Freie Universität Berlin
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Pulsed fluid release from subducting slabs caused by a scale-invariant dehydration process
No full textThe chemical composition of a rock has a first-order effect on the onset and duration of rock dehydration. We present a multiscale dataset of chemical heterogeneities found in a low-temperature serpentinite from the Mirdita ophiolite in Albania, and we explore the effects of such heterogeneities on slab dehydration during subduction. The dataset consists of chemical and geological mappings from the micron to the meter scale, spanning five orders of magnitude. At each scale, we investigate the interplay of metamorphic reactions as well as porosity and fluid production through thermodynamic modeling along a slab Moho P-T path typical for subducting plates. Notably, our results show that chemical heterogeneities are preserved, regardless of the observation scale, even in the case of local homogenization by events such as the lizardite-antigorite transition. Consequently, scale-invariant patterns of porosity evolution and fluid production along the P-T path emerge, with characteristic peaks for each dehydration reaction. As such, the dehydration behavior on the slab scale seems to be controlled by the processes on the millimeter scale, whereby resulting peaks correspond to pulsed slab fluid release localized in space and time at each scale, along the strike and along the dip of the subducting plate
Structure prediction of protein-ligand complexes from sequence information with Umol
No full textProtein-ligand docking is an established tool in drug discovery and development to narrow down potential therapeutics for experimental testing. However, a high-quality protein structure is required and often the protein is treated as fully or partially rigid. Here we develop an AI system that can predict the fully flexible all-atom structure of protein-ligand complexes directly from sequence information. We find that classical docking methods are still superior, but depend upon having crystal structures of the target protein. In addition to predicting flexible all-atom structures, predicted confidence metrics (plDDT) can be used to select accurate predictions as well as to distinguish between strong and weak binders. The advances presented here suggest that the goal of AI-based drug discovery is one step closer, but there is still a way to go to grasp the complexity of protein-ligand interactions fully. Umol is available at: https://github.com/patrickbryant1/Umol
Reaction coordinate flows for model reduction of molecular kinetics
No full textIn this work, we introduce a flow based machine learning approach called reaction coordinate (RC) flow for the discovery of low-dimensional kinetic models of molecular systems. The RC flow utilizes a normalizing flow to design the coordinate transformation and a Brownian dynamics model to approximate the kinetics of RC, where all model parameters can be estimated in a data-driven manner. In contrast to existing model reduction methods for molecular kinetics, RC flow offers a trainable and tractable model of reduced kinetics in continuous time and space due to the invertibility of the normalizing flow. Furthermore, the Brownian dynamics-based reduced kinetic model investigated in this work yields a readily discernible representation of metastable states within the phase space of the molecular system. Numerical experiments demonstrate how effectively the proposed method discovers interpretable and accurate low-dimensional representations of given full-state kinetics from simulations
Application of dimension truncation error analysis to high-dimensional function approximation To appear in: 2022. Springer Verlag, 2024.
No full textParametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty quantification. The model uncertainties are often represented via a series expansion in terms of the parametric variables. In practice, this series expansion needs to be truncated to a finite number of terms, introducing a dimension truncation error to the numerical simulation of a parametric mathematical model. There have been several studies of the dimension truncation error corresponding to different models of the input random field in recent years, but many of these analyses have been carried out within the context of numerical integration. In this paper, we study the L2 dimension truncation error of the parametric model problem. Estimates of this kind arise in the assessment of the dimension truncation error for function approximation in high dimensions. In addition, we show that the dimension truncation error rate is invariant with respect to certain transformations of the parametric variables. Numerical results are presented which showcase the sharpness of the theoretical results
EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation
No full textWe present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state (NESS) systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness, and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an 8D limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics
An effective Hamiltonian for the simulation of open quantum molecular systems
No full textWe discuss the derivation of an effective Hamiltonian for open quantum many-particle systems. The aim is to define an operator that can be used for (molecular) simulations where, through the exchange of energy and matter with the surrounding environment (reservoir), the number of particles, n, becomes a variable of the problem. The Hamiltonian is formally derived from the Von Neumann equation; specifically, we derive an n-hierarchy of equations for the density matrix, ρn, for near equilibrium situations. Such a hierarchy, in case of stationary equilibrium, delivers the standard grand canonical density matrix as it would be expected. We report that a similar Hamiltonian was conjectured, from empirical considerations, in the field of superconductivity. Thus our result also provide a formal basis for this long-standing hypothesis. Finally, an application is discussed for Path Integral simulations of molecular systems
Synchronization and random attractors for reaction jump processes
No full textThis work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at first for the states of the embedded discrete-time Markov chain and then for the augmented Markov chain including also random jump times. We uncover a time-shifted synchronization in the sense that -- after some initial waiting time -- one trajectory exactly replicates another one with a certain time delay. Whether or not such a synchronization behaviour occurs depends on the combination of the initial states. We prove this partial time-shifted synchronization for the special setting of a birth-death process by analyzing the corresponding two-point motion of the embedded Markov chain and determine the structure of the associated random attractor. In this context, we also provide general results on existence and form of random attractors for discrete-time, discrete-space random dynamical systems
High-performance algorithms and applications of long-read mapping and SV detection
No full textAdvances in sequencing technology have facilitated population-scale long-read analysis, in which one of the main challenges is arguably developing high-performance computational pipelines. Sequence alignment and assembly are two main long-read analysis methods. Alignment-based pipelines are commonly more efficient and require less read coverage than assembly-based ones, and thus are more applicable to population-scale analysis. However, alignment-based pipelines are less effective in reconstructing highly diverse structures in ultra-long reads such as intra-read SVs. Here, we propose a new filter-based pipeline that is designed to capture rearrangement signals at an earlier stage than conventional pipelines to improve long-read analysis performance. To this end, we investigated the feasibility and essential methods of the design and assessed the performance of the pipeline. Correspondingly, this work comprises three parts starting with data structure optimizations then module development and finally large-scale assessments. Assessments based on high-quality datasets suggest that filter-based pipelines are comparable to or outperform conventional pipelines in terms of detecting complex intra-read rearrangements and computational efficiency. Therefore, the newly proposed pipeline may further benefit population-scale long-read analysis
Slender vortex filaments in the Boussinesq Approximation
No full textA model for the motion of slender vortex filaments is extended to include the effect of gravity. The model, initially introduced by Callegari and Ting [“Motion of a curved vortex filament with decaying vortical core and axial velocity,” SIAM J. Appl. Math. 35, 148–175 (1978)], is based on a matched asymptotic expansion in which the outer solution, given by the Biot–Savart law, is matched with the inner solution derived from the Navier–Stokes equations. Building on recent work by Harikrishnan et al. [“On the motion of hairpin filaments in the atmospheric boundary layer,” Phys. Fluids 35, 076603 (2023)], the Boussinesq approximation is applied such that the density variations only enter in the gravity term. However, unlike Harikrishnan et al. [“On the motion of hairpin filaments in the atmospheric boundary layer,” Phys. Fluids 35, 076603 (2023)], the density variation enters at a lower order in the asymptotic expansion and, thus, has a more significant impact on the self-induced velocity of the vortex filament. In this regime, which corresponds to the regime studied by Chang and Smith [“The motion of a buoyant vortex filament,” J. Fluid Mech. 857, R1 (2018)], the effect of gravity is given by an alteration of the core constant, which couples the motion of the filament to the motion within the vortical core, in addition to a change in the compatibility conditions (evolution equations), which determine the leading order azimuthal and tangential velocity fields in the vortex core. The results are used to explain certain properties of buoyant vortex rings, as well as qualitatively explore the impact of gravity on tornado-type atmospheric vortices
Leaf: an ultrafast filter for population-scale long-read SV detection
No full textAdvances in sequencing technology have facilitated population-scale long-read structural variant (SV) detection. Arguably, one of the main challenges in population-scale analysis is developing effective computational pipelines. Here, we present a new filter-based pipeline for population-scale long-read SV detection. It better captures SV signals at an early stage than conventional assembly-based or alignment-based pipelines. Assessments in this work suggest that the filter-based pipeline helps better resolve intra-read rearrangements. Moreover, it is also more computationally efficient than conventional pipelines and thus may facilitate population-scale long-read applications