allows pushing-down the execution of database operators into the storage system. We describe how the columnar data processed by AnalyticsDB is mapped to RAMCloud's key-value data model and how the performance advantages of columnar data storage can be preserved.
The combination of fast network technology and the possibility to execute database operators in the storage system opens the discussion for site selection. We construct a system model that allows the estimation of operator execution costs in terms of network transfer, data processed in memory, and wall time. This can be used for database operators that work on one relation at a time - such as a scan or materialize operation - to discuss the site selection problem (data pull vs. operator push). Since a database query translates to the execution of several database operators, it is possible that the optimal site selection varies per operator. For the execution of a database operator that works on two (or more) relations at a time, such as a join, the system model is enriched by additional factors such as the chosen algorithm (e.g. Grace- vs. Distributed Block Nested Loop Join vs. Cyclo-Join), the data partitioning of the respective relations, and their overlapping as well as the allowed resource allocation.
We present an evaluation on a cluster with 60 nodes where all nodes are connected via RDMA-enabled network equipment. We show that query processing performance is about 2.4x slower if everything is done via the data pull operator execution strategy (i.e. RAMCloud is being used only for data access) and about 27% slower if operator execution is also supported inside RAMCloud (in comparison to operating only on main memory inside a server without any network communication at all). The fast-crash recovery feature of RAMCloud can be leveraged to provide high-availability, e.g. a server crash during query execution only delays the query response for about one second. Our solution is elastic in a way that it can adapt to changing workloads a) within seconds, b) without interruption of the ongoing query processing, and c) without manual intervention.
Bacteria respond to changing environmental conditions by switching the global pattern of expressed genes. In response to specific environmental stresses the cell activates several stress-specific molecules such as sigma factors. They reversibly bind the RNA polymerase to form the so-called holoenzyme and direct it towards the appropriate stress response genes. In exponentially growing E. coli cells, the majority of the transcriptional activity is carried out by the housekeeping sigma factor, while stress responses are often under the control of alternative sigma factors. Different sigma factors compete for binding to a limited pool of RNA polymerase (RNAP) core enzymes, providing a mechanism for cross talk between genes or gene classes via the sharing of expression machinery. To quantitatively analyze the contribution of sigma factor competition to global changes in gene expression, we develop a thermodynamic model that describes binding between sigma factors and core RNAP at equilibrium, transcription, non-specific binding to DNA and the modulation of the availability of the molecular components.
Association of housekeeping sigma factor to RNAP is generally favored by its abundance and higher binding affinity to the core. In order to promote transcription by alternative sigma subunits, the bacterial cell modulates the transcriptional efficiency in a reversible manner through several strategies such as anti-sigma factors, 6S RNA and generally any kind of transcriptional regulators (e.g. activators or inhibitors). By shifting the outcome of sigma factor competition for the core, these modulators bias the transcriptional program of the cell. The model is validated by comparison with in vitro competition experiments, with which excellent agreement is found. We observe that transcription is affected via the modulation of the concentrations of the different types of holoenzymes, so saturated promoters are only weakly affected by sigma factor competition. However, in case of overlapping promoters or promoters recognized by two types of sigma factors, we find that even saturated promoters are strongly affected.
Active transcription effectively lowers the affinity between the sigma factor driving it and the core RNAP, resulting in complex cross talk effects and raising the question of how their in vitro measure is relevant in the cell. We also estimate that sigma factor competition is not strongly affected by non-specific binding of core RNAPs, sigma factors, and holoenzymes to DNA. Finally, we analyze the role of increased core RNAP availability upon the shut-down of ribosomal RNA transcription during stringent response. We find that passive up-regulation of alternative sigma-dependent transcription is not only possible, but also displays hypersensitivity based on the sigma factor competition. Our theoretical analysis thus provides support for a significant role of passive control during that global switch of the gene expression program and gives new insights into RNAP partitioning in the cell.
This study examines the course and driving forces of recent vegetation change in the Mongolian steppe. A sediment core covering the last 55years from a small closed-basin lake in central Mongolia was analyzed for its multi-proxy record at annual resolution. Pollen analysis shows that highest abundances of planted Poaceae and highest vegetation diversity occurred during 1977-1992, reflecting agricultural development in the lake area. A decrease in diversity and an increase in Artemisia abundance after 1992 indicate enhanced vegetation degradation in recent times, most probably because of overgrazing and farmland abandonment. Human impact is the main factor for the vegetation degradation within the past decades as revealed by a series of redundancy analyses, while climate change and soil erosion play subordinate roles. High Pediastrum (a green algae) influx, high atomic total organic carbon/total nitrogen (TOC/TN) ratios, abundant coarse detrital grains, and the decrease of C-13(org) and N-15 since about 1977 but particularly after 1992 indicate that abundant terrestrial organic matter and nutrients were transported into the lake and caused lake eutrophication, presumably because of intensified land use. Thus, we infer that the transition to a market economy in Mongolia since the early 1990s not only caused dramatic vegetation degradation but also affected the lake ecosystem through anthropogenic changes in the catchment area.
We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337-355) and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e. g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.
claspfolio 2
(2014)
Building on the award-winning, portfolio-based ASP solver claspfolio, we present claspfolio 2, a modular and open solver architecture that integrates several different portfolio-based algorithm selection approaches and techniques. The claspfolio 2 solver framework supports various feature generators, solver selection approaches, solver portfolios, as well as solver-schedule-based pre-solving techniques. The default configuration of claspfolio 2 relies on a light-weight version of the ASP solver clasp to generate static and dynamic instance features. The flexible open design of claspfolio 2 is a distinguishing factor even beyond ASP. As such, it provides a unique framework for comparing and combining existing portfolio-based algorithm selection approaches and techniques in a single, unified framework. Taking advantage of this, we conducted an extensive experimental study to assess the impact of different feature sets, selection approaches and base solver portfolios. In addition to gaining substantial insights into the utility of the various approaches and techniques, we identified a default configuration of claspfolio 2 that achieves substantial performance gains not only over clasp's default configuration and the earlier version of claspfolio, but also over manually tuned configurations of clasp.
Modern 3D geovisualization systems (3DGeoVSs) are complex and evolving systems that are required to be adaptable and leverage distributed resources, including massive geodata. This article focuses on 3DGeoVSs built based on the principles of service-oriented architectures, standards and image-based representations (SSI) to address practically relevant challenges and potentials. Such systems facilitate resource sharing and agile and efficient system construction and change in an interoperable manner, while exploiting images as efficient, decoupled and interoperable representations. The software architecture of a 3DGeoVS and its underlying visualization model have strong effects on the system's quality attributes and support various system life cycle activities. This article contributes a software reference architecture (SRA) for 3DGeoVSs based on SSI that can be used to design, describe and analyze concrete software architectures with the intended primary benefit of an increase in effectiveness and efficiency in such activities. The SRA integrates existing, proven technology and novel contributions in a unique manner. As the foundation for the SRA, we propose the generalized visualization pipeline model that generalizes and overcomes expressiveness limitations of the prevalent visualization pipeline model. To facilitate exploiting image-based representations (IReps), the SRA integrates approaches for the representation, provisioning and styling of and interaction with IReps. Five applications of the SRA provide proofs of concept for the general applicability and utility of the SRA. A qualitative evaluation indicates the overall suitability of the SRA, its applications and the general approach of building 3DGeoVSs based on SSI.
Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data.
In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.
The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.