We introduce the dual affine Robinson-Schensted correspondence that gives a bijection between the extended affine symmetric group and tuples $(\bar{P},\bar{Q},λ,N)$, where $\bar{P}$ and $\bar{Q}$ are tabloids, $λ$ is a partition, and $N$ is an integer, subject to compatibility conditions. The construction generalizes Fomin's growth diagrams and Viennot's shadow lines for the classical Robinson-Schensted correspondence on the symmetric group, and is dual to the affine matrix ball construction as well as Shi's correspondence, in the sense that the $P$-tabloids are the same, and the $Q$-tabloids are related by affine evacuation. As a consequence, our construction also parametrizes Kazhdan-Lusztig cells in affine type $A$. We conjecture that the growth diagrams we construct admit a natural geometric realization in terms of relative positions of affine flags, similar to the interpretation given by Steinberg and van Leeuwen in the classical case.

This note is the third part of our work devoted to uniqueness sets for spaces of entire functions. Given a discrete set $Λ$ with angular density $Δ$ with respect to the order $ρ$, satisfying some regularity condition, we show that there exists a type-minimizing measure $Δ_0$ with less than $2ρ$ discrete masses. For the case $ρ=2$, the value of the critical uniqueness type is found in geometric terms.

This work presents the design, implementation, and evaluation of a LoRa-based mesh network using the Meshtastic protocol for Smart Campus applications at Universidad Militar Nueva Granada (UMNG). The system integrates heterogeneous hardware nodes including a solar-powered ecological sensing node built around a Raspberry Pi Pico and a Semtech SX1262 transceiver, and mobile trackers based on the Seeed SenseCAP T1000-E managed through a containerized edge gateway running on a Raspberry Pi 4. A Docker Compose microservices stack handles data ingestion via Node-RED, time-series storage in InfluxDB, and real-time visualization through Grafana dashboards. The architecture's performance was evaluated under realistic propagation scenarios at the UMNG Cajicá campus, characterizing link quality using Received Signal Strength Indicator (RSSI) and Signal-to-Noise Ratio (SNR) metrics. Experimental results demonstrate robust mesh connectivity across key university facilities, including an extended-range link of approximately 2.47 km linking the campus gateway to a remote station at Mirador La Cumbre (n = 62 packets received, mean RSSI = -110 dBm, mean SNR = +2.75 dB). This architecture demonstrates that open-source mesh protocols combined with containerized microservices offer an autonomous, highly reproducible infrastructure for environmental monitoring and asset tracking, supporting the transition toward data-driven "Smart Campus" ecosystems without reliance on centralized commercial LoRaWAN operators.

Variational quantum dynamics simulations (VQDS) provide a promising route to simulate real- and imaginary-time quantum dynamics on noisy intermediate-scale quantum devices using fixed-depth circuits. However, their practical performance is strongly limited by sampling noise arising from a finite number of circuit measurements. In this work, we systematically investigate the impact of sampling noise on VQDS, with a focus on ground-state preparation in one-dimensional Ising spin models using imaginary time evolution. We compare different regularization strategies for stabilizing the equations of motion and show that Tikhonov regularization provides robust performance in noisy imaginary-time evolution. We then benchmark measurement-distribution strategies that allocate shots by minimizing a cost function that characterizes the error in solving the equation of motion. Using noisy circuit simulations, we demonstrate that such optimized shot allocation can significantly improve state fidelity and reduce the total measurement cost by more than a factor of two compared to uniform shot distributions. We observe that the best results are found if a sufficiently large number of measurements is guaranteed for all circuits, suggesting that a finite fraction of shots should be distributed evenly. Our results provide practical guidelines for implementing measurement-efficient variational quantum dynamics and ground-state preparation on near-term quantum hardware.

The conventional linear scaling of beamforming gain with the number of antennas is not a fundamental physical limitation, but rather a consequence of the half-wavelength spacings that minimize mutual coupling. Relaxing this constraint facilitates beamforming gains exceeding those of uncoupled arrays along specific directions. This paper shows that, when antenna losses remain sufficiently small, mutual coupling enables the synthesis of super-beams whose endfire gain scales quadratically with the number of antennas. Notably, this quadratic scaling does not necessarily require vanishing spacings, but emerges for spacings slightly below half wavelength as the array aperture increases.

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and several complex variables, starting with a version of the classical theorem of Arnol'd and ending with a result on persistence of Herman rings in families of two-dimensional maps.

Driven by the growing demand for miniaturized spectrometers for in-situ analysis, and point-of-care diagnostics, conventional spectrometers are often constrained by bulky architectures and pathlength-limited spectral resolution. Achieving high-resolution, single-pixel computational spectrometers is therefore critical for the realization of compact, on-chip systems. Here, we report a single-pixel spectrometer enabled by a single 2D material; few-layer GaSe-based photodetector, in which the Schottky barrier height modulation, governed jointly by applied bias and optical excitation, provides an efficient mechanism for spectral encoding without the need for bulky dispersive elements. The device exhibits a high peak-wavelength accuracy of ~0.78 nm across a broad operational bandwidth (300-700 nm) within a compact footprint of ~100 um^2 and resolves closely spaced spectral features with separations down to ~5 nm. The device operates at low bias (+/- 4V) with an ultralow dark current density ~0.3 pA/um^2 at 4V bias. These results establish a simple, scalable route toward compact, cost-effective spectroscopic systems for on-chip spectral sensing and portable hyperspectral imaging applications.

Geometric flows, where an immersed manifold evolves in time according to its own geometry, exhibit important structural properties. For example, surface diffusion dissipates surface area while conserving volume; it is desirable to preserve these properties on discretization. This has motivated a substantial body of research on structure-preserving discretizations for these flows, albeit at low order in time. In this work, we present the first discretization of geometric curvature flows (curve shortening/mean curvature flow and curve/surface diffusion) that preserves the evolution of area and volume at arbitrary order in space and time. The key idea is to introduce auxiliary variables in a particular way so that the derivation of the area dissipation law can be replicated after discretization with continuous Petrov--Galerkin in time. These auxiliary variables are indicated by a general strategy for structure-preservation in time that applies to many other problems. The proposed scheme also preserves mesh quality in the same manner as the minimal deformation rate strategy. We demonstrate its structure-preserving properties and high-order convergence on several benchmark examples.

Object-level management of tiered memory has been studied to address the inefficiencies in page-based systems. However, object-level management for CXL-tiered memory remains underexplored due to CXL's tight performance budget and load/store interface. As a result, existing approaches remain limited in scope, primarily targeting unmanaged-language applications with bespoke runtimes or compiler support. This paper identifies and explores a new design point for object-level CXL management: managed languages and their runtimes. The key observation is that existing managed runtimes already provide highly optimized mechanisms for problems closely related to object-level management, including object relocation and dynamic code generation. However, they still lack the features needed for tiered memory management, such as hotness tracking and relocation policies, and thus must be carefully extended to fully realize this direction. We present Clove, a system that extends existing managed runtimes to support object-level CXL management for managed-language applications. Clove combines profile-guided object hotness tracking with object relocation techniques and policies. Our JVM prototype demonstrates that this extension enables high utilization of fast-tier memory while bounding runtime overhead, reducing application slowdown by 22-84% compared to page-based systems.

We show the stability of a penalty-free asymmetric Nitsche's method using Nédélec edge elements for solving curl-curl-type problems with tangential Dirichlet boundary conditions imposed weakly. The main result is an inf-sup stability estimate for the asymmetric bilinear form under an isolated patch condition on the tetrahedral mesh. Applications to a curl-elliptic problem and a magnetic advection-diffusion problem are discussed.

Nuclear reaction rates are crucial ingredients of solar and stellar models, they directly impact the duration of the life of stars and the energy they produce. In the solar case, the tight observational constraints put on models (Mass, Radius, Luminosity and chemical composition) coupled to our capabilities to probe the solar interior thanks to helioseismology and solar neutrinos provide an exquisite testbed for such physical ingredients. With the recent publication of the Solar Fusion III reaction rates, a new generation of solar models may be computed and put to the test. We aim to investigate the impact of the new Solar Fusion III reaction rates on solar models, both standard and non-standard, as well as the impact of the current uncertainties on some key solar reactions on the predicted neutrino fluxes for boron and the so-called CNO cycle. We compute various theoretical standard solar models as well as non-standard models reproducing the depletion of lithium and beryllium for various abundances, nuclear reaction rates and opacities. We focus on the impact of the solar fusion III reaction rates on both helioseismic inversion results and neutrino fluxes. We find that using the Solar Fusion III reaction rates significantly impact the agreement of solar models both with helioseismic constraints and neutrino flux measurements. While for helioseismic constraints it seems that there is a slight improvement, for neutrino fluxes, the use of the SFIII reaction rates induces a lowering of the beryllium, boron and CNO neutrino fluxes. When investigating the impact of changes on the rates of key reactions within their quoted uncertainties, we find that these changes are far from sufficient to reconcile models and observations, potentially hinting at other processes (e.g. planetary formation as found in other studies).

We formalize a ramification theory for finite covers of knot exteriors. Given a knot group $G_K$ and a finite-index subgroup $U\le G_K$, we define meridional inertia subgroups $U\cap g\langle m\rangle g^{-1}$ and the global ramification subgroup $M_U\triangleleft U$ as their normal closure. We then analyze $M_U$ from three complementary viewpoints: (1) finite quotients, where $U/M_U$ is shown to be the universal ``maximal meridionally unramified'' quotient of $U$; (2) profinite completions, where we identify the closed ramification subgroup $\widehat M_{\widehat U}$ as the closed normal subgroup generated by closed inertia and prove that meridian-preserving isomorphisms of profinite completions preserve inertia and ramification; (3) cohomology, where ``unramified'' $H^1$-classes (discrete and profinite) are characterized as those vanishing on all inertia subgroups, in direct analogy with number-theoretic inertia conditions in Galois cohomology.

From changing fashion trends to views on world leaders and economic policies, large-scale shifts in group positions happen regularly and unexpectedly. How can we track these in the wild? How can we characterize them? Existing work has primarily leveraged stance detection to track shifts of specific groups on a single issue. However, such methods will only find shifts when they accurately pick exactly the right group and right issue. They do not capture the multi-dimensional, multi-resolution stance landscape in which these shifts actually happen. To better model drift and shift in public opinion, we require a framework that can track change at the population level, across a diverse range of issues. We propose a method to infer the potential landscape of stance dynamics, the gradient of which shows large-scale stance shifts, and apply it to show en-mass stance shifts by prominent Canadian political figures across multiple platforms and years. We do this using large-scale stance detection to find stance expressions, dimensionality reduction to find the low-dimensional linear latent space, and potential landscape neural networks to find the potential landscape of that space. This allows us to find a coherent, linear, three-dimensional space that explains 45\% of the variance in stance, where we can explain the specific characteristics of each dimension. We show that while the predictive performance is sufficient to validate its descriptive-ness, in practice its predictive performance is mixed.

In 1991 Bollobás and Frieze found the threshold for the emergence of a spanning triangulation of a triangle in the binomial random graph, up to a logarithmic factor. In this paper, we find the threshold probability for the emergence of a spanning triangulation of a $k$-gon for any $3\leq k\leq n$, up to a constant factor.

WD J005311 is the peculiar stellar remnant of the Galactic supernova from 1181, and appears to have been the merger of two white dwarfs. We present time-resolved spectroscopy of WD J005311 showing emission line variability on a wide range of time-scales. The strong O VI emission feature displays line profile variations (LPVs) on two distinct velocity scales. Broad variations with amplitudes of $\pm$10% of the line flux are seen over the entire O VI line. These broad LPVs likely arise from instabilities in the line-driven wind produced in many Wolf-Rayet stars. There is a hint of coherent structure in the broad LPVs that is consistent with rotation over roughly two hours, although the features survive for less than a full cycle. Low-amplitude, narrow LPVs are also detected within the central $\pm$5000 km/s of the O VI line. We associate these features with an unstable disk formed from the rigidly rotating magnetosphere (RRM) of the remnant white dwarf. We also analyze archival near-ultraviolet photometry of WD J005311 and find a pseudo-periodic oscillation with an hour-long time-scale that maybe associated with the breakout instability of the RRM disk.

Synthetic control methods can produce misleading counterfactual predictions when outcome series contain unit-specific stochastic trends, a common feature of nonstationary macroeconomic data. Existing remedies, such as pre-filtering or differencing, reduce spurious matching but may discard shared nonstationary variation that helps estimate donor weights. We propose Harmonic Synthetic Control (HSC), which replaces this binary choice with a soft allocation mechanism. HSC jointly estimates donor weights and a treated-unit-specific smooth residual component, then extrapolates this component into post-treatment periods using a time-series forecaster. A tuning parameter, selected by rolling-origin cross-validation, governs the division between donor matching and forecasting. As it varies, HSC continuously interpolates between synthetic control applied to differenced outcomes and synthetic control applied to raw outcomes with an intercept or trend. We provide a spectral interpretation showing how HSC downweights low-frequency residual components in donor matching and assigns them to the forecasting branch. A prediction-error decomposition separates weight-estimation distortion from residual-forecasting error. Monte Carlo exercises show that HSC adapts across regimes, performing well when stochastic trends are predominantly common or idiosyncratic, while estimators fixed to one regime can fail in the other.

We construct an impact-parameter-resolved transfer framework for null acoustic rays in the rotating draining-bathtub spacetime. The formalism separates the source-independent ray geometry from the source and detector model by keeping explicit the acoustic redshift, transfer convention, emissivity, emitter velocity field, and source-to-screen mapping. The geometric capture interval provides two clean observables: a shadow centroid that shifts linearly with circulation and a shadow width that grows monotonically with circulation. Observable profiles are obtained from direct ray-source intersections, finite source width or extended-disk integration, detector convolution, and convergence checks, rather than from an approximate semi-analytic ring map. The transfer calculation shows that rotation produces a left-right redshift tilt and a branch-dependent flux imbalance, while the total flux alone remains a degenerate circulation diagnostic. The most useful diagnostics are differential quantities: the shadow centroid, branch-integrated flux asymmetry, peak asymmetry, left-right redshift asymmetry, and global redshift contrast. We also discuss how these observables respond to the transfer convention, intrinsic azimuthal emissivity, the choice of left-right split, finite resolution, and physical limitations such as dispersion, viscosity, and finite-depth corrections.

The Canonical Polyadic (CP) tensor decomposition is a well-known method for interpretable analysis of high-dimensional data. Recently, the Generalized CP method (GCP) was introduced by Hong and Kolda to allow for flexible choice of the loss function in the optimization problem defining the CP model, enabling more interpretable decompositions of strongly non-Gaussian data such as count or binary data. Furthermore, Kolda and Hong introduced a version of GCP that leverages randomization and stochastic optimization to address scalability to large, sparse data sets. In this work, we take these ideas a step further and consider synchronous and asynchronous algorithms for parallel GCP tensor decomposition through the GenTen software package, exploiting both shared and distributed memory parallelism. We build on shared memory parallel CP decomposition algorithms utilizing Kokkos for portability across CPU and GPU architectures to support the random sampling and stochastic optimization methods required by GCP. We then couple this approach to the well-known medium-grained distributed memory parallelism scheme developed for traditional CP decompositions through MPI, providing a synchronous, hybrid MPI+Kokkos, parallel GCP decomposition capability. Finally, we propose an asynchronous distributed parallelism approach building on related techniques for federated learning to achieve even better scalability to large data sets. We study the effectiveness of the proposed synchronous and asynchronous approaches vis-a-vis computational cost and accuracy on synthetic and publicly-available real-world datasets of varying sizes, dimensions, and sparsity patterns using several loss functions.

Globular clusters (GCs) lie scattered around the inner $40\%$ of the virial radius of galaxy clusters, potentially being excellent tracers of the underlying mass distribution. In this paper, we present a statistical method based on assuming that the location of GCs around a galaxy cluster follows an inhomogenous spatial Poisson point process, and we use this method to assess to which galactic component GCs are better tracers of. We apply the method to the galaxy cluster Abell 2744, and we find that the spatial distribution of bright GCs roughly traces the three main interacting clumps in the galaxy cluster, alongside other galaxies with sizeable GC populations. The GC populations are more closely correlated to the predicted mass maps than any other galactic component (Spearman rank coefficients $>0.7$). A perk of this statistical method is that it allows us to distinguish to which map the agreement is closest to. In particular, we find that the Bright Blue GCs are compatible with the mass map solely derived from weak lensing, suggesting that they can provide complementary and independent information on the mass distribution in galaxy clusters with a similar level of detail to that of weak lensing. This statistical method is available in a public repository, and combined with catalogs of GCs in galaxy clusters at different cosmic epochs, it provides an independent method for investigating the mass distribution in these galactic environments.

The evaluation of large language model refusal on malicious-coding tasks now spans at least thirteen publicly released prompt corpora (AdvBench, the CyberSecEval family, RMCBench, RedCode, MCGMark, JailbreakBench, CySecBench, MalwareBench, CIRCLE, MOCHA, ASTRA, Scam2Prompt / Innoc2Scam-bench, and JAWS-Bench), each constructed under a different protocol, released under different licensing terms, and validated (or not) against different inter-rater reliability standards. Existing surveys treat code security, jailbreak taxonomy, or vulnerability detection as the central object and mention these corpora only in passing. This paper reverses that framing: it treats the prompt datasets themselves as the unit of analysis. Following a PRISMA-style protocol, we specify a search strategy, screen the recent literature on coding-LLM refusal evaluation, apply a uniform extraction template to each in-scope corpus, and synthesize the resulting catalogue along construction methodology, prompt-construction taxonomy (modality, turn structure, elicitation style), reproducibility and licensing, and malware-category coverage. The synthesis surfaces three recurring methodological gaps: the absence of human-annotator baselines against which LLM-judge labels can be calibrated, the absence of cross-corpus comparability with refusal-rate statistics measuring non-equivalent constructs, and the fragmentation of malware-category taxonomies, with no canonical schema spanning the thirteen in-scope corpora. The review concludes with proposed methodological directions for next-generation corpora, including pre-registration of inclusion criteria, vendor-diverse multi-judge validation, Fleiss' kappa with bootstrap CI as the reliability baseline, and a candidate canonical taxonomy.

Realistic quantum devices are inherently open and often involve environments with memory. Here, we investigate quantum resource generation in two classes of random circuits, namely, memoryless open and memoryful open random circuits, and compare their behavior with the well-explored random unitary circuit model. We show that environmental memory qualitatively alters the dynamics: while unitary and memoryful circuits exhibit sustained growth and saturation of entanglement and non-stabilizerness (magic); memoryless dynamics leads to a distinct behavior where entanglement decays to zero after transient growth, even though non-stabilizerness remains non-zero, indicating the persistence of nonclassical features beyond entanglement. Consistently, Krylov complexity reveals suppressed spreading of quantum states in memoryless circuits, in contrast to strong growth in unitary and memoryful dynamics, which saturates at the maximum value. Finally, we show that memoryful circuits more effectively approach low-order quantum-state k-designs than the other two circuits. Closed dynamics are therefore usually the most resource-generating, but are ideal; realistic dynamics are open and seem to generate less, but if they possess memory, they can sometimes even outdo closed dynamics.

We develop a semiclassical description of Reissner--Nordström--de Sitter (RN--dS) evaporation by combining a spherically reduced two-dimensional dilaton gravity model with Polyakov anomaly backreaction. The framework captures the causal and thermodynamic structure of the static patch and yields closed adiabatic evolution equations for the mass and charge. With an outward-oriented flux convention, the anomaly-induced Killing-energy flux is $\mathcal F=(N_{\rm eff}/48π)(κ_b^2-κ_c^2)$, while the full mass evolution is $\dot M=-\mathcal F+Φ_b\dot Q$, with $Φ_b=Q/r_b$. We prove analytically that along the entire sub-Nariai neutral Schwarzschild--de Sitter branch $κ_b>κ_c$, so neutral black holes lose mass monotonically. Schwinger pair production provides the discharge channel. In the rapid-discharge regime, controlled charged trajectories become effectively neutral on a timescale short compared with the anomaly-driven Hawking mass-loss time and then follow the neutral SdS channel toward empty de Sitter space. The classical lukewarm locus $T_b=T_c$ is only the nullcline of the anomaly-induced heat flux: the electromagnetic work term tilts the full semiclassical vector field away from this curve, so it is not an invariant trajectory. When sufficiently light charged species provide a rapid-discharge channel, the classical cold/extremal, charged Nariai, ultracold, and lukewarm loci are not semiclassical attractors for controlled nondegenerate trajectories. These results give an adiabatically backreacted derivation of the RN--dS evaporation endpoint in the regime controlled by anomaly-induced flux and rapid charge discharge, and provide the semiclassical background for generalized-second-law monotonicity and conservative quantum-extremal-surface/island estimates.

We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to provide a solution where the given observable has the complementary outcome. Shots are rejected that find logically complementary solutions with similar likelihoods compared to the baseline. Using the Relay-BP decoder, we benchmark the strategy on the $72$-qubit and $144$-qubit bivariate bicycle codes, as well as surgery gadgets for the latter. In comparison to previous post-selection strategies, our results offer an improved logical error rate by over a factor of $4$ on the same circuit and physical error rate, and at the same rate of post-selection. Our strategies are also lightweight, relying only on FPGA-friendly belief propagation, whereas the previous best used repeated rounds of a high-latency BP-OSD decoder.

Stellar granulation produces radial-velocity (RV) jitter at the 1 m/s level in Sun-like stars, limiting Earth-analog detection. A route beyond this limit is to weight spectral lines according to their granulation sensitivity. We apply a line-by-line diagnostic from 3D magneto-convection simulations that measures how each line's Doppler shift and strength respond to convective velocity and thermodynamic fluctuations. Extending our solar study, which used spatial line-profile variability across one granulation snapshot as an efficient proxy for temporal variability, we test whether this diagnostic transfers to cooler stars and examine how sensitivity changes with spectral type. We synthesize high-resolution spectra with MPS-ATLAS from 3D time-dependent MURaM simulations of the Sun and late-G and K dwarfs, focusing on FeI and FeII lines spanning broad ranges of excitation potential and strength. With decreasing $T_{\mathrm{eff}}$, weaker convective velocities and changing ionization balance produce a clearer separation between line families: FeI lines show lower velocity sensitivity and smaller fractional strength variability, while FeII lines are more sensitive. Cumulative contribution functions link spectroscopic velocity jitter to characteristic line-formation temperature. The diagnostic robustly separates stable and granulation-sensitive lines in late-G and K dwarfs, enabling spectral-type-aware cross-correlation masks and line-by-line RV weights. Solar-optimized line selections are therefore not generally portable to cooler stars, particularly when based on equivalent-width stability rather than velocity sensitivity.

Recent matrix-product-state calculations show that the spiral phase in the sawtooth chain has numerical signatures that are difficult to reconcile with an ordinary conformal critical point: a large apparent central charge, slow dynamical scaling, nearly flat excitations, and no detectable dimerization. We develop a bosonization theory for this phenomenology by embedding the sawtooth limit in a zigzag ladder described by two coupled SU(2)$_1$ conformal field theories characterized by an extreme velocity ratio. We show that the sawtooth geometry cancels the leading staggered interaction, leaving a marginal twist interaction that selectively collapses the slow apical spin velocity. Crucially, as this velocity vanishes, the generated apical backscattering interaction diverges only in dimensionless units, causing the energy scale to collapse independently of the spatial correlation length. This mechanism naturally accounts for many of the numerical anomalies and we interpret the perturbative flow as an entrance to local quantum criticality in the strong-coupling regime.

We present ground-based high-resolution spectroscopic pre-eclipse observations of the hot Jupiter CoRoT-2b obtained with the IGRINS spectrograph on Gemini South. Using cross-correlation analysis, we detect the Doppler-shifted signature of the planet's thermal emission with a signal-to-noise ratio of 4.32. Our independent analyses confirm the presence of H$_2$O with a confidence level of 2.6$σ$ and an abundance of log$_{10}$$-5.08^{+0.43}_{-0.43}$, as well as CO with 2.3$σ$ confidence and an abundance of log$_{10}$$-4.21^{+0.48}_{-0.81}$ in CoRoT-2b's atmosphere, using two fully independent data reduction and retrieval pipelines. No significant detections of CH$_4$, CO$_2$, TiO, or VO are reported. While our cross-correlation analysis tentatively suggests the presence of HCN and OH, retrieval analysis does not confirm these molecules. The detected H$_2$O and CO features indicate that CoRoT-2b's dayside spectrum is not featureless, as previously inferred from lower-resolution observations, but instead reveals a complex atmospheric structure. Interestingly, we find a lack of significant molecular features at wavelengths shorter than 1.7 $μm$, potentially due to high-altitude absorbers such as H$^-$, clouds, or observational systematics. From our retrieved abundances of CO and H$_2$O, we constrain a supersolar C/O ratio of $0.91^{+0.08}_{-0.17}$ and a subsolar metallicity. This study provides the first high-resolution constraints on the atmospheric composition of CoRoT-2b and serves as the foundation for future investigations into its peculiar westward hotspot offset. Further phase-resolved observations will be required to explore the underlying atmospheric dynamics in more detail.

We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either symmetry-broken or topological order. We show that the presence of non-trivial topological families of states, including charge pumps and their generalizations, results in phase diagrams being endowed with non-trivial topological textures that can be visualized through Berry phases and their higher-dimensional generalizations. We show that for non-interacting fermion systems with translation invariance, these `higher' Berry phases can be computed using integrals of non-abelian Chern-Simons forms of the Berry-Bloch connection over momentum and parameter spaces. Singularities in these textures correspond to gap-closing loci of `diabolical points', which represent the obstruction to contracting topologically non-trivial families of states, and bulk-boundary correspondence results in a locus of robust boundary modes that terminate at the bulk diabolical points. In the presence of finite chemical potential, we argue that the edge modes are generically robust without any need for fine-tuning for two and higher dimensions, whereas in one dimension they are `estranged' in the phase diagram, i.e. appearing at different parameter values for different edges. We demonstrate our results by constructing several microscopic models of non-interacting fermions. We argue stability to interactions and explore proximate phase diagrams by mapping to continuum field theories.

We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions decay at each singularity, leading to a rich structure of boundary value problems. We derive the weakest quantization conditions compatible with decaying behavior at both singularities, and formulate these conditions in terms of the associated monodromy data. In doing so, we prove the quantization conditions predicted by the topological string/spectral theory duality for a family of deformed Schrödinger equations. More generally, our results point to a hierarchy of spectral problems interpolating between the minimal conditions studied here and the maximally decaying boundary conditions of the $N$-particle quantum Toda chain.

We propose a framework that links the origin of the Standard Model flavour hierarchies to the generation of asymmetric dark matter via leptogenesis. The key new ingredient is a gauged $SO(3)$ flavour symmetry acting on both the visible and dark sectors, whose spontaneous breaking generates fermion mass hierarchies. Right-handed neutrino decays produce a primordial lepton asymmetry, which is redistributed into baryon and dark matter asymmetries by electroweak and flavour sphalerons respectively. Dark matter arises as baryon-like bound states of a confining $SU(3)$, providing a natural rationale for the similar mass scales of visible and dark matter. We analyze flavour, collider, electroweak, and cosmological constraints. Anomaly cancellation requires the presence of mirror fermions, inducing a seesaw-like suppression of new physics effects in the lighter generations, such that different observables are sensitive to different flavour-breaking scales. Meson oscillations provide the dominant constraints, with $K$ and $B_s$ observables constraining the highest and intermediate scales, while the lowest scale may place some mirror fermions potentially within reach of future collider searches and is currently probed by flavour violating $B_s$ decays and electroweak observables. Flavour interactions are also bounded from below by the requirement of a sufficiently fast decay of the symmetric dark matter component, leading to a tightly constrained and predictive scenario testable through several complementary probes.

The North Polar Spur (NPS) is a prominent diffuse X-ray feature whose origin has remained uncertain for decades. Using a uniform analysis of archival \textit{Suzaku} and \textit{XMM--Newton} data with new \textit{Chandra} observations, we constrain its thermal and chemical properties. The NPS emission is fully absorbed by the neutral interstellar medium, demonstrating that the plasma lies beyond the Galactic disk and is not a local supernova remnant or nearby superbubble. The spectra require a two-temperature model with a warm--hot component ($kT \approx 0.2$ keV) and a hotter component ($kT = 0.4$--$0.5$ keV), with emission measures of $(41.8 \pm 4.9) \times 10^{-3}$ and $(12.9 \pm 2.2) \times 10^{-3} \mathrm{cm^{-6}~pc}$, respectively. A key result is the detection of super-solar abundance ratios in the warm--hot phase, with N/O $= 3.6 \pm 0.3$ and Ne/O $= 1.9 \pm 0.1$ solar. A Suzaku observation of the outer South Polar Spur (SPS) shows similar absorption, temperatures, and enhanced abundances (N/O $= 2.9 \pm 0.4$, Ne/O $= 1.6 \pm 0.2$), though with lower emission measures. The similar super-solar abundance ratios suggest a common enrichment history. These properties are consistent with those measured along other sightlines through the X-ray--bright shells of the Galactic bubbles. Together, these results support that the NPS and SPS trace opposite limbs of the Galactic bubbles. The chemical properties suggest a strong contribution from stellar feedback in shaping the Galactic bubbles.