Sustaining exascale performance in production requires engineering choices and operational practices that emerge only under real deployment constraints and demand coordination across system layers. This paper reports experience from three successive campaigns running HPL and HPL-MxP on Aurora, an Intel-based exascale system featuring the first large-scale deployment of Intel discrete GPUs, CPU-attached network interfaces, and the largest production Slingshot-11 interconnect. Aurora progressed from 0.585EF/s on 5,439 nodes to 1.01EF/s on 9,234 nodes in FP64 HPL, while HPL-MxP reached 11.64EF/s, an 11.5x speedup over FP64 enabled by mixed-precision arithmetic and Intel AMX acceleration. We identify and classify by role at production scale the system-level choices that sustained these results, including deterministic locality-aware resource mapping, explicit CPU-GPU pipelining, mixed-precision orchestration, and a hybrid P2P/collective resilience strategy introduced after synchronization stalls at scale. While some observations are Aurora-specific, the broader lessons are likely to apply to tightly coupled heterogeneous systems at extreme scale.

Low-mass galaxies with intense starbursts exhibit spectra dominated by extreme nebular emission and faint stellar continua. These extreme emission-line galaxies (EELGs) are key laboratories to study star formation, feedback, and ionizing photon escape in low-metallicity environments. We exploit the DESI survey to assemble the k-Means of Extreme Nebulae from DEsi outLiers (k-MENDEL), a statistically robust sample of ~16,000 EELGs at 0.01 < z < 0.96 selected via automatic k-means classification. Using SED fitting and Te-based metallicities, we characterize EELGs including "blueberry" and "green pea" galaxies, spanning stellar masses of 10^6-10^10 Msun and SFRs of 0.1-100 Msun/yr. k-MENDEL extends previous SDSS samples toward higher redshifts and lower metallicities (12+log(O/H) ~ 7.0-8.5). EELGs lie systematically above the star-forming main sequence, with sSFRs up to ~100 Gyr^-1. They follow a shallower mass-metallicity relation offset by 0.3-0.5 dex from local relations, closely resembling young galaxies observed with JWST at z > 3-10. The large intrinsic metallicity scatter, even after projecting along the fundamental metallicity relation, indicates strong departures from simple "bathtub" models, suggesting massive inflows of metal-poor gas followed by strong feedback. While ~6% of the sample shows AGN-like signatures, the most extreme star-forming systems reach high ionization (O32 ~ 5-60) comparable to confirmed Lyman-continuum emitters. Our results support the interpretation of EELGs as short-lived, non-equilibrium phases in the evolution of low-mass galaxies and highlight their importance as nearby analogs of galaxies likely driving cosmic reionization (Abridged).

The rapid evolution of software libraries creates a significant challenge for Large Language Models (LLMs), whose static parametric knowledge often becomes stale post-training. While retrieval-augmented generation (RAG) is commonly used to provide up-to-date API specifications, "context-memory conflict" arises when external instructions contradict a model's internal parametric knowledge. This paper presents a systematic empirical study of LLM code generation under API evolution (e.g., API deprecation, API modification, and API addition), by constructing a benchmark of 270 real-world updates from eight Python libraries. We evaluate four LLM families of 11 models. Our results show that without comprehensive documentation, LLMs struggle to prioritize external context, averaging only 42.55% of generated code examples are executable in the target environment. While structured documentation and larger model scales improve LLMs' ability to update adoption, they do not fully resolve executability issues with a low 66.36% executable rate. In addition, reasoning-based strategies (e.g., Self-Reflection) significantly boost LLMs' performance with 11% improvement on executable rate. Our findings highlight the persistence of outdated patterns from LLMs, even when API update specifications are provided, and emphasize the need for evolution-aware benchmarks and techniques.

We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fréchet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator acquires a structural theory that parallels the classical Euclidean smoothing spline. The Euler-Lagrange equation characterizes the solution as a piecewise-geodesic spline, an equivalent kernel controls pointwise risk at the rate $n^{-2/3}$, and the infinite-dimensional variational problem reduces exactly to a finite-dimensional optimization. Such newly established connection reveals a topological phenomenon that has no analogue in Euclidean nonparametric regression and, to our knowledge, has not been studied in the manifold regression literature. On manifolds whose regression curves can wrap around in topologically distinct ways, maps in distinct homotopy classes are separated by energy barriers intrinsic to the geometry of the target, and the Dirichlet penalty makes the estimator sensitive to this structure, recovering the correct topological class with probability tending to one, a phase transition we call topological recovery. A curvature-dependent oracle inequality yields the minimax rate $n^{-2s/(2s+1)}$ for Sobolev order $s$, matching the Euclidean constant on non-positively curved targets, while five geometric obstructions show that the full structural theory is unique to the Dirichlet energy ($s=1$). Simulations on $S^2$, $\mathbb{H}^2$, $SO(3)$, $\mathrm{Sym}^+(2)$, and $T^2$ corroborate the theory, and an application to wind-direction data on $S^1$ illustrates practical advantages.

China has undertaken unprecedented, state-driven vegetation restoration on a continental scale. This large-scale land-surface intervention offers a rare opportunity to assess how deliberate biospheric change influences climate-relevant processes, especially the hydrological cycle. Of particular interest is how increased water use by additional vegetation affects terrestrial water availability, including streamflow that sustains both ecosystems and human society. Here we evaluate the methodological basis for addressing this question in light of recently available data on hydrological change in China. Revisiting the atmospheric branch of the hydrological cycle, we argue that water yield depends fundamentally on vegetation-induced changes in atmospheric circulation. When the effects of vegetation on atmospheric dynamics are neglected, as in moisture-recycling-based approaches, the analysis is predisposed by construction toward diagnosing a negative effect of additional vegetation on water yield. Given the nonlinear dependence of precipitation on atmospheric moisture, we further suggest that streamflow reductions associated with added vegetation in dry regions reflects a transient phase of early ecological succession rather than a long-term outcome. As ecosystems mature and regional moisture regimes evolve, this relationship may reverse, generating a positive feedback between vegetation cover and water availability. We briefly discuss recent observational evidence consistent with this interpretation. We conclude that robust assessment of vegetation impacts on water yield requires frameworks that explicitly couple vegetation change, atmospheric processes, and hydrological responses. Such an approach is essential for distinguishing short-term trade-offs from longer-term system trajectories and for informing sustainable land management under continued ecosystem restoration and conservation.

Bipartition cover probabilities quantify whether a collection of gene trees contains every bipartition of the underlying species tree, a condition that underlies finite-sample guarantees for summary methods such as ASTRAL. We study this problem under the multispecies coalescent (MSC) model and derive topology-free upper bounds on the number of loci required to obtain a bipartition cover with prescribed confidence, improving upon the existing bounds of Uricchio et al. (2016). Practically, our bounds remain below biologically realistic numbers of loci across a substantially broader range of parameter settings, expanding their usefulness for empirical datasets. Theoretically, our analysis sharpens our understanding of coalescence under the MSC model and develops new asymptotics for these bounds and absorption times under Kingman's coalescent in the natural short branch regime. We further compare our new bounds with existing work using simulations under a variety of different species-tree topologies.

Scaling laws for turbulent thermomagnetic convection of a high-Pr fluid in a square cavity are obtained through direct numerical simulations and formulated via theoretical arguments informed by the numerical data. A regime consistent with an ultimate-like scaling $Nu \sim Ra_m^{1/2} and Re \sim Ra_m^{1/2} emerges after the laminar-to-turbulent transition and persists for more than an order of magnitude. Evidence is provided that this heretofore unseen behavior stems from the ability of the magnetic force to facilitate the ejection and advection of thermal plumes across the fluid bulk.

Super-resolution (SR) techniques based on deep learning have recently emerged as a promising approach to enhance the spatial resolution of computational fluid dynamics simulations while containing computational cost. In this paper, we investigate several SR architectures to improve coarse-grid simulations of mesoscale atmospheric flows, with training data generated from simulations of the weakly compressible Euler equations. We compare a baseline convolutional neural network (CNN), an attention-enhanced CNN, a multi-scale CNN designed to capture flow structures across different spatial scales, and a diffusion-based SR model. The methods are evaluated on two standard atmospheric benchmarks: the rising thermal bubble and the density current. Results show that the baseline CNN can accurately reconstruct simpler flow features, while more complex flows require multi-scale architectures. Overall, SR based on the multi-scale CNN provides the best balance of accuracy, robustness, and computational efficiency, outperforming even a state-of-the-art diffusion-based approach. We also analyze the sensitivity of the models to the size of the training dataset, highlighting limitations and trade-offs of the proposed SR strategies.

We study the superconducting diode effect (SDE) in a diffusive superconductor - normal metal (SN) bilayer subjected to an in-plane magnetic field. The supercurrent flows along the layers, perpendicular to the field. The SDE, manifested as an asymmetry in the critical (depairing) currents and kinetic inductance for opposite current directions, arises from an orbital mechanism due to the inhomogeneous distribution of the Meissner currents caused by a spatially varying superfluid density. Recently, Levichev et al. [Phys. Rev. B 108, 094517 (2023)] demonstrated the realization of this effect in such a structure, supporting numerical calculations for an ideal interface with an experiment. In this work, we investigate the influence of a nonideal interface with finite resistance on the SDE. Employing an analytical approach, we focus on limiting cases corresponding to weak intralayer inhomogeneities. We find that the strength of the SDE depends nonmonotonically on the interface resistance when the bilayer thickness is small compared to the coherence length. Remarkably, a nonideal interface can enhance the SDE compared to the ideal case.

We classify superfusion categories describing two-dimensional fermionic systems equipped with the universal fermion-parity symmetry, implemented by a topological defect line (TDL) $Z$, and an additional $\mathbb{Z}_2$ flavor symmetry generated by a $W$ TDL. Depending on whether $W$ is m-type or q-type, its fusion rules lead to three distinct classes, and solving the super-pentagon equations yields 16 consistent superfusion categories. These are labeled by invariants $(ν_W,ν_Z,ν_{WZ})$, which determine the $\mathbb{Z}_8$ anomaly classes of the symmetries generated by $W$, $Z$, and $WZ$. We also provide explicit realizations using multiple Majorana fermions and comment on implications for fermionic CFTs and gapped phases.

Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson electrodynamics to derive the conservation laws of the theory. The energy-momentum tensor is obtained, along with the conserved electric charge and the momentum operator. We consider non-interacting examples for real and complex scalar fields, as well as the Dirac field, within the $κ$-Minkowski spacetime framework. In the latter case, we show that the non-relativistic limit for the $κ$-Minkowski Dirac equation introduces an orbital Zeeman coupling term for the fermionic fields, and the energy shift in the first excited state depends exclusively on the $κ$-parameter.

We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduced in [S. Chu, A. Kurganov, and I. Menshov, Appl. Numer. Math., 209 (2025), pp.155--170], where we first employed the smoothness indicator from [R. Lohner, Comput. Methods. Appl. Mech. Eng., 61 (1987), pp.323--338] to automatically detect ``rough'' and smooth parts of the computed solution, and then used different limiters in the detected regions. This adaptive strategy was based on a threshold needed to sharply separate ``rough'' and smooth regions. In this paper, we propose a different adaption strategy. We use SBM-type limiters and vary one of the limiting parameters continuously to allow a smooth transition between the ``rough'' and smooth areas. This way, compressive and overcompressive limiters are activated in the shock and contact wave vicinities only, while we gradually switch to dissipative limiters in the smooth regions. A series of one- and two-dimensional numerical tests for the Euler equations of gas dynamics demonstrates that the new scheme adaption strategy leads to a higher resolution and reduced numerical dissipation.

Optimally solving decentralized decision-making problems modeled as Dec-POMDPs is known to be NEXP-complete. These optimal solutions are policies based on the entire history of observations and actions of an agent. However, some applications may require more compact policies because of limited compute capabilities, which can be modeled by considering a limited number of memory states (or agent states). While such an agent-state based policy class may not contain the optimal solution, it is still of practical interest to find the best agent-state policy within the class. We focus on an iterated best response style algorithm which guarantees monotonic improvements and convergence to a local optimum in polynomial runtime in the Dec-POMDP model size. In order to obtain a better local optimum, we use a modified objective which incentivizes risk-seeking alongside a conservative policy iteration update. Our empirical results show that our approach performs as well as state-of-the-art approaches on several benchmark Dec-POMDPs, achieving near-optimal performance while having polynomial runtime despite the limited memory. We also show that using more agent states (a larger memory) leads to greater performance. Our approach provides a novel way of incorporating memory constraints on the agents in the Dec-POMDP problem.

Large Language Models (LLMs) offer a promising interface for intent-driven control of autonomous cyber-physical systems, but their direct use in mission-critical Internet of Battlefield Things (IoBT) environments raises significant safety, reliability, and policy-compliance concerns. This paper presents a Policy-Aware Large Language Model Retrieval-Augmented Generation (referred as PA-LLM-RAG), an edge-deployed LLM orchestration framework for IoBT mission control that integrates retrieval-augmented reasoning and independent command verification. The proposed PA-LLM-RAG framework combines a lightweight retrieval module that grounds decisions in operational policies and telemetry with a locally hosted LLM for mission planning and a secondary JudgeLLM for validating user generated commands prior to execution. To evaluate PA-LLM-RAG, we implement a simulated IoBT environment using RoboDK and assess four open-source LLMs across controlled mission scenarios of increasing complexity, including baseline operations, threat detection, coverage recovery, multi-event coordination, and policy-violation requests. Experimental results demonstrate that the framework effectively detects policy-violating commands while maintaining low-latency response suitable for edge deployment. Gemma-2B achieving the highest overall reliability with 4.17 sec latency and 100% success rate. The findings highlight a clear tradeoff between reasoning capacity and responsiveness across models and show that combining deterministic safeguards with JudgeLLM verification significantly improves reliability in LLM-driven IoBT orchestration.

The energy of a graph is the sum of the absolute values of its adjacency eigenvalues. For integral circulant graphs $\ICG(n,\mathcal{D})$ of order $n=p^2q^3$, where $p$ and $q$ are distinct odd primes, we prove that the adjacency eigenvalues of $\ICG(p^2q^3,\Dstar)$, for the divisor set $\Dstar=\{1,p^2,pq,q^2,p^2q^2,pq^3\}$, admit an exact Kronecker factorisation in the prime exponents: they separate completely into a factor depending only on $p$ and a factor depending only on~$q$. This factorisation holds unconditionally for all pairs of distinct odd primes and constitutes the structural core of the paper. From it we derive, unconditionally, the first closed-form polynomial formula for the energy of a two-prime-order integral circulant graph evaluated at $\Dstar$. Exhaustive computation over prime pairs $(p,q)$ confirms that $\Dstar$ is the unique energy maximiser in every tested case; we conjecture that this universality holds for all pairs of distinct odd primes.

We show how equivariant localization can be used to compute the on-shell action for supersymmetric $D=5$ $AdS$ rotating, charged black holes in theories of supergravity with higher derivatives. An exact match with a dual field theory computation of the superconformal index in a Cardy-like limit is achieved.

The Wide-field Spectroscopic Telescope (WST) is a proposed 12-meter segmented facility optimized for seeing limited observations in the visible and designed to operate both a high-multiplex multi-object spectrograph and a panoramic integral field spectrograph (IFS). The WST IFS concept builds on instruments such as MUSE at the VLT (Very Large Telescope), using field splitters and image slicers to reformat a large field into pseudo-slits feeding spectrographs with two optimized spectral channels. This paper presents the spectrograph architecture developed for the WST IFS, aiming to achieve high through put and image quality over a wide wavelength range in a cost-effective manner. We investigate the use of curved detectors as a means to simplify the spectrograph layout, reduce aberrations, and potentially improve efficiency. This study establishes a promising baseline for the IFS spectrographs and assesses the benefits of incorporating curved sensors that can guide the development of future large-scale integral field spectrographs.

We introduce a three-dimensional model for polyelectrolyte hydrogel filaments operating in a fluid environment under an electric field. The formulation builds on a morphoelastic framework for inextensible and unshearable rods, such that the filament's activity is encoded in electric-field-induced spontaneous curvatures, while hydrodynamic interactions are captured via a local approximation of Stokes flows. We employ this framework to investigate the prototypical case of a filament with elliptic cross-section clamped at its base. Under a constant and uniform electric field aligned with its axis, the filament undergoes flutter instability beyond a critical field strength, as revealed by a linear stability analysis. Depending on the model parameters, the instability is characterized by either two- or three-dimensional self-sustained oscillations. We further examine this behaviour through numerical simulations in the post-critical regime, showing that flutter may develop into large amplitude planar oscillations or more complex three-dimensional motions, through a secondary bifurcation. Although the study represents a first step towards extending state-of-the-art models for polyelectrolyte hydrogel filaments to three dimensions, the richness of the resulting dynamics achievable under time-independent forcing underscores the potential of the proposed actuation mechanism for the design of biomimetic cilia and soft robotic systems.

We study theoretical uncertainties in predicting top-quark pair-production near threshold at the LHC using the non-relativistic QCD framework. We include variations in the top-quark mass and width, the strong coupling $α_s$, renormalization and factorization scales, and parton distribution functions, as well as uncertainties from the color-singlet and octet Green's functions that describe quasi-bound toponium formation. These uncertainties are compared with those from standard fixed-order QCD predictions, and implications for ATLAS and CMS analyses are discussed. For the LHC at 13 TeV center-of-mass energy, the integral of the top-quark pair invariant-mass distribution from 340 to 350 GeV is 11.67 pb with ${}^{+1.43}_{-1.47}$ pb uncertainty. The corresponding excess after subtracting the POWHEG-BOX result is 4.15 pb with the same uncertainties.

We develop novel asymptotic-preserving (AP) deterministic particle methods for collisional plasma models, including both Landau--Fokker--Planck and Dougherty collision operators, under hydrodynamic scaling. Our schemes treat the non-stiff transport part explicitly and the stiff collision operators fully implicitly through the energy-conserving Jordan--Kinderlehrer--Otto (JKO) schemes by exploiting their gradient flow structures. This approach extends our previous work on the space-homogeneous Landau equation [arXiv:2409.12296] and introduces a new treatment of the Dougherty operator via a projected gradient flow formulation. We identify the crucial role of Jacobian log-determinant evaluation in stiff regimes and introduce an inner-time quadrature strategy that improves both accuracy and efficiency. Furthermore, we uncover intriguing connections with score-based transport modeling, showing that both explicit and implicit score matching arise as special cases of our unified variational framework and exhibit limitations in the stiff regime. We also develop practical large-scale implementations via neural network parameterization and efficient training strategies. Various numerical examples demonstrate the structure-preserving and AP properties of our schemes for general initial data.

Resolving degenerate quantum eigenspaces - including topologically ordered ground states and frustrated magnets - requires preparing high-fidelity states that span every direction of the target manifold. Existing variational and projective algorithms do not naturally cover a multi-dimensional degenerate subspace without sequential orthogonality constraints. We introduce the quantum randomized subspace iteration (QRSI), a fully parallel construction that conjugates the Hamiltonian by independent random unitaries across as many branches as the degeneracy g, then invokes any chosen eigenstate-preparation primitive on each branch. The target subspace is identified from the resulting ensemble via standard subspace estimation, either classically through the coefficient matrix or on hardware through Gram-matrix measurements. We prove that the construction spans the full eigenspace almost surely and preserves the spectral gap exactly on every branch. For practical use, we show that these guarantees hold whenever the random rotations satisfy an anti-concentration condition over the degenerate manifold, substantially weaker than full Haar randomness. We demonstrate QRSI on the toric code, recovering all four topological ground states, and on random Hamiltonians with planted degeneracies.

Characterization of the trap rf induced a.c. Zeeman shift is essential for achieving high accuracy in optical ion clocks. In this work, we demonstrate the experimental characterization of this shift using highly charged $\mathrm{Ca}^{14+}$. The transverse component of the a.c. magnetic field is measured using the Autler-Townes splitting of the equally-spaced Zeeman components of the $^{3}\mathrm{P}_1$ when the Zeeman splitting is close to resonance with the trap rf drive frequency. We observe the resulting modulation by performing quantum logic spectroscopy using the co-trapped $\mathrm{Be}^{+}$. The longitudinal component is measured from probing the $\mathrm{Be}^{+}$ magnetic field-insensitive hyperfine transition $|F=2,m_F=0 \rangle \rightarrow | F=1,m_F=0 \rangle$. We confirm the small influence of the a.c. Zeeman shift in highly charged ions. The employed techniques can easily be transferred to other multi-level atomic systems.

Recent well-posedness results have identified the Hardy space $L^2_+$ as the natural phase space for continuum Calogero-Moser models, both focusing and defocusing, on the line and on the torus. In this paper, we introduce a symplectic form on this phase space and so are able to realize these models as Hamiltonian systems. Moreover, we demonstrate that previously identified conserved quantities are mutually commuting, reinforcing the notion that these models are completely integrable. We further illustrate the utility of these structures by using them to give a new proof of global well-posedness in the critical space $L^2_+$, under the necessary mass restriction in the focusing case. Our work also brings to light several unforeseen connections: (i) the threshold for well-posedness coincides with that for the nondegeneracy of the symplectic form; (ii) this threshold is connected through Carleman's inequality to the isoperimetric problem in the plane; (iii) the transition from the line to the torus gives rise to a modified dynamical equation.

We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown circular convolution operator $A$. However, in the presence of outliers, even in only a few snapshots, existing approaches often struggle to recover the spectrum. We address this challenge by proposing a novel robust spectral recovery model in the presence of time-sparse corruptions. We propose a robust pipeline that lifts the problem to a sequence of robust low-rank Hankel recovery and completion tasks, followed by Prony-type spectral estimation. Numerical experiments confirm the accurate spectral recovery of the proposed approach and exhibit its superior robustness against state-of-the-art under various settings.

We prove a relative version of Vorst's theorem concerning the equality of the group of all invertible matrices and the group of all elementary matrices over $R[X]$ with respect to an ideal $I\subset R$ such that $R/I$ is regular, where $R$ is a regular $k$-spot. We then introduce a relative version of the symplectic elementary Witt group and show that it fits into a relative version of the Karoubi periodicity sequence. Combining these results, we improve the existing injective stability bounds for relative linear and symplectic $\mathrm{K_1}$-groups of smooth affine algebras over various base fields.

Low-frequency charge noise induced by fluctuating electrostatic disorder is a major limitation for semiconductor hole spin qubits. Here, we analyze the quasistatic response of a hole spin qubit to individual two-level fluctuators (TLFs). We show that, due to the anisotropy of the g-tensor, the qubit response depends on the geometry of the fluctuator-induced dipolar perturbation. We then propose a readout protocol that isolates selected g-tensor components through an accumulated Berry phase and estimate, within our readout model, an order-unity signal-to-noise ratio with a total protocol time in the tens of microseconds. Finally, using microscopic simulations, we compute the quantum Fisher information (QFI) to identify magnetic field directions and confinement regimes in which the qubit is most sensitive to disorder-induced variations of selected g-tensor components.

Audio and speech self-supervised encoder models are now widely used for a lot of different tasks. Many of these models are often trained on clean segmented speech content such as LibriSpeech. In this paper, we look into how the pretraining datasets of such SSL (Self-Supervised Learning) models impact their downstream results. We build a large pretraining corpus of highly diverse TV and Radio broadcast audio content, which we describe with automatic tools. We use these annotations to build smaller subsets, which we use to train audio SSL models. Then, we evaluate the models on multiple downstream tasks such as automatic speech recognition, voice activity and music detection, or speaker recognition. The results show the potential of pretraining SSL models on diverse audio content without restricting it to speech. We also perform a membership inference attack to evaluate the encoder ability to memorize their training datasets, which highlight the importance of data deduplication. This unified training could bridge speech and music machine learning communities.

The classical Neukirch-Uchida theorem states that the absolute Galois group determines a number field up to isomorphism. We prove an analogue of this theorem for 3-manifolds in the framework of arithmetic topology. We study infinite links in 3-manifolds that behave like the set of primes, satisfying a Chebotarev density property. Relative to such a stably Chebotarev link, we define the absolute Galois group of a 3-manifold as the inverse limit of profinite completions of finite sublink complements. Our main result shows that two branched covers of the three-sphere over a stably Chebotarev link are homeomorphic if and only if their absolute Galois groups are isomorphic via a characteristic-preserving isomorphism. The proof translates the key ideas from the number-theoretic argument into topology, relying on Hilbert ramification theory for infinite covers and local-global principles. In doing so, it also provides a systematic justification for viewing Chebotarev links as the precise topological analogue of prime numbers in anabelian geometry. In addition, we discuss further conditions for links to play the role of prime numbers

Multi-arm multi-stage (MAMS) trials have gained popularity, due to their improved efficiency in evaluating multiple treatments. A traditional MAMS trial often decreases the expected sample size of the trial compared to just running a multi-arm approach, but with the drawback of an increase in maximum sample size. For academic led trials this poses a particular challenge, as funding is typically based on the maximum required sample size. To address this, drop-the-loser designs were introduced, where a fixed number of treatments are dropped at each interim stage, thereby reducing the maximum sample size. In this work, we propose an enhanced multi-stage drop-the-loser design that also allows for early stopping of the entire trial for superiority. This approach aims to retain the benefits of a reduced maximum sample size while also lowering the expected sample size. The proposed design is motivated by a trial in atrial fibrillation. We derive analytical expressions for the type I error rate, power, and expected sample size, and compare the proposed design's performance to alternative methods. We outline the key requirements for implementing the proposed design and discuss the contexts in which it should be considered. For the motivating example the results show that the proposed design substantially reduces the expected sample size compared to a standard drop-the-loser design, while lowering the maximum sample size relative to running a traditional MAMS trial or multiple separate trials.

Unlike the more observable phenomenon of group opinion reinforcement, self-censorship online has received comparatively less attention. Our goal in this work is to dissect the phenomena of self-censorship and to examine the implications of restrained expression for participation in public discourse, particularly in polarized contexts. We explore how social media users express their opinions online through analyses of 390 survey responses and 20 semi-structured interviews using a mixed-methods approach. We ask social media users about the differences between their publicly shared opinions and privately held beliefs, highlighting the influence of contextual factors on self-expression. Our findings show that self-censorship is associated with community context; social media users embedded within larger audiences, with lower posting frequency and perceived support, are less likely to express their opinions, and those who do speak often adjust their expressed views to align with perceived group norms. The study complements the rich literature on echo chambers and opinion reinforcement on social media platforms, highlighting the silence within the noise and its potential consequences for public discourse, which have become increasingly pertinent in an era where online platforms are pivotal to social and political narratives.