Papers

Tokamak disruptions caused by tearing modes can be prevented with magnetic feedback. A database of DIII-D locked mode disruptions provides criteria for major disruptions. The main criterion is that the q = 2 rational surface must be sufficiently close to the resistive wall surrounding the plasma to interact with it. This is shown in simulations of a sequence of model equilibria derived from the database. If the wall is ideally conducting, major disruptions do not occur. Magnetic feedback emulates a conducting wall, and can prevent major disruptions. Feedback coils must be designed appropriately, otherwise they are not effective in disruption prevention. Simulations of a model of MST also show the q = 2 criterion for major disruptions, as well as feedback stabilization. Feedback offers an attractive alternative to disruption mitigation by impurity injection.

This paper presents the development strategy for HWO-AGATE (Accurate Guiding and Astrometry Targeting Exoearths), a high-precision relative astrometry instrument concept designed for the future Habitable Worlds Observatory (HWO). The instrument is based on a gigapixel-class focal plane that incorporates the new generation of large-format GigaPyx CMOS sensors developed by Pyxalis. The proposed architecture relies on four 220-megapixel sensors assembled into a focal plane array and coupled with a dedicated calibration system to achieve the astrometric precision required for exoplanet detection and characterization. Preliminary study identified three major technological challenges. First, the performance of the 220-MP detectors must be validated against HWO's astrometric requirements. Second, the development of space-qualified packaging and integration solutions is required for a multi-sensor focal plane, while addressing the electrical and thermal constraints associated with the fast readout of large-format CMOS detectors. Third, an onboard calibration data-processing architecture must be implemented to reduce the raw data volume by approximately two orders of magnitude, enabling efficient operation within spacecraft resource limits. To address these challenges, we propose a comprehensive technology maturation program based on the construction of a representative end-to-end detection chain. The demonstration setup will include a partial focal plane equipped with 220-MP sensors, front-end electronics, a dedicated processing unit, and the calibration subsystem. The objective is to demonstrate compliance with HWO-AGATE requirements and to raise the maturity of large-format CMOS detector technology to Technology Readiness Level 5 (TRL 5). Detector validation and space-qualified packaging activities are already supported through institutional funding and the French national PEPR ORIGINS program in the RETINA (Researching Exoplanets Through Imaging for Narrow-angle Astrometry) project.

We introduce a topological abelian group $\mathrm{K}_1^\Delta(A)$ for every $\mathrm{C}^\ast$-algebra $A$, which is functorial in $A$ and invariant under stabilisations. $\mathrm{K}_1^\Delta$ can distinguish group actions indistinguishable by equivariant (K)K-theory and traces — we illustrate this on the irrational rotation algebra by exhibiting strongly outer actions of $\mathbb Z$ which, via $\mathrm{K}_1^\Delta$, are not (stably) cocycle conjugate. These actions are moreover trivial in $\mathrm{KK}^{\mathbb Z}$ and on the Hausdorffised unitary algebraic $\mathrm{K}_1$ group $\overline{\mathrm{K}}_1^{\mathrm{alg}}(A)$. The Hausdorffisation $\overline{\mathrm{K}}_1^{\Delta}(A)$ of $\mathrm{K}_1^\Delta(A)$ forms the final part of the total stable invariant $\mathrm{\underline{K}T}_{\mathrm{s}}(A)$, which we also introduce. We prove that $\mathrm{\underline{K}T}_{\mathrm{s}}$ classifies $*$-homomorphisms up to approximate unitary equivalence between certain stable $\mathrm{C}^\ast$-algebras which contain a non-zero projection. $\mathrm{K}_1^\Delta(A)$ is new even in the unital setting, but under further assumptions on $A$ recovers the unitary algebraic $\mathrm{K}_1$ group $\mathrm{K}_1^{\mathrm{alg}}(A)$, whereas the Hausdorffisations $\overline{\mathrm{K}}_1^{\Delta}(A)$ and $\overline{\mathrm{K}}_1^{\mathrm{alg}}(A)$ agree for every unital $A$.

This work identifies the dominance regions for discrete, simultaneous-move pursuit-evasion games on graphs. Existing geometric approaches provide efficient characterizations of winning regions, but typically provide only sufficient conditions and rely on open-loop strategies. To address these challenges, we develop a set-based dynamic programming approach to characterize the pursuer's winning and losing regions, providing necessary and sufficient winning conditions under worst-case behavior. The reachability analysis admits a set-chasing interpretation, allowing translation of dominance sets to feedback strategies that adapt to the players' positions in real time. For states where neither player can guarantee victory, we introduce an instantaneous matrix-game formulation and establish upper and lower bounds on the pursuer's winning probability. Simulation results validate the correctness of the dominance-region characterization and the proposed bounds.

In this paper, we study CONFLICT-FREE EDGE CUT (CF-CUT), which is a recently introduced conflict-free version of the MIN-CUT problem that asks to find the minimum number of edges to disconnect a connected graph. The CF-CUT takes as input a connected undirected graph G = (V, E), a conflict graph $\widehat{G}$ such that $E(G) = V(\widehat{G})$, and the objective is to decide whether there exists $F \subseteq E(G)$ such that $G - F$ is disconnected and $F$ is an independent set in $\widehat{G}$. Rauch et. al. [IPL-2025] proved that CF-CUT is NP-Complete and also provided some results on the parameterized complexity of CF-CUT. A related variant MIN CONFLICT-FREE EDGE CUT (MIN-CF-CUT) takes a connected graph $G$, a conflict graph $\widehat{G}$ such that $V(\widehat{G}) = E(G)$, and an integer $k$ as input and asks if there is a set $F$ of at most $k$ edges such that $G - F$ is disconnected and $F$ is an independent set in $\widehat{G}$. In this paper, we extend the work of Rauch et al. [IPL-2025] and provide a systematic study on the CF-CUT and MIN-CF-CUT from the perspective of parameterized complexity and polynomial kernelization. We prove that CF-CUT is NP-hard when the dissociation number of the input graph is at most two. We also complement it by proving that CF-CUT is poly-time solvable when the dissociation number of an input graph is at most one. Additionally, for MIN-CF-CUT, we consider both solution size and various structural parameters of the input graph as parameters, and provide fixed-parameter tractability and W[1]-hardness results when the conflict graph is restricted to various graph classes. We also prove that unless NP $\subseteq$ coNP/poly, MIN-CF-CUT admits no polynomial kernel when parameterized by the vertex cover number of the input graph; and also when parameterized by the sum of the solution size and the vertex integrity of the input graph.

Generalization in multi-arm collaboration can be studied as composing familiar atomic skills in new ways across arms. However, existing evaluations offer limited insight into which training and architectural choices support this ability under different coordination requirements. We introduce ACG-Bench, a benchmark for Arm-wise Compositional Generalization that provides a common testbed for studying skill recomposition in dual-arm policies. It contains 23 task–condition pairs across 8 task families, with 6 in-domain conditions and 17 unseen compositions covering reordering, synchronization, their combination, and cross-task composition. All methods receive the same per-arm atomic prompts, and success requires achieving the task goal while satisfying physical milestones and specified order or timing constraints. Using $\pi_{0.5}$ as a common vision-language-action backbone, we compare representative data-augmentation and architectural strategies with shared source data and a common evaluation protocol. Our architectural study examines arm-token grouping, skill-specific LoRA adapters (SkillLoRA), and arm-wise attention (AWA), highlighting the complementarity of skill-conditioned parameters and attention structure. Combining these choices yields AE-VLA, which achieves 21.53% generalization success in simulation, compared with 2.94% for Single $\pi_{0.5}$, 3.06% for MA-VLA, and 5.53% for two independently controlled $\pi_{0.5}$ policies. On physical SO101 robots, AE-VLA reaches 39.00% mean success across five unseen conditions, compared with 10.00% for the strongest baseline. These findings provide empirical guidance for designing dual-arm policies that generalize beyond fixed training routines.

Multipartite systems of high-dimensional particles can host forms of quantum entanglement inaccessible to qubit systems. A particularly fascinating class is formed by the fully antisymmetric states, also known as supersinglets, which possess a remarkable symmetry: they are invariant under arbitrary collective local unitaries. Here, we explore their entanglement properties and establish their quantum information applications. Using convex optimisation, we show that central entanglement features of supersinglets are remarkably robust to noise, substantially surpassing the robustness of several paradigmatic entangled states under certain relaxations. We then develop witness methods, based on collective-spin or randomised measurements, that certify both the depth and dimensionality of their entanglement. Finally, we identify supersinglets as a natural resource for high-dimensional gradient sensing and prove that they enable Heisenberg scaling. Together, these results reveal supersinglets as an exceptionally robust and versatile class of multipartite entangled states, combining striking symmetry and strong entanglement with concrete potential for quantum sensing.

Lloyd's algorithm and the discrete local (D-local) optimization method (Li et al., 2025) for $k$-means provide only weak local-optimality guarantees, and their solution quality remains sensitive to initialization. In this paper, we introduce $r$-point local optimality, under which no reassignment of at most $r$ samples decreases the objective function, and focus on $r=2$. The main computational obstacle is the $\mathcal{O}(n^2(k^2+d))$ cost of exhaustive two-point certification for $n$ samples in $d$ dimensions and $k$ clusters. To address this challenge, we prove that (i) every improving two-point move of a D-local optimum must involve a cluster shared by both reassignments, and (ii) only certificate-defined boundary points can participate in an improving pair. Exploiting this structure, we propose Boundary-Point-Screened Two-Point Local Search (BPS-2PLS), which terminates at a two-point local optimum. For fixed $k,d$ and nonvanishing cluster occupancy, the number $m$ of retained candidates satisfies $m=\mathcal{O}_{\mathbb{P}}(\log n)$ under i.i.d. sampling from a bounded-support distribution with bounded density or from a Gaussian mixture. Across twelve benchmarks, BPS-2PLS attains the lowest available mean WCSS on ten. In a subsampling study, screening retains 0.10% to 2.81% of samples on average at the largest tested sizes. The code is available at https://github.com/lwl-learning/BPS-2PLS.

We obtain improved Fourier restriction and Kakeya maximal estimates in $\mathbb R^4$. More precisely, by proving the two-ends incidence estimates $\mathbf{TE}\left(\frac{269}{89},\frac{179}{89},\frac{493}{534}\right)$ and $\mathbf{TE}(3.06\ldots,3.06\ldots,0.94\ldots)$, we extend the restriction range to $p>2+ \frac{356}{447}$ and the Kakeya maximal estimate up to dimension $3.06056$. The implications to the known lower-bounds for the Hausdorff dimension of Kakeya sets in $\mathbb{R}^4$ and the Bochner–Riesz conjecture are also studied.

Whether a time-series pattern is anomalous often depends on the operating regime of the monitored process. A missing event can signal a fault in one regime and be routine in another, and the query alone may not reveal which regime applies. We study in-context learning (ICL) for time series anomaly detection (TSAD) through reference-conditioned detection, where a reference record provides evidence about expected behavior and model parameters remain fixed at inference. Supplying the reference is not enough: when training anomalies are recognizable from the query alone, the detector can fit its targets while ignoring the reference. We therefore introduce counterfactual supervision, which pairs one query with two references that support different normal rules and labels the query under each. At positions where the two labels disagree, no detector that ignores the reference can fit both targets. Anlu learns from this supervision by adding a reference memory and zero-initialized gated adapters to a frozen time-series foundation model (TSFM) pretrained for anomaly detection. On the 350 TSB-AD-U evaluation sequences, Anlu raises the mean VUS-PR of the frozen TSFM from 0.542 to 0.607. Replacing the reference with zeros lowers Anlu's score to 0.499.

Geo-restricted content is increasingly common on the Internet, forcing users to rely on circumvention techniques, such as VPNs, to access the web from a seemingly different location. However, these often come with a financial cost and can degrade performance. The rise in popularity of the QUIC protocol, which allows connections to migrate between paths, opens opportunities to circumvent such restrictions. We scan web servers and find that a large portion of geo- blocked content is enforced on the server, at the application layer, rather than on-path. This check is performed once, when the request arrives, and is not repeated as the connection continues. This allows a client to issue its request from a whitelisted IP address and, once the server has accepted it, migrate the connection to an otherwise unauthorized address for the rest of the transfer (post-header migration). It bypasses the block while maximizing direct traffic, thereby reducing eventual circumvention-related costs. Building on this insight, we introduce Stork, an HTTP/2-to-HTTP/3 web proxy that bypasses geo-blocking while introducing negligible additional latency. We demonstrate that our solution is compatible with popular clients and servers. In controlled experiments with 2 MB requests, our proxy migrates 99% of the transferred data onto the unauthorized path. Across real-world targets that support QUIC migration, it migrates at least 75% of the data for more than 52% of them. On real geo-blocked content, post-header migration bypasses the block for 90% of domains, whereas post-handshake migration, as used by prior work, succeeds for only 60%.

Unambiguously detecting a gravitational-wave background (GWB) in pulsar-timing data requires a robust detection statistic. The pulsar timing community currently relies heavily on the cross-correlation-based "optimal statistic." Its design was motivated to avoid false-positive detections from unmodeled pulsar red noise. However, recent work by van Haasteren (2025) suggests that the optimal statistic is not, in fact, optimal. Moreover, the optimal statistic is still susceptible to false positives from misspecified noise. To guard against this, analysts employ quasi-resampling methods such as phase shifts, in which complex phases are randomly assigned to each pulsar strain measurement, thereby destroying any gravitational-wave-induced correlations. Inspired by the concept of phase shifts, we introduce a formalism in which the GWB is measured entirely from phase measurements. We argue that this approach is robust against false positive detections without the need for ad hoc quasi-resampling methods. We demonstrate the feasibility of this formalism by measuring the amplitude and spectral index of a simulated GWB, injected to a simplified mock representation of a pulsar timing array data set. For this example, we use simulation-based-inference and model the phase-based likelihood using a neural circular spline flow. We show that it is possible to adequately recover the spectral parameters of the gravitational wave background signal using the phase-based likelihood. By comparing our results to ones obtained with the optimal statistic, we show how much resolving power comes from amplitude versus phase.

A patient-timeline reconstruction system is auditable only if it keeps the mentions behind each answer, records how facts were revised, and declines to answer when the evidence is not in the text. This study tests these three properties on a fully synthetic corpus (1,000 patients, 3,353 notes, 220 revision edges). Two provenance-aware Evidence Graph operators reduced the node-plus-edge count to 67% and 63% (77-78% of serialized size) while preserving every answer and mention link across 6,813 query points answerable by recency; a fixed-window baseline returned no value for 53.4% of points, unflagged. On evidence-unavailable controls that announce the omission, a BioClinicalBERT gate and a zero-shot LLM gate responded mainly to the announcement. On marker-free controls, BERT abstained on 0 of 81 notes while its accuracy fell from 93.8% to 59.3% across all three relation classes; the LLM's coverage fell from 75.6% to 27.7% on notes its own model family judged undeterminable. Against 482 regenerated gold spans, the LLM's cited evidence reached recall 0.850 and precision 0.864; BERT's span head, trained without span labels, did not localize evidence. A temporally versioned provenance graph stored abstentions as typed, queryable edges. The clean task admits a 0.651-accuracy shortcut, and results describe implementation behaviour on synthetic data, not clinical performance.

Near-term quantum natural language processing (QNLP) experiments often run on classical simulators, so simulator cost is part of the field's practical compute burden, yet accuracy tables do not show it. We measure that cost for a variational quantum classifier (VQC) on binary SST-2 sentiment classification, using PennyLane's state-vector simulator over a controlled grid of 27 configurations: three balanced training-set sizes (N = 200, 500, 1000), three qubit counts (4, 6, 8), and three circuit depths. Each VQC is compared with logistic regression on the same PCA-reduced input; full TF-IDF logistic regression gives an uncompressed reference. The VQC beats its matched baseline in 6 of 27 single-seed comparisons. After reruns at two further seeds, only 1 of these 6 keeps a positive mean advantage larger than its paired seed-to-seed variability, and paired tests on the fixed validation set do not establish it. VQC training is 886-21,127 times slower in measured wall-clock time than the matched classical fit (median 3,158 times); going from 4 to 8 qubits roughly doubles simulator time, and within the tested range per-step cost is well approximated by a linear function of the parameter count. CodeCarbon energy and CO2 estimates are secondary: they imply an almost constant power of about 41 W, so they add little beyond runtime, and we do not build an energy ratio from them. The study is narrow (one dataset, representation, ansatz, simulator, and CPU environment) and is a reproducible feasibility measurement, not a general verdict on QNLP.

A normalized analytic function $f$ defined on the unit disk $\mathbb{D}$ is called $\alpha$-spirallike if $f(\mathbb{D})$ is an $\alpha$-spirallike domain, that is, for every $z\in f(\mathbb{D})$, the $\alpha$-spiral $ze^{-e^{i\alpha}t}$, $t\ge0$, is contained in $f(\mathbb{D})$, or equivalently, if $\operatorname{Re}\!\left(e^{i\alpha} {zf'(z)}/{f(z)}\right)>0$ for all $z\in \mathbb{D}$. The 0-spirallike functions are the usual starlike functions. The function $f$ is parabolic starlike, if $\operatorname{Re}\!\left(\frac{zf'(z)}{f(z)}\right)>\left|\frac{zf'(z)}{f(z)}-1\right|$, and lemniscate starlike if $|(zf'(z)/f(z))^2-1|<1$ respectively. In this paper, we determine the radii of parabolic starlikeness and lemniscate starlikeness of $\alpha$-spirallike functions. Our approach combines geometric characterizations of the underlying regions with the resultant method for eliminating auxiliary variables, leading to explicit equations for the sharp radii. Some known radius results are recovered as special cases.

Can LLMs recognize degradation in their own computational substrate? Inspired by anosognosia, a neurological condition in which patients fail to recognize impairments in their own abilities, we investigate whether LLMs can recognize degradation in their computational substrate induced by quantization. We first show that existing models fail to self-report their quantization state, even when provided with their own generated text as an external cue. Linear probing reveals that, while generated text carries almost no trace of quantization, internal representations contain clear, method-specific fingerprints. Through training, models learn to identify severely degraded outputs such as those of 4-bit models by comparison, yet still fail to do so from a single output. A shared LoRA trained jointly across quantization levels succeeded in reading out internal fingerprints, but fails on unseen quantization methods, merely mapping method-specific fingerprints to labels. Whereas external self-observation can restore awareness in some cases of human anosognosia, our results suggest that the more promising route to enabling such awareness in LLMs may lie in their internal representations. Our results highlight fundamental limits of generalizability to LLM self-monitoring.

Classifying charge traps in amorphous materials requires the electronic state and the network response to be resolved together. We develop state-aligned graph-wavelet fingerprints and apply them to electron trapping in a-Si$_3$N$_4$, where intrinsic-polaronic trapping, coordination-driven trapping, and charge-driven conversion coexist within one ensemble. Across 415 pairs of relaxed neutral and negatively charged cells, alignment of the trap state before and after localisation connects electronic identity to multiscale structural fingerprints. Charge-driven conversion produces substantial reorganisation across graph scales and increases the fingerprint amplitude. The fingerprint change identifies the transformation each site undergoes, while the occupation-induced level shift tracks localisation gain and graph deformation tracks stabilisation. Charge-induced defect formation dominates the deepest spectral-trap decile: 69% form at sites whose Si–N bond breaks on capture, although this route accounts for 44.2% of the classified traps. The fingerprints unify electronic identity, multiscale network reorganisation and energetic stabilisation in a quantitative framework for resolving charge trapping in amorphous materials.

We investigate the translational and rotational dynamics of cyclically sheared suspensions over a broad range of particle concentrations. The transition to an irreversible state is studied using a custom confocal-rheometer and colloidal particles synthesized with chemically identical smooth and lobed surfaces. The particle trajectories and rotations are tracked in three dimensions to reveal enhanced effective diffusivities that exhibit flow induced anisotropy that depends on particle concentration and particle morphology. We show that within the irreversible state, the shear induced anisotropy is determined by interparticle friction and interlocking mechanisms that promote mixing and enforce rotational isotropy.

Evaluating end-to-end autonomous driving under rare, safety-critical vehicle-pedestrian interactions requires photorealistic, sensor-level scenarios. However, trajectory-based scenario generators cannot synthesize raw visual observations, whereas video-based approaches lack controllability. To bridge this gap, we present ControlPed, a novel framework that combines trajectory-level conflict synthesis with 3D Gaussian Splatting (3DGS) to generate photorealistic, motion-controllable safety-critical scenarios. Built upon HazardPed, a dataset derived from 10,352 traffic videos comprising 422 conflict trajectories, HD maps, and 857 annotated 3D human motions, ControlPed first generates conflict trajectories, lifts them into 3D human motion sequences via text-conditioned motion diffusion, and finally renders multi-view sensor observations using animatable 3DGS avatars. Safety evaluation in 88 rendered photorealistic scenarios reveals that seven leading end-to-end driving models suffer a severe performance drop, with their mean HDScore plunging from 88.8 to 47.4, exposing major failure modes under dangerous pedestrian behaviors. The dataset and testing benchmarks will be released to facilitate safety assessment of vehicle-pedestrian interactions.

Biomedical large language model (LLM) evaluation requires auditable assessment of narrow, evolving, source-grounded subspecialty knowledge. Multiple sclerosis MRI (MS-MRI) provides a high-stakes textual-knowledge test case because correct reasoning requires current diagnostic criteria, standardized acquisition and reporting knowledge, longitudinal monitoring concepts, lesion morphology, and recognition of difficult mimics. We present MS-Exam-Gen, a reproducible framework for constructing and auditing a text-based multiple-choice question (MCQ) benchmark for MS-MRI knowledge; it does not evaluate direct MRI image interpretation. MS-Exam-Gen targets source-grounded criteria, protocols, reporting, and differential diagnosis. The framework combines expert-source indexing, exam-oriented topic induction, evidence-grounded MCQ generation, automated quality audits, a same-family consistency screen, and empirical calibration. From a 66-source corpus indexed into 4,289 retrieval chunks, the pipeline produced a locked 3,058-item candidate benchmark spanning 16 topics and 53 subtopics. Evaluation across 12 primary LLM endpoints yielded 36,696 item-level predictions and separated performance over a 42.8-percentage-point accuracy range (89.7% to 46.9%). Across these endpoints, 25.5% of items were missed by at least four. Post-generation audits showed that refreshed construction reduced measurable answer cues, while option-order testing showed that absolute MCQ scores remain position-sensitive. Generated construction labels remain metadata rather than validated psychometric categories. Because expert adjudication and full option-order counterbalancing remain future work, MS-Exam-Gen is not a clinically certified examination. It should be interpreted as an automatically filtered, source-grounded candidate benchmark and reproducible audit workflow for item-level and topic-specific LLM evaluation.

Spectral Barron spaces are Fourier-Lebesgue-type spaces that arise in the approximation of functions by neural networks. Conventional spectral Barron spaces are mostly considered on the whole space or on a bounded domain with certain smoothness assumptions on the boundary. In this work, we investigate spectral Barron spaces for periodic functions, thereby extending the study of spectral Barron spaces to high-dimensional tori and, more generally, to locally compact Abelian groups. These extensions are carried out by considering Fourier series expansions that are isometrically isomorphic to weighted sequence spaces built upon the $\ell^1$ sequence space. We discuss the well-posedness of PDEs in these newly introduced spaces. Two specific inverse problems for evolution equations are investigated, yielding conditional stability within the framework of spectral Barron spaces on the torus.

Market incompleteness causes residual profit and loss after hedging that is accounted for with valuation adjustments and bid-offer spreads acting as model risk buffers for the derivative price. Entropic risk optimisation is a general framework for modelling these adjustments. When the prices are quadratic Gaussian, the coupled equations for price and hedge ratios are solved exactly, with a decomposition of the entropic risk into convexity, dimensionality, funding and strategy contributions that are attributed in the explanation of realised P&L. The results are applicable when the underlying prices follow Gaussian processes, such as fractional Ornstein-Uhlenbeck processes. The article concludes with analysis of the continuous hedging limit for these processes, and a discussion of their application in data-driven regressions.

Zero-shot Neural Architecture Search removes the prohibitive cost of traditional NAS, but its search process is typically based on the evolutionary algorithm (EA); lacking an explicit model of the objective, it often resorts to a near-random search through mutation. Bayesian Optimization offers a principled alternative by modeling the objective and aggregating information across iterations, but scales poorly to the high-dimensional, discrete, graph-structured spaces of modern NAS, restricting its use to only small networks. In this paper, we bring Bayesian Optimization to zero-shot NAS for large-scale architectures by learning a latent space via a Variational Autoencoder trained to reconstruct a novel prefix encoding of architectures and propose a proxy scalarization that combines several zero-shot proxies into a single Bayesian Optimization objective. After only 10,000 iterations of the proposed search algorithm (8 hours on a single GPU), our method found a network architecture which under the given model parameter count constraints achieves state-of-the-art results on three separate tasks – image classification, object detection and semantic segmentation.

We prove that a smooth irreducible proper variety over a number field admits polylogarithmic-size coverings of rational points of bounded height if it admits a tower of finite étale coverings satisfying several conditions. One of the conditions is a height comparison on twists of the finite étale covers. We prove that these conditions hold for abelian varieties.

We analyse solutions of the flow equations of the renormalisation group for the n-point Schwinger functions of scalar field theory in four-dimensional Euclidean space with nonpolynomial boundary conditions. We show that there exist UV asymptotically free solutions of this type which are Bose symmetric, invariant under the Euclidean group, analytic in the flow parameter and the momenta, and satisfy the Osterwalder-Schrader growth condition.

In this work we explore how users interact with sponsored content on social media platforms by collecting and analyzing a large-scale dataset of sponsored Instagram posts. To maintain transparency, we favor robust statistical analysis and explainable models over deep learning techniques. Our pipeline categorizes Instagram accounts along multiple dimensions, including audience size and entity type. We complement this with semantic features extracted from post captions and hashtags, and use these elements to train regression models that forecast engagement. We validate our approach on a dataset comprising over 15M Instagram posts authored by over 700K accounts featuring sponsored content. Our analysis shows that per-post engagement is partly predictable and highly optimized when accounts are segmented by entity type or audience tier. Our models achieve competitive predictive power, while remaining fully transparent about which features drive engagement.

Localizing where an LLM-based agent first fails to uphold security during a repair can show which stage of its workflow needs an additional safeguard. This is difficult for silent failures, which are patches that pass syntactic and functional checks but still contain a security vulnerability. Because such patches give no observable failure signal, existing failure attribution methods, which rely on observed task failures and labelled failure steps, are less suited to them. We propose Security Awareness Gap Evaluation (SAGE), a trace-based method that combines an assessment of the security reasoning recorded at each turn with the reconstructed code history to identify the earliest turn at which a repair diverges from the task's security intent. We evaluate SAGE on 95 confirmed silent failures drawn from 3,684 repair traces produced by six agent frameworks and six base models on SecurityEval and CVEfixes. SAGE assigned an origin in 93 cases. Most origins were an unaddressed security requirement or an inadequate defence choice, and only five coincided with the code change itself. When the agent introduced the vulnerable code, the origin preceded the write in 14 of 19 cases. Repeated scoring and a second judge reproduced the origin type more consistently than the exact turn, and agreement was lowest for traces that kept only the final file.

We solve the functional renormalization group flow of the two-flavor quark-meson model at finite temperature and quark chemical potential with Litim's regulator, using the Kurganov–Tadmor central scheme and the standard grid method, both in the local potential approximation (LPA) and in an LPA$'$ truncation with running wave function renormalization factors for the pion, sigma, and quark fields. Using the Kurganov–Tadmor scheme as a high-resolution benchmark down to very low temperatures, where the Fermi surface produces the sharpest fronts in the field derivative of the potential, we find that, with sufficiently fine resolution, the grid method gives virtually identical results in both truncations. We discuss the difficulties that the wave function renormalization factors bring into the parametrization of the model and into the flow at finite density, related to the choice of the expansion point. Contrary to some expectations, the peculiar backbending of the first-order phase boundary at low temperature, known from LPA, persists in our implementation of the LPA$'$ truncation, both with a fixed and with a running expansion point.

During language acquisition, bilingual children are regularly exposed to code-switched input and use it as a cognitive scaffold to accelerate vocabulary growth and cross-linguistic syntactic mapping. In contrast, computational bilingual models are conventionally pretrained on interleaved monolingual corpora. While introducing synthetic code-switching during pretraining has become a promising strategy to enhance cross-lingual alignment and downstream performance, the structural and developmental parameters governing the success remain poorly understood. In this work, we investigate the efficiency of training with synthetic code-switched data across two typologically distinct language pairs by controlling two key variables: the structural location of code-switches and the dynamic switching rate across training stages. Our results show that training with code-switched data improves cross-lingual alignment for typologically close languages.

The long pulse of the European Spallation Source (ESS) offers unique opportunities to host more than one neutron instrument on a single beam-port. Here, we present two symbiotic instrument concepts designed for previously unexploited neutrons, without imposing significant perturbation on existing or planned beamlines. The first concept employs a doubly focusing dual-monochromator system to vertically translate the neutron beam, enabling compact instruments to be stacked within spatially constrained beam ports inaccessible to conventional instruments. The second extracts excess spectral bandwidth from an existing guide via Bragg reflection upstream of the flagship instrument's chopper system, feeding a second instrument. Both concepts are optimized using gradient-descent Monte Carlo ray-tracing simulations in McStas and benchmarked against existing productive instruments at other sources. Despite operating under significant geometric and flux constraints, the resulting instruments demonstrate performance comparable to well-established reference instruments at the ILL. The two concepts together illustrate a modular and cost-effective route to expanding ESS scientific capacity, using the facility's resources that would otherwise go unused.