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Scatterometry is a tested method for measuring periodic semiconductor structures. Since the sizes of modern semiconductor structures have reached the nanoscale regime, the challenge is to determine the shape of periodic nanostructures with sub-nanometer accuracy. To increase the resolution of scatterometry, short-wavelength radiation like soft X-rays can be used. But, scatterometry with soft X-rays is an inverse problem whose solutions can be ambiguous and its sensitivity should be further increased to determine the shape of even more complicated periodic nanostructures made up of different materials. To achieve unique solutions with smaller uncertainties, scatterometry can leverage the excitation of low-Z materials with soft X-rays. Additional information from soft X-ray fluorescence analysis in a hybrid measurement approach can mitigate the problem of ambiguous solutions from soft X-ray scattering and could further decrease uncertainty. In this work, the hybrid approach is utilized to perform a comparison of solutions from the inverse problem and determine the actual solution over ambiguous solutions.

We construct a unitary operator between Hilbert spaces of generalized eigenfunctions of Coulomb operators and the Laplace-Beltrami operator of hyperbolic space that intertwines their respective Poisson operators on $L^2(\mathbb{S}^{d-1})$. The constructed operator generalizes Fock's unitary transformation, originally defined between the discrete spectra of the attractive Coulomb operator and the Laplace-Beltrami operator on the sphere, to the setting of continuous spectra. Among other connections, this map explains why the scattering matrices are the same in these two different settings, and it also provides an explicit formula for the Poisson operator of the Coulomb Hamiltonian., Comment: 21 pages, 5 figures

We present a study of a general spin Hamiltonian with terms up to fourth order. With the coherent states the semiclassical potential is obtained and with catastrophe theory its parameter space is constructed. When the fourth order parameters are large enough the parameter space has regions where the semiclassical potential has three wells. By applying an oscillating magnetic field a trajectory in parameter space crosses the Maxwell set multiple times resulting in many ground state quantum phase transitions. Using the coherent states we are able to visualize the localization of the ground state on the Bloch sphere as the magnetic field is varied., Comment: 18 pages, 6 figures

Previous studies have shown that eye movement data recorded at 1000 Hz can be used to authenticate individuals. This study explores the effectiveness of eye movement-based biometrics (EMB) by utilizing data from an eye-tracking (ET)-enabled virtual reality (VR) headset (GazeBaseVR) and compares it to the performance using data from a high-end eye tracker (GazeBase) that has been downsampled to 250 Hz. The research also aims to assess the biometric potential of both binocular and monocular eye movement data. GazeBaseVR dataset achieves an equal error rate (EER) of 1.67% and a false rejection rate (FRR) at 10^-4 false acceptance rate (FAR) of 22.73% in a binocular configuration. This study underscores the biometric viability of data obtained from eye-tracking-enabled VR headset., Comment: 9 pages, 6 figures

This paper performs the crucial work of establishing a baseline for gaze-driven authentication performance to begin answering fundamental research questions using a very large dataset of gaze recordings from 9202 people with a level of eye tracking (ET) signal quality equivalent to modern consumer-facing virtual reality (VR) platforms. The size of the employed dataset is at least an order-of-magnitude larger than any other dataset from previous related work. Binocular estimates of the optical and visual axes of the eyes and a minimum duration for enrollment and verification are required for our model to achieve a false rejection rate (FRR) of below 3% at a false acceptance rate (FAR) of 1 in 50,000. In terms of identification accuracy which decreases with gallery size, we estimate that our model would fall below chance-level accuracy for gallery sizes of 148,000 or more. Our major findings indicate that gaze authentication can be as accurate as required by the FIDO standard when driven by a state-of-the-art machine learning architecture and a sufficiently large training dataset., Comment: 31 pages, 20 figures, 5 tables, includes supplementary material

We present an extensive, in-depth analysis of the eye tracking capabilities of the Meta Quest Pro virtual reality headset using a dataset of eye movement recordings collected from 78 participants. In addition to presenting classical signal quality metrics--spatial accuracy, spatial precision and linearity--in ideal settings, we also study the impact of background luminance and headset slippage on device performance. We additionally present a user-centered analysis of eye tracking signal quality, where we highlight the potential differences in user experience as a function of device performance. This work contributes to a growing understanding of eye tracking signal quality in virtual reality headsets, where the performance of applications such as gaze-based interaction, foveated rendering, and social gaze are directly dependent on the quality of eye tracking signal., Comment: 14 pages

We present exact relations between the diffusion coefficients or conductivities, $\kappa_{qq'}/T = \sigma_{qq'}$, of strongly-interacting matter. We show that once the diagonal entries are known in two different charge representations, the off-diagonal coefficients are functions of the diagonal entries once isospin symmetry applies. As an important example, we infer the conductivities on the basis of available calculations from lattice quantum chromodynamics (LQCD) and argue that these computations suffer under the approximations made to achieve them. Further, we argue that the representation of the conductivities w.r.t. to the conserved quark-flavors may deliver more insight into the chemical composition of strongly-interacting matter., Comment: 9 pages, 3 figures

What qualities make a feature useful for biometric performance? In prior research, pre-dating the advent of deep learning (DL) approaches to biometric analysis, a strong relationship between temporal persistence, as indexed by the intraclass correlation coefficient (ICC), and biometric performance (Equal Error Rate, EER) was noted. More generally, the claim was made that good biometric performance resulted from a relatively large set of weakly intercorrelated features with high ICC. The present study aimed to determine whether the same relationships are found in a state-of-the-art DL-based eye movement biometric system (``Eye-Know-You-Too''), as applied to two publicly available eye movement datasets. To this end, we manipulate various aspects of eye-tracking signal quality, which produces variation in biometric performance, and relate that performance to the temporal persistence and intercorrelation of the resulting embeddings. Data quality indices were related to EER with either linear or logarithmic fits, and the resulting model R^2 was noted. As a general matter, we found that temporal persistence was an important predictor of DL-based biometric performance, and also that DL-learned embeddings were generally weakly intercorrelated., Comment: 18 pages, 7 Figures

In the age of personal voice assistants, the question of privacy arises. These digital companions often lack memory of past interactions, while relying heavily on the internet for speech processing, raising privacy concerns. Modern smartphones now enable on-device speech processing, making cloud-based solutions unnecessary. Personal assistants for the elderly should excel at memory recall, especially in medical examinations. The e-ViTA project developed a versatile conversational application with local processing and speaker recognition. This paper highlights the importance of speaker diarization enriched with sensor data fusion for contextualized conversation preservation. The use cases applied to the e-VITA project have shown that truly personalized dialogue is pivotal for individual voice assistants. Secure local processing and sensor data fusion ensure virtual companions meet individual user needs without compromising privacy or data security., Comment: 10 pages, 1 figure, to be presented at https://ihiet-ai.org/, Lausanne in April 2024

Ever since the emergence of large language models (LLMs) and related applications, such as ChatGPT, its performance and error analysis for programming tasks have been subject to research. In this work-in-progress paper, we explore the potential of such LLMs for computing educators and learners, as we analyze the feedback it generates to a given input containing program code. In particular, we aim at (1) exploring how an LLM like ChatGPT responds to students seeking help with their introductory programming tasks, and (2) identifying feedback types in its responses. To achieve these goals, we used students' programming sequences from a dataset gathered within a CS1 course as input for ChatGPT along with questions required to elicit feedback and correct solutions. The results show that ChatGPT performs reasonably well for some of the introductory programming tasks and student errors, which means that students can potentially benefit. However, educators should provide guidance on how to use the provided feedback, as it can contain misleading information for novices., Comment: Accepted to FIE 2023

Graphene nanoribbons (GNRs) exhibit a broad range of physicochemical properties that critically depend on their width and edge topology. While the chemically stable GNRs with armchair edges (AGNRs) are semiconductors with width-tunable band gap, GNRs with zigzag edges (ZGNRs) host spin-polarized edge states, which renders them interesting for applications in spintronic and quantum technologies. However, these states significantly increase their reactivity. For GNRs fabricated via on-surface synthesis under ultrahigh vacuum conditions on metal substrates, the expected reactivity of zigzag edges is a serious concern in view of substrate transfer and device integration under ambient conditions, but corresponding investigations are scarce. Using 10-bromo-9,9':10',9''-teranthracene as a precursor, we have thus synthesized hexanthene (HA) and teranthene (TA) as model compounds for ultrashort GNRs with mixed armchair and zigzag edges, characterized their chemical and electronic structure by means of scanning probe methods, and studied their chemical reactivity upon air exposure by Raman spectroscopy. We present a detailed identification of molecular orbitals and vibrational modes, assign their origin to armchair or zigzag edges, and discuss the chemical reactivity of these edges based on characteristic Raman spectral features.

We present a study of systems of single-molecule magnets using a semiclassical analysis and catastrophe theory. Separatrices in parameter space are constructed which are useful to determine the structure of the Hamiltonians energy levels. In particular the Maxwell set separatrix determines the behavior of the ground state of the system. We consider an external magnetic field with two components, one parallel to the easy magnetization axis of the molecule and the other perpendicular to it. Using the fidelity and heat capacity we were able to detect the signals of the QPTs as a function of the magnetic field components., Comment: 11 pages, 7 figures

This manuscript demonstrates an improved model-based approach for synthetic degradation of previously captured eye movement signals. Signals recorded on a high-quality eye tracking sensor are transformed such that their resulting eye tracking signal quality is similar to recordings captured on a low-quality target device. The proposed model improves the realism of the degraded signals versus prior approaches by introducing a mechanism for degrading spatial accuracy and temporal precision. Moreover, a percentile-matching technique is demonstrated for mimicking the relative distributional structure of the signal quality characteristics of the target data set. The model is demonstrated to improve realism on a per-feature and per-recording basis using data from an EyeLink 1000 eye tracker and an SMI eye tracker embedded within a virtual reality platform. The model improves the median classification accuracy performance metric by 35.7% versus the benchmark model towards the ideal metric of 50%. This paper also expands the literature by providing an application-agnostic realism assessment workflow for synthetically generated eye movement signals., Comment: 12 pages, 10 figures

A multivariate regression model of affine and diffeomorphic transformation sequences - FineMorphs - is presented. Leveraging concepts from shape analysis, model states are optimally "reshaped" by diffeomorphisms generated by smooth vector fields during learning. Affine transformations and vector fields are optimized within an optimal control setting, and the model can naturally reduce (or increase) dimensionality and adapt to large datasets via suboptimal vector fields. An existence proof of solution and necessary conditions for optimality for the model are derived. Experimental results on real datasets from the UCI repository are presented, with favorable results in comparison with state-of-the-art in the literature and densely-connected neural networks in TensorFlow., Comment: 39 pages, 7 figures

Prior research states that frequencies below 75 Hz in eye-tracking data represent the primary eye movement termed ``signal'' while those above 75 Hz are deemed ``noise''. This study examines the biometric significance of this signal-noise distinction and its privacy implications. There are important individual differences in a person's eye movement, which lead to reliable biometric performance in the ``signal'' part. Despite minimal eye-movement information in the ``noise'' recordings, there might be significant individual differences. Our results confirm the ``signal'' predominantly contains identity-specific information, yet the ``noise'' also possesses unexpected identity-specific data. This consistency holds for both short-(approx. 20 min) and long-term (approx. 1 year) biometric evaluations. Understanding the location of identity data within the eye movement spectrum is essential for privacy preservation., Comment: 10 pages, 2 figures, 1 table

The main result of this article characterizes the set of semiclassical measures corresponding to sequences of eigenfunctions of the hydrogen atom. In particular, any Radon probability measure on the fixed negative energy surface $\Sigma_E$ that is invariant under the Hamiltonian flow is a semiclassical measure of a sequence of eigenfunctions of hydrogen. We first prove that there is a sequence of eigenfunctions, called hydrogen coherent states, that converge to a delta measure concentrating on any given geodesic $\gamma$ on $\Sigma_E$, and we finish using a density argument in the weak-* topology., Comment: 15 pages

Serving as the progenitors of electromagnetic and gravitational wave transients, massive stars have received renewed interest in recent years. However, many aspects of their birth and evolution remain opaque, particularly in the context of binary interactions. The centre of our galaxy hosts a rich cohort of very massive stars, which appear to play a prominent role in the ecology of the region. In this paper we investigate the binary properties of the Arches cluster, which is thought to host a large number of very massive stars. A combination of multi-epoch near-IR spectroscopy and photometry was utilised to identify binaries. 13 from 36 cluster members meet our criteria to be classed as RV variable. Combining the spectroscopic data with archival radio and X-ray observations - to detect colliding wind systems - provides a lower limit to the binary fraction of ~43%; increasing to >50% for the O-type hypergiants and WNLha. Dynamical and evolutionary masses reveal the primaries to be uniformly massive (>50M$_{\odot}$). Where available, orbital analysis reveals a number of short period, highly eccentric binaries, which appear to be pre-interaction systems. Such systems are X-ray luminous, with 80% above an empirical bound of $(L_{\rm x}/L_{\rm bol})\sim10^{-7}$ and their orbital configurations suggest formation and evolution via a single star channel; however, we cannot exclude a binary formation channel for a subset. Qualitative comparison to surveys of lower mass OB-type stars confirms that the trend to an extreme binary fraction (>60%) extends to the most massive stars currently forming in the local Universe., Comment: Accepted in MNRAS; In Memoriam: This work is dedicated to the memory of our dearest friend and colleague Simon Clark

We present GazeBaseVR, a large-scale, longitudinal, binocular eye-tracking (ET) dataset collected at 250 Hz with an ET-enabled virtual-reality (VR) headset. GazeBaseVR comprises 5,020 binocular recordings from a diverse population of 407 college-aged participants. Participants were recorded up to six times each over a 26-month period, each time performing a series of five different ET tasks: (1) a vergence task, (2) a horizontal smooth pursuit task, (3) a video-viewing task, (4) a self-paced reading task, and (5) a random oblique saccade task. Many of these participants have also been recorded for two previously published datasets with different ET devices, and some participants were recorded before and after COVID-19 infection and recovery. GazeBaseVR is suitable for a wide range of research on ET data in VR devices, especially eye movement biometrics due to its large population and longitudinal nature. In addition to ET data, additional participant details are provided to enable further research on topics such as fairness., Comment: Data publicly available on figshare at https://doi.org/10.6084/m9.figshare.21308391