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Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without an antipode. The proof relies on mixed dihedral braid relations between Demazure operators and simple reflections. For researchers new to Hopf algebroids we include additional examples from ring theory, representation theory, and algebraic geometry.

We identify the structural impulse responses of quantiles of the outcome variable to a shock. Our estimation strategy explicitly distinguishes treatment from control variables, allowing us to model responses of unconditional quantiles while using controls for identification. Disentangling the effect of adding control variables on identification versus interpretation brings our structural quantile impulse responses conceptually closer to structural mean impulse responses. Applying our methodology to study the impact of financial shocks on lower quantiles of output growth confirms that financial shocks have an outsized effect on growth-at-risk, but the magnitude of our estimates is more extreme than in previous studies.

We employ an optical fiber doped with randomly oriented fluorescent sub-micron diamonds and the novel zero-field resonance protocol to collect information on the localization and orientation of a magnetic-field source and its distribution. Many previous demonstrations of diamond-based magnetic field sensing achieved ultrahigh sensitivities down to the fT range warranted by manipulating spin states of the diamond nitrogen vacancy (NV) centers with externally applied radio or microwaves. The application of such oscillating fields is problematic in distributed magnetic-field measurements and may be incompatible with specific targets. Instead of relying on these approaches, we leveraged cross-relaxations of particular spin-state populations of the NV center under a magnetic field, thus observing zero-field resonances and making external radio frequency fields redundant. Combined with an optical fiber sensitive to the magnetic field along its entire length, remote sensing was realized that returned information on the spatial field distribution without using any moving mechanical elements in the detection system. Variation of the spatial parameters of the investigated field was achieved simply by controlling the current in a pair of induction coils easily integrable with optical fibers without limiting the fiber-specific functionality of the optical readout taking place at a fixed location at the optical fiber output. Lifting of the requirements related to the mechanical scanning of the fiber, the application of external fields, and the orientation of the NV centers against the measured field mark a very practical step forward in optically driven magnetic field sensing, not easily achievable with earlier implementations., Comment: 7 pages, 3 figures

Magnetometry using Nitrogen-Vacancy (NV) color centers in diamond predominantly relies on microwave spectroscopy. However, microwaves may hinder certain studies involving biological systems or thin conductive samples. This work demonstrates a wide-field, microwave-free imaging magnetometer utilizing NV centers in nanodiamonds by exploiting the cross-relaxation feature near zero magnetic fields under ambient conditions without applying microwaves. For this purpose, we measure the center shift, contrast, and linewidth of the zero-field cross-relaxation in 140 nm nanodiamonds drop-cast on a current-carrying conductive pattern while scanning a background magnetic field, achieving a sensitivity of 4.5 $\mathrm{\mu T/\sqrt{Hz}}$. Our work allows for applying the NV zero-field feature in nanodiamonds for magnetic field sensing in the zero and low-field regimes and highlights the potential for microwave-free all-optical wide-field magnetometry based on nanodiamonds., Comment: 8 pages, 5 figures

Existing explanation methods for image classification struggle to provide faithful and plausible explanations. This paper addresses this issue by proposing a post-hoc natural language explanation method that can be applied to any CNN-based classifier without altering its training process or affecting predictive performance. By analysing influential neurons and the corresponding activation maps, the method generates a faithful description of the classifier's decision process in the form of a structured meaning representation, which is then converted into text by a language model. Through this pipeline approach, the generated explanations are grounded in the neural network architecture, providing accurate insight into the classification process while remaining accessible to non-experts. Experimental results show that the NLEs constructed by our method are significantly more plausible and faithful. In particular, user interventions in the neural network structure (masking of neurons) are three times more effective than the baselines., Comment: Findings of EMNLP 2024

We report magnetization changes generated by an electric field in ferromagnetic Ga$_{1-x}$Mn$_x$N grown by molecular beam epitaxy. Two classes of phenomena have been revealed. First, over a wide range of magnetic fields, the magnetoelectric signal is odd in the electric field and reversible. Employing a macroscopic spin model and atomistic Landau-Lifshitz-Gilbert theory with Langevin dynamics, we demonstrate that the magnetoelectric response results from the inverse piezoelectric effect that changes the trigonal single-ion magnetocrystalline anisotropy. Second, in the metastable regime of ferromagnetic hystereses, the magnetoelectric effect becomes non-linear and irreversible in response to a time-dependent electric field, which can reorient the magnetization direction. Interestingly, our observations are similar to those reported for another dilute ferromagnetic semiconductor Cr$_x$(Bi$_{1-y}$Sb$_y$)$_{1-x}$Te$_3$, in which magnetization was monitored as a function of the gate electric field. Those results constitute experimental support for theories describing the effects of time-dependent perturbation upon glasses far from thermal equilibrium in terms of an enhanced effective temperature., Comment: 18 pages, 10 Figures

We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum $\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module category over the monoidal category of type $\pm1$ representations in terms of string diagrams and via generators and relations. The idempotents projecting onto the quantized eigenspaces are described as type $B/D$ analogues of Jones--Wenzl projectors. As an application we introduce and give recursive formulas for analogues of $\Theta$-networks., Comment: This is partially based on the second authors Master Thesis from 2022

We implanted Fe$^+$ ions in nanodiamond (ND) powder containing negatively charged nitrogen-vacancy (NV-) centers and studied their Raman spectra and optically detected magnetic resonance (ODMR) in various applied magnetic fields with green light (532 nm) excitation. In Raman spectra, we observed a blue shift of the NV$^-$ peak associated with the conversion of the electronic sp$^3$ configuration to the disordered sp$^2$ one typical for the carbon/graphite structure. In the ODMR spectra, we observed a red shift of the resonance position caused by local heating by an absorptive environment that recovers after annealing. To reveal the red shift mechanism in ODMR, we created a controlled absorptive environment around ND by adding iron-based Fe$_2$O$_3$ and graphitic sp$^2$ powders to the ND suspension. This admixture caused a substantial increase in the observed shift proportional to the applied laser power, corresponding to an increase in the local temperature by 150-180 K. This surprisingly large shift is absent in non-irradiated NV-ND powders, is associated only with the modification of the local temperature by the absorptive environment of NV-NDs and can be studied using ODMR signals of NV$^-$., Comment: 21 pages, 6 figures

We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schr\"odinger operators, use the characterizations for birth-death chains and stability results to characterize essential self-adjointness for star-like graphs, and give some connections to the $\ell^2$-Liouville property.

One of the significant problems associated with imbalanced data classification is the lack of reliable metrics. This runs primarily from the fact that for most real-life (as well as commonly used benchmark) problems, we do not have information from the user on the actual form of the loss function that should be minimized. Although it is pretty common to have metrics indicating the classification quality within each class, for the end user, the analysis of several such metrics is then required, which in practice causes difficulty in interpreting the usefulness of a given classifier. Hence, many aggregate metrics have been proposed or adopted for the imbalanced data classification problem, but there is still no consensus on which should be used. An additional disadvantage is their ambiguity and systematic bias toward one class. Moreover, their use in analyzing experimental results in recognition of those classification models that perform well for the chosen aggregated metrics is burdened with the drawbacks mentioned above. Hence, the paper proposes a simple approach to analyzing the popular parametric metric $F_\beta$. We point out that it is possible to indicate for a given pool of analyzed classifiers when a given model should be preferred depending on user requirements.

Ploughing phenomena occurring during precise machining processes affect the formation of surface finish and progress of tool wear. Therefore, this study presents an evaluation of ploughing phenomenon by studying the ploughing forces in tool flank face workpiece interface during precise ball end milling of AISI L6 alloy steel. Developed original model of ploughing forces involved the effect of minimum uncut chip thickness hmin and ploughing volume during ball-end milling. Estimated ploughing forces are sensitive to variations of surface inclinations and progressing tool wear. Moreover, intense growth of ploughing force during milling with worn tool is affected by irregular and non-circular profile of worn cutting edge below the stagnant point, and by the appearance of attrition and micro-grooves on tool flank face., Comment: 31 pages, 23 figures

Frictional losses are responsible for significant energy waste in many practical applications, and superlubricity with a coefficient of friction lower than 0.01 is the goal of tribologists. In this paper, metal-on-polymer contact was analysed and close to superlubricity conditions for this material configuration were explored. A new lubricant has been proposed hinge on the phosphorus-based ionic liquid and carbon nanotubes as thickeners. Additionally, carbon nanotube mesh was doped with copper nanoparticles that allowed for the close to superlubricity state in a mild steel/polymer contact configuration under low normal load conditions. The adsorption of phosphorus onto metallic and polymer surfaces has been reported in EDS analysis. The formulation of the new lubricant allowed for stable dispersion with a carbon nanotube content as low as 0.1% wt. The carbon nanotubes and Cu nanoparticles have been analysed using TEM and SEM imaging. A tribological test in a block-on-ring system has been carried out. The wear of material, topography, and surface free energy have been analysed along with SEM/EDS images to explore the underlying mechanisms of friction and wear., Comment: 18 pages

Cells and tissues are constantly exposed to various chemical and physical signals that intricately regulate various physiological and pathological processes. This study explores the integration of two biophysical methods, Traction Force Microscopy (TFM) and Optically-Detected Magnetic Resonance (ODMR), to concurrently assess cellular traction forces and local relative temperature. We present a novel elastic substrate with embedded nitrogen-vacancy microdiamonds, that facilitate ODMR-TFM measurements. Optimization efforts have focused on minimizing the sample illumination and experiment duration to mitigate biological perturbations. Our hybrid ODMR-TFM technique yields precise TFM maps and achieves approximately 1K accuracy in relative temperature measurements. Notably, our setup, employing a simple wide-field fluorescence microscope with standard components, demonstrates the broader feasibility of these techniques in life-science laboratories. By elucidating the physical aspects of cellular behavior beyond the existing methods, this approach opens avenues for a deeper understanding and may inspire diverse biomedical applications., Comment: 19 pages, 5 figures

An effect of alloying of the monoclinic beta- Ga2O3 with Al2O3 and In2O3 on the photoluminescent, thermoluminescent and persistent luminescent properties of Cr3+ ions has been comprehensively investigated. For this purpose, various series of Cr3+ and Ca2+ co-doped microcrystalline phosphors were synthesized by the solution combustion method, including pseudobinary compounds like (Ga-Al)2O3 with up to 20% Al and (Ga-In)2O3 with up to 50% In as well as pseudoternary compounds (Ga Al In)2O3 with balanced proportion of Al, Ga and In. The phase composition and crystal structure of the obtained materials were examined by X-ray powder diffraction technique. Detailed luminescence studies were conducted for the (Ga-Al)2O3 and (Ga-In)2O3 compounds which exhibited a single-phase monoclinic structure. Low-temperature and time-resolved photoluminescence investigations of the Cr-doped pseudobinary compounds unveiled several types of Cr3+ centres, attributed to the Al-, Ga- and In-centred octahedra in the studied alloys. The obtained results underscore the benefit of bandgap engineering through alteration in the host lattice chemical composition for efficient tuning of the thermoluminescent and persistent luminescent properties of the near-infrared-emitting beta Ga2O3:Cr based phosphors. Furthermore, it was demonstrated that modification of the chemical composition of the host lattice also adjusts the thermometric performance of the studied phosphors. Indeed, the specific sensitivity of the beta- Ga2O3:Cr3+ decay time luminescence thermometer showed nearly twofold enhancement when the host lattice was alloyed with 30% of In2O3., Comment: 35 pages, 14 figures

We study the fluorescence of nanodiamond ensembles as a function of static external magnetic field and observe characteristic dip features close to the zero field with potential for magnetometry applications. We analyze the dependence of the features width and contrast of the feature on the size of the diamond (in the range 30 nm to 3 um) and on the strength of a bias magnetic field applied transversely to the field being scanned. We also perform optically detected magnetic resonance (ODMR) measurements to quantify the strain splitting of the zero-field ODMR resonance across various nanodiamond sizes and compare it with the width and contrast measurements of the zero-field fluorescence features for both nanodiamonds and bulk samples. The observed properties provide compelling evidence of cross-relaxation effects in the NV system occurring close to zero magnetic fields. Finally, the potential of this technique for use in practical magnetometry is discussed., Comment: 9 pages, 5 figures

We establish that the summability of the series $\sum\varepsilon_n$ is the necessary and sufficient criterion ensuring that every $(1+\varepsilon_n)$ Markushevich basis in a separable Hilbert space is a Riesz basis. Further we show that if $n\varepsilon_n\to \infty$, then in $\ell_2$ there exists a $(1+\varepsilon_n)$ Markushevich basis that under any permutation is non-equivalent to a Schauder basis. We extend this result to any separable Banach space. Finally we provide examples of Auerbach bases in 1-symmetric separable Banach spaces whose no permutations are equivalent to any Schauder basis or (depending on the space) any unconditional Schauder basis., Comment: We improved the presentation of the proof of Theorem 1.3 and corrected some typos. There are no essential changes except the removal of the last sentence of Example 8.5 which was not correct. The main statement of Example 8.5 remains unchanged. We slightly reformulated the Acknowledgments

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 65 pages, 15 figures; comments welcome

We study heat kernel convergence of induced subgraphs with Neumann boundary conditions. We first establish convergence of the resulting semigroups to the Neumann semigroup in $\ell^2$. While convergence to the Neumann semigroup always holds, convergence to the Dirichlet semigroup in $\ell^2$ turns out to be equivalent to the coincidence of the Dirichlet and Neumann semigroups while convergence in $\ell^1$ is equivalent to stochastic completeness. We then investigate the Feller property for the Neumann semigroup via generalized solutions and give applications to graphs satisfying a condition on the edges as well as birth-death chains.

Current technological advancements of quantum computers highlight the need for application-driven, practical and well-defined methods of benchmarking their performance. As the existing NISQ device's quality of two-qubit gate errors rate is even around one percent and the number of qubits is still limited to a few or several dozen, naturally, we need to propose rather small algorithms instances taken from key promising application areas, such as quantum chemistry, combinatorial optimisation or machine learning. While many techniques for assessing the performance of logical components, such as gate fidelity and qubit coherence exist, it is still challenging to extrapolate those values onto the performance of different quantum algorithms and subroutines. This work aims to introduce a series of initial quantum application benchmarks together with a methodology of execution for measuring the performance and fidelity of the results. The proposed suite refers to several variational algorithms widely used on available NISQ devices but also includes examples of quantum circuits designed for a fault-tolerant quantum computer.

This preprint comprises the first four out of five chapters of the Master's thesis I wrote 2022 under the supervision of Catharina Stroppel and Paul Wedrich at the University of Bonn titled "Categorified Jones-Wenzl projectors and Generalizations". Chapter 1 can serve as introductory literature for researchers or graduate students familiar with Schur-Weyl duality between the symmetric group and the general linear Lie algebra or their quantum counter parts, and who are seeking to learn a type B/D analogue of the famous type A story. Chapter 1 serves as an introduction to the type B combinatorics and blob-diagrammatics. Chapters 2,3, and 4 contain proofs of three main theorem each - the first one is an explicit/computational proof of the easiest case of quantum coideal Schur-Weyl duality involving non-trivial quantizations of weight spaces, the second one shows the generalization of Jones-Wenzl projectors to the type B Temperley-Lieb algebra and the third one uses generalized Reidemeister moves and a functional analytic argument to prove a version of the fact that powers of the type D full-twist converge towards the type D Jones-Wenzl projector., Comment: The categorification part in the title is discussed in the 5th chapter which is not included

$\alpha$-Sn is an elemental topological material, whose topological phases can be tuned by strain and magnetic field. Such tunability offers a substantial potential for topological electronics. However, InSb substrates, commonly used to stabilize $\alpha$-Sn allotrope, suffer from parallel conduction, restricting transport investigations and potential applications. Here, the successful MBE growth of high-quality $\alpha$-Sn layers on insulating, hybrid CdTe/GaAs(001) substrates, with bulk electron mobility approaching 20000 cm$^2$V$^{-1}$s$^{-1}$ is reported. The electronic properties of the samples are systematically investigated by independent complementary techniques, enabling thorough characterization of the 3D Dirac (DSM) and Weyl (WSM) semimetal phases induced by the strains and magnetic field, respectively. Magneto-optical experiments, corroborated with band structure modeling, provide an exhaustive description of the bulk states in the DSM phase. The modeled electronic structure is directly observed in angle-resolved photoemission spectroscopy, which reveals linearly dispersing bands near the Fermi level. The first detailed study of negative longitudinal magnetoresistance relates this effect to the chiral anomaly and, consequently, to the presence of WSM. Observation of the $\pi$ Berry phase in Shubnikov-de Haas oscillations agrees with the topologically non-trivial nature of the investigated samples. Our findings establish $\alpha$-Sn as an attractive topological material for exploring relativistic physics and future applications., Comment: Accepted version; Main text: 37 pages, 7 figures; Supplementary Materials: 29 pages, 13 figures

We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the $q$-regular filtration. This dependency is governed by a martingale analog of the so-called wave cone, which naturally corresponds to the result of De Philippis and Rindler about fine properties of PDE-constrained vector measures. As a corollary we obtain a martingale version of Alberti's rank-one theorem., Comment: 10 pages

We consider weakly null sequences in the Banach space of functions of bounded variation $\mathrm{BV}(\mathbb{R}^d)$. We prove that for any such sequence $\{f_n\}$ the jump parts of the gradients of functions $f_n$ tend to $0$ strongly as measures. It implies that Dunford--Pettis property for the space $\mathrm{SBV}$ is equivalent to the Dunford--Pettis property for the Sobolev space $W^{1,1}.$, Comment: 18 pages; the presentation is sufficiently improved in v2

Cu-based argyrodites have gained much attention as a new class of thermoelectric materials for energy harvesting. However, the phase transition occurring in these materials and low energy conversion performance limited their broad application in thermoelectric converters. In this work, we disclose a newly discovered highly efficient Cu8SiSxSe6-x argyrodite with stabilized high-symmetry cubic phase at above 282 K opening the practical potential of this material for the mid-temperature region applications. The temperature range broadening of the high-symmetry phase existence was possible due to the successful substitution of Se with S in Cu8SiSxSe6-x, which enhances the configurational entropy. The developed argyrodites show excellent thermoelectric performance thanks to the increased density of states effective mass and ultralow lattice thermal conductivity. Further tuning of the carrier concentration through the Cu-deviation improves the thermoelectric performance significantly. The dimensionless thermoelectric figure of merit ZT and estimated energy conversion efficiency {\eta} for Cu7.95SiS3Se3 achieve outstanding values of the 1.45 and 13 %, respectively, offering this argyrodite as a low-cost and Te-free alternative for the thermoelectric energy conversion applications., Comment: 25 pages, 8 figures