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Felix Nagel

Publications and source records attributed to Felix Nagel.

10 recordsLinked to original sources
arXiv2025

Multiplicative convolution with symmetries in Euclidean space and on the sphere

Multiplicative convolution $μ\ast ν$ of two finite signed measures $μ$ and $ν$ on $\mathbb{R}^n$ and a related product $μ\circledast ν$ on the sphere $S^{n-1}$ are studied. For fixed $μ$ the injectivity in $ν$ of both operations is characterised given an arbitrary group of reflections along the coordinate axes. The results for the sphere yield generalised versions of the theorems in Molchanov and Nagel (2021) about convex bodies.

math.PR↗
arXiv2022

Numerical boundary control for semilinear hyperbolic systems

This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer the system towards a desired state. The presented approach is based on a Lyapunov stability analysis and a CWENO-type reconstruction.

math.OC↗
arXiv2020

The impact of physiological stress conditions on protein structure and trypsin inhibition of serine protease inhibitor Kazal type 1 (SPINK1) and its N34S variant

One of the most common mutations in the serine protease inhibitor Kazal type 1 (SPINK1) gene is the N34S variant which is strongly associated with chronic pancreatitis. Although it is assumed that N34S mutation constitutes a high-risk factor, the underlying pathologic mechanism is still unknown. In the present study, we investigated the impact of physiological stress factors on SPINK1 protein structure and trypsin inhibitor function using biophysical methods. Our circular dichroism spectroscopy data revealed differences in the secondary structure of SPINK1 and N34S mutant suggesting protein structural changes induced by the mutation as an impairment that could be disease-relevant. We further confirmed that both SPINK1 (KD of 0.15 +/- 0.06 nM) and its N34S variant (KD of 0.08 +/- 0.02 nM) have similar binding affinity and inhibitory effect towards trypsin as shown by surface plasmon resonance and trypsin inhibition assay studies, respectively. We found that stress conditions such as altered ion concentrations (i.e. potassium, calcium), temperature shifts, as well as environmental pH lead to insignificant differences in trypsin inhibition between SPINK1 and N34S mutant. However, we have shown that the environmental pH induces structural changes in both SPINK1 constructs in a different manner. Our findings suggest protein structural changes in the N34S variant as an impairment of SPINK1 and environmental pH shift as a trigger that could play a role in disease progression of pancreatitis.

q-bio.BM↗
arXiv2019

Diagonal Minkowski classes, zonoid equivalence, and stable laws

We consider the family of convex bodies obtained from an origin symmetric convex body $K$ by multiplication with diagonal matrices, by forming Minkowski sums of the transformed sets, and by taking limits in the Hausdorff metric. Support functions of these convex bodies arise by an integral transform of measures on the family of diagonal matrices, equivalently, on Euclidean space, which we call $K$-transform. In the special case, if $K$ is a segment not lying on any coordinate hyperplane, one obtains the family of zonoids and the cosine transform. In this case two facts are known: the vector space generated by support functions of zonoids is dense in the family of support functions of origin symmetric convex bodies; and the cosine transform is injective. We show that these two properties are equivalent for general $K$. For $K$ being a generalised zonoid, we determine conditions that ensure the injectivity of the $K$-transform. Relations to mixed volumes and to a geometric description of one-sided stable laws are discussed. The later probabilistic application gives rise to a family of convex bodies obtained as limits of sums of diagonally scaled $\ell_p$-balls.

math.MG↗
arXiv2016

Swap-invariant and exchangeable random measures

In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. A random vector $ξ$ in $\mathbb{R}^n$ is called swap-invariant if $\,{\mathbf E}\,\big| \!\sum_j u_j ξ_j \big|\,$ is invariant under all permutations of $(ξ_1, \ldots, ξ_n)$ for each $u \in \mathbb{R}^n$. We extend this notion to random measures. For a swap-invariant random measure $ξ$ on a measure space $(S,\mathcal{S},μ)$ the vector $(ξ(A_1), \ldots, ξ(A_n))$ is swap-invariant for all disjoint $A_j \in \mathcal{S}$ with equal $μ$-measure. Various characterizations of swap-invariant random measures and connections to exchangeable ones are established. We prove the ergodic theorem for swap-invariant random measures and derive a representation in terms of the ergodic limit and an exchangeable random measure. Moreover we show that diffuse swap-invariant random measures on a Borel space are trivial. As for random sequences two new representations are obtained using different ergodic limits.

math.PR↗
arXiv2005

Optimal observables and phase-space ambiguities

Optimal observables are known to lead to minimal statistical errors on parameters for a given normalised event distribution of a physics reaction. Thereby all statistical correlations are taken into account. Therefore, on the one hand they are a useful tool to extract values on a set of parameters from measured data. On the other hand one can calculate the minimal constraints on these parameters achievable by any data-analysis method for the specific reaction. In case the final states can be reconstructed without ambiguities optimal observables have a particularly simple form. We give explicit formulae for the optimal observables for generic reactions in case of ambiguities in the reconstruction of the final state and for general parameterisation of the final-state phase space.

hep-ph↗
arXiv2003

Probing triple gauge couplings with transverse beam polarisation in e+e- -> W+W-

The prospects of measuring triple gauge couplings in W pair production at future linear colliders with transverse beam polarisation are studied. We consider CP conserving and CP violating couplings with both real and imaginary parts. The maximum achievable sensitivity in a simultaneous measurement of all couplings is determined using optimal observables, extending an earlier analysis for longitudinal beam polarisation. We find good sensitivity to the coupling Im(g^R_1 + kappa_R), which is not measurable with longitudinal polarisation. In contrast, for the real parts (including the CP violating couplings) the sensitivity is better if both beams are longitudinally polarised. We conclude that a comprehensive measurement of all triple gauge couplings requires both transverse and longitudinal beam polarisation.

hep-ph↗
arXiv2002

Triple gauge couplings in polarised e-e+ -> W-W+ and their measurement using optimal observables

The sensitivity of optimal integrated observables to electroweak triple gauge couplings is investigated for the process e-e+ -> W-W+ -> 4 fermions at future linear colliders. By a suitable reparameterisation of the couplings we achieve that all 28 coupling parameters have uncorrelated statistical errors and are naturally normalised for this process. Discrete symmetry properties simplify the analysis and allow checks on the stability of numerical results. We investigate the sensitivity to the couplings of the normalised event distribution and the additional constraints that can be obtained from the total rate. Particular emphasis is put on the gain in sensitivity one can achieve with longitudinal beam polarisation. We also point out questions that may best be settled with transversely polarised beams. In particular we find that with purely longitudinal polarisation one linear combination of coupling parameters is hardly measurable by means of the normalised event distribution.

hep-ph↗