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Astronomical spectrographs require frequency calibration through sources like hollow-cathode lamps or absorption-gas cells. Laser frequency combs (LFCs) provide highest accuracy but are facing operational challenges. We aim to provide a precise and accurate frequency solution for the spectrum of molecular iodine absorption by referencing to an LFC that does not cover the same frequency range. We used a Fourier Transform Spectrometer (FTS) to produce a consistent frequency scale for the combined spectrum from an iodine absorption cell at 5200--6200\AA and an LFC at 8200\AA. We used 17,807 comb lines to determine the FTS frequency offset and compared the calibrated iodine spectrum to a synthetic spectrum computed from a molecular potential model. In a single scan, the frequency offset was determined from the comb spectrum with an uncertainty of $\sim$1 cm s$^{-1}$. The distribution of comb line frequencies is consistent with no deviation from linearity. The iodine observation matches the model with an offset of smaller than the model uncertainties of $\sim$1 m s$^{-1}$, which confirms that the FTS zero point is valid outside the range covered by the LFC, and that the frequencies of the iodine absorption model are accurate. We also report small systematic effects regarding the iodine model's energy scale. We conclude that Fourier Transform Spectrometry can transfer LFC accuracy into frequency ranges not originally covered by the comb. This allows us to assign accurate frequency scales to the spectra of customized wavelength calibrators. The calibrators can be optimized for individual spectrograph designs regarding resolution and spectral bandwidth, and requirements on their long-term stability are relaxed because FTS monitoring can be performed during operation. This provides flexibility for the design and operation of calibration sources for high-precision Doppler experiments., Comment: 10 pages, accepted for publication in A&A, abstract shortened for arXiv version

Gaining control over chemical reactions on the quantum level is a central goal of the modern field of cold and ultracold chemistry. Here, we demonstrate a novel method to coherently steer reaction flux of a three-body recombination process across different product spin channels. For this, we employ a magnetically-tunable Feshbach resonance to admix, in a controlled way, a specific spin state to the reacting collision complex. This allows for the control of the reaction flux into the admixed spin channel, which can be used to significantly change the reaction products. Furthermore, we also investigate the influence of an Efimov resonance on the reaction dynamics. We find that while the Efimov resonance can be used to globally enhance three-body recombination, the relative flux between the reaction channels remains unchanged. Our control scheme is general and can be extended to other reaction processes. It also provides new opportunities in combination with other control schemes, such as quantum interference of reaction paths., Comment: 9 pages, 6 figures

We propose a scheme to perform optical pulses that suppress the effect of photon recoil by three orders of magnitude compared to ordinary pulses in the Lamb-Dicke regime. We derive analytical insight about the fundamental limits to the fidelity of optical qubits for trapped atoms and ions. This paves the way towards applications in quantum computing for realizing $>1000$ of gates with an overall fidelity above 99\%., Comment: 5 pages plus appendices and bibliography, 6 figures

A low energy particle confined by a horizontal reflective surface and gravity settles in gravitationally bound quantum states. These gravitational quantum states (GQS) were so far only observed with neutrons. However, the existence of GQS is predicted also for atoms. The GRASIAN collaboration pursues the first observation of GQS of atoms, using a cryogenic hydrogen beam. This endeavor is motivated by the higher densities, which can be expected from hydrogen compared to neutrons, the easier access, the fact that GQS were never observed with atoms and the accessibility to hypothetical short range interactions. In addition to enabling gravitational quantum spectroscopy, such a cryogenic hydrogen beam with very low vertical velocity components - a few cm s$^{-1}$, can be used for precision optical and microwave spectroscopy. In this article, we report on our methods developed to reduce background and to detect atoms with a low horizontal velocity, which are needed for such an experiment. Our recent measurement results on the collimation of the hydrogen beam to 2 mm, the reduction of background and improvement of signal-to-noise and finally our first detection of atoms with velocities < 72 m s$^{-1}$ are presented. Furthermore, we show calculations, estimating the feasibility of the planned experiment and simulations which confirm that we can select vertical velocity components in the order of cm s$^{-1}$.

Power lines are dangerous for low-flying aircraft, especially in low-visibility conditions. Thus, a vision-based system able to analyze the aircraft's surroundings and to provide the pilots with a "second pair of eyes" can contribute to enhancing their safety. To this end, we have developed a deep learning approach to jointly detect power line cables and pylons from images captured at distances of several hundred meters by aircraft-mounted cameras. In doing so, we have combined a modern convolutional architecture with transfer learning and a loss function adapted to curvilinear structure delineation. We use a single network for both detection tasks and demonstrated its performance on two benchmarking datasets. We have integrated it within an onboard system and run it in flight, and have demonstrated with our experiments that it outperforms the prior distant cable detection method on both datasets, while also successfully detecting pylons, given their annotations are available for the data., Comment: Added several declarations at the end of the publication

The mechanism of antiproton-nucleus annihilation at rest is not fully understood, despite substantial previous experimental and theoretical work. In this study we used slow extracted, sub-keV antiprotons from the ASACUSA apparatus at CERN to measure the charged particle multiplicities and their energy deposits from antiproton annihilations at rest on three different nuclei: carbon, molybdenum and gold. The results are compared with predictions from different models in the simulation tools Geant4 and FLUKA. A model that accounts for all the observed features is still missing, as well as measurements at low energies, to validate such models., Comment: 25 pages + 2 cover pages, 16 figures

We show that, in dimension three and higher, the space of harmonic functions vanishing on the cone defined by a generically chosen harmonic quadratic polynomial is two-dimensional. This phenomenon is surprisingly robust, generalizing to arbitrary elliptic differential operators of second order, with the cone replaced by the level set of a solution at a nondegenerate critical value. As long as the tangent cone to the level set at the critical point satisfies a certain genericity condition, the space of solutions vanishing on the level set is at most two-dimensional., Comment: 27 pages, 3 figures

We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity., Comment: 33 pages, 4 figures

Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space denoted as $\mathcal{H}_{\vartheta}$, where $\vartheta\in\{p,bp,r\}$, as an extension of the Hahn sequence space $h$. Our investigation begins with an analysis of several topological properties of $\mathcal{H}_{\vartheta}$, apart from a comprehensive analysis of the relationship between Hahn double sequences and some other classical double sequence spaces. The $\alpha-$dual, algebraic dual and $\beta(bp)-$dual, and $\gamma-$dual of the space $\mathcal{H}_{\vartheta}$ are detrmined. Furthermore, we define the determining set of $\mathcal{H}_{\vartheta}$ and we state the conditions concerning the characterization of four-dimensional (4D) matrix classes $(\mathcal{H}_{\vartheta},\lambda)$, where $\lambda=\{\mathcal{H}_{\vartheta},\mathcal{BV}, \mathcal{BV}_{\vartheta 0}, \mathcal{CS}_{\vartheta},\mathcal{CS}_{\vartheta 0},\mathcal{BS}\}$ and $(\mu,\mathcal{H}_{\vartheta})$, where $\mu=\{\mathcal{L}_u, \mathcal{C}_{\vartheta 0}, \mathcal{C}_{\vartheta},\mathcal{M}_{u}\}$. In conclusion, this research contributes non-standard investigation and various significant results into the space $\mathcal{H}_{\vartheta}$. The conducted results are deepen the understanding of the space $\mathcal{H}_{\vartheta}$ and open up new avenues for further research and applications in sequence space theory.

Reinforcement learning has traditionally focused on learning state-dependent policies to solve optimal control problems in a closed-loop fashion. In this work, we introduce the paradigm of open-loop reinforcement learning where a fixed action sequence is learned instead. We present three new algorithms: one robust model-based method and two sample-efficient model-free methods. Rather than basing our algorithms on Bellman's equation from dynamic programming, our work builds on Pontryagin's principle from the theory of open-loop optimal control. We provide convergence guarantees and evaluate all methods empirically on a pendulum swing-up task, as well as on two high-dimensional MuJoCo tasks, demonstrating remarkable performance compared to existing baselines.

Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative reduced costs. This process continues until the dual values converge to the optimal dual solution to the original problem. A natural phenomenon in CG is the heavy oscillation of the dual values during iterations, which can lead to a substantial slowdown in the convergence rate. Stabilization techniques are devised to accelerate the convergence of dual values by using information beyond the state of the current subproblem. However, there remains a significant gap in obtaining more accurate dual values at an earlier stage. To further narrow this gap, this paper introduces a novel approach consisting of 1) a machine learning approach for accurate prediction of optimal dual solutions and 2) an adaptive stabilization technique that effectively capitalizes on accurate predictions. On the graph coloring problem, we show that our method achieves a significantly improved convergence rate compared to traditional methods., Comment: Accepted by ICML'24

The long-term usability of digital building documents is essential for the maintenance and optimization of infrastructure portfolios. It supports the preservation of building-specific knowledge and the cultural heritage hidden within. However, having to do this throughout the lifecycle of a building - or even indefinitely - remains a major challenge. This is especially true for organizations responsible for large collections of digital building documents, such as public administrations or archives. In this article, we first describe the challenges and requirements associated with preservation tasks, and then introduce the concept of so-called representation information within BIM (Building Information Modeling). This type of information is important to give meaning to the stored bit sequences for a particular community. Then, we design a repository for representation information and introduce some so-called 23 BIMcore content elements. Finally, we focus on BIM and the construction sector and explain how the proposed repository can be used to implement the two concepts introduced in the ISO reference model OAIS (Open Archival Information System), namely the representation information and the context information, as well as the concept of significant properties, which has not yet been explicitly modeled in OAIS., Comment: 14 pages, 4 figures

Particle tracking in turbulent flows is fundamental to the study of the transport of tracers, inertial particles or even active objects in space and time, i.e. the Lagrangian frame of reference. It provides experimental tests of theoretical predictions (e.g. for the statistics of fluid accelerations and particle dispersion) and helps to understand important natural processes where particle inertia is important (e.g. cloud microphysics). While the spatial (Eulerian) properties of turbulent flows have been studied for high, atmospheric Reynolds numbers ($R_\lambda > 10^4$), the profound difficulties in accurately tracking particles in turbulent flows have limited the Reynolds numbers in the Lagrangian reference frame to the Taylor scale Reynolds numbers $R_\lambda \lesssim 10^3$. Here we describe a setup that allowed Lagrangian particle tracking at $R_\lambda$ between 100 and 6000 in the Max Planck Variable Density Turbulence Tunnel (VDTT). We describe the imaging setup within the pressurised facility, the laser illumination, the particles and the particle dispersion mechanism. We verify that the KOBO Cellulobeads D-10 particles are suitable tracers. They carry negligible charge and their Stokes number is small over the full range of experimental conditions. We present typical data from the experiment and discuss the challenges and constraints of the setup.

In Model Predictive Control (MPC), discrepancies between the actual system and the predictive model can lead to substantial tracking errors and significantly degrade performance and reliability. While such discrepancies can be alleviated with more complex models, this often complicates controller design and implementation. By leveraging the fact that many trajectories of interest are periodic, we show that perfect tracking is possible when incorporating a simple observer that estimates and compensates for periodic disturbances. We present the design of the observer and the accompanying tracking MPC scheme, proving that their combination achieves zero tracking error asymptotically, regardless of the complexity of the unmodelled dynamics. We validate the effectiveness of our method, demonstrating asymptotically perfect tracking on a high-dimensional soft robot with nearly 10,000 states and a fivefold reduction in tracking errors compared to a baseline MPC on small-scale autonomous race car experiments., Comment: 8 pages, 3 figures; 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

We present a Rabi-type measurement of two ground-state hydrogen hyperfine transitions performed in two opposite external magnetic field directions. This puts first constraints at the level of 2.3 10^-21 GeV on a set of coefficients of the Standard Model Extension, which were not measured by previous experiments. Moreover, we introduce a novel method, applicable to antihydrogen hyperfine spectroscopy in a beam, that determines the zero-field hyperfine transition frequency from the two transitions measured at the same magnetic field. Our value, nu_0 = 1.420 405 751 63(63) GHz, is in agreement with literature at a relative precision of 0.44 ppb. This is the highest precision achieved on hydrogen in a beam, improving over previous results by a factor of 6., Comment: 8 pages, 5 figures, 2 tables, corresponding author: chloe.m@cern.ch (C. Malbrunot)

Direct-sampling observations of interstellar neutral gas, including hydrogen and deuterium, have been performed for more than one cycle of solar activity by IBEX. IBEX viewing is restricted to directions perpendicular to the spacecraft--Sun line, which limits the observations to several months each year. This restriction is removed in a forthcoming mission Interstellar Mapping and Acceleration Probe. The IMAP-Lo instrument will have a capability of adjusting the angle of its boresight with the spacecraft rotation axis. We continue a series of studies of resulting science opportunities. We adopt a schedule of adjusting the boresight angle suggested by Kubiak et al. 2023 and focus on interstellar hydrogen and deuterium during solar maximum epoch. Based on extensive set of simulations, we identify the times during calendar year and elongation angles of the boresight needed to measure the abundance of D/H at the termination shock and unambiguously observe interstellar H without contribution from interstellar He. Furthermore, IMAP-Lo will be able to resolve the primary and secondary populations, in particular to view the secondary population with little contribution from the primary. We show that the expected signal is sensitive to details of radiation pressure, particularly its dependence on radial speed of the atoms, and to details of the behavior of the distribution function of the primary and secondary populations at the heliopause. Therefore, IMAP-Lo will be able to provide observations needed to address compelling questions of the heliospheric physics, and even general astrophysics.

A pure topological characterization of primitive ideal spaces of separable nuclear C*-algebras is given. We show that a $T_0$-space $X$ is a primitive ideal space of a separable nuclear C*-algebra $A$ if and only if $X$ is point-complete second countable, and there is a continuous pseudo-open and pseudo-epimorphic map from a locally compact Polish space $P$ into $X$. We use this pseudo-open map to construct a Hilbert bi-module $\mathcal{H}$ over $C_0(X)$ such that $X$ is isomorphic to the primitive ideal space of the Cuntz--Pimsner algebra $\mathcal{O}_\mathcal{H}$ generated by $\mathcal{H}$. Moreover, our $\mathcal{O}_\mathcal{H}$ is $KK(X;.,.)$-equivalent to $C_0(P)$ (with the action of $X$ on $C_0(P)$ given be the natural map from $\mathbb{O}(X)$ into $\mathbb{O}(P)$, which is isomorphic to the ideal lattice of $C_0(P)$. Our construction becomes almost functorial in $X$ if we tensor $\mathcal{O}_\mathcal{H}$ with the Cuntz algebra $\mathcal{O}_2$., Comment: This paper was written in 2005 and is now uploaded to the arXiv on the recommendation of several colleagues. The second named author passed away August, 2022

In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka--Lojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem.

Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a na\"ive shadow price Ansatz for maximizing long term returns given average volatility yields a strategy that is, for small bid-ask-spreads, asymptotically optimal at third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices., Comment: 18 pages

In this paper, we address the well-posedness of an evaporation model for a spherical liquid droplet taking into account the convective impact of an air flow in the ambient gas phase. From a mathematical perspective, we are dealing with a coupled ODE-PDE system for the droplet radius, the temperature distribution, and the vapor concentration. The nonlinear coupling arises from the evaporation rate modeled by the Hertz-Knudsen equation. Under physically meaningful assumptions, we prove existence and uniqueness of a weak solution until the droplet has evaporated completely. Numerical simulations are performed to illustrate how different air flows affect the evaporation process.

We give a number of examples of exotic actions of locally compact groups on separable nuclear C*-algebras. In particular, we give examples of the following: (1) Minimal effective actions of ${\mathbb{Z}}$ and $F_n$ on unital nonsimple prime AF algebras. (2) For any second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra. (3) For any amenable second countable noncompact locally compact group, a minimal effective action on a separable nuclear nonsimple prime C*-algebra (unital when the group is ${\mathbb{Z}}$ or ${\mathbb{R}}$) such that the crossed product is $K \otimes {\mathcal{O}}_2$ (${\mathcal{O}}_2$ when the group is ${\mathbb{Z}}$). (4) For any second countable locally compact abelian group which is not discrete, an action on $K \otimes {\mathcal{O}}_2$ such that the crossed product is a nonsimple prime C*-algebra. In most of these situations, we can specify the primitive ideal space of the C*-algebra (of the crossed product in the last item) within a class of spaces., Comment: This paper was nearly done about 10 years ago, but was pushed aside under the press of other projects, and then forgotten. It is now being posted, after Kirchberg's death. The key preprint of Harnisch and Kirchberg was never published and has disappeared from the website of the Universitaet Muenster. It is temporarily at: https://pages.uoregon.edu/ncp/Research/Misc/heft399.pdf

In the search for clues to the matter-antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to $10^{-30}$ e.cm on electron EDM using molecular ions, and relative measurements at the level of $10^{-12}$ in spectroscopy of antihydrogen atoms. Building on these impressive measurements, new experimental directions offer potentials for drastic improvements. We review here some of the new perspectives in those fields and their associated prospects for new physics searches.

Let $G$ be a finite classical group generated by transvections, i.e., one of $\operatorname{SL}_n(q)$, $\operatorname{SU}_n(q)$, $\operatorname{Sp}_{2n}(q)$, or $\operatorname{O}^\pm_{2n}(q)$ ($q$ even), and let $X$ be a generating set for $G$ containing at least one transvection. Building on work of Garonzi, Halasi, and Somlai, we prove that the diameter of the Cayley graph $\operatorname{Cay}(G, X)$ is bounded by $(n \log q)^C$ for some constant $C$. This confirms Babai's conjecture on the diameter of finite simple groups in the case of generating sets containing a transvection. By combining this with a result of the author and Jezernik it follows that if $G$ is one of $\operatorname{SL}_n(q)$, $\operatorname{SU}_n(q)$, $\operatorname{Sp}_{2n}(q)$ and $X$ contains three random generators then with high probability the diameter $\operatorname{Cay}(G, X)$ is bounded by $n^{O(\log q)}$. This confirms Babai's conjecture for non-orthogonal classical simple groups over small fields and three random generators., Comment: 39 pages. Final version

Here, we report a novel and conceptually straightforward technique to detect the spin-polarization directly, with laser spot spatial resolution, at buried ferromagnet/insulator interfaces in ambient settings. This has been accomplished by monitoring the voltage-induced change of the longitudinal MOKE signal as a function of the applied magnetic field and applying an AC voltage across the interface. For the case where the spin polarization enters the VMOKE signal, a simple quantitative model is proposed. A distinct positive majority spin polarization has been found for Fe and Co, whereas Ni exhibits a negative minority spin polarization.

Without using the classification of finite simple groups, we show that the probability that two random elements of $S_n$ generate a primitive group smaller than $A_n$ is at most $\exp(-c(n \log n)^{1/2})$. As a corollary we get Dixon's asymptotic expansion \[ 1 - 1/n - 1/n^2 - 4/n^3 - 23/n^4 - \cdots \] for the probability that two random elements of $S_n$ (or $A_n$) generate a subgroup containing $A_n$., Comment: 4 pages