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Daniel Hoffmann

Publications and source records attributed to Daniel Hoffmann.

9 recordsLinked to original sources
arXiv2023

Construction of adaptive exponential multi-operator splitting methods

We construct splitting methods suitable for the solution of the equations of magnetohydrodynamics (MHD). Due to the physical significance of the involved operators, splittings into three or even four operators with positive coefficients are appropriate for a physically correct and efficient solution of the equations. To efficiently obtain an accurate solution approximation, adaptive choice of the time-steps is important particularly in the light of the unsmooth dynamics of the system. Thus, we construct new method coefficients in conjunction with associated error estimators by optimizing the leading local error term. As a proof of concept, we demonstrate that adaptive splitting faithfully reflects the solution behavior also in the presence of a shock-like behavior for the viscous Burgers equation, which serves as a simplified model problem displaying several features of the Navier-Stokes equation for incompressible flow.

math.NA↗
arXiv2020

Classifier uncertainty: evidence, potential impact, and probabilistic treatment

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of classification performance metrics, based on a probability model of the confusion matrix. Application of our approach to classifiers from the scientific literature and a classification competition shows that uncertainties can be surprisingly large and limit performance evaluation. In fact, some published classifiers are likely to be misleading. The application of our approach is simple and requires only the confusion matrix. It is agnostic of the underlying classifier. Our method can also be used for the estimation of sample sizes that achieve a desired precision of a performance metric.

stat.ML↗
arXiv2017

Locating large flexible ligands on proteins

Many biologically important ligands of proteins are large, flexible, and often charged molecules that bind to extended regions on the protein surface. It is infeasible or expensive to locate such ligands on proteins with standard methods such as docking or molecular dynamics (MD) simulation. The alternative approach proposed here is the scanning of a spatial and angular grid around the protein with smaller fragments of the large ligand. Energy values for complete grids can be computed efficiently with a well-known Fast Fourier Transform accelerated algorithm and a physically meaningful interaction model. We show that the approach can readily incorporate flexibility of protein and ligand. The energy grids (EGs) resulting from the ligand fragment scans can be transformed into probability distributions, and then directly compared to probability distributions estimated from MD simulations and experimental structural data. We test the approach on a diverse set of complexes between proteins and large, flexible ligands, including a complex of Sonic Hedgehog protein and heparin, three heparin sulfate substrates or non-substrates of an epimerase, a multi-branched supramolecular ligand that stabilizes a protein-peptide complex, and a flexible zwitterionic ligand that binds to a surface basin of a Kringle domain. In all cases the EG approach gives results that are in good agreement with experimental data or MD simulations.

q-bio.BM↗
arXiv2017

Trade-off shapes diversity in eco-evolutionary dynamics

We introduce an Interaction and Trade-off based Eco-Evolutionary Model (ITEEM), in which species are competing for common resources in a well-mixed system, and their evolution in interaction trait space is subject to a life-history trade-off between replication rate and competitive ability. We demonstrate that the strength of the trade-off has a fundamental impact on eco-evolutionary dynamics, as it imposes four phases of diversity, including a sharp phase transition. Despite its minimalism, ITEEM produces without further ad hoc features a remarkable range of observed patterns of eco-evolutionary dynamics. Most notably we find self-organization towards structured communities with high and sustainable diversity, in which competing species form interaction cycles similar to rock-paper-scissors games.

q-bio.PE↗
arXiv2016

Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes

The \emph{community}, the assemblage of organisms co-existing in a given space and time, has the potential to become one of the unifying concepts of biology, especially with the advent of high-throughput sequencing experiments that reveal genetic diversity exhaustively. In this spirit we show that a tool from community ecology, the Rank Abundance Distribution (RAD), can be turned by the new MaxRank normalization method into a generic, expressive descriptor for quantitative comparison of communities in many areas of biology. To illustrate the versatility of the method, we analyze RADs from various \emph{generalized communities}, i.e.\ assemblages of genetically diverse cells or organisms, including human B cells, gut microbiomes under antibiotic treatment and of different ages and countries of origin, and other human and environmental microbial communities. We show that normalized RADs enable novel quantitative approaches that help to understand structures and dynamics of complex generalize communities.

q-bio.QM↗
arXiv2014

Existentially closed fields with G-derivations

We prove that the theories of fields with Hasse-Schmidt derivations corresponding to actions of formal groups admit model companions. We also give geometric axiomatizations of these model companions.

math.LO↗
arXiv2012

Integrating Hasse-Schmidt derivations

We study integrating (that is expanding to a Hasse-Schmidt derivation) derivations, and more generally truncated Hasse-Schmidt derivations, satisfying iterativity conditions given by formal group laws. Our results concern the cases of the additive and the multiplicative group laws. We generalize a theorem of Matsumura about integrating nilpotent derivations (such a generalization is implicit in work of Ziegler) and we also generalize a theorem of Tyc about integrating idempotent derivations.

math.AC↗
arXiv1996

Protein dynamics with off-lattice Monte Carlo moves

A Monte Carlo method for dynamics simulation of all-atom protein models is introduced, to reach long times not accessible to conventional molecular dynamics. The considered degrees of freedom are the dihedrals at C$_α$-atoms. Two Monte Carlo moves are used: single rotations about torsion axes, and cooperative rotations in windows of amide planes, changing the conformation globally and locally, respectively. For local moves Jacobians are used to obtain an unbiased distribution of dihedrals. A molecular dynamics energy function adapted to the protein model is employed. A polypeptide is folded into native-like structures by local but not by global moves.

chem-ph↗