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Optimal Reaction Coordinates: Variational Characterization and Sparse Computation
Get PDFReaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that
govern the long-term behavior of high-dimensional stochastic processes. We present a novel
and general variational characterization of optimal RCs and provide conditions for their existence.
Optimal RCs are minimizers of a certain loss function and reduced models based
on them guarantee very good approximation of the long-term dynamics of the original highdimensional
process. We show that, for slow-fast systems, metastable systems, and other
systems with known good RCs, the novel theory reproduces previous insight. Remarkably,
the numerical e�ort required to evaluate the loss function scales only with the complexity of
the underlying, low-dimensional mechanism, and not with that of the full system. The theory
provided lays the foundation for an e�cient and data-sparse computation of RCs via modern
machine learning techniques
Towards a numerical laboratory for investigations of gravity-wave 2 mean-ow interactions in the atmosphere
Get PDFIdealized integral studies of the dynamics of atmospheric inertia-gravity waves (IGWs)
from their sources in the troposphere (e.g., by spontaneous emission from jets and fronts)
to dissipation and mean-
ow e�ects at higher altitudes could contribute to a better treatment
of these processes in IGW parameterizations in numerical weather prediction and
climate simulation. It seems important that numerical codes applied for this purpose are
e�cient and focus on the essentials. Therefore a previously published staggered-grid solver
for f-plane soundproof pseudo-incompressible dynamics is extended here by two main components.
These are 1) a semi-implicit time stepping scheme for the integration of buoyancy
and Coriolis e�ects, and 2) the incorporation of Newtonian heating consistent with
pseudo-incompressible dynamics. This heating function is used to enforce a temperature
pro�le that is baroclinically unstable in the troposphere and it allows the background state
to vary in time. Numerical experiments for several benchmarks are compared against a
buoyancy/Coriolis-explicit third-order Runge-Kutta scheme, verifying the accuracy and ef-
�ciency of the scheme. Preliminary mesoscale simulations with baroclinic-wave activity in
the troposphere show intensive small-scale wave activity at high altitudes, and they also
indicate there the expected reversal of the zonal-mean-zonal winds
Thermally active nanoparticle clusters enslaved by engineered domain wall traps
Get PDFThe stable assembly of fluctuating nanoparticle clusters on a surface represents a techno-
logical challenge of widespread interest for both fundamental and applied research. Here we
demonstrate a technique to stably confine in two dimensions clusters of interacting nano-
particles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to
form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet
film. At each domain, the magnetic stray field generates an effective harmonic potential with
a field tunable stiffness. The experiments are combined with theory to show that the mag-
netic confinement is effectively harmonic and pairwise interactions are of dipolar nature,
leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the sta-
tionary collective states arise from the competition between repulsion, confinement and the
tendency to fill the central potential well. Using a numerical simulation model as a quanti-
tative map between the experiments and theory we explore the field-induced crystallization
process for larger clusters and unveil the existence of three different dynamical regimes. The
present method provides a model platform for investigations of the collective phenomena
emerging when strongly confined nanoparticle clusters are forced to move in an idealized,
harmonic-like potential
From interacting agents to density-based modeling with stochastic PDEs
No full textMany 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
Path probability ratios for Langevin dynamics—Exact and approximate
Get PDFPath reweighting is a principally exact method to estimate dynamic properties from biased simulations—provided that the path probability
ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler–Maruyama scheme
for overdamped Langevin dynamics. Since molecular dynamics simulations use Langevin dynamics rather than overdamped Langevin dynamics,
this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio ML for Langevin dynamics
propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics
propagated by this integrator. We also show that a previously derived approximate path probability ratioMapprox differs from the exactML
only by O(ξ4Δt4) and thus yields highly accurate dynamic reweighting results. (Δt is the integration time step, and ξ is the collision rate.) The
results are tested, and the efficiency of path reweighting is explored using butane as an example
RLM: fast and simplified extraction of read-level methylation metrics from bisulfite sequencing data
No full textBisulfite sequencing data provide value beyond the straightforward methylation assessment by analyzing single-read patterns. Over the past years, various metrics have been established to explore this layer of information. However, limited compatibility with alignment tools, reference genomes or the measurements they provide present a bottleneck for most groups to routinely perform read-level analysis. To address this, we developed RLM, a fast and scalable tool for the computation of several frequently used read-level methylation statistics. RLM supports standard alignment tools, works independently of the reference genome and handles most sequencing experiment designs. RLM can process large input files with a billion reads in just a few hours on common workstations.
Availability and implementation:
https://github.com/sarahet/RL
Thin-Volume Visualization on Curved Domains
No full textThin, curved structures occur in many volumetric datasets. Their analysis using classical volume rendering is difficult because parts of such structures can bend away or hide behind occluding elements. This problem cannot be fully compensated by effective navigation alone, as structure-adapted navigation in the volume is cumbersome and only parts of the structure are visible in each view. We solve this problem by rendering a spatially transformed view of the volume so that an unobstructed visualization of the entire curved structure is obtained. As a result, simple and intuitive navigation becomes possible. The domain of the spatial transform is defined by a triangle mesh that is topologically equivalent to an open disc and that approximates the structure of interest. The rendering is based on ray-casting, in which the rays traverse the original volume. In order to carve out volumes of varying thicknesses, the lengths of the rays as well as the positions of the mesh vertices can be easily modified by interactive painting under view control.
We describe a prototypical implementation and demonstrate the interactive visual inspection of complex structures from digital humanities, biology, medicine, and material sciences. The visual representation of the structure as a whole allows for easy inspection of interesting substructures in their original spatial context. Overall, we show that thin, curved structures in volumetric data can be excellently visualized using ray-casting-based volume rendering of transformed views defined by guiding surface meshes, supplemented by interactive, local modifications of ray lengths and vertex positions
Definition, detection and tracking of persistent structures in atmospheric flows. preprint
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
Erste Befunde aus dem Projekt "MATH+ as a Research Object": Karriereziele, -wissen und -handeln, Nachwuchsförderung und Rekrutierung
No full textDies sind erste Ergebnisse aus dem Projekt "MATH+ as a research object", das Teil des Clusters MATH+ der Exzellenzstrategie von Bund und Ländern zur Stärkung universitärer Spitzenforschung ist.1 In dem Projekt werden die Reproduktionsmechanismen von Geschlechterasymmetrien in der Mathematik sowie das ungleichheitsreduzierende Potenzial karriere- und gleichstellungsunterstützender Maßnahmen untersucht. Das Projekt selbst ist als Teil der Gleichstellungs- und Diversity-Maßnahmen des Clusters konzipiert. Von daher hat es neben einer wissenschaftlichen Perspektive zugleich eine anwendungsorientierte Komponente, nämlich dem Cluster Informationen zu liefern, um empirisch fundiert die Weiterentwicklung dieser Maßnahmen sowie die Verringerung von Geschlechterungleichheiten voranzubringen. Vor diesem Hintergrund haben wir den detaillierten Analysen eine ausführlichere Zusammenfassung vorangestellt, die einen verständlichen und fokussierten Zugang auch für nicht-sozialwissenschaftliche Leser:innnen bieten soll
Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts
No full textThe Covid-19 disease has caused a world-wide pandemic with more than 60 million positive cases and more than 1.4 million deaths by the end of November 2020. As long as effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, self-isolation and quarantine as well as far-reaching shutdowns of economic activity and public life are the only available strategies to prevent the virus from spreading. These interventions must meet conflicting requirements where some objectives, like the minimization of disease-related deaths or the impact on health systems, demand for stronger counter-measures, while others, such as social and economic costs, call for weaker counter-measures. Therefore, finding the optimal compromise of counter-measures requires the solution of a multi-objective optimization problem that is based on accurate prediction of future infection spreading for all combinations of countermeasures under consideration. We present a strategy for construction and solution of such a multi-objective optimization problem with real-world applicability. The strategy is based on a micro-model allowing for accurate prediction via a realistic combination of person-centric data-driven human mobility and behavior, stochastic infection models and disease progression models including micro-level inclusion of governmental intervention strategies. For this micro-model, a surrogate macro-model is constructed and validated that is much less computationally expensive and can therefore be used in the core of a numerical solver for the multi-objective optimization problem. The resulting set of optimal compromises between countermeasures (Pareto front) is discussed and its meaning for policy decisions is outlined.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThe work on this paper was funded by the German Ministry of research and education (BMBF) (project ID: 01KX2022A) and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy via MATH+: The Berlin Mathematics Research Center (EXC-2046/1, project ID: 390685689).Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:Zuse Institute BerlinAll necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesAll data is available through public sources, see refs 1 to 7, and 30.https://covid-sim.info