arXiv subjects

Max Schmidt

Publications and source records attributed to Max Schmidt.

4 recordsLinked to original sources

arXiv2023

Power iteration for matrices with power series entries

We prove the method of power iteration for matrices with at most finite entries from the Levi-Civita field $\mathcal C$ under the assumption that there exists an eigenvalue with the strictly largest in absolute value complex part. In this case the weak convergence of a start vector to the eigenvector, that corresponds to the largest eigenvalue, is proven. Further, we prove that the Rayleigh quotient of the largest eigenvector also converges weakly to the corresponding eigenvalue. As a corollary, the same holds for matrices and polynomials over the Puiseux series field. In addition to that, we deliver an implementation of our method in Python.

math.NA↗

arXiv2023

Amenability for unitary groups of C*-algebras

In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal Z$-stable, UCT C*-algebras with torsionfree K_0 using the progress on the Elliott classification program for nuclear C*-algebras as well as Pestov's study of amenability of gauge groups. Based on work of Kirchberg, we provide a counterexample to a question of Ng, who proposed a different characterization in earlier work.

math.OA↗

arXiv2020

Out-of-Distribution Detection for Automotive Perception

Neural networks (NNs) are widely used for object classification in autonomous driving. However, NNs can fail on input data not well represented by the training dataset, known as out-of-distribution (OOD) data. A mechanism to detect OOD samples is important for safety-critical applications, such as automotive perception, to trigger a safe fallback mode. NNs often rely on softmax normalization for confidence estimation, which can lead to high confidences being assigned to OOD samples, thus hindering the detection of failures. This paper presents a method for determining whether inputs are OOD, which does not require OOD data during training and does not increase the computational cost of inference. The latter property is especially important in automotive applications with limited computational resources and real-time constraints. Our proposed approach outperforms state-of-the-art methods on real-world automotive datasets.

cs.CV↗

arXiv2018

On melt solutions for the growth of CaTiO$_3$ crystals

When calcium titanate crystals are grown from stoichiometric melts, they crystallize in the cubic perovskite structure. Upon cooling to room temperature they undergo subsequent phase transitions to tetragonal and orthorhombic modifications. These phase transitions are disruptive and result in severely damaged crystals. This paper presents differential thermal analysis data for several prospective solvents, with the aim to identify a system offering the possibility to perform crystal growth of undistorted CaTiO$_3$ crystals by crystallizing them significantly below the melting point directly in the low temperature modification. From mixtures CaF$_2$:TiO$_2$:CaTiO$_3$ = 3:1:1 (molar ratio) the growth of undistorted, at least millimeter-sized CaTiO$_3$ crystals is possible.

cond-mat.mtrl-sci↗