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Researcher profile

Thomas Friedrich

Thomas Friedrich contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.DGmath-phmath.MPcond-mat.mtrl-sciphysics.flu-dynBiological Physicscond-mat.softeess.IVhep-thmath.ATmath.RTphysics.ins-detphysics.med-ph

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Published work

17 published item(s)

preprint2026arXiv

Model-aided quantification of patient-specific benefit in mitigating radiation induced lymphopenia by particle therapy of cancer

Treatment-related lymphopenia is a frequent and clinically significant consequence of cancer therapy that can compromise immune-mediated tumor control and worsen patient outcomes. Despite its importance, no mechanistic framework exists to accurately predict the severity of lymphopenia from patient-specific data. Here, we present a biokinetic model that quantitatively describes lymphocyte depletion and recovery during and after radiotherapy, integrating radiation dose-volume distributions, blood circulation dynamics, and distinct kinetics of fast- and slow-recovering lymphocyte populations. The model was calibrated and validated using 56 independent clinical datasets encompassing various tumor sites and treatment modalities. It reproduces observed lymphocyte counts and enables prediction of individual severity of lymphopenia from baseline or early-treatment counts. Applying this framework, we demonstrate that particle therapy reduces lymphocyte depletion by ~30% compared with photon therapy, providing a quantitative explanation for its observed immune-sparing benefit. By linking radiation physics, immune kinetics, and clinical outcomes, our model establishes a mechanistically grounded predictive approach for anticipating systemic immune toxicity. Beyond radiotherapy, this framework offers a generalizable strategy for integrating early biological markers into treatment optimization, advancing personalized and immune-preserving cancer therapy.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Phase retrieval from 4-dimensional electron diffraction datasets

We present a computational imaging mode for large scale electron microscopy data, which retrieves a complex wave from noisy/sparse intensity recordings using a deep learning approach and subsequently reconstructs an image of the specimen from the Convolutional Neural Network (CNN) predicted exit waves. We demonstrate that an appropriate forward model in combination with open data frameworks can be used to generate large synthetic datasets for training. In combination with augmenting the data with Poisson noise corresponding to varying dose-values, we effectively eliminate overfitting issues. The U-NET based architecture of the CNN is adapted to the task at hand and performs well while maintaining a relatively small size and fast performance. The validity of the approach is confirmed by comparing the reconstruction to well-established methods using simulated, as well as real electron microscopy data. The proposed method is shown to be effective particularly in the low dose range, evident by strong suppression of noise, good spatial resolution, and sensitivity to different atom types, enabling the simultaneous visualisation of light and heavy elements and making different atomic species distinguishable. Since the method acts on a very local scale and is comparatively fast it bears the potential to be used for near-real-time reconstruction during data acquisition.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Measuring magnetic moments of polydisperse ferrofluids utilizing the inverse Langevin function

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

The classification of naturally reductive homogeneous spaces in dimensions $n \leq 6$

We present a new method for classifying naturally reductive homogeneous spaces -- i.\,e.~homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion \emph{and} curvature. This method is based on a deeper understanding of the holonomy algebra of connections with parallel skew torsion on Riemannian manifolds and the interplay of such a connection with the geometric structure on the given Riemannian manifold. It allows to reproduce by easier arguments the known classifications in dimensions $3,4$, and $5$, and yields as a new result the classification in dimension $6$. In each dimension, one obtains a `hierarchy' of degeneracy for the torsion form, which we then treat case by case. For the completely degenerate cases, we obtain results that are independent of the dimension. In some situations, we are able to prove that any Riemannian manifold with parallel skew torsion has to be naturally reductive. We show that a `generic' parallel torsion form defines a quasi-Sasakian structure in dimension $5$ and an almost complex structure in dimension $6$.

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preprint2012arXiv

Sp(3) structures on 14-dimensional manifolds

The present article investigates Sp(3) structures on 14-dimensional Riemannian manifolds, a continuation of the recent study of manifolds modeled on rank two symmetric spaces (here: SU(6)/Sp(3)). We derive topological criteria for the existence of such a structure and construct large families of homogeneous examples. As a by-product, we prove a general uniqueness criterion for characteristic connections of G structures and that the notions of biinvariant, canonical, and characteristic connections coincide on Lie groups with biinvariant metric.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Spherical sample holders to improve the susceptibility measurement of superparamagnetic materials

The design of two custom sample holders with a spherical cavity for commercial vibrating sample magnetometer systems is described. For such cavities the magnetization M and the internal magnetic field Hi of a sample are both homogeneous. Consequently, the material parameter M(Hi) of a sample can be determined even for liquids and powders with a high magnetic susceptibility.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

A note on the magnetic spatial forcing of a ferrofluid layer

We report on the response of a thin layer of ferrofluid to a spatially modulated magnetic field. This field is generated by means of a constant current in a special arrangement of aluminum wires. The full surface profile of the liquid layer is recorded by means of the absorption of X-rays. The outcome is analyzed particularly with regard to the magnetic self focusing effect under a deformable fluid layer.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Magnetic traveling-stripe-forcing: enhanced transport in the advent of the Rosensweig instability

A new kind of contactless pumping mechanism is realized in a layer of ferrofluid via a spatio-temporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of X-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood semi-quantitatively by considering the magnetically influenced dispersion relation of the fluid.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

A note on flat metric connections with antisymmetric torsion

In this short note we study flat metric connections with antisymmetric torsion $T \neq 0$. The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on $S^7$. The latter case is interesting from the viewpoint of $G_2$-structures and we discuss its type in the sense of the Fernandez-Gray classification. Moreover, we investigate flat metric connections of vectorial type.

0 citations0 reviewsNo code linkedOpen access
preprint2006arXiv

Eigenvalue estimates for Dirac operators with parallel characteristic torsion

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the torsion $T/3$. This operator plays an eminent role in the investigation of such manifolds and includes as special cases Kostant's ``cubic Dirac operator'' and the Dolbeault operator. In this article, we describe a general method of computation for lower bounds of the eigenvalues of $D^{1/3}$ by a clever deformation of the spinorial connection. In order to get explicit bounds, each geometric structure needs to be investigated separately; we do this in full generality in dimension 4 and for Sasaki manifolds in dimension 5.

0 citations0 reviewsNo code linkedOpen access
preprint2005arXiv

Geometric structures of vectorial type

We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion $Γ$ is a closed 1-form (Proposition \ref{dGamma} and Theorem \ref{Fixspinor}). Using a $\mathrm{G}$-invariant spinor we prove a splitting theorem (Proposition \ref{splitting}). The latter result generalizes and unifies a recent result obtained in \cite{Ivanov&Co}, where this splitting has been proved in dimensions $n=7,8$ only. Finally we investigate geometric structures of vectorial type and admitting a characteristic connection $\nabla^{\mathrm{c}}$. An interesting class of geometric structures generalizing Hopf structures are those with a $\nabla^{\mathrm{c}}$-parallel intrinsic torsion $Γ$. In this case, $Γ$ induces a Killing vector field (Proposition \ref{Killing}) and for some special structure groups it is even parallel.

0 citations0 reviewsNo code linkedOpen access
preprint2003arXiv

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form $\T$ as well as a flux 4-form $\F$. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel $\G_2$-geometries and on the homogeneous Aloff-Wallach space. The constraint $\F \cdot Ψ= 0$ defines a non empty subfamily of solutions. We investigate the constraint $\T \cdot Ψ= 0$, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically.

0 citations0 reviewsNo code linkedOpen access
preprint2003arXiv

On the holonomy of connections with skew-symmetric torsion

We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any spinor. Suitable integral formulas allow us to prove similar properties in case of a compact Riemannian manifold equipped with a metric connection of skew-symmetric torsion. On the Aloff-Wallach space N(1,1) we construct families of connections admitting parallel spinors. Furthermore, we investigate the geometry of these connections as well as the geometry of the underlying Riemannian metric. Finally, we prove that any 7-dimensional 3-Sasakian manifold admits $\mathbb{P}^2$-parameter families of linear metric connections and spinorial connections defined by 4-forms with parallel spinors.

0 citations0 reviewsNo code linkedOpen access
preprint2003arXiv

The Casimir operator of a metric connection with skew-symmetric torsion

For any triple $(M^n, g, \nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $Ω$ acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated $\mathrm{G}_2$-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of $\nabla$-parallel spinors.

0 citations0 reviewsNo code linkedOpen access