We investigate the pseudoscalar ($η_t$) and vector ($ψ_t$) toponium states, as well as the triply-top baryon ($Ω_{ttt}$), using the QCD sum-rule method. This study was motivated by the recent observation of a pseudoscalar enhancement near the $t\bar{t}$ threshold, reported by the CMS and ATLAS collaborations with a statistical significance exceeding $5σ$. In the calculations, we consider both the perturbative and nonperturbative contributions, with the nonperturbative operators taken into account up to dimension eight. The results obtained for the pseudoscalar toponium provide a theoretical estimate that is consistent with the near-threshold events observed in recent experimental studies. The calculated negative binding energy for both the pseudoscalar and vector toponium states reflects the strong correlation within the $t\bar{t}$ system and can be interpreted as $t\bar{t}$ bound states, while the calculated central mass for the $Ω_{ttt}$ slightly exceeds the central value of the sum of the constituent top-quark masses. The results of this study can provide a precise theoretical guide for future experimental investigations of these states, which are composed entirely of top quarks, at high-energy colliders such as the LHC and future facilities like the FCC.

Proximal methods such as the Alternating Direction Method of Multipliers (ADMM) are effective at solving constrained quadratic programs (QPs). To tackle infeasible QPs, slack variables are often introduced to ensure feasibility, which changes the structure of the problem, increases its size, and slows down numerical resolution. In this letter, we propose a simple ADMM scheme to tackle QPs with slack variables without increasing the size of the original problem. The only modification is a slightly different projection in the z-update, while the rest of the algorithm remains standard. We prove that the method is equivalent to applying ADMM to the QP with additional slack variables, even though slack variables are not added. Numerical experiments show speedups of the approach.

We provide a detailed derivation of the Schwarzian modes in the full geometry of the Bañados-Teitelboim-Zanelli (BTZ) black hole at finite temperature, establishing the precise conditions under which they emerge from the general solution, thereby clarifying the absence of rotational modes in the full geometry. In addition, we demonstrate that the same modes can be recovered through a purely geometric Kerr-Schild construction. This equivalent approach offers a new geometric understanding of the Schwarzian sector and highlights the correspondence between perturbative and pure geometric approaches, additionally it provides a connection with double copy.

Offloading communication to existing direct memory access (DMA) engines, available on most state-of-the-art commercial GPUs, has emerged as an interesting and low-cost solution to efficiently overlap computation and communication in machine learning (ML). That said, so far, the reach of DMA offloads has been limited to bandwidth-bound scenarios only (10s of MB to GB transfer sizes). In this work, we aim to break this barrier and expand the reach of DMA communication offloads to even latency-bound regions (KB to low MB). Specifically, we discuss in this work hitherto untapped features available in the state-of-the-art AMD Instinct$^{\mathrm{TM}}$ MI300X GPUs that render DMA communication offloads competitive even for latency-bound regions. We demonstrate the efficacy of these features at the operator-level (ML communication collectives such as all-gather and all-to-all), and also at the end-to-end workload-level (LLM inference). For the former, our optimized DMA offloads close up to 4.5$\times$ performance gap and deliver additional power savings (3-10%) for ML collectives as compared to state-of-the-art GPU core-based communication library, RCCL. For the latter, we demonstrate acceleration for LLM inference: up to 1.5$\times$ lower latency and up to 1.9$\times$ higher throughput over the state-of-the-art vLLM inference framework. We conclude with a discussion of AMD Instinct GPU runtime innovations that stand to expose these features and additionally identify future hardware-software co-design potential to further improve DMA offload efficiency.

Infinitesimal volumes stretch and contract as they coevolve with classical phase space trajectories according to linearized dynamics. Unless these tangent-space dynamics are modified, chaotic evolution causes the volume spanned by evolving tangent vectors to collapse. However, this collapse is unphysical and due to their exponential alignment along the most expanding direction, independent of the compressibility of the phase-space volume. Here, we propose an alternative linearized dynamics and rectify the generalized Liouville equation to preserve phase space volume, even for non-Hamiltonian systems. Within a classical density matrix theory, we define the time evolution operator from the anti-symmetric part of the stability matrix so that phase space volume is time-invariant. The operator generates orthogonal transformations without distorting volume elements, providing an invariant measure for dissipative dynamics and a evolution equation for the density matrix akin to the quantum mechanical Liouville-von Neumann equation. The compressibility of volume elements is determined by a non-orthogonal operator made from the symmetric part of the stability matrix. We analyze complete sets of basis vectors for the tangent space dynamics of chaotic systems, which may be dissipative, transient or driven, without re-orthogonalization of tangent vectors. The linear harmonic oscillator, the Lorenz-Fetter model, and the Hénon-Heiles system demonstrate the computation of the instantaneous Lyapunov exponent spectrum and the local Gibbs entropy flow rate using these bases and show that it is numerically convenient.

We consider a variety of criteria for selecting k representative columns from a real mxn matrix A, when sufficiently few columns are required, i.e., 1<= k<= min{rank(A), m/3}. The criteria include the following optimization problems: absolute volume and S-optimality maximization; norm, pseudo-inverse norm, and condition minimization number in the two-norm, Frobenius norm and Schatten p-norms for p>2; stable rank maximization; and the new criterion of relative volume maximization, which is inversely proportional to a power of the condition number. We show that these criteria are NP hard and many do not admit polynomial time approximation schemes (PTAS). To formulate the optimization problems as decision problems, we derive optimal values for the subset selection criteria, as well as expressions for partitioned pseudo-inverses. The results for minimization of the pseudo-inverse in the Frobenius norm are applicable to trace optimization in A-optimal design.

We aim to reduce the cost of the current bosonic randomized benchmarking proposal. To do this, we introduce two filter functions: one uses immanants, the other uses characters of the special unitary group. These filters avoid computing Clebsch-Gordan coefficients and yield simple variance expressions. The character filter is not only efficient to compute, but also has a constant, low variance. Our filters rely on the same data as the original proposal. We also discuss an example with photon loss and gain. Our numerical evidence shows that a scheme using weak coherent states and intensity measurements can yield estimates close to those obtained without loss or gain. Our work could support simpler platform characterization and streamline data analysis.

Predicting and controlling the transport of colloids in porous media is essential for a broad range of applications, from drug delivery to contaminant remediation. Chemical gradients are ubiquitous in these environments, arising from reactions, precipitation/dissolution, or salinity contrasts, and can drive particle motion via diffusiophoresis. Yet our current understanding mostly comes from idealized settings with sharply imposed solute gradients, whereas in porous media, flow disorder enhances solute dispersion, and leads to diffuse solute fronts. This raises a central question: does front dispersion suppress diffusiophoretic migration of colloids in dead-end pores, rendering the effect negligible at larger scales? We address this question using an idealized one-dimensional dead-end geometry. We derive an analytical model for the spatiotemporal evolution of colloids subjected to slowly varying solute fronts and validate it with numerical simulations and microfluidic experiments. Counterintuitively, we find that diffuseness of solute front enhances removal from dead-end pores: although smoothing reduces instantaneous gradient magnitude, it extends the temporal extent of phoretic forcing, yielding a larger cumulative drift and higher clearance efficiency than sharp fronts. Our results highlight that solute dispersion does not weaken the phoretic migration of colloids from dead-end pores, pointing to the potential relevance of diffusiophoresis at larger scales, with implications for filtration, remediation, and targeted delivery in porous media.

Diffusion magnetic resonance imaging (MRI) has revealed important insights into white matter microstructure, but its application to gray matter remains comparatively less explored. Here, we investigate whether global patterns of gray-matter microstructure can be captured through neurite orientation dispersion and density imaging (NODDI) and whether such patterns are predictive of cognitive performance. Using diffusion MRI and behavioral data from the Human Connectome Project Young Adult study, we derive region averaged NODDI parameters and apply principal component analysis (PCA) to construct general gray-matter microstructure factors. We find that the factor derived from isotropic volume fraction explained substantial inter-individual variability and was significantly correlated with specific cognitive scores collected from the NIH Toolbox. In particular, the isotropic volume fraction factor is linked to reading and vocabulary performance and to cognitive fluidity. Our findings demonstrate that PCA-based global indicators of gray-matter microstructure provide complementary markers of structure-function relationships, extending beyond region-specific analyses. Our results suggest that general microstructure factors may serve as population-level exploratory biomarkers for studying cognition and cortical organization.

When a metastable state decays into radiation, there must be entanglement between the radiation and the decaying system, as well as between radiation collected at late and early times. We study the interplay between these two types of entanglement in simple Gaussian models in the Markov approximation. We define, via a windowed Fourier transform, multimode quantum states associated with radiation fragments produced at different times and compute the corresponding entanglement entropy increments. On the basis of these results, we argue that such entropy increments are useful entanglement measures, especially in cases, such as Hawking radiation, where one wishes to separate the radiation into ``old'' and ``new.''

We present relativistic $N$-body simulations of a $Λ_{\rm s}$CDM - sign-switching cosmological constant (CC) - scenario under general relativity and compare its nonlinear matter power spectrum to $Λ$CDM at ${z = 15,\,2,\,1,\,0}$, using best-fit parameters from Planck-only and a combined ''full'' dataset. During the AdS-like CC ($Λ_{\rm s}<0$) phase, prior to the transition redshift $z_\dagger$, reduced Hubble friction dynamically enhances the growth of perturbations; after the switch, with dS-like CC ($Λ_{\rm s}>0$), the larger late-time expansion rate partly suppresses, but does not erase, the earlier amplification. Consequently, the ratio $P_{Λ_{\rm s}\rm CDM}/P_{Λ\rm CDM}$ exhibits a pronounced, redshift-dependent shape feature: a crest peaking at ${\sim 20-25\%}$ around ${k \simeq 1-3\,h\,\mathrm{Mpc}^{-1}}$ near the transition, which then migrates to larger physical scales and persists to ${z = 0}$ as a robust ${\sim 15-20\%}$ uplift at ${k \simeq 0.6-1.0\,h\,\mathrm{Mpc}^{-1}}$. These wavenumbers correspond to group or poor-cluster environments and lie within the sensitivity range of weak lensing, galaxy-galaxy lensing, cluster counts, and tSZ power, providing a concrete, falsifiable target that cannot be mimicked by a scale-independent change in $σ_8$ or $S_8$. The timing (earlier for Planck-only, later for the full dataset) and the amplitude of the crest align with the ''cosmic noon'' epoch (${z \simeq 1-2}$), offering a gravitational prior for the observed peak in the cosmic star-formation rate.

The enhancement and attenuation of near-field radiative heat transfer between polaritonic SiC, SiN and SiO2 subwavelength membranes is analyzed. Fluctuational electrodynamics simulations combined with a modal analysis show that all membranes support corner and edge modes, which can induce a large 5.1-fold enhancement for SiC and a 2.1-fold attenuation for SiO2 of the heat transfer coefficient with respect to that between infinite surfaces. The enhancement or attenuation is directly related to material losses which reduce the density of available electromagnetic states between the membranes.

We present BayeSN-TD, an enhanced implementation of the probabilistic type Ia supernova (SN Ia) BayeSN SED model, designed for fitting multiply-imaged, gravitationally lensed type Ia supernovae (glSNe Ia). BayeSN-TD fits for magnifications and time-delays across multiple images while marginalising over an achromatic, Gaussian process-based treatment of microlensing, to allow for time-dependent deviations from a typical SN Ia SED caused by gravitational lensing by stars in the lensing system. BayeSN-TD is able to robustly infer time delays and produce well-calibrated uncertainties, even when applied to simulations based on a different SED model and incorporating chromatic microlensing, strongly validating its suitability for time-delay cosmography. We then apply BayeSN-TD to publicly available photometry of the glSN Ia SN H0pe, inferring time delays between images BA and BC of $ΔT_{BA}=121.9^{+9.5}_{-7.5}$ days and $ΔT_{BC}=63.2^{+3.2}_{-3.3}$ days along with absolute magnifications $β$ for each image, $β_A = 2.38^{+0.72}_{-0.54}$, $β_B=5.27^{+1.25}_{-1.02}$ and $β_C=3.93^{+1.00}_{-0.75}$. Combining our constraints on time-delays and magnifications with existing lens models of this system, we infer $H_0=69.3^{+12.6}_{-7.8}$ km s$^{-1}$ Mpc$^{-1}$, consistent with previous analysis of this system; incorporating additional constraints based on spectroscopy yields $H_0=66.8^{+13.4}_{-5.4}$ km s$^{-1}$ Mpc$^{-1}$. While this is not yet precise enough to draw a meaningful conclusion with regard to the `Hubble tension', upcoming analysis of SN H0pe with more accurate photometry enabled by template images, and other glSNe, will provide stronger constraints on $H_0$; BayeSN-TD will be a valuable tool for these analyses.

Comparing probability measures modulo unknown rigid transformations is a central challenge in geometric data analysis. Classical optimal transport (OT) distances, including Wasserstein and sliced Wasserstein, are sensitive to rotations and reflections, whereas Gromov-Wasserstein (GW) and Procrustes-Wasserstein (PW) distances are invariant to isometries but computationally prohibitive for large datasets. We introduce Rigid-Invariant Sliced Wasserstein via Independent Embeddings (RISWIE), a scalable distance that combines the invariance of NP-hard approaches with the efficiency of projection-based OT. RISWIE utilizes data-adaptive bases and matches optimal signed permutations along axes according to distributional similarity to achieve rigid invariance with nearly linear complexity in the sample size. We prove bounds relating RISWIE to GW in special cases and demonstrate dimension-independent statistical stability. Our experiments on cellular imaging and 3D human meshes demonstrate that RISWIE outperforms GW and PW in clustering tasks and discriminative capability while significantly reducing runtime.

Future missions, including the Habitable Worlds Observatory, will aim to image Earth-like exoplanets around Sun-like stars in reflected light. Determining whether an exoplanet is in the habitable zone of its star may be difficult in multi-planet systems when the observer does not know in advance which detection corresponds to which planet. This "confusion" problem will be a concern for future missions due to the high occurrence rate of multi-planet systems, and will be exacerbated by lack of prior knowledge about planets' orbital parameters or characteristics. We address the exoplanet confusion problem by applying a photometry model to update an orbit ranking scheme for a "deconfuser" tool . This helps to account for phase variation of planets throughout their orbits. We demonstrate the updated ranking scheme as a proof-of-concept on a subset of known to be confused simulated multi-planet systems among three inclination groupings (low, medium, and high). We find that incorporating photometry improves correctly interpreting previously confused orbits in more than half of these particularly challenging cases. These results emphasize that photometry is useful for orbit discrimination and deconfusion of directly imaged multi-planet systems, providing a framework for including photometry alongside astrometry when fitting orbits to detections.

JWST's exquisite data have opened the doors to new possibilities in detecting broad classes of astronomical objects, but also to new challenges in classifying those objects. In this work, we introduce SESHAT, the Stellar Evolutionary Stage Heuristic Assessment Tool for the identification of Young Stellar Objects, field stars (main sequence through asymptotic giant branch), brown dwarfs, white dwarfs, and galaxies, from any JWST photometry. This identification is done using the machine learning method XGBoost to analyze thousands of rows of synthetic photometry, modified at run-time to match the filters available in the data to be classified. We validate this tool on real data of both star-forming regions and cosmological fields, and find we are able to reproduce the observed classes of objects to a minimum of 85\% recall across every class, with all available data, without additional information on the ellipticity or spatial distribution of the objects. Furthermore, this tool can be used to test the filter choices for JWST proposals by verifying whether the chosen filters are sufficient to identify the desired class of objects. SESHAT is released as a Python package to the community for general use.

The practical use of future climate projections from global circulation models (GCMs) is often limited by their coarse spatial resolution, requiring downscaling to generate high-resolution data. Regional climate models (RCMs) provide this refinement, but are computationally expensive. To address this issue, machine learning (ML) models can learn the downscaling function, mapping coarse GCM outputs to high-resolution fields. Among these, generative approaches aim to capture the full conditional distribution of RCM data given coarse-scale GCM data, which is characterized by large variability and thus challenging to model accurately. We introduce EnScale, a generative ML framework emulating the full GCM-to-RCM map by training on multiple pairs of GCM and corresponding RCM data. It first adjusts large-scale mismatches between GCM and coarsened RCM data, followed by a super-resolution step to generate high-resolution fields. To efficiently model the high-dimensional output, the super-resolution step employs a novel class of sparse local stochastic layers. Both steps employ generative models optimized with the energy score, a proper scoring rule. Compared to state-of-the-art ML downscaling approaches, our setup reduces computational cost by about one order of magnitude. EnScale jointly emulates multiple variables -- temperature, precipitation, solar radiation, and wind -- spatially consistent over Central Europe. In addition, we propose a variant EnScale-t that enables temporally consistent downscaling. We establish a comprehensive evaluation framework across various categories including calibration, spatial and temporal structure, extremes, and multivariate dependencies. Comparison with diverse benchmarks demonstrates EnScale(-t)'s competitive performance and computational efficiency, offering a promising approach for accurate and temporally consistent RCM emulation.

Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning framework that employs a hybrid $β$-Variational Autoencoder-Generative Adversarial Network ($β$-VAE-GAN) architecture with masked convolutions to extract dominant flow features into a compact latent space while preserving fidelity at solid-fluid interfaces. A bidirectional transformer then models the temporal evolution of these features, learning to predict flow trajectories from minimal sensor inputs. This two-stage approach enables the transformer to map sensor measurements to dominant flow variables identified by the autoencoder, advancing reduced-order modeling capabilities for real-time flow prediction. The effectiveness of the framework is demonstrated through application to a problem relevant to vortex-induced vibration (VIV) energy harvesting systems, reconstructing the turbulent flow around a one-degree-of-freedom moving cylinder. Validated against experimental data spanning fluid-structure interaction regimes of interest, VIVALDy accurately predicts different flow states using only the cylinder displacement. The framework demonstrates adequate performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions, enabling efficient prediction of the turbulent flow phenomena governing vortex-induced vibration.

We propose a new theoretical method to describe the monitored dynamics of bosonic many-body systems based on the concept of the most likely trajectory. We show how such trajectory can be identified from the probability distribution of quantum trajectories, i.e. measurement readouts, and how it successfully captures the monitored dynamics beyond the average state. We prove the method to be exact in the case of Gaussian theories and then extend it to the interacting Sine-Gordon model. Although no longer exact in this framework, the method captures the dynamics through a self-consistent time-dependent harmonic approximation and reveals an entanglement phase transition in the steady state from an area-law to a logarithmic-law scaling.

X-ray interferometry is an emerging imaging modality with a wide variety of potential clinical applications, including lung imaging. A grating interferometer uses a diffraction grating to produce a periodic interference pattern and measures how a patient or sample perturbs the pattern, producing three unique images that highlight X-ray absorption, refraction, and small angle scattering, known as the attenuation, differential-phase, and dark-field images, respectively. Inaccuracies in grating position and multi-harmonic fringes produce Moiré artifacts when assuming the fringe pattern is perfectly sinusoidal and the phase steps are evenly spaced. We have developed an image recovery algorithm that estimates the true phase stepping positions using multiple harmonics and total variation regularization, removing the Moiré artifacts present in the attenuation, differential-phase, and dark-field images. We demonstrate the algorithm's utility for the Talbot-Lau and Modulated Phase Grating Interferometers by imaging multiple samples, including PMMA microspheres and a euthanized mouse.

Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of optimal control for a class of coupled reaction-diffusion systems. The couplings are justified by the shared regulatory mechanisms encountered in synthetic biology. Furthermore, we introduce inputs and polynomial input-gain functions to guarantee well-posedness of the control system while maintaining biological relevance. As a result, we formulate an optimal control problem and derive necessary optimality conditions. We demonstrate our framework on an instance of such equations modeling the Nodal-Lefty interactions in mammalian cells. Numerical simulations showcase the effectiveness in directing pattern towards diverse targeted ones.

We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to both absolutely continuous and discrete measures. Central to our approach is a refinement operator based on McCann's interpolants, which preserves the geodesic structure of measure flows and serves as an upsampling mechanism. Building on this, we introduce the optimality number, a scalar that quantifies deviations of a sequence from Wasserstein geodesicity across scales, enabling the detection of irregular dynamics and anomalies. We establish key theoretical guarantees, including stability of the transform and geometric decay of coefficients, ensuring robustness and interpretability of the multiscale representation. Finally, we demonstrate the versatility of our methodology through numerical experiments: denoising and anomaly detection in Gaussian flows, analysis of point cloud dynamics under vector fields, and the multiscale characterization of neural network learning trajectories.

Recently, the KM3NeT experiment reported the detection of a neutrino with exceptionally high energy E = 220 PeV, whose origin remains unclear. The corresponding value of the neutrino flux is in tension with the results of other high-energy neutrino experiments. In this study, we discuss the possibility that this neutrino is cosmogenic, i. e., produced by ultra-high energy cosmic rays (UHECR) during their propagation through the intergalactic medium. We adopt the UHECR flux models derived by the Telescope Array experiment, which features a predominantly light mass composition. We show that the predictions of the cosmogenic neutrino flux in these models are consistent with the measurements of the KM3NeT-only and with that of the "global neutrino observatory" at approximately 2$σ$ level. Notably, this result is achieved in a minimal version of the UHECR flux models, that assume one source population with a standard cosmological evolution. We also estimate the corresponding cosmogenic gamma-ray flux and show that it is consistent with Fermi-LAT IGRB measurements and UHE gamma-ray limits; the improvement of the latter can probe these predictions in future.

We study interference effects in the dynamics of a spin-$1/2$ particle propagating in two dimensions in a disordered potential and subject to a generalized spin-orbit coupling. With the particle initially in a spin-polarized plane wave state, in the short-time regime, before the spin and momentum distributions reach their steady states, we observe a transient backscattering peak offset from the exact backscattering direction, coexisting with a coherent backscattering dip. We present an intuitive explanation of this momentum offset using a non-Abelian gauge transformation. We also describe the full time evolution of the transient peak, from its buildup to its decay with a precise prediction of the dephasing time within a perturbative framework for multiple scattering. Our results can be applied to general spatially uniform SU(2) gauge fields, including the synthetic gauge field in ultracold atoms.

The Internet, the world's largest and most pervasive network, lacks a transparent, granular view of its traffic patterns, volumes, and growth trends, hindering the networking community's understanding of its dynamics. This paper leverages publicly available Internet Exchange Point traffic statistics to address this gap, presenting a comprehensive two-year study (2023-2024) from 472 IXPs worldwide, capturing approximately 300 Tbps of peak daily aggregate traffic by late 2024. Our analysis reveals a 49.2% global traffic increase (24.5% annualized), uncovers regionally distinct diurnal patterns and event-driven anomalies, and demonstrates stable utilization rates, reflecting predictable infrastructure scaling. By analyzing biases and confirming high self-similarity, we establish IXP traffic as a robust proxy for overall Internet growth and usage behavior. With transparent, replicable data--covering 87% of the worldwide IXP port capacity--and plans to release our dataset, this study offers a verifiable foundation for long-term Internet traffic monitoring. In particular, our findings shed light on the interplay between network design and function, providing an accessible framework for researchers and operators to explore the Internet's evolving ecosystem.

We develop a unified theory for the nonadiabatic wave-packet dynamics of Bloch electrons subject to slowly varying spatial and temporal perturbations. Extending the conventional wave-packet ansatz to include interband contributions, we derive equations for the interband coefficients using the time-dependent variational principle, referred to as the wave-packet coefficient equation. Solving these equations and integrating out interband contributions yields the leading-order nonadiabatic corrections to the wave-packet Lagrangian. These corrections appear in three forms: (i) a nonadiabatic metric in real and momentum space, which we identify with the energy-gap-renormalized quantum metric, (ii) modified Berry connections associated with the motion of the wave-packet center, and (iii) an energy correction arising from spatial and temporal variations of the Hamiltonian. This metric reformulates the wave-packet dynamics as geodesic motion in phase space, enabling an analogue-gravity perspective in condensed matter systems. As an application, we analyze one-dimensional Dirac electron systems under a slowly varying exchange field $\bm{m}$. Our results demonstrate that variations in the magnitude of $\bm{m}$ are important to nonadiabatic dynamics, in sharp contrast to the adiabatic regime where directional variations of $\bm{m}$ are crucial.

We present version 2.1 of the public code {\sc precession}, a Python module for studying the post-Newtonian dynamics of precessing black hole binaries. In this release, we extend the code to handle eccentric orbits. This extension leverages the existing numerical infrastructure wherever possible, introducing a semi-automatic method to adapt circular-orbit functions to the eccentric case via a Python decorator. Additional new features include orbit- and precession-averaged evolutionary equations for the eccentricity, as well as revised expressions to convert between post-Newtonian separation and gravitational-wave emission frequency.

By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum degree. This answers an open question of Chen, Liu and You. Notice that our conclusion would be false if we did not require the graph to be finite. We actually classify all connected graphs with non-negative Lin-Lu-Yau curvature and edge-connectivity smaller than their minimum degree. In particular, they are all infinite.

We investigate the dynamics of the three-state Potts quantum spin chain in the extreme ferromagnetic limit using a perturbative expansion in the transverse magnetic field. We demonstrate that a perturbative approach provides access to important features beyond the reach of previous studies, most notably the description of resonant excitations and the analytic prediction of post-quench time evolution. A central focus is the oblique quench regime - a feature unique to the Potts model with no Ising counterpart - in which unconfined kink excitations hybridise with the two-kink bound states. We provide a detailed examination of the analytic structure of the two-kink scattering amplitude, tracing the transformation of stable excitations into resonances near stability thresholds. Our analytical results for the excitation spectra and magnetisation dynamics show excellent agreement with numerical simulations of non-equilibrium dynamics.

Wavefront distortions are a leading source of systematic uncertainty in light-pulse atom interferometry, limiting absolute measurements of gravitational acceleration at the 30 nm/s$^2$ level. Here, we demonstrate in situ spatially resolved measurement of the interferometer phase in a Mach-Zehnder atom interferometer as a tool to characterize and correct wavefront bias. By introducing controllable curvature of the Raman light using an adjustable collimation retro-reflector, we show that the bias due to parabolic wavefront curvature can be measured with 1 mrad uncertainty and that finite-size corrections impact the measured phase curvature. This measurement process could be adopted in optimized atom interferometer gravimeters to reduce wavefront bias uncertainty below the nm/s$^2$ level.