Papers

Thermal conduction plays an important role in energy transport during solar flares. Flares heat the solar atmosphere to tens of MK which, combined with mean free paths in excess of 1Mm, can cause the heat flux to become non-local. We use the magnetohydrodynamic Lare2d code to simulate a reconnective heating event with three different thermal conduction models: classical Spitzer-Harm (SH) along the magnetic field, local transport with a heat flux limiter (FL), and the non-local Schurtz, Nicolai, Busquet (SNB) model which is routinely used in laser-plasma codes and has been bench- marked against full Vlasov-Fokker-Planck treatment. The evolution of the atmosphere post heating is compared between simulations using each of these models. Due to a supressed heat flux, SNB gives rise to significantly higher peak temperatures than SH. Further, with SNB transport chromospheric evaporation occurs later and has stronger extreme ultraviolet emission intensity. FL simulations have similar temperature evolution and chromospheric evaporation to SNB, however different values of the flux limiter work best for peak temperature, downflow velocity and EUV emission intensity, and so there is no one optimal value for all cases. We conclude that the SNB model provides a practicable solution to incorporate non-local thermal transport at MHD scales, which will be crucial to improve the realism and accuracy of the next generation of solar flare simulations.

We report the first calculation of the lowest-known energy configuration for $N=100\,000$ classical point charges confined to a disk and interacting via the $1/r$ Coulomb potential - a system size never before achieved for the Thomson problem in a disk, more than doubling the previous record of $N=40\,886$ reported by Amore and Zarate. An adaptive defect-targeting subdomain optimization strategy yields an approximately linear growth of the wall-clock time per cycle with $N$; for $N=100\,000$ a single $24$-core CPU workstation without GPU acceleration required $\approx31$ hours. The energy $E_{\min}=7.80466624157\times10^{9}$ deviates from the standard empirical asymptotic expansion by only $2.525\times10^{-7}$. We demonstrate that this remarkable agreement provides a stringent test of the rigorous next-order asymptotic theory for Riesz interactions, while the residual deviation is consistent with an $O(N^{4/3})$ boundary-layer correction whose absence from the standard fitting basis biases the empirical $N^{3/2}$ coefficient away from its exact crystalline value, thereby tying the deviation to the two-dimensional crystallization conjecture. Bond-orientational order analysis reveals a polycrystalline bulk threaded by radial grain boundaries, establishing a new benchmark for two-dimensional Coulomb systems.

Flat bands with vanishing group velocity and quenched kinetic energy provide fertile ground for correlated states and exotic phenomena such as unconventional superconductivity. Yet, engineering and characterizing flat bands in quantum materials is time-consuming and costly, limiting the exploration of the vast design space of possible flat band systems. Acoustic metamaterials offer an accessible alternative: they can be easily simulated, cheaply fabricated, and quickly measured. Here we present a complete workflow to rapidly prototype flat band systems using acoustic metamaterials. Our design directly implements a tight-binding model using air cavities as lattice sites connected by channels that control hopping, allowing it to generalize to diverse lattice geometries. Using the kagome lattice as a proof-of-concept, we demonstrate excellent agreement between tight-binding theory, finite-element simulations, and experimental measurements. We then design a family of extended kagome lattices whose added sites cancel successively longer-range hopping, flattening the flat band. With fabrication and measurement requiring hours rather than months and a total cost orders of magnitude lower than quantum materials, our approach enables rapid iteration through candidate lattices, facilitating the discovery of new flat band physics in quantum materials.

The Hessian of the energy with respect to the nuclear positions is indispensable in atomistic modelling. However, constructing this matrix requires $O(N)$ Hessian vector products, traditionally limiting high-accuracy Hessians to small systems. Machine learning interatomic potentials (MLIPs) have accelerated atomistic modelling by providing highly accurate energies and forces at $O(N)$ cost, yet the resulting $O(N^2)$ cost of Hessians remains a practical bottleneck for large systems. Based on the insight that we can derive the sparsity pattern for an MLIP's Hessians in closed form, we show in this paper how to use techniques from sparse automatic differentiation to reduce the cost of a local MLIP's Hessians to a system-size-independent number of Hessian-vector products, yielding overall $O(N)$ total cost without any approximations. We benchmark our approach on a variety of systems ranging from alkane chains to water clusters to $A\beta40$ conformers. Depending on the MLIP configuration, we achieve the linear scaling regime already on relatively small systems, resulting in large runtime reductions between 2$\times$-15$\times$ for these systems. This opens up the possibility of scaling high-accuracy MLIP Hessians to very large systems, such as proteins that were previously inaccessible.

Braess paradox is a well-known phenomenon that originates when latency at Wardrop equilibrium in traffic networks decreases because of removing edges. The possibility of having the paradox was called vulnerability by Roughgarden in 2006 and was characterized later on by graph-theoretical notions, both for undirected and for directed graphs. In this paper we provide an algorithm for the incremental case of checking vulnerability for dynamically evolving graphs. The crucial idea to keep the amortized cost linear for every edge addition is that we do not need to run the vulnerability algorithm on the whole graph, but only on a well-identified subgraph, determined by the edge that we are adding. Overall, to add m edges, we pay a cost of O(m2); this aligns with the O(m2) cost of the state-of-the-art static algorithm for vulnerability.

While a centralized approach involving patient consent to collect and analyze data centrally would theoretically offer the best data quality and predictive performance, it is not always feasible in practice. Federated Learning (FL) architectures have shown to be a very promising approach to use and access distributed disease related resources within the GDPR boundaries. In a previous case report, we described the preconditions at the participating sites and necessary administrative and process related steps to prepare data, people and infrastructure for improving subtype identification and assessing treatment options in pancreatic cancer. We update this report sharing our experience in tackling the challenges and show preliminary results of the actual federated learning AI pipelines. At the participating sites, we have to identify and annotate the data being accessible after extraction and transformation in a local FL hub - in our case a centrally developed and distributively deployed Docker container. This container comprises the FL scripts generating local models. We apply a newly developed FL algorithm considering all local features, including partial overlapping features specific to the local sites. Theoretically, an annotation in a cancer setting should succeed using the German oncology core data set (oBDS), which is already utilized for mandatory reporting to cancer registries, and can be sustained in the FL setting. The FL algorithms deal robustly with partially overlapping features as we showed with public data sets. Major roadblocks including straightening operational concepts for the infrastructures, ethics approval for such novel architectures and support for every site have been addressed. However, scaling up this approach in the future faces hurdles; while including broader multi-modal data sets should be feasible, large-scale deployment to more sites remains challenging.

Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the local existence of reduced-order equations, they typically lack explicit quantitative estimates on the size of the neighbourhoods in which these representations faithfully capture the full bifurcation structure. In recent work, we have addressed this limitation by deriving bounds on the domain of validity of this reduction using first-order conditions on the vector field together with a quantitative result for the implicit function theorem. In this article we explore beyond, and adopt second-order conditions that incorporate the Hessians of the vector field to develop these bounds, and obtain a new set of results. We then investigate the applicability of these newly derived bounds to Hopfield-like networked dynamical systems, evaluate these bounds for pitchfork bifurcations on connected regular graphs, and finally examine the relationship between the two certified domains for this class of systems.

We prove the Brendle isoperimetric inequality for varifolds of finite mass and finite total first variation, allowing an arbitrary singular part. The distributional mean curvature is assumed only integrable. The result applies to integral varifolds and, more generally, to rectifiable varifolds with a positive lower density bound and weight measure concentrated on countably many $C^2$ submanifolds. The proof uses optimal transport and a locality theorem for the tangential Laplacian of an ambient convex function. The isoperimetric constant is sharp in codimensions one and two.

Traditional physics laboratory courses often focus on experiments with well-known results, limiting students' engagement in authentic scientific practices. Course-based undergraduate research experiences (CUREs), where students engage in real research with unknown outcomes, have been shown to support positive student outcomes, such as increased self-efficacy, persistence, and engagement in scientific practices. However, discipline-specific studies of CUREs in physics remain limited. We describe the development, structure, and initial implementation of a photovoltaics-focused CURE in a second-year undergraduate physics laboratory course at the University of Colorado Boulder. To examine how students experienced the course, we analyzed end-of-semester reflection assignments using the five CURE components (i.e., scientific practices, discovery, relevance, collaboration, and iteration), as well as established dimensions of research authenticity, as analytic frameworks. Students described experiences associated with all five CURE components, with collaboration, relevance, and scientific practices appearing most prominently in their reflections. Students also associated authentic research with meaningful scientific contribution, engagement in authentic scientific practices, and navigating the uncertainty and setbacks inherent in research, although fewer explicitly identified themselves as researchers or scientists. A subset of students additionally connected the course to their immediate thinking about future academic and professional pathways. This work contributes both a discipline-specific model for implementing CUREs in experimental physics laboratory courses and provides insight into how students interpret and experience authentic research within this course context.

Axion relic pockets are phase-transition remnants consisting of regions of false vacuum stabilised from collapse by a hot axion gas. Axion relic pockets can comprise dark matter, but little is known about their phenomenology. We consider trapped axions coupled to electromagnetism and derive the axion to photon conversion rate accounting for the pocket's compactness and spherical geometry. As a case study, we show that axion-photon conversion occurs in atomic electric fields, leading to high-energy electromagnetic cascades that may be detectable by neutrino, cosmic-ray, and dark-matter experiments. The distribution of electromagnetic showers is inherently isotropic, and upward-going showers provide a smoking-gun signal for the model. Using recent data from the IceCube neutrino telescope, we derive the first limits from terrestrial experiments on axion relic pockets as dark matter. However, for the simplest realisation of the model, only a small part of the parameter space can give signals strong enough to be constrained by current data. We also comment on the prospects for discovering axion relic pockets using fluorescence and radio Cherenkov detection by atmospheric instruments and balloon-borne payloads, as well as traditional dark matter direct detection experiments. These results provide the necessary tools to initiate phenomenological studies of axion relic pockets across different environments.

In modern blockchains, efficient, fair, and faulttolerant information dissemination is critical for performance and security. Several stages of the transaction lifecycle are affected, from the creation and dissemination of transactions to the dissemination of blocks in the consensus layer. Mempool protocols, such as L{Ø}, already address some of modern blockchains' security threats. However, others remain unless fairness is embedded most fundamentally in the dissemination layer used by these protocols to share transactions and blocks and to reconcile mempools. This paper introduces HERMES, a novel dissemination protocol for mempools that leverages robust minimal structures to optimize data propagation, balance load, and ensure fairness despite faults and Byzantine actors. Specifically, we address front-running attacks by randomizing the choice of an overlay structure while forcing nodes to prove adherence to the mempools' dissemination policies and the random choice made. Experimental results show significant performance improvements compared to traditional broadcast protocols for both permissioned and permissionless blockchains.

We report the experimental observation and characterization of Replica Symmetry Breaking (RSB) manifestation while analyzing the transverse intensity profile of pulses in filamentation experiments using sapphire crystal and distilled water, excited by a femtosecond laser centered at 800 nm. The RSB arises from the competition between self-focusing and plasma defocusing, subject to local fluctuations in the nonlinear refractive index generated by plasma via multiphoton excitation, which subsequently promotes frustration among modes. Our results confirm the existence of glassy-like photonic states not only in multifilamentation, as previously reported [W. Ettoumi, J. Kasparian, and J. Wolf, "Spin-glass model governs laser multiple filamentation," Phys. Rev. Lett., vol. 115, no. 3, pp. 033902, 2015], but also in the generation of a single filament and in filamentation accompanied by conical emission. These findings improve the understanding of statistical nonlinear optics by establishing connections with magnetism and highlighting the glassy-like behavior of light in the context of ultrafast optical phenomena.

We present an elementary proof of the bivariate nested Artin-Popescu approximation theorem: it ensures the existence of a nested algebraic power series solution of a given polynomial (functional) equation. Such equations often appear in enumerative combinatorics, e.g., when counting lattice walks in the first quadrant. The ad hoc proofs of the algebraicity of the generating functions, as e.g. proposed by Bousquet-Mélou and Jehanne , can thus be replaced by applying the theorem without need to resort to the extremely difficult general case solved by Popescu. Our method of proof follows closely the arguments of Denef and Lipshitz who treat a more general case (namely, the Artin approximation for Weierstrass systems). This is combined with the techniques of Hauser and Woblistin for the description of the overall geometry of the infinite dimensional variety formed by all power series solutions. Putting both approaches together now provides combinatorialists with an accessible proof for the bivariate nested Artin-Popescu approximation theorem.

Large Language Models (LLMs) are increasingly used in cybersecurity, where accurate analysis often requires multi-step and context-dependent reasoning over complex and heterogeneous data. However, existing prompting approaches typically focus on eliciting reasoning without explicitly considering how intermediate reasoning steps are structurally organized. We introduce Security Reasoning Topology, which models reasoning through three representative structures: Linear, Branching, and Graph. To evaluate their effects, we conduct controlled experiments on three cybersecurity datasets covering MITRE ATT&CK network traffic, cyber threat intelligence (CTI), and CVE vulnerability analysis. We evaluate multiple LLMs, including Llama 2 (7B, 13B, 70B), GPT-5.1, and Mistral Large 3, while keeping task inputs consistent and controlling reasoning structure through system-level prompting. Results show that reasoning topology substantially affects performance: Graph reasoning achieves the highest overall accuracy, improving over few-shot prompting by 9.8-12.2 percentage points across datasets, while Branching provides a strong intermediate solution. The results further show that the effect of reasoning topology remains consistent across model families and scales, highlighting reasoning topology as an important design factor for LLM-based cybersecurity analysis.

Neutron and X-ray perfect-crystal interferometers (PCIs) are powerful platforms for studies of fundamental physics and phase-contrast imaging. Further enhancing several PCI capabilities requires reducing crystal blade thickness to the micron scale, which minimizes dynamical-diffraction image blur, permits operation in the pendellösung regime where blade thickness controls beam splitting, and reduces absorption for simultaneous neutron and X-ray operation. However, fabricating multiple crystal blades with identical micrometer-scale thicknesses over centimeter-scale areas remains a major challenge. Here, using a non-etching sub-micron fabrication technique, we demonstrate silicon triple-Laue interferometers with equal-blade-thicknesses of 110 $\mu$m and 350 $\mu$m, operated with both neutrons and X-rays. These devices are the thinnest PCIs realized to date, enabling a factor-of-six reduction in dynamical-diffraction beam spreading for improved phase-contrast imaging, while reaching the single pendellösung length regime in which crystal thickness provides an experimentally accessible control parameter for engineered quantum-optical beam splitting of plane-wave inputs. These results motivate multi-blade PCI designs utilizing identical half-pendellösung crystal lamellae that are proposed for neutron spin–orbit and electric dipole moment measurements.

Robotic perception often requires solving large nonlinear least-squares (NLS) problems. While sparsity has been widely exploited to scale solvers, a complementary and underused structure is separability: some variables, such as visual landmarks, appear linearly in the residuals and admit a closed-form solution once the remaining variables, such as poses, are fixed. Variable projection (VarPro) exploits this structure by analytically eliminating the linear variables, yielding a reduced problem with favorable computational properties. However, its use in robotic perception has been limited by gauge symmetries, such as invariance to global translations and rotations, which introduce challenges for standard VarPro methods. We present SPARSER (Sparsity Preserving Analytic Reduction for Separable Robotic Perception), a VarPro framework for gauge-symmetric problems that jointly exploits separability and sparsity. Our method constructs a matrix-free Schur complement operator for efficient evaluation of reduced costs, gradients, and Hessian-vector products, enabling integration with iterative NLS solvers. We characterize the applicable problem class, identify common cases admitting further analytical simplifications, and show that IRLS-based robust costs preserve most of the exploitable structure. Across synthetic and real SLAM, SNL, and SfM benchmarks, SPARSER is on average $5\times$–$7\times$ faster than state-of-the-art baselines on CPU and GPU, with gains exceeding $40\times$ on individual datasets. On outlier-corrupted multi-robot SLAM data, the robust variant is $2\times$–$16\times$ faster than a state-of-the-art GNC solver. We release open-source C++ code and all datasets.

This paper presents the first systematic study of $[F]$-irregular graphs, a concept that parallels classical $F$-irregularity. For a fixed graph $F$, a graph $G$ is $[F]$-irregular if the numbers of its induced subgraphs isomorphic to $F$ containing a given vertex are pairwise distinct for all vertices of $G$. We prove that there exist infinitely many $[P_n]$-irregular graphs for any path $P_n$ of order $n \ge 3$. We establish that a non-trivial $[P_3]$-irregular graph of order $k$ exists if and only if $k \ge 7$. Finally, we propose the Strong Conjecture on $[F]$-irregular graphs.

Autobiographical remembering supports identity, well-being, and social connection in later life, yet voice-based memory technologies largely rely on isolated prompts. We designed and built MeBo, a fully functional relational voice-based memory companion, through participatory design with 11 older adults. Their accounts shaped four Design Strategies that guided MeBo's interaction design and multi-agent implementation. In a mixed-methods evaluation with 20 older adults, participants found MeBo exceptionally usable (SUS = 87.75), enjoyable, sociable, emotionally responsive, and trustworthy. Participants reported higher positive affect and momentary social connection and lower negative affect after the session than before. Participants described how MeBo followed their stories, returned to earlier memories, adapted to their preferences, and made its growing memory visible and controllable. MeBo's relational framing surfaces tensions around what it should remember, who may access memories produced through interaction, and what becomes of them when the user or MeBo is no longer present.

The interplay between lattice and electron degrees of freedom gives rise to competing ordered states in quantum materials, which can lead to a series of subsequent symmetry breaking transitions. While the differences are often subtle, these phases can be distinguished by their remaining point group symmetries. Here, we use infrared optical spectroscopy to probe symmetry breaking at the charge density wave transition of 1$T$-TiSe$_{2}$. We uncover a previously unobserved splitting of a doubly degenerate $E_u$ optical phonon at $T_{\mathrm{CDW}}\approx$ 190 K that constitutes direct evidence for the breaking of three-fold rotational symmetry. Our finding rules out proposals where the CDW transition to a low temperature chiral or nematic phase takes place through an intermediary state that preserves three-fold symmetry. The energy difference between the two former $E_{u}$ partners can only be explained by large $C_{3}$ breaking distortions of the same order of magnitude as previously observed changes in bond lengths, suggesting that $C_{3}$ symmetry breaking plays a dominant role in the CDW transition. The linewidth of the single phonon mode above $T_{\mathrm{CDW}}$ could be consistent with a fluctuating state where three-fold symmetry is also broken.

This article extends Stein's functional method to establish explicit rates of convergence in the Wasserstein-1 distance for Donsker's invariance principle under weak dependence. Our approach first reduces the problem of bounding distances between distributions on a function space to estimating distances between finite-dimensional marginals. We then employ the block technique, which is standard in Stein's methodology, to handle dependence. While our analysis focuses on $\phi$-mixing sequences, the method extends to other forms of weak dependence admitting suitable covariance inequalities.

Data-driven protection may complement conventional relays in distribution grids whose operating conditions vary with distributed generation, switching events, and changing short-circuit levels. We study line-selective tripping from static trajectories of a realistically simulated CIGRE medium-voltage network using offline reinforcement learning. A convolutional Q-network receives causal voltage-current phasor and apparent-impedance features, optionally together with raw waveforms, and is trained with conservative Q-learning (CQL). A controlled sensitivity study evaluates two observation windows, reward variants, and three CQL weights under a common split and training protocol; one exploratory post-hoc run additionally increases the discount factor from $\gamma$=0.95 to 0.99. On 225 held-out episodes, the best per-timestep result is obtained with combined input and CQL weight $\alpha$=0.9, reaching precision 0.9993, recall 0.9496, and F1-score 0.9738. Because dense per-timestep scores do not encode the terminal semantics of relay operation, we also evaluate the first non-wait action in each episode. The default combined-input agent selects the correct line-trip action first in 98.13% of 214 fault episodes, but trips in 72.73% of the 11 non-fault episodes. In the post-hoc run, the corresponding rates are 98.60% and 54.55%, respectively. The results show that dense predictive performance and terminal protection behavior can lead to different model rankings. Offline CQL therefore demonstrates strong faulted-line selection on the simulated fault episodes, while the static trajectories, small non-fault set, and single-seed post-hoc design preclude conclusions about practical relay security or deployment readiness.

We study scalable peer-to-peer dynamic average consensus (DC) for multi-robot systems under finite-range, finite-rate, and interference-constrained communication. We introduce Adaptive Communication for Dynamic Average Consensus (AC-DC), which jointly adapts Who communicates with whom, When, and over What parts of the consensus state, using local inputs and successfully received neighbor information. Each robot's consensus state estimates the current average of the robots' local inputs. AC-DC updates these estimates as local inputs change and averages the values exchanged between robot pairs. In AC-DC, robot pairs update without waiting for every robot to complete a communication round, and the selected-state messages carry consensus state coordinates independent of team size for a fixed state representation. We apply AC-DC to dynamic-priority multi-robot ergodic search: one consensus stream estimates team visitation for motion coordination, while the other fuses regional measurement information to update uncertainty maps and search targets. Across twelve settings with up to 80 robots and 20 paired trials per setting, AC-DC has the lowest mean (i) normalized covariance-trace area under the curve (AUC) and (ii) attempted modeled communication payload among the compared decentralized methods. Averaged across settings, AC-DC achieves paired AUC reductions of 27.5% relative to state-of-the-art baselines, with 8.7x less communication traffic. As the number of robots increases, we observe that AC-DC's communication payload approaches that of the ideal centralized baseline (one ground compute-station communicating directly with all robots): with 120 robots in a fixed 600 x 600 m scaling test, AC-DC uses 19.3 MB versus 19.2 MB for the ideal centralized baseline, while remaining peer-to-peer.

Consider a number field $K$, a polarized endomorphism $f:X\to X$ on a normal projective variety, and a non-exceptional point $\alpha$ for $f$. We show that the extension $K(f^{-\infty}(\alpha))/K$ generated by the backward orbit of $\alpha$ is virtually abelian if and only if $f$ is an exceptional map with CM and $\alpha$ is $f$-preperiodic. This answers a conjecture of Andrews and Petsche and extends it to higher dimensions. To this end, we develop the theory of exceptional maps on normal projective varieties over $\mathbb{C}$ and prove that commuting polarized endomorphisms of multiplicatively independent degrees are exceptional.

We study the Cauchy problem for the one-dimensional full compressible Navier–Stokes equations with viscosity $\mu(\theta)=\tilde\mu\theta^\alpha$ and heat conductivity $\kappa(\theta)=\tilde\kappa\theta^\beta$. For each fixed $\beta\ge0$, we prove the global stability of the combination of a viscous contact wave with rarefaction waves, provided that the viscosity exponent $\alpha$ and the total wave strength are sufficiently small. The initial perturbation may be large in $H^1$, and the specific volume and temperature are assumed to have positive initial lower bounds. The solution remains uniformly bounded in $H^1$ relative to the wave, and converges uniformly to that wave as time tends to infinity. We show that both the specific volume and the temperature admit time-uniform lower and upper bound. Estimates for the logarithmic volume derivative and the temperature gradient then close the $H^1$ estimates without requiring a second derivative of the initial specific volume.

Transcendence questions of periods and quasi-periods of Anderson modules, as well as the hyperderivatives thereof, are of major interest in number theory over function fields. In the case of Drinfeld modules, this question was answered by the second author. In this paper, we show that these results hold for general Anderson $t$-modules under certain assumptions on their Galois representations. The proofs use the explicit description of the $\mathfrak{p}$-adic Galois representation of the first author by means of a rigid analytic trivialization of the associated $t$-motive, as well as prolongations of $t$-modules and $t$-motives. The general result is applied to determine algebraic relations between periods and quasi-periods, and their hyperderivatives, of finitely many Drinfeld modules. Along the way, our results provide more evidence for the Mumford-Tate conjecture for Anderson modules.

Repeated execution of the target model during autoregressive decoding is a major source of LLM inference latency. Unlike linear speculation, which follows a single candidate chain, tree-structured speculation retains multiple branches from shared prefixes; under the same budget, this broader coverage can improve acceptance and efficiency. Adapting it to DeepSeek-V4 is nontrivial: its CSA/HCA online compressed attention concentrates the difficulty on the target-verify side, where branches diverging from a shared prefix compress into different states, breaking cross-branch state consistency. We integrate tree-structured speculative decoding into the DeepSeek-V4-Flash pipeline via branch-aware causal verification, temporary state isolation, and accepted-path state refresh, keeping verification and compressed-state updates consistent across branches. Across budgets D=5 to D=8, batch sizes 1 to 64, and three datasets (GSM8K, MBPP, ShareGPT), tree speculation achieves a higher accepted length than the matched linear configurations in all settings (e.g., at D=8 about 2.83–3.41 versus 2.39–2.84) and improves throughput in nearly all configurations—marginal only at the smallest budget—by up to about 18.5%. More importantly, the gains follow stable, transferable regularities: the relative gain grows with the budget and is most pronounced for less predictable workloads at small-to-medium batch sizes, while beyond a certain budget throughput plateaus and decouples from the still-rising accepted length. These results show that retaining multiple candidate paths under the same budget can effectively improve DeepSeek-V4 decoding efficiency, and offer experience for adapting speculative decoding to future models with compressed, sparse, or structured context representations.

Watanabe constructed many nontrivial family diffeomorphisms in $\pi_*\text{Diff}_\partial(D^4)$, which were obtained by doing clasper surgeries on trivalent graphs. In this paper, we generalize the barbell diffeomorphism discovered by Budney and Gabai and construct a series of nontrivial elements in $\pi_{k-1}\text{Diff}_\partial(M_{k+1}')$ with $M_{k+1}'=\natural_{k+1} S^2\times D^2$ the $(k+1)$-cuff barbell, which we call higher barbell diffeomorphisms. We show that Watanabe's constructions can be realized as implanted higher barbell diffeomorphisms in $D^4$ if the trivalent graph is homologically nonzero in the graph complex. Combining this realization with Watanabe's detection theorem, we establish the nontriviality of these implanted higher barbell diffeomorphisms.

The exotic magnetic properties of the pyrochlore Pr$_2$Zr$_2$O$_7$ are determined by the coupling of spin, orbital, and lattice degrees of freedom. Magnetism in this material originates from the non-Kramers Pr$^{3+}$ ion, and the exotic behavior has been discussed both in the framework of dipole-quadrupole properties of magnetic moments and disorder splitting the non-Kramers doublet. We use magneto-Raman spectroscopy to probe the crystal electric field (CEF) excitations of Pr$^{3+}$ in magnetic fields up to 14 T applied along the [100] and [111] crystallographic directions at 2 K. For $\mathrm{B}\parallel[100]$, the field evolution of the Raman active crystal field modes is quantitatively described by conventional Zeeman splitting of the Pr$^{3+}$ ground state doublet, including the thermally populated upper Zeeman branch at elevated temperature. For $\mathrm{}{B}\parallel[111]$, the spectra separate into responses from the triangular and kagome sublattices, and the CEF excitations of Pr$^{3+}$ on the triangular lattice exhibit the expected Zeeman shift consistent with full moments polarization. In contrast, the CEF excitations of Pr$^{3+}$ on the kagome lattice do not split as expected and instead broaden strongly with increasing field. This behavior is inconsistent with a static polarized configuration and is captured phenomenologically by a motional-narrowing description in which the kagome plane moments fluctuate between Zeeman-split levels on a meV timescale. This result offers a natural explanation for the reduced magnetization observed in $\mathrm{}{B}\parallel[111]$ and provides further evidence of the dipole-quadrupole properties of magnetic moments. It highlights Raman scattering as a sensitive probe of exotic spin-orbital dynamics in frustrated magnets.

In this article, we study germs of biholomorphisms of $(\C^n,0)$, $n\geq 2$ fixing the origin, the linear part at which has all its eigenvalues on the unit circle. We prove the existence of a sectorial transformation to a polynomial normal form of a non-degenerate 1-resonant biholomorphism under a Diophantine condition. We also give their holomorphic classification. We show that the sectorial automorphisms of the polynomial normal form are exponentially flat perturbations of the identity. We deduce the Gevrey character of the formal normalizing transformation and we show how the Gevrey index depends on the Diophantine exponent.

The cotangent space to any subvariety of a Grassmannian is naturally identified with a space of linear homomorphisms. We use this to define a new statistic on a subvariety of a Grassmannian, called conormal rank. We show that Chow–Lam forms and their natural generalizations have low conormal rank, and moreover that hypersurfaces of sufficiently low conormal rank are all of this form, generalizing a result of Gelfand–Kapranov–Zelevinsky. We also compute the conormal rank of many families of varieties, including Schubert varieties, torus orbit closures, and positroid varieties.