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The generation of entangled photons from radiative cascades has enabled milestone experiments in quantum information science with several applications in photonic quantum technologies. Significant efforts are being devoted to pushing the performances of near-deterministic entangled-photon sources based on single quantum emitters often embedded in photonic cavities, so to boost the flux of photon pairs. The general postulate is that the emitter generates photons in a nearly maximally entangled state of polarization, ready for application purposes. Here, we demonstrate that this assumption is unjustified. We show that in radiative cascades there exists an interplay between photon polarization and emission wavevector, strongly affecting quantum correlations when emitters are embedded in micro-cavities. We discuss how the polarization entanglement of photon pairs from a biexciton-exciton cascade in quantum dots strongly depends on their propagation wavevector, and it can even vanish for large emission angles. Our experimental results, backed by theoretical modelling, yield a brand-new understanding of cascaded emission for various quantum emitters. In addition, our model provides quantitative guidelines for designing optical microcavities that retain both a high degree of entanglement and collection efficiency, moving the community one step further towards an ideal source of entangled photons for quantum technologies.

Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult. Matrix-free loop convergence algorithms deform entire space-time fields (loops) until they satisfy the evolution equations. Initial guesses for these robust variational convergence algorithms are thus periodic space-time fields in a high-dimensional state space, rendering their generation highly challenging. Usually guesses are generated with recurrency methods, which are most suited to shorter and more stable periodic orbits. Here we propose an alternative, data-driven method for generating initial guesses: while the dimension of the space used to discretize fluid flows is prohibitively large to construct suitable initial guesses, the dissipative dynamics will collapse onto a chaotic attractor of far lower dimension. We use an autoencoder to obtain a low-dimensional representation of the discretized physical space for the one-dimensional Kuramoto-Sivashinksy equation, in chaotic and hyperchaotic regimes. In this low-dimensional latent space, we construct loops based on the latent POD modes with random periodic coefficients, which are then decoded to physical space and used as initial guesses. These loops are found to be realistic initial guesses and, together with variational convergence algorithms, these guesses help us to quickly converge to UPOs. We further attempt to 'glue' known UPOs in the latent space to create guesses for longer ones. This gluing procedure is successful and points towards a hierarchy of UPOs where longer UPOs shadow sequences of shorter ones.

The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension of a chaotic attractor in a partial differential equation (PDE) is less than three, even though that attractor is embedded within an infinite-dimensional space. Here we study the Kuramoto-Sivashinsky PDE at the onset of chaos. We use two different dimensionality-reduction techniques - proper orthogonal decomposition and an autoencoder neural network - to find two different approximate embeddings of the chaotic attractor into three dimensions. By finding the projection of the attractor's UPOs in these reduced spaces and examining their linking numbers, we construct templates for the branched manifold which encodes the topological properties of the attractor. The templates obtained using two different dimensionality reduction methods mirror each other. Hence, the organization of the periodic orbits is identical (up to a global change of sign) and consistent symbolic names for low-period UPOs are derived. This is strong evidence that the dimensional reduction is robust, in this case, and that an accurate topological characterization of the chaotic attractor of the chaotic PDE has been achieved.

The new class of compact quasi-axisymmetric stellarators with a wide range of field periods offers the unique potential to combine the advantages of the two leading magnetic confinement fusion devices, tokamaks and stellarators. Here we present the first numerical optimization of this class which has so far only been obtained analytically. Our approach finds significantly improved quasi-axisymmetric equilibria at aspect ratio $< 2.5$, resulting in no losses of alpha particles at reactor volume while also satisfying improved magnetohydrodynamic stability and a self-consistent plasma current.

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are typically noisy, which implies that both the regression inputs and outputs are corrupted by noise. However, most of the literature considers only noise in the regression outputs. In this paper, we show how to account for the noise in the regression inputs in an extended Gaussian process framework to approximate scalar and multidimensional systems. We demonstrate the potential of our framework by comparing it to different state-of-the-art methods in several simulation examples., Comment: 6 pages

Chemical evolution models predict a gradual build-up of $^{13}$C in the universe, based on empirical nuclear reaction rates and assumptions on the properties of stellar populations. However, old metal-poor stars within the Galaxy contain more $^{13}$C than is predicted, suggesting that further refinements to the models are necessary. Gas at high redshift provides important supplementary information at metallicities $-2\lesssim$ [Fe/H] $\lesssim-1$, for which there are only a few measurements in the Galaxy. We obtained new, high-quality, VLT/ESPRESSO observations of the QSO B1331+170 and used them to measure $^{12}$C/$^{13}$C in the damped Lyman-$\alpha$ system (DLA) at $z_{abs}=1.776$, with [Fe/H]=-1.27. AI-VPFIT, an Artificial Intelligence tool based on genetic algorithms and guided by a spectroscopic information criterion, was used to explore different possible kinematic structures of the carbon gas. Three hundred independent AI-VPFIT models of the absorption system were produced using pre-set $^{12}$C/$^{13}$C values, ranging from 4 to 500. Our results show that $^{12}$C/$^{13}$C$=28.5^{+51.5}_{-10.4}$, suggesting a possibility of $^{13}$C production at low metallicity., Comment: 11 pages, 6 figures. Three appendices. To appear in MNRAS

We present here the preliminary design of the RIZ module, one of the visible spectrographs of the ANDES instrument 1. It is a fiber-fed high-resolution, high-stability spectrograph. Its design follows the guidelines of successful predecessors such as HARPS and ESPRESSO. In this paper we present the status of the spectrograph at the preliminary design stage. The spectrograph will be a warm, vacuum-operated, thermally controlled and fiber-fed echelle spectrograph. Following the phase A design, the huge etendue of the telescope will be reformed in the instrument with a long slit made of smaller fibers. We discuss the system design of the spectrographs system., Comment: Paper submitted to the SPIE astronomical telescope and instrumentation 2024, conference title : Ground-based and Airborne Instrumentation for Astronomy X, paper reference number : 13096-171

The low-energy collective excitations of semiconductors and insulators often couple strongly to light, allowing them to be probed optically. We argue here that in fractional Chern insulators intra-band collective excitations are dark in the sense that they couple anomalously weakly to light. This conclusion is based on a relationship between ideal quantum geometry and the structure factor of a Chern band, and on a classical plasma analogy motivated by the vortexibility property of ideal Chern bands., Comment: Main text: 5 pages, 3 figures, Supmat: 5 pages, 1 figure; Comments are welcome

Ground-based astronomy is unavoidably subject to the adverse effect of atmospheric turbulence, a.k.a. the seeing, which blurs the images and limits the achievable spatial resolution. For spectroscopic observations, it leads to slit or fiber-injection losses, since not all photons distributed over the extended seeing disk can be captured. These losses might have a very substantial impact on the overall efficiency of a spectrograph and are naturally highly variable. Assessing the fiber-injection losses requires accurate information about the image quality (IQ) delivered by the telescope to the instrument over the course of the observations, which, however, is often not directly available. ESPRESSO provides acquisition and field-stabilization images attached to the science data and thus offers the opportunity for a post-processing analysis. Here, we present a novel method to infer the IQ profile and fiber-injection losses from the integrated field-stabilization images, utilizing the spill-over light that does not get injected into the fiber. We validate these measurements against the IQ observed in the acquisition images and determine that our method delivers unbiased estimates with a scatter of 0.11" for the FWHM of the profile and 15% in terms of fiber-injection losses. This compares favorably to the estimates derived from either the differential image motion monitor (DIMM) or the telescope guide probe sensors and therefore represents a valuable tool to characterize the instrument efficiency and to correct raw spectra for fiber-injection losses., Comment: Accepted for publication with MNRAS

Spin and valley flavor polarization plays a central role in the many-body physics of flat band graphene, with fermi surface reconstructions often accompanied by quantized anomalous Hall and superconducting state observed in a variety of experimental systems. Here we describe an optical technique that sensitively and selectively detects flavor textures via the exciton response of a proximal transition metal dichalcogenide layer. Through a systematic study of rhombohedral and rotationally faulted graphene bilayers and trilayers, we show that when the semiconducting dichalcogenide is in direct contact with the graphene, the exciton response is most sensitive to the large momentum rearrangement of the Fermi surface, providing information that is distinct from and complementary to electrical compressibility measurements. The wide-field imaging capability of optical probes allows us to obtain spatial maps of flavor orders with high throughput, and with broad temperature and device compatibility. Our work paves the way for optical probing and imaging of flavor orders in flat band graphene systems., Comment: 29 pages, 4 figures, with supplementary materials

Green Tsetlin (GT) is a Tsetlin Machine (TM) framework developed to solve real-world problems using TMs. Several frameworks already exist that provide access to TM implementations. However, these either lack features or have a research-first focus. GT is an easy-to-use framework that aims to lower the complexity and provide a production-ready TM implementation that is great for experienced practitioners and beginners. To this end, GT establishes a clear separation between training and inference. A C++ backend with a Python interface provides competitive training and inference performance, with the option of running in pure Python. It also integrates support for critical components such as exporting trained models, hyper-parameter search, and cross-validation out-of-the-box.

This paper introduces the Sparse Tsetlin Machine (STM), a novel Tsetlin Machine (TM) that processes sparse data efficiently. Traditionally, the TM does not consider data characteristics such as sparsity, commonly seen in NLP applications and other bag-of-word-based representations. Consequently, a TM must initialize, store, and process a significant number of zero values, resulting in excessive memory usage and computational time. Previous attempts at creating a sparse TM have predominantly been unsuccessful, primarily due to their inability to identify which literals are sufficient for TM training. By introducing Active Literals (AL), the STM can focus exclusively on literals that actively contribute to the current data representation, significantly decreasing memory footprint and computational time while demonstrating competitive classification performance., Comment: 8 pages, 8 figures

Achieving a truly accurate wavelength calibration of high-dispersion echelle spectrographs is a challenging task but crucially needed for certain science cases, e.g. to test for a possible variation of the fine-structure constant in quasar spectra. One of the spectrographs best suited for this mission is VLT/ESPRESSO. Nevertheless, previous studies have identified significant discrepancies between the classical wavelength solutions and the one derived independently from the laser frequency comb. The dominant parts of these systematics were intra-order distortions, most-likely related to a deviation of the instrumental line-spread function from the assumed Gaussian shape. Here, we therefore present a study focused on a detailed modeling of the ESPRESSO instrumental line-spread function. We demonstrate that it is strongly asymmetric, non-Gaussian, different for the two slices and fibers, and varies significantly along the spectral orders. Incorporating the determined non-parametric model in the wavelength calibration process drastically improves the wavelength calibration accuracy, reducing the discrepancies between the two independent wavelength solutions from 50m/s to about 10m/s. The most striking success is, however, that the different fibers and slices now provide fully consistent measurements with a scatter of just a couple m/s. This demonstrates that the instrument-related systematics can be nearly eliminated over most of the spectral range by properly taking into account the complex shape of the instrumental line-spread function and paves the way for further optimizations of the wavelength calibration process., Comment: Accepted for publication in MNRAS

In a vertical channel driven by an imposed horizontal temperature gradient, numerical simulations have previously shown steady, time-periodic and chaotic dynamics. We explore the observed dynamics by constructing invariant solutions of the three-dimensional Oberbeck-Boussinesq equations, characterizing the stability of these equilibria and periodic orbits, and following the bifurcation structure of the solution branches under parametric continuation in Rayleigh number. We find that in a narrow vertically-periodic domain of aspect ratio ten, the flow is dominated by the competition between three and four co-rotating rolls. We demonstrate that branches of three and four-roll equilibria are connected and can be understood in terms of their discrete symmetries. Specifically, the D4 symmetry of the four-roll branch dictates the existence of qualitatively different intermediate branches that themselves connect to the three-roll branch in a transcritical bifurcation due to D3 symmetry. The physical appearance, disappearance, merging and splitting of rolls along the connecting branch provide a physical and phenomenological illustration of the equivariant theory of D3-D4 mode interaction. We observe other manifestations of the competition between three and four rolls, in which the symmetry in time or in the transverse direction is broken, leading to limit cycles or wavy rolls, respectively. Our work highlights the interest of combining numerical simulations, bifurcation theory, and group theory, in order to understand the transitions between and origin of flow patterns.

Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and turbulence. In a three-dimensional domain extended in both the vertical and the transverse dimensions, Gao et al. (2018) have observed a variety of convection patterns which are not described by linear stability analysis. We investigate the fully non-linear dynamics of vertical convection using a dynamical-systems approach based on the Oberbeck-Boussinesq equations. We compute the invariant solutions of these equations and the bifurcations that are responsible for the creation and termination of various branches. We map out a sequence of local bifurcations from the laminar base state, including simultaneous bifurcations involving patterned steady states with different symmetries. This atypical phenomenon of multiple branches simultaneously bifurcating from a single parent branch is explained by the role of D4 symmetry. In addition, two global bifurcations are identified: first, a homoclinic cycle from modulated transverse rolls and second, a heteroclinic cycle linking two symmetry-related diamond-roll patterns. These are confirmed by phase space projections as well as the functional form of the divergence of the period close to the bifurcation points. The heteroclinic orbit is shown to be robust and to result from a 1:2 mode interaction. The intricacy of this bifurcation diagram highlights the essential role played by dynamical systems theory and computation in hydrodynamic configurations.

A two-dimensional extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities is derived. Prior work has demonstrated that the emergent dynamics of these systems is characterized by a slow evolution of mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this emergent behavior, an efficient fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability (and temporal scale separation) is maintained. For 2D systems that are spatially-extended in one direction, the fluctuation eigenfunctions are labeled by their wavenumbers characterizing spatial variability in that direction, and the marginal mode(s) also must coincide with the fastest-growing mode(s) over all admissible wavenumbers. Here, we introduce two equivalent procedures for deriving an ordinary differential equation governing the slow evolution of the wavenumber of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasi-coherent states in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally-turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows where scale separation justifies a QL approximation of the dynamics.

Primordial abundances of light elements are sensitive to the physics of the early Universe and can directly constrain cosmological quantities, such as the baryon-to-photon ratio $\eta_{10}$, the baryon density and the number of neutrino families. Deuterium is especially suited for these studies: its primordial abundance is sensitive and monotonically dependent on $\eta_{10}$, allowing an independent measurement of the cosmic baryon density that can be compared, for instance, against the Planck satellite data. The primordial deuterium abundance can be measured in high $H_I$ column density absorption systems towards distant quasars. We report here a new measurement, based on high-resolution ESPRESSO data, of the primordial $D_I$ abundance of a system at redshift $z \sim 3.572$, towards PKS1937-101. Using only ESPRESSO data, we find a D/H ratio of $2.638\pm0.128 \times 10^{-5}$, while including the available UVES data improves the precision, leading to a ratio of $2.608 \pm 0.102 \times 10^{-5}$. The results of this analysis agree with those of the most precise existing measurements. We find that the relatively low column density of this system ($\log{N_{\rm H_I}/ {\rm cm}^{-2}}\sim18 $) introduces modelling uncertainties, which become the main contributor to the error budget., Comment: Accepted for publication in MNRAS. 16 pages, 10 figures and 6 tables (4 in main text, 2 in Appendix). Full model is available at the end of the manuscript

The gravitationally lensed quasar J014516.6-094517 at z=2.719 has been observed with the ESPRESSO instrument at the ESO VLT to obtain high-fidelity spectra of the two images A and B with a resolving power R=70000. At the redshifts under investigation (2.1 < z < 2.7), the Lyman forests along the two sightlines are separated by sub-kiloparsec physical distances and exhibit a strong correlation. We find that the two forests are indistinguishable at the present level of signal-to-noise ratio and do not show any global velocity shift, with the cross-correlation peaking at $\Delta v = 12 \pm 48$ m/s. The distribution of the difference in velocity of individual Lyman-$\alpha$ features is compatible with a null average and a mean absolute deviation of 930 m/s. Significant differences in NHI column density are not detected, putting a limit to the RMS fluctuation in the baryon density on $\leq 1$ proper kpc scales of $\Delta \rho / \rho < 3$%. On the other hand, metal lines show significant differences both in velocity structure and in column density. A toy model shows that the difference in velocity of the metal features between the two sightlines is compatible with the the motions of the baryonic component associated to dark matter halos of typical mass $M\simeq 2\times 10^{10} M_\odot$, also compatible with the observed incidence of the metal systems. The present observations confirm the feasibility of the Sandage test of the cosmic redshift drift with high-fidelity spectroscopy of the Lyman forest of distant, bright quasars, but also provide an element of caution about the intrinsic noise associated to the usage of metal features for the same purpose., Comment: 17 pages, 10 figures, 5 tables, accepted for publication in MNRAS

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. In the proposed scheme, we take advantage of the properties of Gaussian processes. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we analyze under which conditions incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in a simulation case study and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions., Comment: 16 pages

Superlattice potential modulation can produce flat minibands in Bernal-stacked bilayer graphene. In this work we study how band topology and interaction-induced symmetry-broken phases in this system are controlled by tuning the displacement field and the shape and strength of the superlattice potential. We use an analytic perturbative analysis to demonstrate that topological flat bands are favored by a honeycomb-lattice-shaped potential, and numerics to show that the robustness of topological bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, the strength of the displacement field and the superlattice potential tune phase transitions between quantum anomalous Hall insulator, trivial insulator, and metallic states. We present mean-field phase diagrams in a gate voltage parameter space at filling factor $\nu=1$, and discuss the prospects of realizing quantum anomalous Hall insulators and fractional Chern insulators when the superlattice potential modulation is produced by dielectric patterning or adjacent moir\'e materials.

A current concern in the field of Artificial Intelligence (AI) is to ensure the trustworthiness of AI systems. The development of explainability methods is one prominent way to address this, which has often resulted in the assumption that the use of explainability will lead to an increase in the trust of users and wider society. However, the dynamics between explainability and trust are not well established and empirical investigations of their relation remain mixed or inconclusive. In this paper we provide a detailed description of the concepts of user trust and distrust in AI and their relation to appropriate reliance. For that we draw from the fields of machine learning, human-computer interaction, and the social sciences. Furthermore, we have created a survey of existing empirical studies that investigate the effects of AI systems and XAI methods on user (dis)trust. With clarifying the concepts and summarizing the empirical investigations, we aim to provide researchers, who examine user trust in AI, with an improved starting point for developing user studies to measure and evaluate the user's attitude towards and reliance on AI systems.

We report the successful adaptation of the quasi-boson approximation, a technique traditionally employed in nuclear physics, to the analysis of the two-dimensional electron gas. We show that the correlation energy estimated from this approximation agrees closely with the results obtained from quantum Monte Carlo simulations. Our methodology comprehensively incorporates the exchange self-energy, direct scattering, and exchange scattering for a particle-hole pair excited out of the mean-field groundstate within the equation-of-motion framework. The linearization of the equation of motion leads to a generalized-random-phase-approximation (gRPA) eigenvalue equation whose spectrum indicates that the plasmon dispersion remains unaffected by exchange effects, while the particle-hole continuum experiences a marked upward shift due to the exchange self-energy. Notably, the plasmon mode retains its collective nature within the particle-hole continuum, up to moderately short wavelength ($q\sim 0.3 k_F$ at metallic density $r_s=4$). Using the gRPA excitation spectrum, we calculate the zero-point energy of the quasi-boson Hamiltonian, thereby approximating the correlation energy of the original Hamiltonian. This research highlights the potential and effectiveness of applying the quasi-boson approximation to the gRPA spectrum, a fundamental technique in nuclear physics, to extended condensed matter systems., Comment: 7 pages, 4 figures

Solid-state quantum emitters embedded in circular Bragg resonators are attractive due to their ability to emit quantum states of light with high brightness and low multi-photon probability. As for any emitter-microcavity system, fabrication imperfections limit the spatial and spectral overlap of the emitter with the cavity mode, thus limiting their coupling strength. Here, we show that an initial spectral mismatch can be corrected after device fabrication by repeated wet chemical etching steps. We demonstrate ~16 nm wavelength tuning for optical modes in AlGaAs resonators on oxide, leading to a 4-fold Purcell enhancement of the emission of single embedded GaAs quantum dots. Numerical calculations reproduce the observations and suggest that the achievable performance of the resonator is only marginally affected in the explored tuning range. We expect the method to be applicable also to circular Bragg resonators based on other material platforms, thus increasing the device yield of cavity-enhanced solid-state quantum emitters.

We present polarized |S|=0.99$\pm$0.01, and unpolarized |S|=0.03$\pm$0.01 emission from a single emitter embedded in a single, cylindrically symmetric device design. We show that the polarization stems from a position offset of the single emitter with respect to the cavity center, which breaks the cylindrical symmetry, and a position-dependent coupling to the frequency degenerate eigenmodes of the resonator structure. The experimental results are interpreted by using numerical simulations and by experimental mapping of the polarization-resolved far-field emission patterns. Our findings can be generalized to any nanophotonic structure where two orthogonal eigenmodes are not fully spatially overlapping., Comment: 15 pages, 5 figures

Although hyperthyroidism is a common disease, the pharmaceutical therapy is based on a trial-and-error approach. We extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of one antithyroid agent, namely methimazole (MMI), can be considered and use a model predictive control (MPC) scheme to determine suitable dosages., Comment: 2 pages

In recent years the use of Artificial Intelligence (AI) has become increasingly prevalent in a growing number of fields. As AI systems are being adopted in more high-stakes areas such as medicine and finance, ensuring that they are trustworthy is of increasing importance. A concern that is prominently addressed by the development and application of explainability methods, which are purported to increase trust from its users and wider society. While an increase in trust may be desirable, an analysis of literature from different research fields shows that an exclusive focus on increasing trust may not be warranted. Something which is well exemplified by the recent development in AI chatbots, which while highly coherent tend to make up facts. In this contribution, we investigate the concepts of trust, trustworthiness, and user reliance. In order to foster appropriate reliance on AI we need to prevent both disuse of these systems as well as overtrust. From our analysis of research on interpersonal trust, trust in automation, and trust in (X)AI, we identify the potential merit of the distinction between trust and distrust (in AI). We propose that alongside trust a healthy amount of distrust is of additional value for mitigating disuse and overtrust. We argue that by considering and evaluating both trust and distrust, we can ensure that users can rely appropriately on trustworthy AI, which can both be useful as well as fallible., Comment: This preprint has not undergone peer review or any post-submission improvements or corrections. The version of records of this contribution is published in Explainable Artificial Intelligence First World Conference, xAI 2023, Lisbon, Portugal, July 26-28, 2023, Proceedings, Part III (CCIS, volume 1903) and is available at https://doi.org/10.1007/978-3-031-44070-0

Astronomical precision spectroscopy underpins searches for life beyond Earth, direct observation of the expanding Universe and constraining the potential variability of physical constants across cosmological scales. Laser frequency combs can provide the critically required accurate and precise calibration to the astronomical spectrographs. For cosmological studies, extending the calibration with such astrocombs to the ultraviolet spectral range is highly desirable, however, strong material dispersion and large spectral separation from the established infrared laser oscillators have made this exceedingly challenging. Here, we demonstrate for the first time astronomical spectrograph calibrations with an astrocomb in the ultraviolet spectral range below 400 nm. This is accomplished via chip-integrated highly nonlinear photonics in periodically-poled, nano-fabricated lithium niobate waveguides in conjunction with a robust infrared electro-optic comb generator, as well as a chip-integrated microresonator comb. These results demonstrate a viable route towards astronomical precision spectroscopy in the ultraviolet and may contribute to unlocking the full potential of next generation ground- and future space-based astronomical instruments.

Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many solutions inaccessible and thus hindering progress towards a dynamical description of turbulence in terms of invariant solutions. We compute equilibria of three-dimensional wall-bounded shear flows using an adjoint-based matrix-free variational approach. To address the challenge of computing pressure in the presence of solid walls, we develop a formulation that circumvents the explicit construction of pressure and instead employs the influence matrix method. Together with a data-driven convergence acceleration technique based on dynamic mode decomposition, this yields a practically feasible alternative to state-of-the-art Newton methods for converging equilibrium solutions. We compute multiple equilibria of plane Couette flow starting from inaccurate guesses extracted from a turbulent time series. The variational method outperforms Newton(-hookstep) iterations in successfully converging from poor initial guesses, suggesting a larger convergence radius.

In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we replace the mathematical model of the system by the posterior mean of the Gaussian process. To account for the uncertainty of the learned model, we exploit the posterior variance of the learned Gaussian process in the weighting matrices of the cost function of the proposed MHE scheme. We prove practical robust exponential stability of the resulting estimator using a recently proposed Lyapunov-based proof technique. Finally, the performance of the Gaussian process based MHE scheme is illustrated via a nonlinear system., Comment: 8 pages