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Hot subdwarfs (sdO/B) are the stripped helium cores of red giants formed by binary interactions. Close hot subdwarf binaries with massive white dwarf companions have been proposed as possible progenitors of thermonuclear supernovae type Ia (SN Ia). If the supernova is triggered by stable mass transfer from the helium star, the companion should survive the explosion and should be accelerated to high velocities. The hypervelocity star US 708 is regarded as the prototype for such an ejected companion. To find more of those objects we conducted an extensive spectroscopic survey. Candidates for such fast stars have been selected from the spectroscopic database of the Sloan Digital Sky Survey (SDSS) and several ground-based proper motion surveys. Follow-up spectroscopy has been obtained with several 4m- to 10m-class telescopes. Combining the results from quantitative spectroscopic analyses with space-based astrometry from \textit{Gaia} Early Data Release 3 (EDR3) we determined the atmospheric and kinematic parameters of 53 fast hot subdwarf stars. None of these stars is unbound to the Galaxy, although some have Galactic restframe velocities close to the Galactic escape velocity. 21 stars are apparently single objects, which crossed the Galactic disc within their lifetimes in the sdO/B stage and could be regarded as potential candidates for the SN Ia ejection scenario. However, the properties of the full sample are more consistent with a pure old Galactic halo population. We therefore conclude that the fast sdO/B stars we found are likely to be extreme halo stars., Comment: 22 pages, A&A accepted

We propose a new full discretization of the Biot's equations in poroelasticity. The construction is driven by the inf-sup theory, which we recently developed. It builds upon the four-field formulation of the equations obtained by introducing the total pressure and the total fluid content. We discretize in space with Lagrange finite elements and in time with backward Euler. We establish inf-sup stability and quasi-optimality of the proposed discretization, with robust constants with respect to all material parameters. We further construct an interpolant showing how the error decays for smooth solutions.

We analyze the two-field formulation of the quasi-static Biot's equations by means of the inf-sup theory. For this purpose, we exploit an equivalent four-field formulation of the equations, introducing the so-called total pressure and total fluid content as independent variables. We establish existence, uniqueness and stability of the solution. Our stability estimate is two-sided and robust, meaning that the regularity established for the solution matches the regularity requirements for the data and the involved constants are independent of all material parameters. We prove also that additional regularity in space of the data implies, in some cases, corresponding additional regularity in space of the solution. These results are instrumental to the design and the analysis of discretizations enjoying accurate stability and error estimates.

The Burton-Miller method is a widely used approach in acoustics to enhance the stability of the boundary element method for exterior Helmholtz problems at so-called critical frequencies. This method depends on a coupling parameter $\eta$ and it can be shown that as long as $\eta$ has an imaginary part different from 0, the boundary integral formulation for the Helmholtz equation has a unique solution at all frequencies. A popular choice for this parameter is $\eta = \frac{\mathrm{i}}{k}$, where $k$ is the wavenumber. It can be shown that this choice is quasi optimal, at least in the high frequency limit. However, especially in the low frequency region, where the critical frequencies are still sparsely distributed, different choices for this factor result in a smaller condition number and a smaller error of the solution. In this work, alternative choices for this factor are compared based on numerical experiments. Additionally, a way to enhance the Burton-Miller solution with $\eta = \frac{\mathrm{i}}{k}$ for a sound hard scatterer in the low frequency region by an additional step of a modified Richardson iteration is introduced., Comment: 14 pages, 9 figures

For a commutative finite $\mathbb{Z}$-algebra, i.e., for a commutative ring $R$ whose additive group is finitely generated, it is known that the group of units of $R$ is finitely generated, as well. Our main results are algorithms to compute generators and the structure of this group. This is achieved by reducing the task first to the case of reduced rings, then to torsion-free reduced rings, and finally to an order in a reduced ring. The simplified cases are treated via a calculation of exponent lattices and various algorithms to compute the minimal primes, primitive idempotents, and other basic objects. All algorithms have been implemented and are available as a SageMath package. Whenever possible, the time complexity of the described methods is tracked carefully., Comment: 16 pages; published in the journal of Groups, Complexity, Cryptology

Let $K$ be a field and $P=K[x_1,\dots,x_n]$. The technique of elimination by substitution is based on discovering a coherently $Z=(z_1,\dots,z_s)$-separating tuple of polynomials $(f_1,\dots,f_s)$ in an ideal $I$, i.e., on finding polynomials such that $f_i = z_i - h_i$ with $h_i \in K[X \setminus Z]$. Here we elaborate on this technique in the case when $P$ is non-negatively graded. The existence of a coherently $Z$-separating tuple is reduced to solving several $P_0$-module membership problems. Best separable re-embeddings, i.e., isomorphisms $P/I \longrightarrow K[X \setminus Z] / (I \cap K[X \setminus Z])$ with maximal $\#Z$, are found degree-by-degree. They turn out to yield optimal re-embeddings in the positively graded case. Viewing $P_0 \longrightarrow P/I$ as a fibration over an affine space, we show that its fibers allow optimal $Z$-separating re-embeddings, and we provide a criterion for a fiber to be isomorphic to an affine space. In the last section we introduce a new technique based on the solution of a unimodular matrix problem which enables us to construct automorphisms of $P$ such that additional $Z$-separating re-embeddings are possible. One of the main outcomes is an algorithm which allows us to explicitly compute a homogeneous isomorphism between $P/I$ and a non-negatively graded polynomial ring if $P/I$ is regular., Comment: 26 pages

Localizing linearly moving sound sources using microphone arrays is challenging as the transient nature of the signal leads to relatively short observation periods. Commonly, a moving focus is used and most methods operate at least partially in the time domain. In contrast, this manuscript presents an inverse source localization algorithm for uniformly moving single-frequency sources that acts entirely in the frequency domain. For this, a 2.5D approach is utilized and a transfer function between sources and a microphone grid is derived. By solving a least squares problem using the data at the microphone grid, the unknown source distribution in the moving frame can be determined. First, the time signals need to be transformed from time into frequency domain using a windowed discrete Fourier transform (DFT), which leads to spectral leakage that depends on the length of the time interval and the analysis window used. To include spectral leakage in the numerical model, the calculation of the transfer matrix is modified using the Fourier transform of the analysis window in the DFT applied to the measurements. Currently, this approach is limited to single-frequency sources as this restriction allows for simplified calculations and reduces the computational effort. The least squares problem is solved using a Tikhonov regularization and an L-curve approach. As moving sources are considered, utilizing the Doppler effect enhances the stability of the system by combining the transfer functions for multiple frequencies in the measured signals. The performance is validated using simulated data of a moving point source with or without a reflecting ground. Numerical experiments are performed to show the effect of the choice of frequencies in the receiver spectrum, the effect of the DFT, the source frequency, the distance between source and receiver, and the robustness with respect to noise., Comment: 35 pages, 17 figures

Sleep stage classification is a widely discussed topic, due to its importance in the diagnosis of sleep disorders, e.g. insomnia. Analysis of the brain activity during sleep is necessary to gain further insight into the processing that occurs in our brains. We want to use permutation entropy as a model for this analysis. Therefore, the signal processing in terms of electroencephalography is described. This results in a time discrete signal, that can be further processed by applying the method of permutation entropy, which is a modification of the Shannon entropy as a measure of information processing. The method is applied to 18 data sets, nine electroencephalography measurements of patients suffering from insomnia and nine of people without a sleep disorder. A strong correlation between the permutation entropy value and the sleep stages was found during the simulation runs. The results are analysed and presented using boxplot diagrams of the permutation entropy over the sleep stages. Furthermore, it is investigated that there is a steady decrease in the value when the patient is in a deeper sleep. This suggests that the method is a good parameter for sleep stage classification. Finally, we propose an extension of the conceptual model to other pathological conditions and also to the analysis of brain activity during surgery., Comment: 14 pages, 5 figures, included in abstract volume of the 11th EUROSIM Congress on Modelling and Simulation

This paper introduces the XOR-OR-AND normal form (XNF) for logical formulas. It is a generalization of the well-known Conjunctive Normal Form (CNF) where literals are replaced by XORs of literals. As a first theoretic result, we show that every CNF formula is equisatisfiable to a formula in 2-XNF, i.e., a formula in XNF where each clause involves at most two XORs of literals. Subsequently, we present an algorithm which converts Boolean polynomials efficiently from their Algebraic Normal Form (ANF) to formulas in 2-XNF. Experiments with the cipher ASCON-128 show that cryptographic problems, which by design are based strongly on XOR-operations, can be represented using far fewer variables and clauses in 2-XNF than in CNF. In order to take advantage of this compact representation, new SAT solvers based on input formulas in 2-XNF need to be designed. By taking inspiration from graph-based 2-CNF SAT solving, we devise a new DPLL-based SAT solver for formulas in 2-XNF. Among others, we present advanced pre- and in-processing techniques. Finally, we give timings for random 2-XNF instances and instances related to key recovery attacks on round reduced ASCON-128, where our solver outperforms state-of-the-art alternative solving approaches., Comment: 27 pages, 3 figures; revised version; source code available at http://github.com/j-danner/2xnf_sat_solving

The calculation of the acoustic field in or around objects is an important task in acoustic engineering. To numerically solve this task, the boundary element method (BEM) is a commonly used method especially for infinite domains. The open source tool Mesh2HRTF and its BEM core NumCalc provide users with a collection of free software for acoustic simulations without the need of having an in-depth knowledge into numerical methods. However, we feel that users should have a basic understanding with respect to the methods behind the software they are using. We are convinced that this basic understanding helps in avoiding common mistakes and also helps to understand the requirements to use the software. To provide this background is the first motivation for this paper. A second motivation for this paper is to demonstrate the accuracy of NumCalc when solving benchmark problems. Thus, users can get an idea about the accuracy they can expect when using NumCalc as well as the memory and CPU requirements of NumCalc. A third motivation for this paper is to give users detailed information about some parts of the actual implementation that are usually not mentioned in literature, e.g., the specific version of the fast multipole method and its clustering process or how to use frequency-dependent admittance boundary conditions., Comment: 50 pages, 20 figures, corrected typo in Eq. (14)

For a finite $\mathbb{Z}$-algebra $R$, i.e., for a $\mathbb{Z}$-algebra which is a finitely generated $\mathbb{Z}$-module, we assume that $R$ is explicitly given by a system of $\mathbb{Z}$-module generators $G$, its relation module ${\rm Syz}(G)$, and the structure constants of the multiplication in $R$. In this setting we develop and analyze efficient algorithms for computing essential information about $R$. First we provide polynomial time algorithms for solving linear systems of equations over $R$ and for basic ideal-theoretic operations in $R$. Then we develop ZPP (zero-error probabilitic polynomial time) algorithms to compute the nilradical and the maximal ideals of 0-dimensional affine algebras $K[x_1,\dots,x_n]/I$ with $K=\mathbb{Q}$ or $K=\mathbb{F}_p$. The task of finding the associated primes of a finite $\mathbb{Z}$-algebra $R$ is reduced to these cases and solved in ZPPIF (ZPP plus one integer factorization). With the same complexity, we calculate the connected components of the set of minimal associated primes ${\rm minPrimes}(R)$ and then the primitive idempotents of $R$. Finally, we prove that knowing an explicit representation of $R$ is polynomial time equivalent to knowing a strong Gr\"obner basis of an ideal $I$ such that $R = \mathbb{Z}[x_1,\dots,x_n]/I$., Comment: Published in journal of Groups, Complexity, Cryptology

For a finite $\mathbb{Z}$-algebra $R$, i.e., for a ring which is not necessarily associative or unitary, but whose additive group is finitely generated, we construct a decomposition of $R/{\rm Ann}(R)$ into directly indecomposable factors under weak hypotheses. The method is based on constructing and decomposing a ring of scalars $S$, and then lifting the decomposition of $S$ to the bilinear map given by the multiplication of $R$, and finally to $R/{\rm Ann}(R)$. All steps of the construction are given as explicit algorithms and it is shown that the entire procedure has a probabilistic polynomial time complexity in the bit size of the input, except for the possible need to calculate the prime factorization of one integer. In particular, in the case when ${\rm Ann}(R) = 0$, these algorithms compute a direct decomposition of $R$ into directly indecomposable factors., Comment: 31 pages

Given an ideal $I$ in a polynomial ring $K[x_1,\dots,x_n]$ over a field $K$, we present a complete algorithm to compute the binomial part of $I$, i.e., the subideal ${\rm Bin}(I)$ of $I$ generated by all monomials and binomials in $I$. This is achieved step-by-step. First we collect and extend several algorithms for computing exponent lattices in different kinds of fields. Then we generalize them to compute exponent lattices of units in 0-dimensional $K$-algebras, where we have to generalize the computation of the separable part of an algebra to non-perfect fields in characteristic $p$. Next we examine the computation of unit lattices in affine $K$-algebras, as well as their associated characters and lattice ideals. This allows us to calculate ${\rm Bin}(I)$ when $I$ is saturated with respect to the indeterminates by reducing the task to the 0-dimensional case. Finally, we treat the computation of ${\rm Bin}(I)$ for general ideals by computing their cellular decomposition and dealing with finitely many special ideals called $(s,t)$-binomial parts. All algorithms have been implemented in SageMath., Comment: 29 pages

This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The formalization uncovered a number of problems with the existing proofs in the literature. The paper describes how these problems were corrected in the formalization. The work was carried out in the proof assistant Isabelle., Comment: to be published at CADE-29

Given an affine algebra $R=K[x_1,\dots,x_n]/I$ over a field $K$, where $I$ is an ideal in the polynomial ring $P=K[x_1,\dots,x_n]$, we examine the task of effectively calculating re-embeddings of $I$, i.e., of presentations $R=P'/I'$ such that $P'=K[y_1,\dots,y_m]$ has fewer indeterminates. For cases when the number of indeterminates $n$ is large and Gr\"obner basis computations are infeasible, we have previously introduced the method of $Z$-separating re-embeddings. This method tries to detect polynomials of a special shape in $I$ which allow us to eliminate the indeterminates in the tuple $Z$ by a simple substitution process. Here we improve this approach by showing that suitable candidate tuples $Z$ can be found using the Gr\"obner fan of the linear part of $I$. Then we describe a method to compute the Gr\"obner fan of a linear ideal, and we improve this computation in the case of binomial linear ideals using a cotangent equivalence relation. Finally, we apply the improved technique in the case of the defining ideals of border basis schemes., Comment: 21 pages. Minor corrections and improvements. To appear in "Beitr\"age zur Algebra und Geometrie". arXiv admin note: substantial text overlap with arXiv:2207.08115

The extraction of text in high quality is essential for text-based document analysis tasks like Document Classification or Named Entity Recognition. Unfortunately, this is not always ensured, as poor scan quality and the resulting artifacts lead to errors in the Optical Character Recognition (OCR) process. Current approaches using Convolutional Neural Networks show promising results for background removal tasks but fail correcting artifacts like pixelation or compression errors. For general images, Transformer backbones are getting integrated more frequently in well-known neural network structures for denoising tasks. In this work, a modified UNet structure using a Swin Transformer backbone is presented to remove typical artifacts in scanned documents. Multi-headed cross-attention skip connections are used to more selectively learn features in respective levels of abstraction. The performance of this approach is examined regarding compression errors, pixelation and random noise. An improvement in text extraction quality with a reduced error rate of up to 53.9% on the synthetic data is archived. The pretrained base-model can be easily adapted to new artifacts. The cross-attention skip connections allow to integrate textual information extracted from the encoder or in form of commands to more selectively control the models outcome. The latter is shown by means of an example application.

In this paper, we address the challenging problem of detecting bearing faults in railway vehicles by analyzing acoustic signals recorded during regular operation. For this, we introduce Mel Frequency Cepstral Coefficients (MFCCs) as features, which form the input to a simple Multi-Layer Perceptron classifier. The proposed method is evaluated with real-world data that was obtained for state-of-the-art commuter railway vehicles in a measurement campaign. The experiments show that with the chosen MFCC features bearing faults can be reliably detected even for bearing damages that were not included in training., Comment: Accepted at the ICPHM 2023

In this article, we present our contribution to the ICPHM 2023 Data Challenge on Industrial Systems' Health Monitoring using Vibration Analysis. For the task of classifying sun gear faults in a gearbox, we propose a residual Convolutional Neural Network that operates on raw three-channel time-domain vibration signals. In conjunction with data augmentation and regularization techniques, the proposed model yields very good results in a multi-class classification scenario with real-world data despite its relatively small size, i.e., with less than 30,000 trainable parameters. Even when presented with data obtained from multiple operating conditions, the network is still capable to accurately predict the condition of the gearbox under inspection., Comment: Accepted at the IEEE Conference on Prognostics and Health Management (ICPHM) 2023

{In this paper, we address the challenging problem of detecting bearing faults from vibration signals. For this, several time- and frequency-domain features have been proposed already in the past. However, these features are usually evaluated on data originating from relatively simple scenarios and a significant performance loss can be observed if more realistic scenarios are considered. To overcome this, we introduce Mel-Frequency Cepstral Coefficients (MFCCs) and features extracted from the Amplitude Modulation Spectrogram (AMS) as features for the detection of bearing faults. Both AMS and MFCCs were originally introduced in the context of audio signal processing but it is demonstrated that a significantly improved classification performance can be obtained by using these features. Furthermore, to tackle the characteristic data imbalance problem in the context of bearing fault detection, i.e., typically much more data from healthy bearings than from damaged bearings is available, we propose to train a One-class \ac{SVM} with data from healthy bearings only. Bearing faults are then classified by the detection of outliers. Our approach is evaluated with data measured in a highly challenging scenario comprising a state-of-the-art commuter railway engine which is supplied by an industrial power converter and coupled to a load machine., Comment: Accepted at Inter-Noise 2021