We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the singular set are sufficiently mean-convex. Our proof uses initial data sets where a suitably chosen second fundamental form transfers convexity defects between different singularity components.

For precision atomic magnetometry, inert buffer gas is included in alkali-metal vapor cells to significantly broaden hyperfine transitions, which facilitates optical pumping and reduces diffusive relaxation, while also providing non-radiative excited state quenching. We show low-buffer gas pressure (below 50 Torr) alkali vapor cells with resolved hyperfine manifolds can also yield high-performance magnetometers. For high polarization in $^{87}$Rb, we optically pump $F=2$ states with narrow linewidth $σ_+$ light, while tuning a probe beam to depopulate $F=1$ states ($Δν= 6.8$ GHz from $F=2$). The probe tuning then also provides $F=2$ detection with high optical rotation and low probe broadening; we demonstrate top-bottom gradiometry, within a single 25 Torr, 0.5 cc cell, that yields an Earth's field free-precession magnetometer sensitivity of 18 fT/$\sqrt{\text{Hz}}$ with a 1 kHz bandwidth, as well as RF magnetometer sensitivity of 12 fT/$\sqrt{\text{Hz}}$ in a small band about 110 kHz.

We present a curated dataset of planar displacement fields from eight fatigue crack growth experiments obtained via full-field digital image correlation (DIC). The dataset covers multiple aerospace-grade aluminium alloys, specimen geometries, material orientations, and load configurations, providing a diverse experimental basis for data-driven fracture mechanics research. Crack tip locations are consistently annotated using an iterative correction procedure applied to all measurements, and fracture mechanical descriptors like stress-intensity factors are provided as additional labels. The dataset comprises 8,794 unique experimentally observed displacement fields and a total of 70,352 supervised samples generated through standardized interpolation and augmentation. DIC data is provided as uniformly interpolated displacement grids at three standardized resolutions 28 x 28, 64 x 64, and 128 x 128 pixels, each available in three dataset sizes to support scalable use cases ranging from educational applications to high-capacity model development. Accompanying metadata and a Python interface facilitate filtering, loading, and integration into reproducible machine learning and fracture mechanics workflows.

We study the generalized rank weight distribution of a linear code. First, we provide a MacWilliams-type identity which relates the distributions of a code and its dual. Then, we give a formula for the enumerator polynomial. Finally, we explicitly compute the distribution of an MRD code.

Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale modeling of these materials is defining the macroscopic polarization. In a periodic crystal, the usual definition of the polarization as the first moment of the charge density in a unit cell is found to depend qualitatively - allowing even a change in the sign - and quantitatively on the choice of unit cell. We examine this issue using a rigorous approach based on the framework of 2-scale convergence. By examining the continuum limit of when the lattice spacing is much smaller than the characteristic dimensions of the body, we show that the 2-scale limit provides both a bulk polarization as well as a surface charge density supported on the boundary of the body. Further, different choices of the periodic unit cell of the body lead to correspondingly different partial unit cells at the boundary; these choices give to different bulk polarization and surface charges but compensate such that the electric field and energy are independent of the choice of unit cell.

These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$-Positivity Preserver, and their Generators''. The lecture was given at the University of Konstanz in the winter semester 2025/26.

This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive set of ultra high-frequency equity and foreign exchange tick data recorded at millisecond precision, allowing us to examine the price evolution at the individual order level. We show that in both theory and practice, traditional measures of jump variation based on lower-frequency data tend to spuriously assign a burst of volatility to the jump component. As a result, the true price variation coming from jumps is overstated. Our estimates based on tick data suggest that the jump variation is an order of magnitude smaller than typical estimates found in the existing literature.

Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference on individuals' unobserved disease statuses over time, which form a high-dimensional and highly correlated state space. We introduce a novel Bayesian (data-augmentation Markov chain Monte Carlo) algorithm for jointly estimating the model parameters and unobserved disease statuses, which we call the Rippler algorithm. This is a non-centred method that can be applied to any individual-based state-transition model. We compare the Rippler algorithm to the state-of-the-art inference methods for individual-based stochastic epidemic models and find that it performs better than these methods as the number of disease states in the model increases.

We address data assimilation for linear and nonlinear dynamical systems via the so-called \emph{model reference adaptive system}. Continuing our theoretical developments in \cite{Tram_Kaltenbacher_2021}, we deliver the first practical implementation of this approach for online parameter identification with time series data. Our semi-implicit scheme couples a modified state equation with a parameter evolution law that is driven by model-data residuals. We demonstrate four benchmark problems of increasing complexity: the Darcy flow, the Fisher-KPP equation, a nonlinear potential equation and finally, an Allen-Cahn type equation. Across all cases, explicit model reference adaptive system construction, verified assumptions and numerically stable reconstructions underline our proposed method as a reliable, versatile tool for data assimilation and real-time inversion.

We report the discovery of a new massive giant planet, HD 164604 c ($a_c = 5.556_{-0.10}^{+0.093}$ au, $e_c = 0.196_{-0.078}^{+0.078}$ and $m_c = 9.5_{-1.25}^{+1.2}$ or $7.6_{-1.0}^{+1.0}\,M_{\rm Jup}$), orbiting a K3.5 dwarf, The result is based on the combined analysis of high-precision radial-velocity data, Hipparcos, and Gaia DR2 and DR3 astrometry. We refine the orbital parameters of the inner planet HD 164604 b to $a_b = 1.362_{-0.012}^{+0.012}$ au, $e_b = 0.479_{-0.021}^{+0.027}$, and $m_b = 13.2_{-1.5}^{+1.8}\,M_{\rm Jup}$ (or $8.8_{-1.5}^{+1.9}\,M_{\rm Jup}$). Depending on the two possible orbital orientations of HD 164604 c, the true mutual inclination between the two planets is $ψ_{bc}=5.0^{+3.7}_{-2.2}$$^\circ$ (prograde) or $162.1^{+7.1}_{-4.7}$$^\circ$ (retrograde). Long-term N-body integrations show that most orbits with the retrograde configuration remain dynamically stable for at least 10 Myr, while orbits with the prograde motion might rapidly evolve into chaos or lead to ejection. The retrograde architecture points to a violent dynamical history, possibly involving von Zeipel-Lidov-Kozai cycles or three-body scattering, while the prograde scenario might be consistent with coplanar and mild disk migration. Future Gaia DR4 astrometry will break the inclination degeneracy and distinguish between prograde and retrograde orbits for HD 164604 c.

A robust stellar initial mass function (IMF) is crucial in any studies related to star formation. However, the direct measurement of the stellar IMF is confined to the local universe, limited by the resolving power of telescopes. Recently, a new method for accessing the stellar IMF beyond the local universe has been developed. The observed detection rate of transient lensed stars -- individual, massive, thus luminous stars in strongly lensed galaxies that are temporarily detectable upon stellar microlensing -- can serve as a probe to break the IMF-star formation history degeneracy in studies utilizing spectral energy distribution fitting, hence providing a window to look at the IMF at a subsample of gravitationally lensed galaxies. In this proceeding, I summarize the contributed talk given at IAUS402 entitled the same as this contribution and highlight some key results, which currently show no evidence for a top-heavy IMF in $z \approx 1$ galaxies.

The double copy is by now a well-established relationship between scattering amplitudes and classical solutions in gauge and gravity (field) theories, and is itself inspired by amplitude relations in string theory. In this paper, we generalise the classical double copy to the motion of strings, taking as a case study the motion of an open string in a background abelian gauge field. We argue that the double copy of this situation is a closed string moving in a spacetime background arising as the double copy of the gauge theory background. The gauge theory background we consider is that of a constant electric field, which has a critical value beyond which the open string motion is pathological. We find no counterpart of this behaviour in the double copy, and interpret this result. We then examine how the closed string nevertheless still knows about the single copy gauge theory. Our results pave the way for more systematic study of the double copy in a classical string context, thus going beyond the KLT relations for amplitudes in flat space.

Retinal implants aim to restore functional vision despite photoreceptor degeneration, yet are fundamentally constrained by low resolution electrode arrays and patient-specific perceptual distortions. Most deployed encoders rely on task-agnostic downsampling and linear brightness-to-amplitude mappings, which are suboptimal under realistic perceptual models. While global inverse problems have been formulated as neural networks, such approaches can be fast at inference, and can achieve high reconstruction fidelity, but require training and have limited generalizability to arbitrary inputs. We cast stimulus encoding as a constrained sparse least-squares problem under a linearized perceptual forward model. Our key observation is that the resulting perception matrix can be highly sparse, depending on patient and implant configuration. Building on this, we apply an efficient projected residual norm steepest descent solver that exploits sparsity and supports stimulus bounds via projection. In silico experiments across four simulated patients and implant resolutions from $15\times15$ to $100\times100$ electrodes demonstrate improved reconstruction fidelity, with up to $+0.265$ SSIM increase, $+12.4\,\mathrm{dB}$ PSNR, and $81.4\%$ MAE reduction on Fashion-MNIST compared to Lanczos downsampling.

We analyze the rare semileptonic decays $B_{c}^+ \to D^{\ast+}(\to P_1 P_2)\ell^{+}\ell^{-}$, with $P_1 P_2 = D^+ π^0$ or $D^0 π^+$, and $\ell=μ, τ$. We focus on the impact of weak annihilation contributions alongside penguin, box, and long-distance effects. Using the effective Hamiltonian for $b \to d \ell^+ \ell^-$ transitions and $B_c \to D^{*}$ form factors from covariant confined quark model inputs, we compute the differential branching ratios, forward-backward asymmetry, longitudinal helicity fraction of the $D^{\ast}$, and various normalized angular coefficients. The results of the observables show that weak annihilation effects are sizable, particularly at low $q^2$, significantly modifying several observables and shifting zero-crossings. Resonance effects dominate at high $q^2$, restricting reliable analysis windows. We conclude that the inclusion of weak annihilation is essential for precise Standard Model predictions and for isolating possible New Physics effects in $B_c^+ \to D^{*+} \ell^+ \ell^-$ decays.

Pollux is a high-resolution spectropolarimeter proposed by an European consortium for HWO. The current design of Pollux features four spectropolarimetric channels, three of which are in the UV range. For the near-UV (NUV) [236-472 nm] and mid-UV (MUV) [118-236 nm] channels, the polarimeters consist of waveplates and prisms made of MgF2, a birefringent material. However, no such birefringent material can be used for the far-UV (FUV) channel [100-123 nm]. Therefore, the polarimeter for this FUV channel is composed solely of mirrors in an innovative assembly. In this talk, we aim to detail the architecture of the test bench that will allow us to validate the performance of these different polarimeters, as part of the HWO GOMaP. Given that we are working in the vacuum ultraviolet (VUV) range, the test bench operates in a vacuum chamber in a clean room. We will discuss the adaptable architecture of the bench based on wavelength and the measurement methodology that we will implement to test if the polarimeters achieve the precision of $10^{-3}$ required for the Pollux instrument. With this test bench, we will successfully increase the Technology Readiness Level (TRL) of UV spectropolarimeters and, for the first time, develop a means to test FUV spectropolarimetry.

We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $Ψ$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle Ψ^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $η$ and retaining terms through $O(η^2)$, we find that $\langle Ψ^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result - with the event horizon radius modified by the presence of $η$. Our result parallels earlier analyses for Schwarzschild black holes pierced by a cosmic string.

For generalized Frenkel-Kontorova models subjected to almost-periodic media, employing both the KAM method and the approach of `anti-integrable' limits, two different types of equilibria are obtained in \cite{an2024kamtheoryalmostperiodicequilibria} and \cite{du2024anti} respectively. We study the phonon gap around these equilibria and we find that the KAM equilibria do not have a phonon gap but the equilibria obtained by anti-integrable limits do have.

High backgrounds and detector ageing impact the track finding in the Belle II central drift chamber, reducing both track purity and track efficiency in events. This necessitates the development of new track finding algorithms to mitigate detector performance degradation. Building on our previous success with an end-to-end multi-track reconstruction algorithm for the Belle II experiment at the SuperKEKB collider (arXiv:2411.13596), we have extended the algorithm to incorporate inputs from both the drift chamber and the silicon vertex tracking detector, creating a multi-modal network. We employ graph neural networks to handle the irregular detector structure and object condensation to address the unknown, varying number of particles in each event. This approach simultaneously identifies all tracks in an event and determines their respective parameters. We demonstrate the algorithm's effectiveness using a realistic full detector simulation, which incorporates beam-induced backgrounds and noise modelled from actual collision data. The simultaneous reconstruction of the information from the two detectors yields a track efficiency improvement from 48.0 % to 74.7 % for uniformly displaced particles up to 100 cm, while increasing the track purity by 5.5 percentage points. We provide a detailed comparison of its track-finding performance against the current Belle II baseline across various event topologies.

Fast radio burst (FRB) is mysterious phenomenon with millisecond-duration radio pulses observed mostly from cosmological distance. The association between FRB 200428 and a magnetar X-ray burst (MXB) from SGR J1935+2154 has significantly advanced the understanding of FRB and magnetar bursts. However, it is uncertain whether this association between MXB and FRB (i.e. MXB/FRB 200428) is genuine or just coincidental only based on this single event. Here we report the discovery of a bright ($\rm\sim7.6\times10^{-7}\,erg \cdot cm^{-2}$ in 1-250 keV) magnetar X-ray burst detected by GECAM on October 14th, 2022 (dubbed as MXB 221014) from SGR J1935+2154, which is associated with a FRB detected by CHIME and GBT. We conducted a detailed temporal and spectral analysis of MXB 221014 with GECAM data and find that it is a bright and typical ($T_{90}\sim$250 ms) X-ray burst from this magnetar. Interestingly, we find two narrow X-ray pulses in the MXB, one of which temporally aligns with the main pulse of the FRB 221014 $\sim5.70$ ms latter than the peak time of FRB 221014), resembling the feature found in MXB/FRB 200428. Furthermore, we did comprehensive comparison between MXB/FRB 221014 and MXB/FRB 200428, and find that while the two events share several common features, they also exhibit distinct differences, highlighting the variety of the MXB-FRB association morphology. This finding not only confirms the association between MXB and FRB but also provides new insights into the mechanism of and the relationship between FRB and MXB.

Beyond cosmic noon, galaxies appear as faint whispers amid noise, yet this epoch is key to understanding massive galaxy assembly. ALMA's sensitivity to cold dust and [C II] emission allows us to probe their interstellar medium, but faint signals make robust denoising essential. We evaluate and benchmark denoising strategies including Principal Component Analysis, Independent Component Analysis, sparse unsupervised representations: iterative soft thresholding with 2D-1D wavelets, and supervised deep learning with a 3D U-Net, to identify techniques that suppress noise while preserving flux and morphology across peak SNRs of 2.5-8, applied to (i) synthetic spectral cubes of rotating toy disk galaxies, (ii) synthetic [C II] IFU cubes from FIRE simulations, and (iii) ALMA [C II] observations of CRISTAL galaxies and W2246-0526. Performance is assessed via RMSE, conservation of flux and spectra, noise reduction, and SNR improvement of the central galaxy. For synthetic cubes: PCA and ICA provide marginal improvement; IST reduces noise effectively at moderate SNRs but can suppress emission at low SNRs; and the U-Net outperforms IST, though it can produce quantifiable hallucinations at lower-SNRs. For moderate-SNR observations (ALMA-CRISTAL), U-Net and IST achieve comparable performance, conserving >91% flux and increasing SNR by >6. However, for observations with complex morphologies absent in the training set (W2246), the U-Net underperforms relative to IST, recovering ~80% flux, while IST robustly conserves flux and improves SNR by ~3, highlighting generalisation challenges and the need for physically-motivated training priors. We conclude that IST is a robust unsupervised denoiser for moderate-SNR data, and a synthetically trained U-Net generalises effectively to real data, dependent on training priors. This framework offers a pathway for transferable denoising for ALMA, VLT/MUSE, and JWST.

In this work we study arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are thus particularly suited for problems that include both diffusive and advective terms. The family of numerical schemes proposed in this work hinge on hybrid spaces with unknowns located at elements and faces. They support general meshes, are locally conservative and, compared with traditional Discontinuous Galerkin discretizations, lead to smaller algebraic systems once static condensation has been applied. We carry out a complete stability and convergence analysis, which appears to be the first of its kind. The performance of the method is illustrated on scalar and vector three-dimensional diffusion-advection-reaction problems.

We study the propagation of massless scalar waves in static, spherically symmetric Lorentz-violating wormhole spacetimes within a geometric-optical framework. Starting from a general metric characterized by an arbitrary lapse function and areal radius, we derive curvature invariants, establish regularity conditions at the wormhole throat, and reduce the Klein-Gordon equation to a Helmholtz-type radial wave equation. This formulation naturally leads to a position- and frequency-dependent effective refractive index determined by the underlying spacetime geometry and Lorentz-violating structure, resulting in effective frequency-dependent wave-optical behavior. We show that divergences of the refractive index coincide with Killing horizons, while curvature-induced turning points control reflection, transmission, and confinement of scalar waves. By analyzing constant, linear, and quadratic lapse profiles, we identify horizonless transmission regimes, asymmetric wave propagation, and multi-horizon trapping structures. Our results reveal that Lorentz violation can significantly modify wave-optical properties of curved spacetime, generating graded-index analogues and geometric confinement of modes without curvature singularities. This unified optical perspective provides a robust framework for investigating wave scattering, resonances, and potential observational signatures in Lorentz-violating gravitational backgrounds.

H-band spectra contain very limited spectral information for stars at the most metal-poor tail ( Fe/H < -2.5) because the available Fe lines in FGK stars in this wavelength range are weak. The first paper in this series successfully identified a sample of 327 very metal-poor stars (with [Fe/H] < -2) from the APOGEE database, 289 of which are on the red giant branch. The spectra of these stars were not properly analysed by the APOGEE main pipeline because they are very metal poor. In this work, we measure metallicities for these stars using the abundances of the elements Mg and Si. We demonstrate that the absorption lines of the elements Mg and Si are of good quality despite the challenging combination of (low) metallicity, wavelength regime, spectral resolution, and signal-to-noise ratios available for these spectra. A specialised pipeline was designed to measure the abundance of Mg and Si in APOGEE spectra and yielded a robust estimate of the overall metallicity. In order to provide reliable measurements, we tested three different sets of assumptions for Mg and Si enhancement. We present Mg and Si abundances as well as overall metallicities for 327 stars, all of which had previously gotten null values from the main APOGEE pipeline for either the calibrated M/H or [Fe/H] . The typical uncertainties for our measurements are 0.2 dex. We found five stars in our sample with unusual [Si/Mg] abundances higher than 0.5, and we connect this signature to globular cluster stars, and this might be related to specific supernova events. Our data suggest a concentration of high [Si/Mg] stars in the Sextans dwarf galaxy. Other dwarf galaxies are found to agree well with results in the literature. Our derived metallicities range between -3.1 $\leq$ [M/H] $\leq$ -2.25, thereby pushing the metal-poor tail of APOGEE results down by 0.6 dex.

We present a simple methodology to compute the anomalous Hall conductivity (AHC) as a function of the canting angles in ferromagnets and altermagnets, starting from a nonmagnetic Hamiltonian obtained from first-principles calculations that preserves the full symmetry of the crystal structure. Magnetism is introduced by including on-site spin splitting, spin-orbit coupling, and spin-canting angles. As a representative material, we study SrRuO$_3$, which supports spin canting and exhibits a sign change of the AHC. In the ferromagnetic phase, the low-energy AHC is found to be close to zero at the Fermi level, in agreement with experimental observations. We show that the dependence of the AHC on the relevant physical parameters is most pronounced in the central region of the electronic bandwidth. We determine the symmetry-allowed components of the AHC for different magnetic orders in the large family of transition-metal perovskite ABO$_3$ compounds with space group $62$, including the spontaneous in-plane anomalous Hall effect. Within density functional theory, we evaluate the range of spin-canting angles in SrRuO$_3$ and demonstrate that it is suppressed as electronic correlations increase. By analyzing the AHC as a function of the canting angle, we find that the collinear magnetic configurations contribute most to the AHC, while spin canting plays a secondary role in determining its magnitude in non-collinear ferromagnets and altermagnets. However, canting can become relevant and induce a sign change of the AHC when the collinear magnetic state exhibits an AHC close to zero. Finally, we investigate the locations of Weyl points in the Brillouin zone and their evolution as a function of the canting angle.

We experimentally investigate four-wave mixing (FWM) of matter waves in two geometric configurations in $^{39}$K Bose-Einstein condensates with the atomic interaction tuned via Feshbach resonances. For one configuration with the single-spin component, the FWM yield increases with a larger scattering length. For the two-spin component configuration, we specifically investigate FWM in both the droplet and gas parameter regimes. We find that the FWM yield reaches its maximum near the critical parameter region between the gas and droplet phases. Our research can help to optimize the FWM yield for matter-wave amplification and entangled atom pair generation, making it conducive to applications in quantum information processing and precision measurement.

We present our novel evolutionary algorithm for generating Special Quasirandom Structures (SQS) designed to optimize the computational efficiency of Density Functional Theory (DFT) computations. Operating on the premise that symmetry proxies non-randomness, we rigorously filter out 1.P1 candidate structures prior to evaluating correlation functions. Our extinction-based workflow includes the seeding, filtration, evaluation, extinction, and repopulation phases to produce efficient supercells with maximal local environmental distinctness. We compare our results against those generated by established software packages, on the example of the W\textsubscript{70}Cr\textsubscript{30} alloy. Although standard tools achieve (marginally) lower correlation errors, our best-performing structures require approximately five times fewer unique displacements for phonon calculations. This approach sacrifices negligible quantitative disorder accuracy to significantly reduce the computational cost of modeling thermal properties.

SMS-based phishing (smishing) attacks have surged, yet training effective on-device detectors requires labelled threat data that quickly becomes outdated. To deal with this issue, we present Agentic Knowledge Distillation, which consists of a powerful LLM acts as an autonomous teacher that fine-tunes a smaller student SLM, deployable for security tasks without human intervention. The teacher LLM autonomously generates synthetic data and iteratively refines a smaller on-device student model until performance plateaus. We compare four LLMs in this teacher role (Claude Opus 4.5, GPT 5.2 Codex, Gemini 3 Pro, and DeepSeek V3.2) on SMS spam/smishing detection with two student SLMs (Qwen2.5-0.5B and SmolLM2-135M). Our results show that performance varies substantially depending on the teacher LLM, with the best configuration achieving 94.31% accuracy and 96.25% recall. We also compare against a Direct Preference Optimisation (DPO) baseline that uses the same synthetic knowledge and LoRA setup but without iterative feedback or targeted refinement; agentic knowledge distillation substantially outperforms it (e.g. 86-94% vs 50-80% accuracy), showing that closed-loop feedback and targeted refinement are critical. These findings demonstrate that agentic knowledge distillation can rapidly yield effective security classifiers for edge deployment, but outcomes depend strongly on which teacher LLM is used.

On-time performance is a critical challenge in the airline industry, leading to large operational and customer dissatisfaction costs. The tail assignment problem builds the sequences of flights or routes followed by individual airplanes. While airlines cannot avoid some sources of delay, choosing routes wisely limits propagation along these. This paper addresses the stochastic tail assignment problem at Air France. We propose a column generation approach for this problem. The key ingredient is the pricing algorithm, which is a stochastic shortest path problem. We use dedicated bounds to discard paths in an enumeration algorithm, and introduce new bounds based on a lattice ordering of the set of piecewise linear convex functions to strike a balance between bounds quality and computational cost. A diving heuristic enables us to retrieve integer solutions. Numerical experiments on real-world Air France instances demonstrate that our algorithms lead to an average 0.28% optimality gap on instances with up to 600 flight legs in a few hours of computing time. The resulting solutions effectively balance operational costs and delay resilience, outperforming previous approaches based on minimum turn time.

For any number field $K$ and integer $0\leq r \leq 4$, we prove that there are infinitely many elliptic curves over $K$ of rank $r$. Our elliptic curves are obtained by specializing well-chosen nonisotrivial elliptic curves over the function field $K(T)$. We use a result of Kai, which generalizes work of Green, Tao and Ziegler to number fields, to choose our specializations so that we have control over the bad primes and can perform a $2$-descent to compute ranks.

Controlling ensembles of weakly coupled spins typically requires computationally expensive multispin optimisations. We present a compact framework that enables control of weakly coupled spin systems (of any spin), but using RF pulses optimised for a single spin-1/2. We do this by explicitly creating a GRAPE pulse with fixed 'active' evolution times using single spin-1/2 methods, and pulsing on one spin at a time. By enforcing this form uniformly across offsets ('band-schematic' pulses),chemical shift and scalar coupling evolution of the entire system can be precisely controlled. We demonstrate the approach by constructing band-schematic pulses and a continuously irradiated joint INEPT (JINEPT) that achieves band-selective transfer $I_z \rightarrow 2I_zS_z$. The framework is implemented in the software Seedless, which both rapidly generates such pulses and analyses the schematic form of arbitrary pulses, enabling robust multi-spin control, without multi-spin optimisation.