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Volker Schmidt

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cond-mat.mtrl-sci Applications math.ST Statistics Theory Biological Physics Computation Machine Learning math.PR Subcellular Processes

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preprint2026arXiv

Statistical analysis of virion-cell interactions mediated by peptide nanofibrils and peptide amphiphiles using STEM tomography

Peptide nanofibrils (PNFs) and peptide amphiphiles (PAs) are promising tools for enhancing viral transduction and gene transfer. However, quantitative insight into how their supramolecular architecture governs virion-cell interactions is limited. Here, we introduce a framework for the acquisition, processing, and statistical analysis of scanning transmission electron microscopy (STEM) tomograms to objectively quantify peptide-virion-cell interactions. Using four transduction-enhancing peptides (D4, Vectofusin-1, palmitic acid-PA (pal-PA), and eicosapentaenoic-PA (eic-PA)), peptide aggregate morphology, interfacial contact areas, and the spatial organization of virions with respect to peptides and cells were analyzed using advanced geometric descriptors. All peptides efficiently captured virions, resulting in few free virions, but they differ in how strictly virions were spatially confined near the cell surface. These differences reflect alternative spatial organization strategies, which are likely crucial factors influencing transduction-enhancing efficacy. Our approach provides a novel, generalizable method to evaluate infection-enhancing nanomaterials and guides the rational design of next-generation peptide assemblies for therapeutic viral delivery.

preprint2023arXiv

Multidimensional characterization of particle morphology and mineralogical composition using CT data and R-vine copulas

Computed tomography (CT) can capture volumes large enough to measure a statistically meaningful number of micron-sized particles with a sufficiently good resolution to allow for the analysis of individual particles. However, the development of methods to efficiently investigate such image data and interpretably model the observed particle features is still an active field of research. When image data of particles exhibiting a wide range of shapes and sizes is considered, traditional image segmentation methods, such as the classic watershed algorithm, struggle to recognize particles with satisfying accuracy. Thus, more advanced methods of machine learning must be utilized for image segmentation to improve the validity of subsequent analyzes. Moreover, CT data does not include information about the mineralogical composition of particles and, therefore, additional SEM-EDS image data has to be acquired. In this paper, micro-CT image data of a particle system mostly consisting of zinnwaldite-quartz composites is considered. First, an image segmentation method is applied which uses deep convolutional neural networks, in particular an adaptation of the U-net architecture. This has the advantage of requiring less hand-labeling than other machine learning methods, while also being more flexible with the possibility of transfer learning. Then, fully parameterized models based on vine copulas are designed to determine multivariate probability distributions of descriptor vectors for the size, shape, texture and composition of particles -- allowing for the estimation and interpretable characterization of interdependencies between particle descriptors. For model fitting, the segmented three-dimensional CT data and co-registered two-dimensional SEM-EDS data are used.

preprint2022arXiv

Classification of FIB/SEM-tomography images for highly porous multiphase materials using random forest classifiers

FIB/SEM tomography represents an indispensable tool for the characterization of three-dimensional nanostructures in battery research and many other fields. However, contrast and 3D classification/reconstruction problems occur in many cases, which strongly limits the applicability of the technique especially on porous materials, like those used for electrode materials in batteries or fuel cells. Distinguishing the different components like active Li storage particles and carbon/binder materials is difficult and often prevents a reliable quantitative analysis of image data, or may even lead to wrong conclusions about structure-property relationships. In this contribution, we present a novel approach for data classification in three-dimensional image data obtained by FIB/SEM tomography and its applications to NMC battery electrode materials. We use two different image signals, namely the signal of the angled SE2 chamber detector and the Inlens detector signal, combine both signals and train a random forest, i.e. a particular machine learning algorithm. We demonstrate that this approach can overcome current limitations of existing techniques suitable for multi-phase measurements and that it allows for quantitative data reconstruction even where current state-of the art techniques fail, or demand for large training sets. This approach may yield as guideline for future research using FIB/SEM tomography.

preprint2022arXiv

Quantitative comparison of different approaches for reconstructing the carbon-binder domain from tomographic image data of cathodes in lithium-ion batteries and its influence on electrochemical properties

It is well known that the spatial distribution of the carbon-binder domain (CBD) offers a large potential to further optimize lithium-ion batteries. However, it is challenging to reconstruct the CBD from tomographic image data obtained by synchrotron tomography. In the present paper, we consider several approaches to segment 3D image data of two different cathodes into three phases, namely active material, CBD and pores. More precisely, we focus on global thresholding, a local closing approach based on EDX data, a k-means clustering method, and a procedure based on a neural network that has been trained by correlative microscopy, i.e., based on data gained by synchrotron tomography and FIB-SEM data representing the same electrode. We quantify the impact of the considered segmentation approaches on morphological characteristics as well as on the resulting performance by spatially-resolved transport simulations. Furthermore, we use experimentally determined electrochemical properties to identify an appropriate range for the effective transport parameter of the CBD. The developed methodology is applied to two differently manufactured cathodes, namely an ultra-thick unstructured cathode and a two-layer cathode with varying CBD content in both layers. This comparison elucidates the impact of a specific structuring concept on the 3D microstructure of cathodes.

preprint2015arXiv

Fitting Laguerre tessellation approximations to tomographic image data

The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.

preprint2014arXiv

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $χ^2$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $β$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.

preprint2012arXiv

Non-parametric asymptotic statistics for the Palm mark distribution of β-mixing marked point processes

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic χ^2-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean-square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable β-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. Our method needs a central limit theorem for β-mixing random fields which is proved by extending Bernstein's blocking technique to non-cubic index sets and seems to be of interest in its own right. By large-scale model-based simulations the performance of our test is studied in dependence of the model parameters which determine the range of spatial correlations.

preprint2007arXiv

Scaling limits for random fields with long-range dependence

This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $λ$ of the sets grows to infinity and the mean volume $ρ$ of the sets tends to zero. Assuming that the volume distribution has a regularly varying tail with infinite variance, we show that the centered and renormalized random field can have three different limits, depending on the relative speed at which $λ$ and $ρ$ are scaled. If $λ$ grows much faster than $ρ$ shrinks, the limit is Gaussian with long-range dependence, while in the opposite case, the limit is independently scattered with infinite second moments. In a special intermediate scaling regime, there exists a nontrivial limiting random field that is not stable.