Freie Universität Berlin
Repository: Freie Universität Berlin (FU), Math Department (fu_mi_publications)Not a member yet
2251 research outputs found
Sort by
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
No full textWe study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of a parabolic PDE with a random thermal diffusion coefficient, steered by a control function. To account for the presence of uncertainty in the optimal control problem, the objective function is composed with a risk measure. We focus on two risk measures, both involving high-dimensional integrals over the stochastic variables: the expected value and the (nonlinear) entropic risk measure. The high-dimensional integrals are computed numerically using specially designed QMC methods and, under moderate assumptions on the input random field, the error rate is shown to be essentially linear, independently of the stochastic dimension of the problem—and thereby superior to ordinary Monte Carlo methods. Numerical results demonstrate the effectiveness of our method
Lattice-Based Kernel Approximation and Serendipitous Weights for Parametric PDEs in Very High Dimensions
No full textWe describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing the input random field of the system using the model proposed by Kaarnioja, Kuo, and Sloan (SIAM J. Numer. Anal. 2020), in which a countable number of independent random variables enter the random field as periodic functions, it was shown by Kaarnioja, Kazashi, Kuo, Nobile, and Sloan (Numer. Math. 2022) that the lattice-based kernel interpolant can be constructed for the PDE solution as a function of the stochastic variables in a highly efficient manner using fast Fourier transform (FFT). In this work, we discuss the connection between our model and the popular “affine and uniform model” studied widely in the literature of uncertainty quantification for PDEs with uncertain coefficients. We also propose a new class of product weights entering the construction of the kernel interpolant, which dramatically improve the computational performance of the kernel interpolant for PDE problems with uncertain coefficients, and allow us to tackle function approximation problems up to very high dimensionalities. Numerical experiments are presented to showcase the performance of the new weights
Scaling law for the size dependence of a short-ranged quantum gas
No full textIn a recent work [Reible et al., Phys. Rev. Res. 5, 023156 (2023)], it was shown that the mean particle-particle interaction across an ideal surface that divides a system into two parts can be employed to estimate the size dependence for the thermodynamic accuracy of the system. In this work we propose its application to systems with finite-range interactions that model dense quantum gases and derive an approximate size-dependence scaling law. In addition, we show that the application of the criterion is equivalent to the determination of a free-energy response to a perturbation. The latter result confirms the complementarity of the criterion to other estimates of finite-size effects based on direct simulations and empirical structure or energy convergence criteria
Clinical Effectiveness of Ritonavir-Boosted Nirmatrelvir—A Literature Review
No full textNirmatrelvir/Ritonavir is an oral treatment for mild to moderate COVID-19 cases with a high risk for a severe course of the disease. For this paper, a comprehensive literature review was performed, leading to a summary of currently available data on Nirmatrelvir/Ritonavir’s ability to reduce the risk of progressing to a severe disease state. Herein, the focus lies on publications that include comparisons between patients receiving Nirmatrelvir/Ritonavir and a control group. The findings can be summarized as follows: Data from the time when the Delta-variant was dominant show that Nirmatrelvir/Ritonavir reduced the risk of hospitalization or death by 88.9% for unvaccinated, non-hospitalized high-risk individuals. Data from the time when the Omicron variant was dominant found decreased relative risk reductions for various vaccination statuses: between 26% and 65% for hospitalization. The presented papers that differentiate between unvaccinated and vaccinated individuals agree that unvaccinated patients benefit more from treatment with Nirmatrelvir/Ritonavir. However, when it comes to the dependency of potential on age and comorbidities, further studies are necessary. From the available data, one can conclude that Nirmatrelvir/Ritonavir cannot substitute vaccinations; however, its low manufacturing cost and easy administration make it a valuable tool in fighting COVID-19, especially for countries with low vaccination rates
Retentiveness of rare earth elements in garnet with implications for garnet Lu-Hf chronology
No full textIncorporation of rare earth elements (REE) in garnet enables garnet chronology (Sm-Nd, Lu-Hf), and imparts a garnet-stable signature on cogenetic phases, which allows petrochronology and general petrogenetic tracing of garnet stability in minerals and melts. Constraints on the uptake and redistribution mechanisms, as well as on the diffusive behaviour of REE in garnet are required for allowing accurate interpretation of REE signatures and ages. Garnet REE profiles are often measured to gain insight into the nature and cause of REE zoning. Interpretation of such profiles is nevertheless complicated by poor constraints on the extent of diffusive relaxation. This is especially relevant for Lu, which, according to experiments, has a relatively high diffusivity and thus may re-equilibrate with possible consequences for Lu-Hf chronology. To provide new insight into the REE systematics of garnet, we applied quantitative trace-element mapping of garnet grains from metamorphic rocks that record peak temperatures above 750°C and cooling rates as low as 1.5°C Ma−1. Garnet in all samples preserves Rayleigh-type or oscillatory growth zoning with sharply defined interfacial angles that match the garnet habit. Re-equilibration of REE compositions appears restricted to domains with nebulous and patchy zoning, which likely form by interface-coupled dissolution and re-precipitation reactions mediated by fluids or melts, rather than REE volume diffusion. The possible effect of Lu diffusion in the analysed grains was investigated by comparing the observations to the results from 2D numerical modelling using Lu diffusivities from recent diffusion experiments. This test indicates that Lu diffuses significantly slower in natural garnet than experiments predict. The retentiveness of REE in garnet demonstrates the reliability of REE signatures in magmatic tracing and petrochronology and establishes Lu-Hf chronology as a robust means of dating garnet growth and recrystallization in metamorphic rocks, including those that underwent high- or ultrahigh-temperature conditions
Improved Protein Complex Prediction with AlphaFold-Multimer by Denoising the MSA Profile
No full textStructure prediction of protein complexes has improved significantly with AlphaFold2 and AlphaFold-multimer (AFM), but only 60% of dimers are accurately predicted. Here, we learn a bias to the MSA representation that improves the predictions by performing gradient descent through the AFM network. We demonstrate the performance on seven difficult targets from CASP15 and increase the average MMscore to 0.76 compared to 0.63 with AFM. We evaluate the procedure on 487 protein complexes where AFM fails and obtain an increased success rate (MMscore>0.75) of 33% on these difficult targets. Our protocol, AFProfile, provides a way to direct predictions towards a defined target function guided by the MSA. We expect gradient descent over the MSA to be useful for different tasks
An optimal control perspective on diffusion-based generative modeling
No full textWe establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we can formulate diffusion-based generative modeling as a minimization of the Kullback-Leibler divergence between suitable measures in path space. Finally, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. We demonstrate that our time-reversed diffusion sampler (DIS) can outperform other diffusion-based sampling approaches on multiple numerical examples
A novel approach to hydrodynamics for long-range generalized exclusion
No full textWe consider a class of generalized long-range exclusion processes evolving either on Z or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and destination sites, and it is such that the particle displacement has an infinite expectation, but some tail bounds are satisfied. We study the superballisitic scaling limit of the particle density and prove that its space-time evolution is concentrated on the set of weak solutions to a non-local transport equation. Since the stationary states of the dynamics are unknown, we develop a new approach to such a limit relying only on the algebraic structure of the Markovian generator
Pressure gain combustion for gas turbines: Analysis of a fully coupled engine model
No full textThe ``Shockless Explosion Combustion" (SEC) concept for gas turbine combustors, introduced in 2014, approximates constant volume combustion (CVC) by harnessing acoustic confinement of autoigniting gas packets. The resulting pressure waves simultaneously transmit combustion energy to a turbine plenum and facilitate the combustor's recharging against an average pressure gain. Challenges in actualizing an SEC-driven gas turbine include i) the creation of charge stratifications for nearly homogeneous autoignition, ii) protecting the turbo components from combustion-induced pressure fluctuations, iii) providing evidence that efficiency gains comparable to those of CVC over deflagrative combustion can be realized, and iv) designing an effective one-way intake valve. This work addresses challenges i)-iii) utilizing computational engine models incorporating a quasi-one-dimensional combustor, zero- and two-dimensional compressor and turbine plena, and quasi-stationary turbo components. Two SEC operational modes are identified which fire at roughly one and two times the combustors' acoustic frequencies. Results for SEC-driven gas turbines with compressor pressure ratios of 6:1 and 20:1 reveal 1.5-fold mean pressure gains across the combustors. Assuming ideally efficient compressors and turbines, efficiency gains over engines with deflagration-based combustors of 30% and 18% are realized, respectively. With absolute values of 52% and 66%, the obtained efficiencies are close to the theoretical Humphrey cycle efficiencies of 54% and 65% for the mentioned pre-compression ratios. Detailed thermodynamic cycle analyses for individual gas parcels suggest that there is room for further efficiency gains through optimized plenum and combustor designs
Reconstructing extrachromosomal DNA structural heterogeneity from long-read sequencing data using Decoil
No full textCircular extrachromosomal DNA (ecDNA) is a form of oncogene amplification found across cancer types and associated with poor outcome in patients. ecDNA can be structurally complex and can contain rearranged DNA sequences derived from multiple chromosome locations. As the structure of ecDNA can impact oncogene regulation and may indicate mechanisms of its formation, disentangling it at high resolution from sequencing data is essential. Even though methods have been developed to identify and reconstruct ecDNA in cancer genome sequencing, it remains challenging to resolve complex ecDNA structures, in particular amplicons with shared genomic footprints. We here introduce Decoil, a computational method that combines a breakpoint-graph approach with LASSO regression to reconstruct complex ecDNA and deconvolve co-occurring ecDNA elements with overlapping genomic footprints from long-read nanopore sequencing. Decoil outperforms de novo assembly and alignment-based methods in simulated long-read sequencing data for both simple and complex ecDNAs. Applying Decoil on whole-genome sequencing data uncovered different ecDNA topologies and explored ecDNA structure heterogeneity in neuroblastoma tumors and cell lines, indicating that this method may improve ecDNA structural analyses in cancer