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  • 2015-2019  (70)
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  • 1
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    A Variational Bayesian Algorithm for Clustering of Large and Complex Networks (2015)
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    Publication Date: 2020-10-09
    Description: We propose the Blockloading algorithm for the clustering of large and complex graphs with tens of thousands of vertices according to a Stochastic Block Model (SBM). Blockloading is based on generalized Variational Bayesian EM (VBEM) schemes and works for weighted and unweighted graphs. Existing Variational (Bayesian) EM methods have to consider each possible number of clusters sepa- rately to determine the optimal number of clusters and are prone to converge to local optima making multiple restarts necessary. These factors impose a severe restriction on the size and complexity of graphs these methods can handle. In con- trast, the Blockloading algorithm restricts restarts to subnetworks in a way that provides error correction of an existing cluster assignment. The number of clusters need not be specified in advance because Blockloading will return it as a result. We show that Blockloading outperforms all other variational methods regarding reliability of the results and computational efficiency.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 2
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    Finding dominant structures of nonreversible Markov processes (2015)
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    Publication Date: 2020-10-09
    Description: Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 3
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    Influence of pH and sequence in peptide aggregation via molecular simulation (2015)
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    Publication Date: 2021-12-23
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 4
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    Influence of pH and sequence in peptide aggregation via molecular simulation (2015)
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    Publication Date: 2020-10-09
    Description: We employ a recently developed coarse-grained model for peptides and proteins where the effect of pH is automatically included. We explore the effect of pH in the aggregation process of the amyloidogenic peptide KTVIIE and two related sequences, using three different pH environments. Simulations using large systems (24 peptides chains per box) allow us to correctly account for the formation of realistic peptide aggregates. We evaluate the thermodynamic and kinetic implications of changes in sequence and pH upon peptide aggregation, and we discuss how a minimalistic coarse- grained model can account for these details.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 5
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    Prior estimation and Bayesian inference from large cohort data sets (2016)
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    Publication Date: 2021-07-06
    Description: One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterisations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Using these population data, we propose an iterative algorithm for contructing an informative prior distribution, which then serves as the basis for computing patient-specific posteriors and obtaining individual predictions. We demonsrate the performance of our method by applying it to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 6
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    Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems (2017)
    Details
    Publication Date: 2020-03-20
    Description: Well-mixed stochastic chemical kinetics are properly modelled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows to express various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 7
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    Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems (2017)
    Details
    Publication Date: 2020-03-20
    Description: Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 8
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    Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries (2016)
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    Publication Date: 2020-09-24
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 9
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    Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach (2018)
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    Publication Date: 2020-03-20
    Description: Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 10
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    From interacting agents to density-based modeling with stochastic PDEs (2019)
    Details
    Publication Date: 2021-11-02
    Description: Many real-world processes can naturally be modeled as systems of interacting agents. However, the long-term simulation of such agent-based models is often intractable when the system becomes too large. In this paper, starting from a stochastic spatio-temporal agent-based model (ABM), we present a reduced model in terms of stochastic PDEs that describes the evolution of agent number densities for large populations. We discuss the algorithmic details of both approaches; regarding the SPDE model, we apply Finite Element discretization in space which not only ensures efficient simulation but also serves as a regularization of the SPDE. Illustrative examples for the spreading of an innovation among agents are given and used for comparing ABM and SPDE models.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
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