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An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration
No full textThe traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e. the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e. a bottom boundary condition that allows for a vertical energy flux and non-reflecting boundary at the top, the atmosphere at rest becomes prone to a novel unstable mode. The validity of assuming a meridionally homogeneous flow is investigated via scale analysis. Numerical experiments were conducted, and Rayleigh damping was used as a numerical approximation for the non-reflecting top boundary. Our three main results are as follows: (i) experiments involving the full Coriolis terms exhibit an exponentially growing instability, yet experiments subjected to the traditional approximation remain stable; (ii) the experimental instability growth rate is close to the theoretical value; (iii) a perturbed version of the unstable mode arises even under sub-optimal bottom boundary conditions. Finally, we conclude our study by discussing the limitations, implications and remaining open questions. Specifically, the influence on numerical deep-atmosphere models and possible physical interpretations of the unstable mode are discussed
Fredholm integral equations for function approximation and the training of neural networks
Get PDFWe present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of the first kind by Ritz-Galerkin discretization, Tikhonov regularization and tensor-train methods. Practical application to supervised learning problems of regression and classification type confirm that the resulting algorithms are competitive with state-of-the-art neural network-based methods.
Patrick , Aizhan , Ral
Ensemble-based gradient inference for particle methods in optimization and sampling
No full textWe propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation of some potential in an ensemble contains implicit information about first or higher order derivatives, which can be made explicit with little computational effort (ensemble-based gradient inference -- EGI). We suggest to use this information for the improvement of established ensemble-based numerical methods for optimization and sampling such as Consensus-based optimization and Langevin-based samplers. Numerical studies indicate that the augmented algorithms are often superior to their gradient-free variants, in particular the augmented methods help the ensembles to escape their initial domain, to explore multimodal, non-Gaussian settings and to speed up the collapse at the end of optimization dynamics.} The code for the numerical examples in this manuscript can be found in the paper's Github repository (https://github.com/MercuryBench/ensemble-based-gradient.git).
Claudia , Claudia , Philip
SARS-CoV-2 Evolution on a Dynamic Immune Landscape
No full textSince the onset of the pandemic, many SARS-CoV-2 variants have emerged, exhibiting substantial evolution in the virus spike protein, the main target of neutralizing antibodies. A plausible hypothesis proposes that the virus evolves to evade antibody-mediated neutralization (vaccine-or infection-induced) to maximize its ability to infect an immunologically experienced population. While virus infection induces neutralizing antibodies, viral evolution may thus navigate on a dynamic immune landscape that resulted from the infection history in different regions. Global inequalities in vaccine distribution and differences in infection-prevention measures have shaped this global immunological landscape, resulting in uneven geographic distributions of SARS-CoV-2 variants. Consequently, predicting which variant will spread within particular regions has become increasingly challenging. To tackle this challenge, we developed a comprehensive mechanistic model of the dynamic immunological landscape of SARS-CoV-2. We utilized deep-mutational scanning data and antibody pharmacokinetics to compute time-dependent cross-neutralization between arbitrary variants. Combined with infection history and molecular surveillance data, we could predict the variant-specific relative number of susceptibles over time, exemplified for Germany. This quantity precisely matched historical variant dynamics, predicted future variant dynamics, and could explain global differences in variant dynamics. Our work strongly supports the hypothesis that SARS-CoV-2 evolution is driven by escape from humoral immunity, allows contextualizing risk assessment of variants
A fuzzy classification framework to identify equivalent atoms in complex materials and molecules
No full textThe nature of an atom in a bonded structure—such as in molecules, in nanoparticles, or in solids, at surfaces or interfaces—depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with equivalent environments is a frequent task, to gain an understanding of the material function, to interpret experimental results, or to simply restrict demanding first-principles calculations. However, while routine, this task can often be challenging for complex molecules or non-ideal materials with breaks in symmetries or long-range order. To automatize this task, we here present a general machine-learning framework to identify groups of (nearly) equivalent atoms. The initial classification rests on the representation of the local atomic environment through a high-dimensional smooth overlap of atomic positions (SOAP) vector. Recognizing that not least thermal vibrations may lead to deviations from ideal positions, we then achieve a fuzzy classification by mean-shift clustering within a low-dimensional embedded representation of the SOAP points as obtained through multidimensional scaling. The performance of this classification framework is demonstrated for simple aromatic molecules and crystalline Pd surface examples
Das Decision Theatre Lab: transdisziplinäre Lehr- und Lernformate in der Mathematik. In: Konstantin Kirpijanov, Thorsten Philipp und Thorsten Roelcke (Hrsg.). Transferwissenschaften: , Verlag Peter Lang, S. 221-238. ISBN (Hardcover) ; (DOI - open access)
No full textWissenstransfer und kooperative Forschung an den Schnittstellen von Universität, Wirtschaft, Politik, Zivilgesellschaft und Kultur gewinnen für alle an Wissensproduktion und Innovationsprozessen beteiligten Akteure und Institutionen zunehmend an Relevanz. Schlüsselwörter wie Transferwissenschaften, Transdisziplinarität und transformative Wissenschaft bestimmen inzwischen die wissenschaftstheoretische Debatte, doch bleiben deren konzeptionelle und terminologische Grundlagen vielfach unklar und umstritten. Welche Mehrwerte, Funktionen, Potentiale und Aporien verbinden sich mit der Idee der Transferwissenschaften? Wie verändert sich ihr Stellenwert in der aktuellen wissenschaftlichen Auseinandersetzung? Inwieweit geht sie mit einer Innovation hochschuldidaktischer Methoden einher
Linear: a framework to enable existing software to resolve structural variants in long reads with flexible and efficient alignment-free statistical models
No full textAlignment is the cornerstone of many long-read pipelines and plays an essential role in resolving structural variants (SVs). However, forced alignments of SVs embedded in long reads, inflexibility of integrating novel SVs models and computational inefficiency remain problems. Here, we investigate the feasibility of resolving long-read SVs with alignment-free algorithms. We ask: (1) Is it possible to resolve long-read SVs with alignment-free approaches? and (2) Does it provide an advantage over existing approaches? To this end, we implemented the framework named Linear, which can flexibly integrate alignment-free algorithms such as the generative model for long-read SV detection. Furthermore, Linear addresses the problem of compatibility of alignment-free approaches with existing software. It takes as input long reads and outputs standardized results existing software can directly process. We conducted large-scale assessments in this work and the results show that the sensitivity, and flexibility of Linear outperform alignment-based pipelines. Moreover, the computational efficiency is orders of magnitude faster
Machine learned coarse-grained protein force-fields: Are we there yet?
No full textThe successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges
Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics
No full textCoarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several small- to medium-sized protein simulations, reproducing the CG equilibrium distribution, and preserving dynamics of all-atom simulations such as protein folding events
Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles
No full textThis theoretical study concerns a pH oscillator based on the urea–urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyze the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms