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Spectral Properties of Effective Dynamics from Conditional Expectations
Get PDFAbstract: The reduction of high-dimensional systems to effective models on a smaller set of variables
is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes,
a general procedure to find effective equations is the conditioning approach. In this paper, we are
interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to
the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction
approximation error for reversible systems. We also present numerical examples indicating that,
if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced
generator, it seems largely insensitive to the time window used for the KM estimators. We analyze
the implications of these observations for systems driven by underdamped Langevin dynamics,
and show how meaningful effective dynamics can be defined in this setting
GENERIC for dissipative solids with bulk-interface interaction
Get PDFThe modeling framework of GENERIC was originally introduced by Grmela and Öttinger for
thermodynamically closed systems. It is phrased with the aid of the energy and entropy as driving
functionals for reversible and dissipative processes and suitable geometric structures. Based on
the definition functional derivatives we propose a GENERIC framework for systems with bulkinterface
interaction and apply it to discuss the GENERIC structure of models for delamination
processes
Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading
No full textWe investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori–Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies
Testing assembly strategies of Francisella tularensis genomes to infer an evolutionary conservation analysis of genomic structures
No full textBackground
We benchmarked sequencing technology and assembly strategies for short-read, long-read, and hybrid assemblers in respect to correctness, contiguity, and completeness of assemblies in genomes of Francisella tularensis. Benchmarking allowed in-depth analyses of genomic structures of the Francisella pathogenicity islands and insertion sequences. Five major high-throughput sequencing technologies were applied, including next-generation “short-read” and third-generation “long-read” sequencing methods.
Results
We focused on short-read assemblers, hybrid assemblers, and analysis of the genomic structure with particular emphasis on insertion sequences and the Francisella pathogenicity island. The A5-miseq pipeline performed best for MiSeq data, Mira for Ion Torrent data, and ABySS for HiSeq data from eight short-read assembly methods. Two approaches were applied to benchmark long-read and hybrid assembly strategies: long-read-first assembly followed by correction with short reads (Canu/Pilon, Flye/Pilon) and short-read-first assembly along with scaffolding based on long reads (Unicyler, SPAdes). Hybrid assembly can resolve large repetitive regions best with a “long-read first” approach.
Conclusions
Genomic structures of the Francisella pathogenicity islands frequently showed misassembly. Insertion sequences (IS) could be used to perform an evolutionary conservation analysis. A phylogenetic structure of insertion sequences and the evolution within the clades elucidated the clade structure of the highly conservative F. tularensis
Data-driven model reduction of agent-based systems using the Koopman generator
No full textThe dynamical behavior of social systems can be described by agent-based models. Although single agents follow easily explainable rules, complex time-evolving patterns emerge due to their interaction. The simulation and analysis of such agent-based models, however, is often prohibitively time-consuming if the number of agents is large. In this paper, we show how Koopman operator theory can be used to derive reduced models of agent-based systems using only simulation data. Our goal is to learn coarse-grained models and to represent the reduced dynamics by ordinary or stochastic differential equations. The new variables are, for instance, aggregated state variables of the agent-based model, modeling the collective behavior of larger groups or the entire population. Using benchmark problems with known coarse-grained models, we demonstrate that the obtained reduced systems are in good agreement with the analytical results, provided that the numbers of agents is sufficiently large
From Adaptive Resolution to Molecular Dynamics of Open Systems
No full textWe provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method’s advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments
Thermolab: a thermodynamics laboratory for nonlinear transport processes in open systems
No full textWe developed a numerical thermodynamics laboratory called “Thermolab” to study the effects of the thermodynamic behavior of non-ideal solution models on reactive transport processes in open systems. The equations of state of internally consistent thermodynamic datasets are implemented in MATLAB functions and form the basis for calculating Gibbs energy. A linear algebraic approach is used in Thermolab to compute Gibbs energy of mixing for multi-component phases to study the impact of the non-ideality of solution models on transport processes. The Gibbs energies are benchmarked with experimental data, phase diagrams and other thermodynamic software. Constrained Gibbs minimization is exemplified with MATLAB codes and iterative refinement of composition of mixtures may be used to increase precision and accuracy. All needed transport variables such as densities, phase compositions, and chemical potentials are obtained from Gibbs energy of the stable phases after the minimization in Thermolab. We demonstrate the use of precomputed local equilibrium data obtained with Thermolab in reactive transport models. In reactive fluid flow the shape and the velocity of the reaction front vary depending on the non-linearity of the partitioning of a component in fluid and solid. We argue that non-ideality of solution models has to be taken into account and further explored in reactive transport models. Thermolab Gibbs energies can be used in Cahn-Hilliard models for non-linear diffusion and phase growth. This presents a transient process towards equilibrium and avoids computational problems arising during precomputing of equilibrium data
Wear Testing of Knee Implants
Get PDFHardware wear tests for knee implants, necessary for market authorization, are expensive and time-consuming. Faster than realtime wear simulations have the potential to speed up the design process for implants by providing frequent and early feedback
Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations
No full textBoolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators
Markov Chain Importance Sampling—A Highly Efficient Estimator for MCMC
No full textMarkov chain algorithms are ubiquitous in machine learning and statistics and many other disciplines. Typically, these algorithms can be formulated as acceptance rejection methods. In this work, we present a novel estimator applicable to these methods, dubbed Markov chain importance sampling, which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides a novel way of correcting the discretization error. Our estimator satisfies a central limit theorem and improves on error per CPU cycle, often to a large extent. As a by-product it enables estimating the normalizing constant, an important quantity in Bayesian machine learning and statistics. Supplementary materials for this article are available online