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On the boundary layer arising from fast internal waves dynamics
No full textIn this paper, we investigate the boundary layer arising from the fast internal waves in the Boussinesq equations with the Brunt-Vaisälä frequency of order O(1/ε). For the homogeneous-in-height stratification, previous work by \emph{Desjardins, Lannes, Saut, 3(1):153--192, Water Waves, 2021} establishes uniform-in-ϵ estimates locally in time, with additional constraints on the boundary data initially, which essentially restricts the dynamics in the spatially periodic domain. Removing such constraints, our goal is to investigate the general near-boundary behavior. We observe that the fast internal waves will give rise to large growth of the spatial derivatives in the normal direction of the solutions in the vicinity of the boundary. To capture this phenomenon, we introduce an inviscid boundary layer using a natural scaling. In addition, we investigate the well-posedness of such a boundary layer system in the space of analytic functions
A simple refined DNA minimizer operator enables 2-fold faster computation
No full textMotivation
The minimizer concept is a data structure for sequence sketching. The standard canonical minimizer selects a subset of k-mers from the given DNA sequence by comparing the forward and reverse k-mers in a window simultaneously according to a predefined selection scheme. It is widely employed by sequence analysis such as read mapping and assembly. k-mer density, k-mer repetitiveness (e.g. k-mer bias), and computational efficiency are three critical measurements for minimizer selection schemes. However, there exist trade-offs between kinds of minimizer variants. Generic, effective, and efficient are always the requirements for high-performance minimizer algorithms.
Results
We propose a simple minimizer operator as a refinement of the standard canonical minimizer. It takes only a few operations to compute. However, it can improve the k-mer repetitiveness, especially for the lexicographic order. It applies to other selection schemes of total orders (e.g. random orders). Moreover, it is computationally efficient and the density is close to that of the standard minimizer. The refined minimizer may benefit high-performance applications like binning and read mapping.
Availability and implementation
The source code of the benchmark in this work is available at the github repository https://github.com/xp3i4/mini_benchmar
Thermal isomerization rates in retinal analogues using Ab-Initio molecular dynamics
No full textFor a detailed understanding of chemical processes in nature and industry, we need accurate models of chemical reactions in complex environments. While Eyring transition state theory is commonly used for modeling chemical reactions, it is most accurate for small molecules in the gas phase. A wide range of alternative rate theories exist that can better capture reactions involving complex molecules and environmental effects. However, they require that the chemical reaction is sampled by molecular dynamics simulations. This is a formidable challenge since the accessible simulation timescales are many orders of magnitude smaller than typical timescales of chemical reactions. To overcome these limitations, rare event methods involving enhanced molecular dynamics sampling are employed. In this work, thermal isomerization of retinal is studied using tight-binding density functional theory. Results from transition state theory are compared to those obtained from enhanced sampling. Rates obtained from dynamical reweighting using infrequent metadynamics simulations were in close agreement with those from transition state theory. Meanwhile, rates obtained from application of Kramers' rate equation to a sampled free energy profile along a torsional dihedral reaction coordinate were found to be up to three orders of magnitude higher. This discrepancy raises concerns about applying rate methods to one-dimensional reaction coordinates in chemical reactions
Local well-posedness of a system coupling compressible atmospheric dynamics and a micro-physics model of moisture in air
No full textWe establish here the local-in-time well-posedness of strong solutions with large initial data to a system coupling compressible atmospheric dynamics with a refined moisture model introduced in Hittmeir and Klein (Theor. Comput. Fluid Dyn. 32:137--164, 2018). This micro-physics moisture model is a refinement of the one communicated by Klein and Majda (Theor. Comput. Fluid Dyn. 20:525--551, 2006), which serves as a foundation of multi-scale asymptotic expansions for moist deep convection in the atmosphere. Specifically, we show, in this paper, that the system of compressible Navier--Stokes equations coupled with the moisture dynamics is well-posed. In particular, the micro-physics of moisture model incorporates the phase changes of water in moist air
Neural parameter calibration and uncertainty quantification for epidemic forecasting
No full textThe recent COVID-19 pandemic has thrown the importance of accurately forecasting contagion dynamics and learning infection parameters into sharp focus. At the same time, effective policy-making requires knowledge of the uncertainty on such predictions, in order, for instance, to be able to ready hospitals and intensive care units for a worst-case scenario without needlessly wasting resources. In this work, we apply a novel and powerful computational method to the problem of learning probability densities on contagion parameters and providing uncertainty quantification for pandemic projections. Using a neural network, we calibrate an ODE model to data of the spread of COVID-19 in Berlin in 2020, achieving both a significantly more accurate calibration and prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The uncertainties on our predictions provide meaningful confidence intervals e.g. on infection figures and hospitalisation rates, while training and running the neural scheme takes minutes where MCMC takes hours. We show convergence of our method to the true posterior on a simplified SIR model of epidemics, and also demonstrate our method’s learning capabilities on a reduced dataset, where a complex model is learned from a small number of compartments for which data is available
Sub-membrane actin rings compartmentalize the plasma membrane
No full textThe compartmentalization of the plasma membrane (PM) is a fundamental feature of cells. The diffusivity of membrane proteins is significantly lower in biological than in artificial membranes. This is likely due to actin filaments, but assays to prove a direct dependence remain elusive. We recently showed that periodic actin rings in the neuronal axon initial segment (AIS) confine membrane protein motion between them. Still, the local enrichment of ion channels offers an alternative explanation. Here we show, using computational modeling, that in contrast to actin rings, ion channels in the AIS cannot mediate confinement. Furthermore, we show, employing a combinatorial approach of single particle tracking and super-resolution microscopy, that actin rings are close to the PM and that they confine membrane proteins in several neuronal cell types. Finally, we show that actin disruption leads to loss of compartmentalization. Taken together, we here develop a system for the investigation of membrane compartmentalization and show that actin rings compartmentalize the PM
Partial mean-field model for neurotransmission dynamics
No full textThis article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios
A Koopman-Takens theorem: Linear least squares prediction of nonlinear time series
No full textThe least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations. We consider observation sequences of deterministic dynamics, and ask: Which pairs of observation function and dynamics are predictable? If one allows for nonlinear mappings of time-delayed observations, then Takens' well-known theorem implies that a set of pairs, large in a specific topological sense, exists for which an exact prediction is possible. We show that a similar statement applies for the linear least squares filter in the infinite-delay limit, by considering the forecast problem for invertible measure-preserving maps and the Koopman operator on square-integrable functions
Dynamical Reweighting for Biased Rare Event Simulations
No full textDynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces
Combining LLMs and Knowledge Graphs to Reduce Hallucinations in Question Answering
No full textAdvancements in natural language processing have revolutionized the way we can interact with digital information systems, such as databases, making them more accessible. However, challenges persist, especially when accuracy is critical, as in the biomedical domain. A key issue is the hallucination problem, where models generate information unsupported by the underlying data, potentially leading to dangerous misinformation. This paper presents a novel approach designed to bridge this gap by combining Large Language Models (LLM) and Knowledge Graphs (KG) to improve the accuracy and reliability of question-answering systems, on the example of a biomedical KG. Built on the LangChain framework, our method incorporates a query checker that ensures the syntactical and semantic validity of LLM-generated queries, which are then used to extract information from a Knowledge Graph, substantially reducing errors like hallucinations. We evaluated the overall performance using a new benchmark dataset of 50 biomedical questions, testing several LLMs, including GPT-4 Turbo and llama3:70b. Our results indicate that while GPT-4 Turbo outperforms other models in generating accurate queries, open-source models like llama3:70b show promise with appropriate prompt engineering. To make this approach accessible, a user-friendly web-based interface has been developed, allowing users to input natural language queries, view generated and corrected Cypher queries, and verify the resulting paths for accuracy. Overall, this hybrid approach effectively addresses common issues such as data gaps and hallucinations, offering a reliable and intuitive solution for question answering systems. The source code for generating the results of this paper and for the user-interface can be found in our Git repository