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Exploring the Absorption Spectrum of Simulated Water from MHz to Infrared
No full textAbsorption spectra of liquid water at 300 K are calculated from both classical and density functional theory molecular dynamics simulation data, which together span from 1 MHz to hundreds of THz, agreeing well with experimental data qualitatively and quantitatively over the entire range, including the IR modes, the microwave peak, and the intermediate THz bands. The spectra are decomposed into single-molecular and collective components, as well as into components due to molecular reorientations and changes in induced molecular dipole moments. These decompositions shed light on the motions underlying the librational and translational (hydrogen-bond stretching) bands at 20 and 5 THz, respectively; interactions between donor protons and acceptor lone pair electrons are shown to be important for the line shape in both librational and translational regimes, and in- and out-of-phase librational dimer modes are observed and explored
EPIFANY: A Method for Efficient High-Confidence Protein Inference
No full textAccurate protein inference in the presence of shared peptides is still one of the key problems in bottom-up proteomics. Most protein inference tools employing simple heuristic inference strategies are efficient but exhibit reduced accuracy. More advanced probabilistic methods often exhibit better inference quality but tend to be too slow for large data sets. Here, we present a novel protein inference method, EPIFANY, combining a loopy belief propagation algorithm with convolution trees for efficient processing of Bayesian networks. We demonstrate that EPIFANY combines the reliable protein inference of Bayesian methods with significantly shorter runtimes. On the 2016 iPRG protein inference benchmark data, EPIFANY is the only tested method that finds all true-positive proteins at a 5% protein false discovery rate (FDR) without strict prefiltering on the peptide-spectrum match (PSM) level, yielding an increase in identification performance (+10% in the number of true positives and +14% in partial AUC) compared to previous approaches. Even very large data sets with hundreds of thousands of spectra (which are intractable with other Bayesian and some non-Bayesian tools) can be processed with EPIFANY within minutes. The increased inference quality including shared peptides results in better protein inference results and thus increased robustness of the biological hypotheses generated. EPIFANY is available as open-source software for all major platforms at https://OpenMS.de/epifany
A Rigorous Theory of Conditional Mean Embeddings
No full textConditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces by providing a linear-algebraic relation for the kernel mean embeddings of the respective joint and conditional probability distributions. Both centered and uncentered covariance operators have been used to define CMEs in the existing literature. In this paper, we develop a mathematically rigorous theory for both variants, discuss the merits and problems of each, and significantly weaken the conditions for applicability of CMEs. In the course of this, we demonstrate a beautiful connection to Gaussian conditioning in Hilbert spaces
Finite-size corrections for the static structure factor of a liquid slab with open boundaries
Get PDFThe presence of a confining boundary can modify the local structure of a liquid markedly. In addition, small samples of
finite size are known to exhibit systematic deviations of thermodynamic quantities relative to their bulk values. Here, we
consider the static structure factor of a liquid sample in slab geometry with open boundaries at the surfaces, which can
be thought of as virtually cutting out the sample from a macroscopically large, homogeneous fluid. This situation is a
relevant limit for the interpretation of grazing-incidence diffraction experiments at liquid interfaces and films. We derive
an exact, closed expression for the slab structure factor, with the bulk structure factor as the only input. This shows
that such free boundary conditions cause significant differences between the two structure factors, in particular at small
wavenumbers. An asymptotic analysis of this result yields the scaling exponent and an accurate, useful approximation of
these finite-size corrections. Furthermore, the open boundaries permit the interpretation of the slab as an open system,
supporting particle exchange with a reservoir. We relate the slab structure factor to the particle number fluctuations and
discuss conditions under which the subvolume of the slab represents a grand canonical ensemble with chemical potential
� and temperature T. Thus, the open slab serves as a test-bed for the small-system thermodynamics in a �T reservoir.
We provide a microscopically justified and exact result for the size dependence of the isothermal compressibility. Our
findings are corroborated by simulation data for Lennard-Jones liquids at two representative temperatures
A domain mapping approach for elliptic equations posed on random bulk and surface domains
No full textIn this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface systems. In particular, we present the necessary geometric analysis required by the domain mapping method to reformulate elliptic equations on random surfaces onto a fixed deterministic surface using a prescribed stochastic parametrisation of the random domain. An abstract analysis of a finite element discretisation coupled with a Monte-Carlo sampling is presented for the resulting elliptic equations with random coefficients posed over the fixed curved reference domain and optimal error estimates are derived. The results from the abstract framework are applied to a model elliptic problem on a random surface and a coupled elliptic bulk-surface system and the theoretical convergence rates are confirmed by numerical experiments
Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications
No full textThis work is motivated by the goal of designing simulation software for technical devices that, at their functional core, rely on atomistic‐scale processes embedded in a larger‐scale fluid environment. The core of the problem is the conceptual and technical approach for coupling particle and continuum representations of a fluid. The state of the art for key aspects including physical modeling, mathematical formalization, computational implementation, and applications, is discussed and organized in a consistent picture across the relevant physical regimes
Combining Phage Display and Next-generation Sequencing for Materials Sciences: A Case Study on Probing Polypropylene Surfaces
No full textPhage display biopanning with Illumina next-generation sequencing (NGS) is applied to reveal insights into peptide-based adhesion domains for polypropylene (PP). One biopanning round followed by NGS selects robust PP-binding peptides that are not evident by Sanger sequencing. NGS provides a significant statistical base that enables motif analysis, statistics on positional residue depletion/enrichment, and data analysis to suppress false-positive sequences from amplification bias. The selected sequences are employed as water-based primers for PP–metal adhesion to condition PP surfaces and increase adhesive strength by 100% relative to nonprimed PP
Mathematik: Geschlechterforschung in disziplinären Zwischenräumen
No full textFragen zur Relevanz der Kategorie Geschlecht für und innerhalb der Mathematik werden außerhalb des Faches verhandelt. Sie umfassen die Felder Geschichte, Soziologie, Didaktik und Wissenschaftstheorie und bewegen sich in disziplinären Zwischenräumen, da auch Philosophie, Bildungs- und Kulturwissenschaften sich kaum auf die Befassung mit Mathematik und mathematischer Fachkultur einlassen
Investigation of the hydration shell of a membrane in an open system molecular dynamics simulation
No full textWe analyze structural properties of hydration for a biological membrane with the open boundary adaptive resolution molecular dynamics approach in its latest version. A large region of noninteracting pointlike particles (tracers) acts as a reservoir of molecules and energy for the atomistically resolved membrane-water interface. The drastic simplification of the environment and its simple coupling to the high-resolution region has been successfully tested in a previous work on pure liquid water, and this work represents the method's first application to a system with high structural complexity. The successful results and novel methodology allow us to suggest a complementary view to the controversial question of the definition of the hydration shell for a membrane. The adaptive resolution technique allows for a physically well-founded statistical mechanics definition of the hydration shell by quantifying the minimal size of the region where the atomistic resolution of the molecules is strictly required while the rest of the system plays the role of a generic, structureless thermodynamic reservoir
On the incorporation of box-constraints for ensemble Kalman inversion
No full textThe Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties in various areas of applications. In recent years, a complete analysis of the method has been developed for linear inverse problems adopting an optimization viewpoint. However, many applications require the incorporation of additional constraints on the parameters, e.g. arising due to physical constraints. We propose a new variant of the ensemble Kalman inversion to include box constraints on the unknown parameters motivated by the theory of projected preconditioned gradient flows. Based on the continuous time limit of the constrained ensemble Kalman inversion, we discuss a complete convergence analysis for linear forward problems. We adopt techniques from filtering, such as variance inflation, which are crucial in order to improve the performance and establish a correct descent. These benefits are highlighted through a number of numerical examples on various inverse problems based on partial differential equations