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Model reduction and uncertainty quantification of multiscale diffusions with parameter uncertainties using nonlinear expectations
No full textAbstract: In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of the slow process in the limit of infinite scale separation. The aim of our work is two-fold: Firstly, we want to propose a general framework for averaging and homogenisation of multiscale systems with parametric uncertainties in the drift or in the diffusion coefficient. Secondly, we want to use this framework to quantify the uncertainty in the reduced system by deriving a limit equation that represents a worst-case scenario for any given (possibly path-dependent) quantity of interest. We do so by reformulating the slow-fast system as an optimal control problem in which the unknown parameter plays the role of a control variable that can take values in a closed bounded set. For systems with unknown diffusion coefficient, the underlying stochastic control problem admits an interpretation in terms of a stochastic differential equation driven by a G-Brownian motion. We prove convergence of the slow process with respect to the nonlinear expectation on the probability space induced by the G-Brownian motion. The idea here is to formulate the nonlinear dynamic programming equation of the underlying control problem as a forward-backward stochastic differential equation in the G-Brownian motion framework (in brief: G-FBSDE), for which convergence can be proved by standard means. We illustrate the theoretical findings with two simple numerical examples, exploiting the connection between fully nonlinear dynamic programming equations and second-order BSDE (2BSDE): a linear quadratic Gaussian regulator problem and a bilinear multiplicative triad that is a standard benchmark system in turbulence and climate modelling
Mechanical test data of quartz sand, garnet sand, gypsum powder (plaster), kaolin and sand-plaster mixtures used as granular analogue materials in geoscience laboratory experiments
No full textThis dataset provides mechanical test data for quartz sand (“MAM1ST-300”, Sibelco, Mol, Belgium), gypsum powder (plaster; “Goldband”, Knauf), kaolin clay powder, garnet sand, and mixtures of quartz sand and gypsum powder, used at the Analogue Laboratory of the Department of Geography at the Vrije Universiteit Brussel, Brussels, Belgium, for simulating brittle rocks in the upper crust (Poppe et al., 2019). The measured properties are density ρ, tensile strength T0, shear strength σ, obtained by density measurements, ring-shear tests (RST; at Helmholtz Centre Potsdam GFZ, Germany), direct shear tests, traction tests (at University of Maine, Le Mans, France) and extension tests. The obtained tensile strengths and shear strengths reconstruct two-dimensional failure envelopes for each material. By fitting linear Coulomb and non-linear combined Griffith failure criteria to the characterised failure envelopes (Jaeger et al., 2007), the internal friction coefficient µC, Coulomb cohesion CC and Griffith cohesion CG are obtained. The influence of the material emplacement technique has been investigated in Poppe et al. (2021) to which this data set is supplementary, by repeat characterisation of the above physical parameters under three emplacement conditions, i.e. sieving, pouring (non-dried state) and compaction after pouring (oven-dried state).
We find that densities of the materials and mixtures range from ~1600 kg.m³ (sieved) and ~1700 kg.m³ (compacted) for pure quartz sand to ~600 kg.m³ (poured) to ~900 kg.m³ (compacted) for pure plaster. Tensile strengths range from ~166 Pa (sand) to ~425 Pa (plaster). Velocity ring-shear tests on a 90 wt% quartz sand – 10 wt% plaster mixture show a minor shear rate-weakening of <2% per ten-fold increase in shear velocity. The materials show a behavior ranging from Mohr-Coulomb behavior for the materials with coarser grain size (sands) to combined Griffith-Mohr-Coulomb behavior for the powder materials (plaster, kaolin), with the sand-plaster mixtures occupying a spectrum between both end-members. Peak friction coefficients range from ~0.5 (sand) to ~0.6 (plaster) with a maximum of ~0.9 (80:20 wt% sand:plaster), peak Coulomb cohesions range from 13 Pa (sand) to 248 Pa (plaster), peak Griffith cohesions range from ~10 Pa (sand) to ~425 Pa (plaster)
Insights into reaction kinetics in confined space: real time observation of water formation under a silica cover
No full textWe offer a comprehensive approach to determine howphysical confinement can affect the water formation reaction. By using free-standing crystalline SiO2bilayer supported on Ru(0001) as a model system,we studied the water formation reaction under confinement in situ and inreal time. Low-energy electron microscopy reveals that the reaction proceedsvia the formation of reaction fronts propagating across the Ru(0001) surface.The Arrhenius analyses of the front velocity yield apparent activationenergies (Eaapp) of 0.32 eV for the confined and 0.59 eV for the nonconfinedreaction. DFT simulations indicate that the rate-determining step remainsunchanged upon confinement, therefore ruling out the widely acceptedtransition state effect. Additionally, H2O accumulation cannot explain thechange inEaappfor the confined cases studied because its concentrationremains low. Instead, numerical simulations of the proposed kinetic modelsuggest that the H2adsorption process plays a decisive role in reproducing the Arrhenius plot
Transfer Operators from Optimal Transport Plans for Coherent Set Detection
No full textAbstract
The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows. For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow’s domain. The other is concerned with reconstructing a flow field from observations of its action on a measure, which we address by optimal transport. We show that the framework of optimal transport is well suited for delivering the formal requirements on which a coherent-set analysis can be based on. The necessary noise-robustness requirement of coherence can be matched by the computationally efficient concept of unbalanced regularized optimal transport. Moreover, the applied regularization can be interpreted as an optimal way of retrieving the full dynamics given the extremely restricted information of an initial and a final particle distribution moving according to Brownian motion
Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Get PDFOptimal control of diffusion processes is intimately connected to the problem of solving
certain Hamilton–Jacobi–Bellman equations. Building on recent machine learning inspired
approaches towards high-dimensional PDEs, we investigate the potential of iterative diffusion
optimisation techniques, in particular considering applications in importance sampling and
rare event simulation, and focusing on problems without diffusion control, with linearly
controlled drift and running costs that depend quadratically on the control. More generally,
our methods apply to nonlinear parabolic PDEs with a certain shift invariance. The choice of
an appropriate loss function being a central element in the algorithmic design, we develop a
principled framework based on divergences between path measures, encompassing various
existing methods. Motivated by connections to forward-backward SDEs, we propose and
study the novel log-variance divergence, showing favourable properties of corresponding
Monte Carlo estimators. The promise of the developed approach is exemplified by a range
of high-dimensional and metastable numerical examples
Positive Selection in Gene Regulatory Factors Suggests Adaptive Pleiotropic Changes During Human Evolution
No full textGene regulatory factors (GRFs), such as transcription factors, co-factors and histone-modifying enzymes, play many important roles in modifying gene expression in biological processes. They have also been proposed to underlie speciation and adaptation. To investigate potential contributions of GRFs to primate evolution, we analyzed GRF genes in 27 publicly available primate genomes. Genes coding for zinc finger (ZNF) proteins, especially ZNFs with a Krüppel-associated box (KRAB) domain were the most abundant TFs in all genomes. Gene numbers per TF family differed between all species. To detect signs of positive selection in GRF genes we investigated more than 3,000 human GRFs with their more than 70,000 orthologs in 26 non-human primates. We implemented two independent tests for positive selection, the branch-site-model of the PAML suite and aBSREL of the HyPhy suite, focusing on the human and great ape branch. Our workflow included rigorous procedures to reduce the number of false positives: excluding distantly similar orthologs, manual corrections of alignments, and considering only genes and sites detected by both tests for positive selection. Furthermore, we verified the candidate sites for selection by investigating their variation within human and non-human great ape population data. In order to approximately assign a date to positively selected sites in the human lineage, we analyzed archaic human genomes. Our work revealed with high confidence five GRFs that have been positively selected on the human lineage and one GRF that has been positively selected on the great ape lineage. These GRFs are scattered on different chromosomes and have been previously linked to diverse functions. For some of them a role in speciation and/or adaptation can be proposed based on the expression pattern or association with human diseases, but it seems that they all contributed independently to human evolution. Four of the positively selected GRFs are KRAB-ZNF proteins, that induce changes in target genes co-expression and/or through arms race with transposable elements. Since each positively selected GRF contains several sites with evidence for positive selection, we suggest that these GRFs participated pleiotropically to phenotypic adaptations in humans
Canalization and developmental stability of the yellow-necked mouse (Apodemus flavicollis) mandible and cranium related to age and nematode parasitism
No full textBackground
Mammalian mandible and cranium are well-established model systems for studying canalization and developmental stability (DS) as two elements of developmental homeostasis. Nematode infections are usually acquired in early life and increase in intensity with age, while canalization and DS of rodent skulls could vary through late postnatal ontogeny. We aimed to estimate magnitudes and describe patterns of mandibular and cranial canalization and DS related to age and parasite intensity (diversity) in adult yellow-necked mice (Apodemus flavicollis).
Results
We found the absence of age-related changes in the levels of canalization for mandibular and cranial size and DS for mandibular size. However, individual measures of mandibular and cranial shape variance increased, while individual measures of mandibular shape fluctuating asymmetry (FA) decreased with age. We detected mandibular and cranial shape changes during postnatal ontogeny, but revealed no age-related dynamics of their covariance structure among and within individuals. Categories regarding parasitism differed in the level of canalization for cranial size and the level of DS for cranial shape. We observed differences in age-related dynamics of the level of canalization between non-parasitized and parasitized animals, as well as between yellow-necked mice parasitized by different number of nematode species. Likewise, individual measures of mandibular and cranial shape FA decreased with age for the mandible in the less parasitized category and increased for the cranium in the most parasitized category.
Conclusions
Our age-related results partly agree with previous findings. However, no rodent study so far has explored age-related changes in the magnitude of FA for mandibular size or mandibular and cranial FA covariance structure. This is the first study dealing with the nematode parasitism-related canalization and DS in rodents. We showed that nematode parasitism does not affect mandibular and cranial shape variation and covariance structure among and within individuals. However, parasite intensity (diversity) is related to ontogenetic dynamics of the levels of canalization and DS. Overall, additional studies on animals from natural populations are required before drawing some general conclusions
Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics
No full textA novel approach to simulate simple protein–ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein–protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein–protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package
Airborne virus transmission via respiratory droplets: Effects of droplet evaporation and sedimentation
No full textAirborne transmission is considered as an important route for the spread of infectious diseases, such as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), and is primarily determined by the droplet sedimentation time, that is, the time droplets spend in air before reaching the ground. Evaporation increases the sedimentation time by reducing the droplet mass. In fact, small droplets can, depending on their solute content, almost completely evaporate during their descent to the ground and remain airborne as so-called droplet nuclei for a long time. Considering that viruses possibly remain infectious in aerosols for hours, droplet nuclei formation can substantially increase the infectious viral air load. Accordingly, the physical-chemical factors that control droplet evaporation and sedimentation times and play important roles in determining the infection risk from airborne respiratory droplets are reviewed in this article
Reachability Analysis of Randomly Perturbed Hamiltonian Systems
No full textAbstract
In this paper, we revisit energy-based concepts of controllability and reformulate them for control-affine nonlinear systems perturbed by white noise. Specifically, we discuss the relation between controllability of deterministic systems and the corresponding stochastic control systems in the limit of small noise and in the case in which the target state is a measurable subset of the state space. We derive computable expression for hitting probabilities and mean first hitting times in terms of empirical Gramians, when the dynamics is given by a Hamiltonian system perturbed by dissipation and noise, and provide an easily computable expression for the corresponding controllability function as a function of a subset of the state variables