Metastable failures are hard to detect, prevent, and mitigate. During a metastable failure, a system exhibits self-sustaining bad behavior even in the absence of adversarial conditions. Prior work focuses on symptoms and has portrayed metastable failures as instances of self-sustaining overload. This characterization leaves the underlying failure causes and dynamics unknown, and does not account for metastable failures that do not manifest as overload. We present the first causal characterization of metastable failures by identifying their origin in metastable faults, i.e., structural destabilizing cycles of interaction among systems components that, in isolation, are stabilizing. Metastable failures arise when scheduling decisions let these destabilizing interactions gain the upper hand over the individual components' stabilizing tendencies. We then derive a methodology to predict metastable failures, and to build metastable-fault-tolerant (MFT) systems. We apply our methodology to three case studies, showcasing the generality of our results.

We present a novel, practical attack on the IPv6 Fragment ID generation algorithm of XNU, which is the kernel used by Apple products such as macOS and iOS. This attack exploits a race-condition vulnerability in the algorithm's pseudorandom number generator (PRNG) to cryptanalytically break, learn the internal state of the generator, and consequently predict fragment IDs, which, in turn, facilitates an IPv6 fragment spoofing attack. As far as we know, this is the first cryptanalytic attack that is based on exploiting race-conditions. With fragment spoofing, it is possible to partially manipulate UDP datagrams and TCP segments. We showcase a new type of attack on NFS (UDP) where an off-path attacker modifies a file as it is written, and an attack on HTTP (TCP) where an off-path attacker modifies an HTTP request. Apple assigned this vulnerability the CVE identifier CVE-2024-27823 and patched all its XNU-based products against the attack.

Evidence accumulation models provide a formal framework for studying decision making as a dynamic process unfolding over time. While these models have been extensively developed and reviewed in laboratory paradigms, their structured application in complex, ecologically valid domains has received comparatively little attention. Road traffic is a particularly relevant context for studying sustained, embodied perception action behavior, where decisions unfold under time pressure and involve continuous control and ongoing perception-action coupling. Examining how EAMs have been applied in this domain may therefore offer insights beyond discrete laboratory tasks toward decision making in real-world behavior. This semi-systematic review synthesizes 28 studies (2014-2026) applying EAMs to traffic-related behavior. We organize the literature along two dimensions: 1) modelling level, distinguishing models at the level of discrete decision-making and models at the level of continuous action control, and 2) model architecture, distinguishing evidence accumulation as either a stand-alone decision model or an embedded component within broader perception-action or interaction frameworks. These distinctions are associated with systematic differences in model architecture, parameterization, data usage, and validation strategies, reflecting task specific demands. By providing a structured overview of these patterns, this review clarifies how EAMs are currently instantiated in traffic contexts and highlights methodological challenges and future directions both in traffic modelling and in modelling of decision-making more broadly. Promising directions include laboratory work on evidence accumulation in sustained and time-varying tasks, interactive multi-individual decision-making, and the use of neurophysiological measures to identify the perceptual evidence underlying complex perception-action behavior.

Recent diffusion accelerators exploit activation sparsity by skipping near-zero GELU outputs, reporting 52--85% element-level sparsity. However, systolic-array hardware processes activations at column granularity, where a single non-zero element forces the entire column to be computed. We present the first systematic column-level sparsity characterization across seven diffusion workloads spanning three workload groups and four modalities. Our measurements reveal that element-level sparsity overstates hardware-exploitable sparsity by up to 78 percentage points and exposes a three-way taxonomy. UNet+transformer workloads exhibit activation concentration with workload-dependent cycle reductions up to 30.6%. Pure-transformer DiT shows dispersion, yielding 12.4%. Motion/dance transformer workloads range from modest reductions to 50.8% for MLD, driven by its extreme token dimension and expansion ratio. Cycle-level simulation on a GDDR6-based accelerator confirms that memory stalls account for up to 84--89% of total cycles and that layout sensitivity tracks the profiling-based taxonomy. A full accuracy sweep across five thresholds reveals that UNet+transformer workloads degrade gracefully, while motion models exhibit an accuracy cliff between the primary operating point and the next threshold. Our characterization shows that workload group and model dimensions jointly determine whether column-level memory layout optimization is beneficial, and element-level sparsity alone is insufficient for that prediction.

GPU workloads with large memory footprints frequently suffer from redundant L2 TLB misses in which a recently evicted translation is immediately re-walked at full page-walk cost. We characterize these dead-entry misses across 24 GPU workloads, finding they account for up to 99% of L2 TLB misses in the most TLB-sensitive applications, yet their performance impact varies widely depending on memory access structure. Workloads where warps share the same virtual page suffer from burst amplification, where a single eviction stalls many warps simultaneously waiting for one translation to return. In contrast, workloads where each warp accesses a distinct set of pages face a capacity-overflow problem that no replacement policy can resolve, a distinction validated by huge page experiments. Building on this two-class taxonomy, we design DEPOT (Dead-Entry PrOTection), a 1 KB Bloom filter mechanism that prevents recently evicted translations from being displaced immediately upon reinstallation, delivering up to 72% IPC improvement on interference-driven workloads with zero overhead on others, and composing with the state-of-the-art TLB prefetching and compaction mechanism, for 2 to 7% additional gain.

We develop a unified geometric framework for local non-adiabaticity in driven quantum systems. We show that the previously introduced AMT non adiabaticity parameter arises as a special realization of a more general geometric instability criterion governed by the normalized Fubini Study distinguishability speed. The local geometric evolution speed is identified as the physically relevant quantity controlling the onset of non-adiabatic instability. We introduce a universal dimensionless instability parameter measuring the competition between quantum-state evolution speed and spectral-gap protection. This quantity provides a local, gauge-invariant, and basis-independent criterion for arbitrary driven Hamiltonians. Near quantum critical points, the instability parameter diverges through inverse gap amplification, recovering the Kibble Zurek freeze-out condition directly from local geometric data. We prove that monotonic occupation-dependent nonlinear regulators geometrically compress the quantum metric, establishing a self-limitation theorem in which nonlinear spectral deformation confines the accessible region of projective Hilbert space under strong driving. The multimode extension yields a matrix-valued instability criterion that identifies collective instability channels invisible to scalar descriptions. The framework naturally extends to open quantum systems through the Bures metric and quantum Fisher geometry, where thermal mixing and Lindblad decay increase the instability threshold through geometric suppression of state distinguishability. The instability threshold further implies a universal geometric lower bound on coherent control time and quantum gate duration.

We investigate optical memory efficiency and storage time across $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ isotopes on both the D$_1$ and D$_2$ transitions. Maximum efficiency of up to $44\%$ was achieved using the D$_1$ line in both isotopes, with up to 1.5 ms storage time. %Maximum efficiencies of $44\%$ were measured for both isotopes on the D$_1$ line, in agreement within $1σ$, while the longest storage time reached is $1.5$ ms. These performance levels are enabled by warm vapor rubidium buffer-gas filled cells, large optical depth, and a near-resonant EIT scheme optimized with respect to the one- and two-photon detuning. Our results provide practical guidelines for optimizing the performance of warm rubidium vapor optical memories in simplified experimental configurations. We expect that the optimization approach employed here, specifically operating at elevated temperatures while identifying the optimal single-photon and two-photon detunings, should lead to improved performance of the quantum memory.

Ultrastrong coupling between matter and cavity vacuum fields can turn the electromagnetic vacuum into a structured quantum environment, thereby opening passive routes for modifying and manipulating material properties. Recent work has identified light--matter entanglement as an important ingredient in these property changes, which raises the question of where the relevant vacuum correlations actually reside. Landau polaritons provide chiral ultrastrong coupling systems in which one circular cavity polarization forms the bright polariton branches. Here, using a quantum information approach, we show that an exact chiral charge in a multimode Hopfield model routes the dominant anomalous correlations, squeezing, and cavity--matter entanglement into the opposite polarization. We find that, using parameters extracted from a multimode Landau polariton system, this hidden sector correlates the cyclotron resonance with finite momentum magnetoplasmons through Gaussian discord, while pairwise matter--matter entanglement remains absent. We further predict a polarization anisotropy of dressed vacuum electric field fluctuations as a signature of this chiral routing. These results identify chirality as a symmetry principle for organizing ultrastrong coupling vacua and show that quantum information tools provide a powerful framework for revealing the salient properties of Landau polaritons.

Can gradient descent be accelerated by just choosing better stepsizes? Surprisingly, the answer is yes. This short expository article provides an accessible introduction to this phenomenon of stepsize hedging.

Interstellar scintillation probes the properties of the ionized interstellar medium as well as the dynamical behavior of pulsars themselves. Using the Five-hundred-meter Aperture Spherical Radio Telescope, we obtained hour-long observations of PSRs~J0837+0610, J1136+1551, and J1239+2453. We detected a single scintillation arc in PSRs~J0837+0610 and J1239+2453, and identified three distinct arcs in PSR~J1136+1551. Our analysis reveals that the arc curvature scales with observing frequency as $η\propto ν^{-2.0\pm0.6}$ for PSR J0837+0610, and as $η\propto ν^{-1.9\pm0.6}$ for PSR J1239+2453. For PSR J1136+1551, the two clearest arcs exhibit scaling relations of $η\propto ν^{-1.6\pm0.6}$ and $η\propto ν^{-2.0\pm0.4}$, respectively. However, the frequency dependence of the third arc could not be constrained due to its low signal-to-noise ratio at higher frequencies. Moreover, the corresponding scattering screens are measured at distances ranging from 30 to 420 pc from Earth. However, long-term scintillation monitoring or VLBI observations are needed to reliably measure the scattering screen.

Underdetermined quadratic interpolation is a central model-construction tool in model-based derivative-free trust-region methods: it limits sampling costs but leaves an affine family of interpolating quadratics. Classical solvers select one element of this family by prescribing a fixed norm or model-change measure, such as the least-Frobenius-change Hessian update in Powell-type methods. We introduce BUP-TR (Bayesian Underdetermined Projection Trust-Region), which instead completes the model by projecting a prior quadratic onto the affine interpolation set in the precision norm supplied by the prior. The same precision matrix defines a spectral geometry certificate, MAP-poisedness, and a repair mechanism for interpolation sets. Under standard smoothness assumptions, uniform precision bounds, MAP-poisedness, and a trust-region-scale prior-accuracy condition, the hard-MAP models are fully linear. Consequently, BUP-TR attains global first-order convergence and O(epsilon^{-2}) evaluation complexity, with geometry-repair evaluations included. A NEWUOA-style implementation, BUP-NEWUOA, improves fixed-budget performance on the reported benchmark suite at moderate and stringent accuracy targets while retaining the computational structure of a Powell-type trust-region method.

We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial.

Magnetic fields play a crucial yet complex role in star formation, while their connection between large-scale filamentary clouds and small-scale young stellar objects remains poorly understood. We present new continuum polarization observations from the JCMT, ACA, and ALMA that provide continuous magnetic field measurements from approximately 5 pc down to approximately 4000 au, tracing for the first time the evolution of field morphology seamlessly across all key scales within a massive star-forming system. Our polarization maps reveal multiple U-shaped magnetic field structures pointing toward the central protocluster, aligned with accreting filaments from parsec to subparsec scales and converging at the compact center. This morphology suggests an environment of colliding flows that drag magnetic fields and trigger massive protocluster formation. On approximately 4000 au scales, we identify compact U-shaped fields likely guiding the kinematics of streamers accreting onto dense cores. The increasing curvature of these U-shaped patterns is a direct measure of a growing magnetic field tension force, implying a magnetic field strength scaling index of 0.50 +/- 0.10. These results indicate that the field, possibly enhanced by large-scale flow collisions, becomes strong enough to regulate star formation, linking parsec-scale colliding flows, a subparsec hub-filament system, and the triggering of massive star formation.

Regulatory institutions (from content moderation platforms to financial supervisors) observe, deliberate, and intervene only after a characteristic delay. We ask whether this processing lag alone can destabilize a multi-agent system that would otherwise remain stable, without exogenous shocks, coordination among agents, or malicious actors. We study this in two stages. First, we analyze a delayed replicator equation in which autonomous agents benefit from radical behavior but face punishment based on a lagged institutional alarm signal. We derive a closed-form critical delay beyond which the unique interior equilibrium loses stability through a Hopf bifurcation, and prove via center manifold reduction that the bifurcation is supercritical (bounded oscillations, not explosive growth) for the entire sigmoid response family. Second, we embed N=240 agents on a network with reinforcement learning (tabular Q-learning) and cross institutional delay with three decision architectures: fixed-policy, reactive (a memoryless threshold heuristic), and Q-learning. The hierarchy is opposite to the naive expectation that learning amplifies instability. Reactive agents are perfectly stable without delay yet collapse once delay is introduced (96% runaway by delay >= 8); fixed-policy agents are immune (0% at all delays); Q-learning agents are only partially resilient (66% at delay 20). The destabilizing ingredient is reactivity to delayed signals, not learning: agents that immediately exploit low-alarm windows trigger oscillatory feedback loops, while learning buffers this through punishment memory encoded in value functions. Throughout, "runaway" denotes bounded large-amplitude oscillation crossing a radical-fraction threshold, consistent with the supercritical bifurcation, not unbounded growth.

We calculate the Sudakov-limited maximum phase-space density associated with the linearly polarized gluon TMD coefficient $h_1^{\perp g}$ in the saturation region. Using Mueller's occupancy argument together with the small-$x$ Weizsäcker-Williams (WW) and dipole gluon distributions of Metz and Zhou, we find $n_{h,{\rm DP}}^{\rm max}=2n_g^{\rm max}\sim2α_s^{-3/2}$ for the dipole distribution in the same phase-space normalization. This dipole result is a process-dependent TMD proxy, not a literal gluon number density. For the WW distribution, the deep-saturation tensor coefficient lacks the logarithmic enhancement needed for the Mueller saddle, so the maximum is pushed toward the saturation boundary. We also perform a numerical Collins-Soper evolution study and find that the $J_2$ Bessel weight in the tensor TMD definition reduces the resolved peak, giving $c_h^{\rm num}\simeq6.6$--$7.1$ for representative EIC scales.

We give examples of proper minimal immersions in Euclidean space with very rapid area growth. The first is a proper embedding into $\bf{R}^4$ that yields a stable minimal surface, while the second is a proper immersion into $\bf{R}^3$. These results are motivated by [CM1] that shows that proper minimal submanifolds confined in space satisfy strong structural constraints.

In chapter 9 of his book "The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal", Woodin shows how to force the Strong Chang Conjecture over models of determinacy using $\mathbb{P}_{\mathrm{max}}$. We show here how a modification of the proof implies that such extensions actually verify the stronger cofinal version of the conjecture. This stronger version has important consequences on the semi-properness of small forcing, allowing us to prove the consistency of the theory "ZFC + Namba forcing is semiproper + $Θ^{UB}=ω_3$". We then use the constructions of this proof to also show that Woodin $(\ast)_{UB}$ axiom implies the conjecture.

We study a symmetry problem for the $h$-polynomials of edge rings of bipartite graphs. Let $G$ be a bipartite graph and write $h(\mathbb{k}[G];t)=h_0+h_1t+\cdots+h_st^s$. We prove that if $\Bbbk[G]$ is pseudo-Gorenstein and $h_1=h_{s-1}$, then $\Bbbk[G]$ is Gorenstein. Equivalently, under these assumptions the $h$-polynomial of $\Bbbk[G]$ is palindromic. The proof treats the $2$-connected case first by translating the numerical condition $h_1=h_{s-1}$ into a tight-separation condition for non-edges, and then passes to arbitrary bipartite graphs using the block decomposition. We also construct a blockwise minimal Gorenstein closure, obtained by adjoining all non-edges not separated by tight acceptable sets, and show that this construction preserves the next-to-leading coefficient of the $h$-polynomial.

The Empirical Bayes (EB) procedure of Hauer et al. (2002) is the workhorse of highway safety analysis: it combines a Safety Performance Function with observed crash counts to produce shrinkage estimates of segment-level crash rates. EB delivers practicality by holding several quantities fixed at calibration: SPF coefficients, per-type overdispersion, observed ADT, and a fixed exposure exponent. These assumptions strain when ADT is missing on a majority of segments. We present a fully Bayesian hierarchical model that moves beyond EB by relaxing each of these assumptions in a single joint inference. Fit on Ohio's road inventory (408,304 segments, 2.9 million crashes, 2013-2025), the model jointly imputes missing ADT and estimates per-segment crash rates with uncertainty. Posterior predictive checks of an initial fixed-exposure model expose a tail misfit; relaxing the exposure structure to a per-functional-class exposure exponent and an estimated length exponent, in place of a single scalar and a fixed offset, resolves it and improves out-of-sample predictive accuracy (PSIS-LOO $Δ\mathrm{elpd}$ = 9,394, SE 238). Crash count is sublinear in traffic in every class (exposure exponents 0.49-0.70, all $<1$, the safety-in-numbers effect) and sublinear in segment length ($β_{\mathrm{len}} = 0.69$). Partial pooling substantially improves out-of-sample predictive accuracy over complete pooling (PSIS-LOO $Δ\mathrm{elpd}$ = 4,780, SE 225). The Bayesian ADT submodel attains $R^2_{\log} = 0.756$ by encoding county and functional class as hierarchical priors, versus $0.653$ for a LightGBM restricted to the same continuous predictors. The output is a posterior crash rate distribution per segment, replacing the median-by-type point estimates used in our prior risk-aware routing framework.

In observational cosmology, the dark energy density and equation of state are effective quantities reconstructed at the background level under a set of assumptions. These include the FLRW framework, the standard Friedmann equation of General Relativity, and separately conserved non-relativistic matter at late times. Recent analyses involving DESI BAO measurements combined with CMB and supernova data have shown mild preference for dynamical dark energy featuring phantom or phantom-crossing behaviour. While the statistical significance of these trends remains limited, and unresolved systematics or modelling uncertainties may still be important, the resulting discussions have highlighted the need for a clearer interpretation of effective dark energy reconstruction. In particular, effective phantom behaviour does not necessarily imply the existence of a fundamental phantom field, microscopic ghost instabilities, violation of the null energy condition by the fundamental stress tensor, or a catastrophic cosmic future. The purpose of this work is to clarify these distinctions, independently of whether the current observational preference for dynamical dark energy survives future data. We discuss the definition of effective dark energy in cosmology, the interpretation of phantom and phantom-crossing behaviour, introduce a simple kinematic criterion for identifying effective phantom evolution directly from the expansion history, and review physical mechanisms through which effective phantom behaviour may arise without fundamental pathologies. While familiar within the dark energy reconstruction community, these distinctions are often left implicit in broader discussions of dynamical dark energy. We hope that this work will remain useful beyond the present observational situation as a clarification of what observationally reconstructed dark energy does and does not imply.

We prove that infinite Galois extensions of number fields with Galois group of finite exponent have the Northcott property. The main novelty of our approach lies in the application of a theorem of Segal on profinite groups.

We present results on dark energy evolution, assuming a time-dependent equation of state $w(a)=w_0+w_a(1-a)$, from growth and geometric probes using the full six-year Dark Energy Survey dataset: type Ia supernovae, baryon acoustic oscillations, and weak gravitational lensing and galaxy clustering (3$\times$2pt). The combination yields $w_0=-0.84^{+0.10}_{-0.10}$ and $w_a=-0.44^{+0.60}_{-0.55}$, the tightest constraints ever obtained from a single survey, with $2.2σ$ deviation from a cosmological constant. Adding the DESI DR2 BAO data yields $w_0=-0.84^{+0.06}_{-0.07}$ and $w_a=-0.53^{+0.33}_{-0.28}$, representing the most stringent low-redshift-only test of dynamical dark energy to date, with a $2.3σ$ deviation. In this combination, adding 3$\times$2pt doubles the constraining power. Finally, when combined with primary CMB information, we obtain $w_0=-0.82^{+0.05}_{-0.05}$, $w_a=-0.63^{+0.21}_{-0.18}$, with a $3.0σ$ deviation. We find that including 3$\times$2pt in the previously studied SN + DESI BAO + CMB combination leaves the significance essentially unchanged ($3.2 σ$ to $3.0σ$) while improving the figure of merit by $\sim$10\%. We systematically investigate the impact of leaving out each one of the probes and find that the significance of the deviation from a cosmological constant ranges from 2.3 to 3.2$σ$, with best-fit parameters consistently in the region $w_0 >-1$ and $w_a <0$. Excluding SN from the all data combination yields a $2.6σ$ departure from $Λ$CDM, providing a cross-check independent of supernova photometric calibration. These results support the weak preference for evolving dark energy reported by several recent cosmological analyses. By combining growth and geometric probes from a single survey, this work realizes the multi-probe dark energy program envisioned at the inception of DES.

Two integrable systems are constructed in a 2 + 1-dimensional space. Every of these systems involve two evolutions with negative numbers.

Machine learning systems face diverse threats that undermine robustness, privacy, and fairness. Although many defenses have been proposed, each typically addresses a single risk in isolation. Real-world deployments, however, require these defenses to be composed to meet multiple guarantees simultaneously. The process of composing defenses is complex and not well understood, and its impact on performance and security remains unclear. We present Landseer, a modular framework for integrating machine learning (ML) defenses into the ML lifecycle and systematically evaluating their composition. Landseer encapsulates defenses as containerized modules, allowing existing and new techniques to be plugged in with minimal effort. Its evaluation engine automates experiments across multiple metrics, supporting the study of defenses both individually and in combination. In a preliminary study, we identified 35 state-of-the-art machine learning defenses. After filtering for reproducibility, we analyzed their performance using Landseer's unified evaluation process. Our findings reveal gaps in replicability across defense families and provide insights into the challenges and opportunities in integrating multiple defenses, establishing a foundation for improving the reliability of machine learning systems.

We prove that the topological flow category $\mathcal{M}$ arising from a Morse-Smale pair $(f,ξ)$ on a smooth closed manifold $X$ is equivalent, as an $\infty$-category, to Lurie's $\infty$-category $\mathrm{Sing}_A(X)$ of exit paths in $X$ with respect to the stratification by the stable manifolds of $ξ$. The objects of $\mathcal{M}$ are the critical points of $f$, and for every pair of critical points, the space of morphisms of $\mathcal{M}$ between these is the space of possibly broken trajectories of $ξ$ connecting them; it can be identified up to homotopy with the space of unbroken ones. The latter maps naturally to the space of exit paths connecting these critical points; we prove this map to be a weak homotopy equivalence. Then, we combine these ingredients with several others to construct a zigzag of equivalences between the homotopy coherent nerve of $\mathcal{M}$, denoted $\mathcal{N}(\mathcal{M})$, and $\mathrm{Sing}_A(X)$. The $n$-simplices of $\mathcal{N}(\mathcal{M})$ are homotopy coherent diagrams of $n$ composable morphisms of $\mathcal{M}$; we introduce the notion of unbroken diagram, yielding an $\infty$-subcategory of $\mathcal{N}(\mathcal{M})$, which we refer to as the flow coherent nerve of $\mathcal{M}$. The simplices of the latter give rise to stratified maps out of a family of stratified cubes, into $X$. We organize this family into a functor from the category of finite ordered sequences of critical points, to the category of $A$-stratified topological spaces, and we prove a comparison result with the usual stratified geometric realization functor. We finally use a theorem of Tanaka that associates a functor of $\infty$-categories to a map a semi-simplicial sets satisfying some conditions. Our theorem has implications regarding constructible sheaves and the description of homotopy types in terms of flow categories.

A central challenge in precision cosmology with galaxy surveys is to extract non-Gaussian information from large-scale structure while controlling systematic uncertainties such as tracer bias. Conventional clustering statistics, such as the two-point correlation function (2PCF), capture limited nonlinear information and typically require explicit bias modeling, which can introduce systematic errors if the adopted bias prescription is inaccurate. To address this problem, we introduce $R^{\rm wst}$, a bias-robust statistic constructed from $m$-mode ratios of the wavelet scattering transform (WST). Using simulation-based inference, we train a Gaussian-process-regression emulator on the \texttt{Kun} simulation suite and use \texttt{JiuTian} simulations for covariance estimation and validation. The emulator achieves percent-level accuracy, sufficient for the expected observational uncertainties. We show that $R^{\rm wst}$ yields unbiased constraints on $Ω_m$, $σ_8$, $n_s$, and $w_0$, and improves the breaking of the $Ω_m$--$σ_8$ degeneracy by about a factor of two compared with 2PCF. Its constraining power remains stable across a broad range of tracer-bias scenarios, demonstrating that $R^{\rm wst}$ can mitigate bias-induced systematics without explicit bias modeling. These results establish $R^{\rm wst}$ as a powerful and robust statistic for precision cosmology with Stage-IV surveys.

We consider the ODE/IM correspondence for the value $c=-2$ of the Virasoro central charge (free-fermion point) and the associated quantum KdV model $-$ the quantization of the second hamiltonian structure of the classical periodic KdV model. We prove that the ODE/IM correspondence is complete (in the sense of V. Bazhanov, S. Lukyanov, and A. Zamolodchikov), namely that any solution of the Bethe equations coincides with the spectrum of a rational extension of the (quantum) harmonic oscillator. To this end, on the ODE side we consider Crum$-$Darboux transformations of the harmonic oscillator and the associated Laguerre Wronskians, which are remarkable special functions parametrized by pairs of partitions which we study in depth. As a further result, on the IM side, we diagonalize explicitly the first three hamiltonian operators of quantum KdV (in the free field representation): the eigenstates are Schur functions and the eigenvalues are shifted symmetric functions on partitions. We give two applications of this result: i) we prove that the eigenvalues are given by the evaluation of the Newton symmetric polynomials at the poles of the associated monster potentials, as further conjectured by V. Bazhanov, S. Lukyanov, and A. Zamolodchikov; ii) we show that these hamiltonian operators also belong to the algebra of hamiltonian operators obtained by quantizing the first hamiltonian structure of the classical periodic dispersionless KdV model.

The Discrete Source Classifier (DSC) provides probabilistic classifications of sources in Gaia Data Release 4 (GDR4) based on empirically-trained Bayesian classifiers. Using Gaia astrometry, photometry, and low-resolution spectra (XP), DSC classifies all sources as quasars, galaxies, or stars. DSC comprises three trained neural networks and three combinations of their probabilities. When evaluated as a function of brightness and sky position on a test set excluding the Magellanic Clouds, the DSC purity in GDR4 has improved for a small loss in completeness. The average performance of the best classifiers at magnitudes brighter than G=20 is at least 88% completeness and 96% purity for the extragalactic classes, namely the quasar and galaxy classes. At fainter magnitudes, performance is lower due to increased noise. The average performance at magnitudes of 20$\leq$G<20.5 is a minimum of 55% completeness and 71% purity for the extragalactic classes. At G>20.5 mag, completeness is considerably reduced, primarily for the models that depend on the XP spectra. Furthermore, we train additional models on Gaia optical data together with mid-infrared photometry from the CatWISE2020 catalogue. Inclusion of infrared photometry increases the completeness of extragalactic samples at G>20 mag between 9 and 29 percentage points, at the cost of reducing purity between 1 and 9 percentage points. In GDR4, the best DSC-combined classifier prioritising completeness identifies three million quasars and two million galaxies, but with expected high contamination among fainter sources. In contrast, the combined classifiers prioritising purity identify approximately two million quasars and 1.3 million galaxies with an expected lower level of contamination. Finally, we provide recommendations for enhancing the purity of the DSC extragalactic selection by applying quality cuts to the Gaia photometry and astrometry.

Identifying possible clusters in datasets and estimating their hierarchical modularity are central tasks in pattern recognition. In the present work, concepts and methodologies are described for performing these tasks while considering only the density of mergings obtained from hierarchical representations (dendrograms) of data inter-relationship along a scale variable. More specifically, the mergings of subclusters along the scale variable are obtained, yielding a respective merging density function. After this function is balanced along the scale variable, peak detection is applied in order to estimate, within a specified resolution, the respective hierarchical clusters and their hierarchical modularity. The potential of the reported approach is illustrated for some types of data and dendrograms, and the possibility of recursive cluster detection is also considered.

We reinterpret the lukewarm sector of four-dimensional Reissner--Nordström--de Sitter black holes as the exact zero-dissipation thermal manifold of an effective two-horizon nonequilibrium system. In the fixed-charge sector, the inter-horizon thermal affinity controls the entropy production and vanishes precisely on the lukewarm branch. The corresponding linearized thermal mode is governed by an exact relaxation coefficient \(K_L(ρ)\), with \(ρ=r_+/r_c\), and changes stability at the critical ratio \[ ρ_*=\frac{1+\sqrt{3}-\sqrt{2}\,3^{1/4}}{2}\approx 0.4354, \] where the relaxation time diverges as \(τ\sim |ρ-ρ_*|^{-1}\). We then encode this critical structure in a minimal Bragg--Williams functional and an Onsager--Machlup action for the effective trajectories of the thermal mode. In this way, the lukewarm branch is promoted from a geometric equal-temperature locus to a critical inter-horizon thermal manifold.