Papers

We aim to provide a cookbook for purely astrometric selection of quasars with Gaia DR3 and to provide an example of its use for the identification of very luminous $z>2$ quasars. We analyse the Gaia DR3 astrometry of confirmed quasars and stationary sources. We show that the proper motion signal to noise $\mu/\sigma_{\mu}$ follows a Rayleigh-like distribution. We also show the importance of properly taking into account the correlation between proper motions in right ascension and declination, as well as the non-linear error propagation. We adopt the Mahalanobis distance to the null proper-motion hypothesis. A scaled $\chi^2$ distribution with $k=2$ and scale $s=1.1485$ is fitted to Gaia-CRF3; the corresponding $\pm2\sigma$ Gaussian-equivalent threshold is $D^2_{M(\mu)}<7.097$. The final criteria combine this with the parallax condition and $\mathrm{ruwe}<1.4$. Applying the new criteria to the SDSS DR16Q confirmed quasars, the recovery rate is $90.25\%$. The suggested purely astrometric selection significantly improves both completeness and purity compared to other strategies used in the literature, reaching a quasar purity of approximately $95\%$ ($\sim2\sigma$ Gaussian-equivalent). It can be used to improve the selection purity and completeness for future quasar surveys. As an example, we use the suggested strategi to locate 24 very bright $z>2$ quasars without redshifts in the literature. Our proposed astrometric selection strategy recovers 95% of known quasars. Its potential use for new discoveries is demonstrated by the identification of 24 very luminous $z>2$ quasars. Ten of these are new discoveries and for an additional seven we correct the redshifts determined by other methods.}

This paper addresses the local convergence analysis of the stabilized sequential quadratic programming method for a class of composite optimization problems with convex piecewise linear- quadratic (CPLQ) modeling functions. We demonstrate that an appropriate second-order sufficient condition (SOSC) -formulated for composite problems- alone is sufficient to guarantee local superlin- ear convergence of the primal-dual sequence generated by this method. Furthermore, we examine the relaxation of the SOSC and show that it can be replaced with a weaker noncriticality of the associated Lagrange multiplier, provided, the modeling function is polyhedral and a relative interior condition is satisfied. We also present counterexamples showing that the relative interior condition is indispensable and that this relaxation fails for general CPLQ modeling functions.

World-action models (WAMs) predict a robot's actions together with the observations those actions will produce. However, the strongest models rely on video diffusion transformers that are far too computationally expensive for resource-constrained edge devices. We present SmolWAM, a latent WAM that we derive from the 2B-parameter Cosmos Policy by keeping its pretrained trunk and rebuilding its inference interface: single-frame visual latents, cached text features that preserve the trunk's attention sinks, 12 of 28 transformer blocks, and 1,008 tokens from which actions and future visual latents are read out in one rectified-flow step. Trained in 3.6 GPU-hours, SmolWAM succeeds in 95.5% of 400 LIBERO episodes at 57 ms and 2.3 TFLOP per 16-action chunk with 2.4 GiB of GPU memory, 11x faster than its teacher with 18.5x fewer FLOPs and 3.2x less memory, and its world head still forecasts scene motion.

If cosmic acceleration is driven by a positive cosmological constant, the universe approaches an eternally accelerating de Sitter state, whose interpretation in quantum gravity remains elusive. We develop a framework in which acceleration is instead a transient stage of dark-sector relaxation towards compositional equilibrium: matter and dark energy approach a stationary density ratio, eventually diluting like pressureless matter. Guided by linear response theory and Onsager's near-equilibrium regression hypothesis, we describe this evolution through a composition variable measuring departure from equilibrium. Extending constant fractional relaxation to the full background evolution yields the dark-energy equation of state $w=w_0a^{-n}$, where $n$ is the relaxation rate per e-fold of expansion. This history connects early dark-energy suppression, an upward phantom crossing and a density maximum to a pressureless scaling future. Using DESI DR2 BAO and Planck distance priors, with and without three alternative supernova compilations, we find a nominal $2.6$–$3.6\sigma$ preference for nonzero relaxation over constant $w$. The composition framework also motivates a constitutive prescription for linear perturbations that remains regular at phantom crossing. Near equilibrium, regular long-wavelength composition disturbances relax at the background rate to leading order, while small-scale fluctuations propagate as damped sound waves. We prove, however, that for separately conserved matter and dark energy, the pointwise constitutive relation cannot sustain a regular, gradient-stable negative-pressure branch throughout its full past evolution. We explore modifications of the pressure response and their consistency with neighbouring homogeneous histories, identifying requirements for extending the near-equilibrium description to the full cosmological evolution.

We obtain sharp isoperimetric-type upper bounds for Steklov eigenvalues on warped products whose bases are compact Riemannian manifolds with boundary and whose fibres are closed Riemannian manifolds. These bounds involve the volume of the warped product and of its boundary, as well as the eigenvalues of the Laplace operator on the fibre and the Steklov eigenvalues of the base. After separation of variables, these bounds are obtained by comparison with auxiliary Helmholtz-Steklov problems on the base involving weighted Laplace operators naturally induced by the warping function. We also study the effect of various natural geometric constraints, such as the warping function being identically equal to one on the boundary. The proofs make use of various spectral approximation methods, including homogenisation on manifolds when the fibres are one-dimensional.

Cooperative multi-agent tasks often impose constraints on a shared objective or collective safety. A team level violation cost function can measure this constraint outcome, but does not distinguish which agents' actions most strongly influence that violation. We present SafeDiSTL, a constrained multi-agent reinforcement learning framework that allows for credit assignment even with joint constraint measurements. We use Signal Temporal Logic (STL) robustness to measure episode-level violation through running-maximum cost increments. Smooth full-episode robustness and differentiable dynamics provide action sensitivities, which allocate each cost increment across agents at the same decision time. These sensitivities account for delayed effects when weighting agents' shares of each cost increment. We study the framework in cooperative payload transport, connected navigation, and networked traffic control tasks. SafeDiSTL achieves 1.6-5.1x the safe-success rate in transport, improves navigation safe-success by 11.1%, and delivers 50-68% more throughput in traffic when compared to constrained baselines. Results demonstrate a strong improvement of the learned policy in dealing with shared constraint while retaining the performance of unconstrained policies.

As engineering systems are optimized to reduce weight and improve performance, vibration behavior, including nonlinear effects, is becoming increasingly important to analyze. While methods such as harmonic balance are popular for analyzing periodic nonlinear vibration behavior, these analyses often only consider deterministic loading. However, real applications experience additional noise in the excitation, and alternative approaches are frequently limited to smaller models. This work expands on a recent approach to calculate a time-varying covariance using a linearized system around a periodic nonlinear response. Specifically, numerical conditioning is addressed and improved for cases increasing from a few degrees of freedom to hundreds of degrees of freedom. The algorithm is then extended to capture correlations across both space and time via a period-spanning covariance matrix. Model reduction is proposed for this calculation to maintain computational efficiency. The period-spanning covariance matrix is used to sample full stochastic cycles and estimate fatigue-relevant statistics up to 1393 times faster than stochastic time integration. Importantly, the present methodology uses the same gradient information as stability analyses and continuation solutions, so it can easily be applied for many nonlinear analyses. The methodology is demonstrated for two beam systems: one with unsteady aerodynamic forces and another with a Bouc-Wen frictional tip force. For the aeroelastic model, statistics are accurately estimated via the present approach. For the frictional system, some errors are introduced compared to stochastic time integration and are attributed to the linear time-periodic nature of the system used in the present stochastic calculations. However, estimated stochastic statistics remain useful given the significant reduction in computation time.

Efficient attention mechanisms, such as linear and sliding window attention, aim to reduce the computational complexity of Transformers from quadratic to linear. However, their degraded in-context recall often necessitates interleaving full attention layers, leaving the quadratic bottleneck unresolved in long-context processing. To address this, we introduce Orthros attention, which shifts the efficiency paradigm from structural allocation to phase-aware decoupling. As a unified module, it dynamically switches its computation pattern across different phases of sequence processing, enabling linear complexity prefilling and full attention decoding. Our design grants Orthros attention a lower asymptotic complexity compared to vanilla Transformers in prevalent long-context scenarios characterized by heavy prefilling and light decoding. Beyond theoretical formulation and complexity analysis, extensive empirical evaluations demonstrate Orthros's superiority across multiple dimensions. First, we validate its fundamental language modeling capabilities, demonstrating scalability across varying model sizes and strong competitiveness in comprehensive architectural comparisons. Second, Orthros exhibits exceptional conversion feasibility via a data-efficient Transformer-to-Orthros conversion, yielding performance that even surpasses the original Transformer. Finally, Orthros achieves a $21.9\times$ prefilling speedup over Transformers with end-to-end inference gains, while preserving long-context capabilities, as demonstrated by near-perfect 128K needle-in-a-haystack results and Transformer-level performance on real-world in-context recall tasks. Overall, these advantages in high performance, flexibility, and efficiency position Orthros as a promising candidate to succeed the Transformer in industrial applications.

We study the Arens regularity of the Fremlin projective tensor product of Banach lattice algebras. We firrst introduce and investigate L-weakly almost periodic functionals, a class of functionals defind in terms of L-weak compactness of their orbits. We obtain a characterization of these functionals in terms of bounded disjoint sequences and use it to analyze the Fremlin projective tensor product. In particular, we prove that, for nontrivial Banach attice algebras A and B, Arens regularity of A j jB implies Arens regularity of both A and B. The converse, however, fails: we construct two Arens regular Banach lattice algebras whose Fremlin projective tensor product is not Arens regular. We also establish several sufficient conditions for the Arens regularity of A j jB, including conditions involving the positive Schur property and order continuity of the norm on the space of regular operators. Finally, we show that when both factors are Banach f-algebras, their Fremlin projective tensor product is Arens regular.

The rapid development of personalized video generation has raised serious concerns over identity privacy, as a few facial videos of a person now suffice to reproduce their identity in synthetic videos. This report presents the first-place solutions to both phases of the ECCV 2026 LifeGenIP Challenge on Unlearnable Videos, which aims to protect facial videos from unauthorized customization under a limited and imperceptible perturbation budget. For Phase 1, we introduce Reference Capacity Collapse, a pair of complementary losses that degrade the information carried by the reference condition while keeping subsequent video representations dependent on it, together with a Motion-Guided EOT mechanism that improves robustness across unknown inference conditions. Phase 2 further considers tuning-based customization and unseen generative models. To address both threats within a single perturbation, we design a two-layer framework that protects the facial and background regions separately, constructing structure-aligned perturbations from a synthetic target identity in the former and strengthening the white-box disruption of Phase 1 in the latter. Our method achieves nearly perfect protection under white-box reference-based customization, and remains effective under other customization paradigms, various models, and temporal attacks. Both solutions are built upon our recent work LETHE. We hope our solutions can inspire future work on protecting facial videos against unauthorized customization. Our code is available at https://github.com/AntigoneRandy/KVeil.

Scaling generalist robotic policies is limited by the high cost of collecting embodied interaction data. Large-scale egocentric human videos offer a rich alternative, but they lack robot action labels, and existing action annotation methods are often noisy under real-world visual complexity and diverse manipulation dynamics. We introduce LAPT-Scale, a scalable latent action pre-training paradigm with two components: LAPT-Scale-LAM learns continuous latent actions by explaining frame-to-frame visual transitions in human videos and uses them as human-derived supervision, while LAPT-Scale-Policy trains a VLA policy through human-video latent-action pre-training, target-robot embodiment alignment, and task-specific post-training. Unlike prior vector-quantized LAMs, LAPT-Scale-LAM uses a continuous latent space to preserve fine-grained motion and interaction dynamics. We further combine perceptual, semantic, and optical-flow alignment signals to improve transition-level supervision beyond pixel reconstruction. Trained on 23.3K hours of egocentric video, LAPT-Scale-LAM provides implicit action supervision for policy pre-training, yielding consistent scaling gains and improving real-robot success from 63.3% to 85.0% as annotated human video scales from 1K to 5K hours. The learned policy also generalizes to unseen visual conditions.

Sensitivity analysis asks how strong unmeasured confounding would have to be before an observational conclusion changes. Several R packages already calculate established sensitivity quantities, but their outputs use different parameters, objects, and plotting conventions. In this article, we describe confoundvis 0.3.0, an R package designed as a common interface for these analyses. The package stores results from the impact threshold of a confounding variable, the robustness of inference to replacement, partial-R^2 omitted-variable bias analysis, E-values, and Rosenbaum bounds for matched pairs in one confoundsens object. Each result keeps its own parameter and its own published formula. The same functions then draw robustness curves, locate the points at which a conclusion changes, write plain-language reports, and collect several analyses in one table. When a framework describes a confounder by two associations, the package also draws the two-parameter surface on which the familiar single number lies and, where such benchmarks are defined, places measured covariates on the surface. We demonstrate the package with the right heart catheterization data and with a matched-pair study of welders. The native calculations agree with sensemakr, konfound, DOS2, sensitivity2x2xk, and sensitivitymv to numerical or grid precision, and imported EValue results reproduce the reported E-values. The purpose of confoundvis is not to replace the underlying methods or to place their sensitivity parameters on a common scale. Its purpose is to provide a consistent workflow for drawing, comparing, and reporting the results that those methods produce.

Origin-destination (OD) flow forecasting supports urban mobility decisions by predicting the volume and patterns of human movement across a city. Most existing public OD benchmarks provide only a partial view of citywide mobility, covering a single transport service or at most two modes. With partial mode coverage, observed demand changes are difficult to separate into shifts across transport modes and changes in total travel. We introduce SeoulMMOD, a large-scale public benchmark for citywide multimodal mobility in Seoul. SeoulMMOD provides three years of hourly OD flows estimating total mobility for 6 urban travel modes across 25 districts and 426 sub-districts, together with travel-time, travel-distance, calendar, rainfall, and point-of-interest (POI) signals. Using SeoulMMOD, we benchmark 14 forecasting baselines under a common protocol and analyse the effects of spatial scaling, joint versus mode-separate training, and cross-year generalization. Results show that several spatio-temporal models that work at district level do not scale to sub-district OD forecasting, and that naive joint multi-mode training does not consistently improve accuracy. Together, the dataset and benchmark establish a reproducible testbed for multi-mode, multi-year OD forecasting at the city scale.

A plate withdrawn from a bath of partially wetting liquid entrains a film above a critical velocity. Here, we show that this critical threshold can be substantially increased by the presence of a laminar gas flow opposed to the plate velocity that exerts a tangential shear stress on the liquid-gas interface. Using two-phase immiscible Navier-Stokes simulations and confining the gas to a narrow channel, we derive a closed-form expression for the interfacial stress, which combined with lubrication theory relates the thickness of the film and the contact line velocity to the applied shear stress. As the gas velocity is increased, the film thins and the contact line velocity slows down, until the imposed shear overcomes the drag of the moving plate and entrainment is arrested. As in the quiescent case, the velocity mismatch between plate and contact line is independent of the plate velocity and is set by the applied shear alone. We find that one set of varying gas flow simulations, with constant critical plate velocity, therefore determines the critical gas flow for every smaller plate velocity.

Chiroptical nonlinearity is vital for modern optics and photonics. However, it remains a central challenge to obtain a material simultaneously with large second-order nonlinearity and strong nonlinear optical chirality. Here we uncover the strong chiroptical nonlinearity in COF-330-a, owing to the formation of unique chiral, polar structure with large p-electron conjugation via structural transformation. A large effective second-order nonlinear susceptibility of ~ 101 pm/V and a strong nonlinear chiroptical response (SHG-CD: -1.60 to +1.66) have been demonstrated in individual COF-330-a microcrystals, transcending the performance trade-off limitation in conventional chiroptical materials. These findings open a new avenue for designing nonlinear chiroptical materials which harness the duality of polarity and chirality and chemical versatility of COFs.

We investigate the anomaly-induced transport properties of a holographic superconductor exhibiting spontaneous symmetry breaking. The holographic model incorporates vector and axial gauge fields, an additional non-anomalous $U(1)$ symmetry, and a charged scalar field that drives the phase transition. Working in the probe limit, we numerically construct the superconducting background under two alternative scalar field quantizations, corresponding to operators with scaling dimensions $\Delta=1$ and $\Delta=3$ (denoted as the $O_1$ and $O_2$ theories, respectively). Using Kubo formulae, we compute the chiral magnetic conductivities and examine their response to the scalar condensate. Our findings demonstrate that spontaneous symmetry breaking allows anomaly-induced transport to extend beyond anomalous currents, significantly impacting the non-anomalous sector as well. Remarkably, this effect appears in both theories, indicating that the influence on the non-anomalous sector is independent of the chosen quantization. The comparison of our numerical results with the analytical limits for $O_i \to 0$ and $O_i \to \infty$ $(i=1,2)$ reveals consistent behavior across both theories.

Understanding the turbulent structure of molecular clouds is essential for linking galactic environment to the regulation of star formation. Although Galactic molecular clouds have been studied extensively, extending turbulence-mode analysis beyond the Milky Way remains challenging because of the limited spatial resolution and dynamic range of extragalactic observations. We assess the applicability of the Brunt & Federrath (2014; BF14) framework to molecular clouds in M33. We apply BF14 to 128 $^{13}$CO(2-1) clouds, selecting a primary quality-controlled sample of 54 clouds and a more restrictive 25-cloud subsample defined using a stricter extraction-padding criterion (PAD=2) for quantitative analysis.Tests of cloud and noise power spectra, Fourier-space cutoffs, extraction padding, and Monte Carlo uncertainties demonstrate that the retained spatial frequencies are dominated by astrophysical signal and that the inferred turbulence-mode fractions are robust against reasonable analysis choices. Both samples yield consistent distributions of the solenoidal fraction, with mean values of $R \simeq 0.22$ for both samples and median values of $R \simeq 0.18$ and $0.17$, respectively, indicating that compressive motions dominate the turbulent energy budget. No strong systematic variations of $R$ are found with galactocentric distance or tracers of recent star formation. These results demonstrate that, despite the challenging spatial resolution of current extragalactic molecular-line observations, the BF14 framework can be applied reliably to nearby galaxies using spectroscopic observations alone. To our knowledge, this constitutes the first application of the full BF14 formalism to extragalactic molecular-cloud observations.

We study multiwinner voting with $n$ voters and $m$ candidates, where the goal is to select a committee of size $k$. Voters have unit-sum cardinal utilities but report only coarse information induced by $t$ utility thresholds. In particular, each voter partitions the candidates into approval sets, with the utilities of all candidates in the same set lying between the same pair of consecutive thresholds. We model the utility of each voter for a committee as a normalized monotone symmetric norm, capturing, among others, additive welfare, best-representative utility, top-$r$ welfare, $\ell_p$ welfare, and normalized non-increasing ordered weighted averages. We design a deterministic rule with distortion at most $2(2m)^{1/t}$ and a randomized rule with distortion at most $2\min\{m^{1/(t+1)},m/k\}$. These guarantees hold for every committee size $k$ and every norm in our framework. Consequently, a single threshold yields distortion $O(m)$ for deterministic rules and $O(\sqrt{m})$ for randomized rules, while $O(\log m)$ thresholds suffice for constant distortion. We complement these results with norm-dependent lower bounds that asymptotically match our upper bounds for constant committee sizes, including the single-winner case.

Counterfactual inference asks how an observed outcome might have differed under different circumstances, such as whether a patient would have recovered had they received a different treatment. Such questions arise whenever decisions depend on the outcomes of alternatives that were not observed. Answering counterfactual queries generally requires knowledge of the underlying causal structure, which is often unavailable in practice. A common approach is therefore to first estimate the causal graph from observational data and then perform counterfactual inference. However, errors in the estimated causal graph can propagate to downstream counterfactual predictions. To address this challenge, we introduce the Counterfactual Graph Neural Process (CFGNP), an end-to-end approach that answers counterfactual queries directly from observational data without first estimating a causal graph. CFGNP uses Graph Neural Networks (GNNs) to exploit the dual-graph structure by restricting cross-world message passing to corresponding factual–counterfactual variables. Across synthetic and image-based benchmarks, CFGNP achieves stronger predictive performance than existing approaches, including on the German Loan benchmark, where it reduces MSE from $4.51 \times 10^{-2}$ to $0.19 \times 10^{-2}$. Furthermore, on synthetic causal graphs, a model trained only on 10-node graphs maintains strong predictive performance on graphs with up to 30 nodes, without retraining.

We study the list chromatic number of generalized Johnson graphs. Recall that the vertices of such graphs are all possible $r$-element subsets of $[n] = \{1, \dotsc, n\}$ and an edge is drawn between two vertices if and only if corresponding sets have exactly $s$ common elements. We prove that for any fixed $s \geq 1$ and $r \geq 2s + 2$ we have $\chi_L(G(n,r,s)) = \Theta(n^{s+1}\ln n)$. In case where $s = 0$ we prove that for all $4\ln n \leq r \leq n/20$ we have $\chi_L(G(n,r,0)) \geq \frac{n}{120}\ln\left(\frac{en}{r}\right)$. Together with previous results of Bulankina, Inozemtsev and Kupavskii this proves that $\chi_L(G(n,r,0)) = \Theta\left(n\ln\left(\frac{en}{r}\right)\right)$ uniformly for $2 \leq r \leq (1/2-\varepsilon)n$.

Legal language understanding requires reasoning over semi-structured regulatory documents, yet standard pre-training objectives do not explicitly target this structural capability. Because current legal language models rely solely on masked language modeling, they treat statutory text as flat token sequences and ignore the underlying hierarchical constraints. To bridge this gap, we present a multi-task pre-training approach for German traffic law (StVO). Our approach combines three complementary objectives: Next Sentence Prediction (NSP), Knowledge Graph (KG) Guided Clustering (CLU), and Knowledge Graph (KG) Aware Paragraph Classification (CLS). This approach explicitly encodes structured legal knowledge directly into the model weights. This encoding enables zero-shot legal reasoning at inference time and removes the need for discrete graph traversal. We evaluate our approach across nine Transformer-based encoders and 324 experimental runs. On synthetic StVO question answering, our models demonstrate consistent relative improvements between 10.3% and 155.0% over baselines. Furthermore, relative to the established LexGLUE baselines (Chalkidis et al., 2022), our models improve over prior results on four of seven legal benchmarks. It also achieves consistent zero-shot transfer gains between 3.4% and 15.8% on Austrian driving regulations. These experimental results indicate that our training approach generalizes successfully beyond the initial training legal domain.

This study aimed to reconstruct a regulatory network suitable for systems biology analysis of diabetic bone marrow. Three artificial intelligence large language models independently analysed 18 Discovery and 43 Validation publications. Investigator guided integration produced a frozen network of 62 biological entities and 79 directed interactions. Open source software Gephi created a visual representation before and after main node removal. The plausibility of the reconstructed interactions was tested against independent curated knowledge resources, including the Kyoto Encyclopedia of Genes and Genomes, connectomeDB2025, Reactome, and Gene Ontology. Further analysis examined physiological correspondence, missing edge sensitivity, and graph constrained interrogation. Functional modules encompassed endothelial perivascular support, stem cell retention and trafficking, neural circadian regulation, inflammatory myelopoiesis, metabolic stress, and epigenetic regulation. They intersected through shared effects on endothelial function and stem cell behaviour. The endothelium was the principal connecting node. Computational removal of the endothelial node increased network fragmentation and diameter, while average directed path length remained essentially unchanged. External resources supported 60/79 interactions (75.9%); 19 remained unresolved, with none classified as contradictory. Complementary assessments supported biological plausibility and faithful interrogation of the reconstructed network. This investigator led dialogue with artificial intelligence provides a foundation for a systems level understanding of diabetic bone marrow dysfunction. The approach may facilitate the generation of testable hypotheses and the identification of mechanistic targets for coordinated restoration of disrupted niche interactions.

Vision Mamba has recently emerged as an efficient alternative to convolutional and Transformer-based architectures by modeling long-range spatial dependencies through recurrent state evolution. Existing studies primarily improve token serialization, scanning strategies, or expert routing, yet largely overlook a state level question question: how should recurrent states be organized for spatially heterogeneous visual restoration? In this paper, we show that forcing tokens with heterogeneous update behaviors to recurrently modify a shared hidden state leads to persistent cross-content interference, which we term State Contention. We further argue that effective recurrent modeling should organize state evolution according to token compatibility rather than token ordering. Based on this observation, we introduce State Isolation, a new recurrent state organization principle for Vision Mamba,tokens with compatible state-update tendencies evolve within independent recurrent state streams. To instantiate this principle, we propose IsoMamba, a $\Delta$-guided architecture that constructs model-intrinsic update representations, discovers update-compatible token groups through label-free clustering, and routes them to isolated Mamba experts following a cluster–route–isolate paradigm. In addition, we develop a dynamic channel-wise reweighting objective to compensate for wavelength-dependent reconstruction difficulty in underwater images. Extensive experiments demonstrate that IsoMamba consistently achieves state-of-the-art performance on multiple underwater image enhancement benchmarks while providing cleaner hidden state responses, validating the effectiveness of state isolated recurrent modeling.

We analyze archival high spectral resolution ESPaDOnS spectropolarimetric observations (R = $\lambda/\Delta\lambda$ = 68000) of three targeted locations within the filamentary nebula surrounding NGC 1275. We present here the analysis of the main filaments emission lines, namely: [NII]$\lambda6584$, H$\alpha$, and [NII]$\lambda6548$, across our three pointings displaying clear detectable emission, with one also showing additional [SII]$\lambda6716$ and [SII]$\lambda6731$ emission line doublet. Using a Markov Chain Monte-Carlo (MCMC) algorithm and thanks to the exceptionally high spectral resolution of the observations, we resolve for the first time each of the emission lines within one of the pointings into a set of three emission components with a remarkable velocity dispersion contrast ($\sigma_1 \sim 25$ km/s, $\sigma_2 \sim 90$ km/s and $\sigma_3 \sim 208$ km/s). We also perform flux ratios of the three detected emission components, which reveal differences in electron density and ionization sources. Consequently, the ESPaDOnS observations appear to reveal for the first time the overlap of an outer quiescent filament and a central turbulent filament likely affected by the AGN activity at a distance of $\sim 6.8''$ ($\sim 2.5$ kpc) from the central BCG. Finally, ESPaDOnS polarimetric data of one of the pointing allows us to confirm an average linear polarization degree of $\sim 0.15-0.14\%$ and an angle of polarization of $5.3\pm25.7^\circ$ for the optical emission of the filaments, as well as polarization dips associated with the H$\alpha$ emission line and its multiple emission components. We interpret these features and measurements as tentative polarization due to dust scattering.

We show that the cotangent bundle of a holomorphically flexible Stein manifold has the symplectic density property. As application we deduce holomorphic approximation for Hamiltonian diffeomorphisms of real cotangent bundles by complex symplectic automorphisms of the complexified cotangent bundles, which preserve the real bundle, in the Carleman sense, i.e. in the Whitney topology.

Federated clustering can support applications such as patient stratification across hospitals and customer segmentation across distributed financial datasets. Responsible AI calls for fair representation of demographic groups and support for data deletion, motivated in part by rights such as the GDPR's right to erasure. These goals interact: deleting records can change the balance between groups and alter the clustering of the remaining population. We study exact machine unlearning for federated socially fair $k$-means, whose objective is to minimize the largest group-average squared distance to the nearest center. Our approach keeps separate local summaries for each group, so summaries at unaffected institutions remain valid as global fairness weights change. For two groups, we prove an initialization approximation guarantee independent of client group proportions under ideal sampling, and we show that same-seed replay reproduces retraining exactly. Reuse pays off most when a whole client withdraws: across three datasets, replay is $35.8\times$ faster than retraining for the initialization-only model and remains $2.4\times$ and $1.7\times$ faster with one and two fair-refinement rounds, which improve worst-group cost. For individual record deletions, gains are modest (about $1.06\times$), and certifying cached assignments can cost more than it saves. These results map where exact unlearning can profitably reuse computation. Code and reproducibility materials are available at https://github.com/arareddy/mufsc.

We revisit autobidding equilibria in GSP sponsored shopping auctions, recently proposed and studied in Dütting et al. On the existence side, we show that autobidding equilibria under both budget constraints (ABE-B) and return-on-investment constraints (ABE-R) always exist and, moreover, always admit equilibria with polynomial-size support over the allocation space. On the computational side, we show that computing an exact equilibrium is in FIXP, and that computing an approximate equilibrium is in PPAD. We also prove that computing an approximate equilibrium is PPAD-hard for both ABE-B and ABE-R. Together, these results provide a fairly comprehensive picture of the computational complexity of autobidding equilibria in GSP sponsored shopping auctions.

Non-Bloch band theory recovers the open-boundary spectrum of a non-Hermitian chain from its Bloch Hamiltonian evaluated along the generalised Brillouin zone rather than the unit circle. We develop its finite-size counterpart for banded Toeplitz matrices with real open-boundary spectrum. Reality of the spectrum forces the generalised Brillouin zone to be parametrised by an analytic polar curve, so the known sufficient condition for a real spectrum is also necessary under some mild non-degeneracy conditions. At finite size $n$, the eigenvalues of the original and the symmetrised Bloch Hamiltonians are given by samples at $n$ quantised momenta from the same limiting band, although separated by a phase mismatch of order $1/n$ which we obtain in closed form. Iterating this correction $K$ times yields a quantisation rule on the generalised Brillouin zone reproducing the finite spectrum with an error $\mathcal{O}(n^{-K-1})$ for any fixed $K$. At finite size, the generalised Brillouin zone itself is unchanged and only its parametrisation depends on $n$.

Grain boundaries (GBs), including twin boundaries (TBs), play a critical role in plastic deformation by interacting with dislocations. The deformation and strengthening mechanisms in $\beta$-Sn are of significant interest because Sn-based alloys are widely used as solder materials. Recent experiments have shown deformation-induced faceting in $\beta$-Sn arising from twin-dislocation interactions. Using molecular dynamics (MD) simulations informed by a recently developed machine-learned interatomic potential (MLIP), we demonstrate a $\langle c\rangle$ dislocation-absorption mediated faceting reaction along $(301)$ TBs in $\beta$-Sn in which facet length grows with the number of absorbed dislocations. We show that the predicted facet length is consistent with isotropic elasticity theory only when the disclination character of the asymmetric twin facet is taken into account. We discuss analogies to faceting reactions in other low symmetry metals and hypothesize that the ubiquity of $(301)$ twins in $\beta$-Sn stems from their ability to grow rapidly through a forest of dislocation obstacles.

Projection methods are among the most widely used techniques for solving convex feasibility problems due to their simplicity and robustness. However, classical projection-based algorithms and existing circumcentered-reflection methods generally provide only asymptotic convergence. In this paper, we introduce a relaxed version of the centralized circumcentered-reflection method (cCRM) obtained through an extrapolation of the circumcenter step. We first analyze the two-set case and then extend the proposed approach to the successive framework for multiple convex sets, including under- and over-relaxation and a backtracking strategy. The convergence analysis establishes Fejér monotonicity and global convergence under suitable conditions, while local error-bound assumptions yield linear convergence and standard regularity assumptions imply superlinear convergence. Motivated by finitely convergent projection methods based on perturbed feasible sets, we further investigate a perturbed relaxed formulation designed to achieve finite termination. Numerical experiments show good practical performance, comparable to and competitive with the finitely convergent PACA method. The results also provide clear numerical evidence of finite termination in the tested instances.