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All of arXiv

Wednesday 30 September

Combinatorics

Separating Notions of Graph Width: the Adaptive, Normal, Linear, Entropic, and Submodular Width

Matthias Lanzinger, Timo Camillo Merkl and Dan Suciu

We describe one explicit simple graph G on 32 vertices whose adaptive, normal, linear, entropic, and submodular widths are pairwise distinct. We compute all these widths exactly, except for the entropic width, where we only give a lower and upper bound. We use Ingleton's inequality and the Zhang-Yeung inequality for upper bounds, and give explicit constructions of modular, normal, linear, entropic, and non-entropic polymatroids for lower bounds.
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Differential Geometry

On Lorentzian Lie groups of Nonzero Constant Curvature

Mohamed Boucetta

We investigate Lie groups endowed with left-invariant Lorentzian metrics of nonzero constant sectional curvature. We first revisit Heintze's theory and obtain a characterization of the Lie algebras of Riemannian Lie groups of negative constant curvature. We also extend classical results of Nomizu and Barnet to the pseudo-Riemannian setting by constructing a large family of Lie groups carrying incomplete left-invariant metrics of constant sectional curvature. We then describe Lorentzian Lie algebras of nonzero constant curvature according to the causal nature of their center and derived ideal. This description is complete except when the derived ideal is Lorentzian, for which we obtain a complete classification in dimension four. We show that every left-invariant Lorentzian metric of nonzero constant curvature on \(\mathrm{SL}(2,\mathbb R)\) is bi-invariant and complete. Moreover, a semisimple Lie group admits a complete left-invariant Lorentzian metric of nonzero constant curvature if and only if it is locally isomorphic to \(\mathrm{SL}(2,\mathbb R)\). We also characterize \(\mathrm{SL}(2,\mathbb R)\) through the existence of a noncentral spacelike left-invariant Killing vector field. Finally, we classify Lorentzian Lie algebras of nonzero constant curvature in dimensions at most four.
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Data Structures and Algorithms

Component-Weighted Centroid Search for Exact Incremental BPE

Harshit Verma and Rex Ying

Exact incremental tokenizers keep the tokenization of a growing text up to date, so a long prompt or agent trace is not retokenized each time it grows. Jiang and Gong's algorithm does this for byte-pair encoding (BPE) in $O(\log^2 t)$ worst-case time per byte, where $t$ is the length of the longest token. Its search passes through $O(\log t)$ nested subproblems and runs a binary search over the possible branches at each one. We weight each branch by the size of the subproblem it leads to. Each step then costs about one probe for every halving of the remaining candidates, and a whole update costs $O(\log t)$, as much as one binary search over all candidates. Output and asymptotic memory are unchanged. We also construct valid BPE vocabularies on which the original search provably needs $\Theta(\log^2 t)$ probes and ours $\Theta(\log t)$, and a Rust implementation reproduces both counts exactly. On six real vocabularies the two searches run at about the same speed on ordinary text, while on long runs of spaces or hyphens the weighted search is up to 2.5$\times$ faster.
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Analysis of PDEs

Inverting the geodesic ray transform with finite measurements: stability and reconstruction

Yernat M. Assylbekov

We study the inversion of the geodesic ray transform from finitely many local averages of its data. Under suitable geometric assumptions, we prove Lipschitz stability on any fixed finite-dimensional reconstruction space when the measurement partition is sufficiently fine. We develop convergent reconstruction algorithms based on Steepest Gradient Descent and Conjugate Gradients and implement them using piecewise constant finite element spaces. Numerical experiments in 2D and 3D illustrate the influence of geometry and measurement discretization on reconstruction quality.
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Computer Vision

Can We Anticipate Violence? Multimodal Learning from Pre-Incident Behavioral Cues

Sindhuja Penchala, Mohammed Yusuf Mujawar, Noorbakhsh Amiri Golilarz et al. (+2 more)

Detecting violence after it begins is important from recognizing behavioral cues that appear immediately beforehand. This work studies short-horizon pre-incident risk recognition from multimodal video signals. We construct a binary Normal-versus-Risky setting from temporally annotated XD-Violence clips, using 443 samples with source-level separation across training, validation, and test sets. Each sample consists of a variable-length pre-incident clip, with its duration determined by the observable behavioral context preceding the incident. The inci- dent itself is excluded from all input clips. We evaluate three complementary information sources: facial-region appearance, temporally aligned audio, and body-motion features derived from tracked keypoints. Controlled ablations are performed with Swin-Tiny, ViT-Tiny, and DeiT-Tiny to measure the contribution of each modality under the same split. Results show that combining all modalities is more effective than using any other combination alone. The best configuration, Deit-Tiny with audio, facial appearance, and motion, achieves 91.21% accuracy, 88.96% balanced accuracy, 93.65% F1-score, and 96.38% ROC-AUC on the held-out test set. These results suggest that complementary appearance, acoustic, and kinematic cues provide useful evidence for recognizing elevated pre-incident risk.
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All authors Sindhuja Penchala, Mohammed Yusuf Mujawar, Noorbakhsh Amiri Golilarz, Sudip Mittal, Shahram Rahimi

Systems and Control

Duration-Aware Ramp Adequacy Screening

Qian Zhang, Aidan Looney, Chao Tian et al. (+2 more)

Ramp products are widely used in regional electricity markets to procure intertemporal flexibility in anticipation of net demand changes. However, the design of such ramp products often lacks a clear specification of ramping duration, potentially leading to infeasible dispatch solutions. This paper develops a duration-aware ramp adequacy screening method that evaluates whether the currently committed and dispatched fleet can meet the anticipated net-demand ramp requirement across different durations. A negative ramp adequacy margin identifies an insufficient-duration set in which the fleet lacks adequate ramp capability. Evaluating this margin across duration supports product-duration selection, while tracking it over time provides a metric for assessing ramp adequacy under different products and dispatch policies. We further formulate rolling-window ramp-reserve procurement with horizon-dependent forecast uncertainty and show that a product can affect ramp capability beyond its designated duration through changes in dispatch positioning. Building on this framework, we develop a forecast-free ramp-reserve scarcity dispatch policy that prioritizes resources according to their remaining ramp-up durations and, in the transmission-unconstrained setting, achieves the same minimum operational security loss as a perfect-foresight benchmark. Studies on a 10-generator system and a 2751-bus synthetic Texas grid demonstrate the value of the proposed framework for early detection of ramp scarcity, product design and evaluation, and screening-guided emergency dispatch.
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All authors Qian Zhang, Aidan Looney, Chao Tian, Xu Andy Sun, Le Xie

Robotics

Identifiable Decomposition of Submovements in Human Hand Trajectories

Adrian Prados, James Hermus, Ramon Barber et al. (+1 more)

Voluntary movements have long been hypothesised to be comprised of discrete primitives called submovements, as a descriptive model of human motor behaviour. However, existing methods scale poorly, and no principled method exists to determine whether a decomposition is informative. We propose a spatiotemporal kernel correlation between primitive pairs as an identifiability criterion. Submovement-Identifiable Decomposition (Sub-ID) embeds this criterion in its adaptive-ridge regularisation, biasing the optimiser toward low-correlation solutions. Identifiability is lost when primitives become collinear and recovered when they diverge spatially. On synthetic data, Sub-ID recovers ground-truth parameter distributions where existing methods fail; furthermore, when primitives overlap too heavily to be distinguished, the method explicitly detects this ambiguity rather than outputting misleading results. Sub-ID extracts submovements from real three-dimensional, long-horizon movements, a regime no prior method addresses. This method has the potential to identify physiologically grounded primitives for motor control research and imitation learning.
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All authors Adrian Prados, James Hermus, Ramon Barber, Sylvain Calinon

Earth and Planetary Astrophysics

Project CERES: Nuclear Thermal Transportation and In-Situ Propellant Production A Foundational Architecture for Solar System Logistics

S.P. Worden and F.G. Kennedy

Project CERES proposes a reusable deep-space transportation architecture centered on the dwarf planet Ceres, combining nuclear thermal propulsion (NTP) with in-situ production of water, hydrogen, oxygen and ammonia. Its first flight, a Pathfinder that surveys Ceres and returns samples, also bears on the question of life: Dawn found the ingredients of prebiotic chemistry there, and returned material would show just how far that chemistry went. We survey every direct Earth-Ceres opportunity from 2032 through 2042 with ephemeris-based Lambert analysis and compare chemical, gravity-assisted, nuclear-electric and nuclear thermal vehicles under one parametric mass model. Impulsive requirements vary from 10.2 to 14.1 km/s across the decade. A 900 s NTP stage delivering 35 t closes near 220 t in low Earth orbit and does so at every surveyed window; chemical delivery is marginal and sensitive to opportunity and staging, and nuclear-electric propulsion requires multi-megawatt power to match one-to-two-year trip times. Refueling at Ceres reduces the launch mass of an Earth-Ceres-Earth sortie by 61%, and the specific impulse of the propellant the node produces decides whether Ceres water becomes cargo or tanker mass. We conclude that Ceres uniquely combines abundant volatiles, exceptionally low gravity and a strategic Main Belt position, and that nuclear thermal propulsion is the only propulsion class that closes mass, time and the return leg together. Together they convert deep-space exploration from independent expeditions into a network operating on a timetable.
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Materials Science

Training and memory in a randomly driven fractal gel

Chloe W. Lindeman, Joshua D. Clugston, Justin C. Goodrich et al. (+3 more)

A variety of disordered materials, including jammed particulate systems and crumpled paper, can be trained to exhibit memory of a cyclic strain amplitude. Only recently, however, have questions emerged around the whether random driving can impart similar training. Here, we employ x-ray photon correlation spectroscopy to study a fractal nanoparticle gel trained via either deterministic cyclic shear or random shear bounded by strain amplitudes $-\gamma_t$ and $+\gamma_t$. Both types of training lead to microstructural reversibility, with a slower and more irregular training for the random protocol. In both cases, the shear induces redistribution of internal stress in the gel with corresponding irreversible strain displacements whose magnitudes decrease during training. Finally, we show that memory of the random driving can be read out and quantified using a standard protocol.
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All authors Chloe W. Lindeman, Joshua D. Clugston, Justin C. Goodrich, Mark Sutton, James L. Harden, Robert L. Leheny

Quantum Gases

Room-temperature polariton supersolids

Yuanhao Gong, Jingwen Ma, Shuang Zhang et al. (+2 more)

Exploring exotic quantum phases of matter at room temperature represents a frontier challenge in modern physics. The supersolid phase, uniquely merging crystalline order with frictionless superfluid flow, stands among the most intriguing macroscopic quantum phenomena. However, all previous demonstrations of supersolidity, whether in ultracold atomic gases or III-V semiconductor-based polariton systems, have been strictly confined to cryogenic temperatures. Here, we report the observation of room-temperature supersolids in photonic-crystal polariton condensates. By integrating a room-temperature-stable perovskite semiconductor with a dispersion-engineered photonic-crystal waveguide, we create a polariton condensate with multi-mode dispersion landscapes and pronounced parametric nonlinearities. Above a critical condensation density, the interacting condensates spontaneously break continuous translational symmetry, creating a non-rigid supersolid phase that simultaneously exhibits emergent crystalline order and global quantum coherence. This work establishes a room-temperature platform for investigating quantum hydrodynamics and developing coherent quantum simulation devices.
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All authors Yuanhao Gong, Jingwen Ma, Shuang Zhang, Xiaobo Yin, Xiang Zhang

High Energy Physics (Phenomenology)

PINNing the pion: conformal deep learning for $F_\pi(s)$ and the $(g-2)_\mu$ hadronic contribution

Mayank Goel, Subhadip Mitra and Monalisa Patra

Extracting the pion electromagnetic form factor $F_{\pi}(s)$ through phenomenological curve-fitting models introduces model dependence, unphysical artefacts, and kinematic inconsistencies. We introduce a Physics-Informed Neural Network (PINN) embedded in a conformal $z$-plane that constructs $F_{\pi}(s)$ directly from first principles across spacelike and timelike domains: charge normalisation and Schwarz reflection are enforced by construction, while Cauchy-Riemann analyticity, dispersion relations, Watson's theorem, and perturbative QCD asymptotics enter through the loss functional. Thus, the fundamental S-matrix principles dictate the form factor's behaviour while data act as constraints. Mapping the cut complex plane onto the unit disk bounds the Hessian norm and prevents Neural Tangent Kernel spectral starvation, two known failure modes of deep-learning optimisation. Besides $e^+e^-$ scattering data, we also incorporate $\tau$-decay data through a switch that isolates the pure isovector form factor natively, bypassing model-dependent isospin-breaking pre-corrections. The network organically yields an interior zero-free form factor, while the framework tests experimental tensions around the $\rho(770)$ peak against analyticity and dispersion constraints. We obtain model-independent estimates of the pion charge radius, $\langle r_{\pi}^2 \rangle = 0.435 \pm 0.008_{\text{stat}} \pm 0.007_{\text{cali}}$ fm$^2$, the second-sheet pole parameters, $m_{\rho}^{\text{pole}} = 761.72\pm 1.04$ MeV and $\Gamma_{\rho}^{\text{pole}} = 135.99 \pm 1.20$ MeV, and the two-pion contribution to the muon anomalous magnetic moment, $a_{\mu}^{\pi\pi} = (506.48 \pm 2.02_{\text{stat}} \pm 1.70_{\text{cali}}) \times 10^{-10}$.
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Robotics

Multi-Link Safety Filtering for VLA Policies Around Moving Hazards

Yatharth Agarwal and Vijay Raghunathan

A vision-language-action (VLA) policy can finish a manipulation task while knocking over objects unrelated to it, so task success alone does not show that the policy is safe to deploy in clutter. We study how to keep a pretrained VLA policy clear of such hazards at run time without retraining it, which requires guarding more of the arm than the end effector, following the hazard as it moves, and sharing onboard compute with the policy. Our training-free shield covers the gripper, wrist, and forearm with five ellipsoids and filters every commanded motion through one barrier program against a keep-out ellipsoid fitted from RGB-D perception at reset. Sparse optical flow then carries that ellipsoid's center along with the hazard, with no repeated detection or refitting. Over six simulated hazard-motion conditions, the shield lowers collision from $65.62\%$ to $27.27\%$ and raises safe-success, task completion without collision, from $29.35\%$ to $50.43\%$. Ablations show that guarding the arm links protects beyond end-effector shielding, and that tracking recovers most of the protection lost when the hazard estimate is frozen at reset. On heterogeneous edge hardware, the five-ellipsoid barrier runs on the CPU in $2.2$~ms at the 99th percentile, and trimming the vision–language prefix and taking fewer flow-matching steps shortens each $\pi_{0.5}$ policy call on the integrated GPU from $343$ to $177.3$~ms. On a physical SO-101 arm across four tasks, the arm touched the hazard in 3 of 16 shielded episodes versus 11 of 16 unshielded ones. Project page: https://yathag.github.io/multilink-safety-filter/
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Numerical Analysis

A Reduced Coupling-Space Multigrid Schur Preconditioner for Fictitious-Domain Interface Problems

Najwa Alshehri

We study a reduced multigrid Schur preconditioner for the fictitious-domain method with distributed Lagrange multipliers applied to elliptic interface problems. The method replaces the costly background solve by a multigrid approximation and treats the resulting correction only in the multiplier coupling space through a Woodbury formula. Numerical experiments show a marked improvement over the baseline preconditioner and consistently rapid convergence under mesh refinement and coefficient contrast.
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Accelerator Physics

Compact ultrafast intense LWFA-driven crystal-based source of $\gamma$-radiation, positrons and neutrons

Alexei Sytov, Hyeon Myung Jeong, Leejin Bae et al. (+5 more)

Compact sources of intense $\gamma$-rays, positrons and neutrons can bring radiation and particle-beam capabilities to small university-scale laboratories that would otherwise rely on large accelerator facilities. Here we propose and simulate a compact, laser-driven source that combines laser plasma wakefield acceleration (LWFA) with oriented crystalline targets to enhance the conversion of relativistic electron beams into high-energy photons and secondary particles. Electrons aligned with major crystallographic directions undergo coherent interactions, including channeling radiation and coherent bremsstrahlung, producing substantially enhanced photon emission compared with amorphous targets. Moreover, the strong angular-spectral correlation of the emitted radiation enables the generation of collimated $\gamma$-ray beams with reduced spectral bandwidth. Consequently, crystal-enhanced emission can increase particle-production efficiency, namely that of positrons through $\gamma$ conversion into electron-positron pairs and of neutrons through photonuclear reactions. Using Geant4 simulations, we investigate electron energies of 300 MeV, 1 GeV and 3 GeV interacting with an oriented tungsten crystal. Crystal orientation increases the $\gamma$-ray, positron and neutron yields by up to a factor of $\sim2$, reaching production rates of $\sim10^{24}\gamma/s$, $\sim10^{23}e^+/s$ and $\sim10^{21}neutrons/s$ for a 200 pC electron bunch with a duration of a few fs. The collimated $\gamma$-ray brightness reaches $\sim10^{24}\gamma/s/mm^2/mrad^2/0.1\%BW$, with an enhancement of 6-8 compared with random crystal alignment. We further demonstrate tunable quasi-monochromatic radiation through coherent bremsstrahlung in a thin diamond crystal, reaching a brilliance of $\sim3.5\cdot10^{20}\gamma/s/mm^2/mrad^2/0.1\%BW$. Furthermore, we discuss the potential applications of the technique proposed.
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All authors Alexei Sytov, Hyeon Myung Jeong, Leejin Bae, Iryna Chaikovska, Hyoeun Choi, Gianfranco Paternò, Laura Bandiera, Inhyuk Nam

Statistical Mechanics

Many-body topology in parity-preserving tensor networks

Maksimilian Usoltcev, Nguyen Hanh Dung, Carolin Wille et al. (+2 more)

Planar parity-preserving tensor networks (ppTNs) admit a fermionic formulation in which the Gaussian, efficiently contractible limit is deformed by local interactions. We investigate how many-body methods can be used to analyze such contractions in a minimal two-parameter ppTN. Its contraction is simultaneously an interacting fermionic partition function, a loop gas, a deformed toric-code norm, and a quartic Ising model, allowing the same phase diagram to be approached with complementary tools. At its center lies a `topological island', characterized beyond the Gaussian limit by a boundary-twist $\mathbb Z_2$ indicator that reduces to Chern-number parity and admits a loop-winding interpretation under duality. Fermionic perturbation theory predicts the interacting phase boundaries, tensor-network numerics establish their critical behavior, and the loop and spin descriptions reveal a self-dual line with a $c=1$ four-state-Potts multicritical fixed point.
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All authors Maksimilian Usoltcev, Nguyen Hanh Dung, Carolin Wille, Matteo Rizzi, Alexander Altland

Machine Learning

DashVMC: Real-Time Discrete World Model Control in Geometry Dash

Florent Tariolle and Florian Yger

World-model agents are usually evaluated in simulators that can wait for the policy; live games impose the opposite constraint, requiring capture, prediction, and action before the next frame. We present DashVMC, which learns a compact, action-conditioned world model from approximately two hours of recorded Geometry Dash gameplay. To test whether the learned dynamics are actionable, a controller is initialized by behavioural cloning (BC) and refined with Proximal Policy Optimization (PPO) entirely in frozen-model rollouts, without further interaction with the live game. Across three controller seeds, the refined policies survive longer than their BC initializations on all three official levels and a held-out community layout. At deployment, the baseline skips visual generation and sustains a 60-Hz capture-to-action loop on a consumer GPU. Action-conditioned continuations and rollout diagnostics show that the model remains useful for control despite imperfect long-horizon fidelity.
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Strongly Correlated Electrons

Entropy-Driven Altermagnetism from Thermal Magnons

Tanaya Halder, Ashis K. Nandy and Anamitra Mukherjee

We identify a route to altermagnetism driven by entropy upon heating and demonstrate it in a minimal square-lattice antiferromagnet. An exchange modulation is entropically favored because the resulting momentum-dependent magnon splitting increases the magnon entropy, thereby lowering the free energy and favoring altermagnetism. We derive an instability criterion for this exchange-modulated state, predict its temperature-driven reentrant behavior, and show that its overlap with Néel order defines a finite-temperature altermagnetic phase. Variational spin-wave theory, spin–lattice Monte Carlo, and cluster diagonalization establish the entropy-driven instability and its coexistence with magnetic order. The resulting state supports a transverse spin conductivity. The mechanism provides a route to thermally induced altermagnetism in compensated magnets coupled to sufficiently soft physical modes.
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Quantum Physics

An exponential query advantage from access to Stinespring dilation unitaries in quantum channel learning

Manaki Arihara, Satoshi Yoshida, Philip Taranto et al. (+1 more)

We present a learning task for quantum channels that exhibits an exponential separation in query complexity (in terms of the number of qubits) between two access models: i) black-box channel access and ii) access to a Stinespring dilation unitary of the channel along with its inverse. We consider the task of learning how close the unknown channel is to the set of unitary channels. This is characterized by the optimal average gate fidelity (OAGF), defined as the average gate fidelity maximized over all unitary channels. For constant Kraus rank and a dilation environment of dimension $\operatorname{polylog}(d)$, we provide an algorithm that estimates the OAGF to fixed additive accuracy using $\operatorname{polylog}(d)$ queries to the Stinespring dilation unitary and its inverse. In contradistinction, under the black-box access model, this estimation requires at least $\Omega(\sqrt{d})$ queries, even for channels of constant Kraus rank and constant additive accuracy. As a corollary, we rule out a universal simulator that uses only $\operatorname{poly}(\log d,q)$ queries to the unknown channel to approximate the output of arbitrary $q$-query algorithms with access to a randomly-sampled Stinespring dilation unitary and its inverse, even to sufficiently small constant error. These results demonstrate that access to the system-environment joint evolution and its inverse can provide an exponential advantage in estimating an intrinsic property of a quantum channel.
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All authors Manaki Arihara, Satoshi Yoshida, Philip Taranto, Mio Murao

Instrumentation and Methods for Astrophysics

Toward the Italian Astronomical Community's Contribution to HWO: Science, Technology, and Instrument Concepts

A. Fontana, F. Annibali, N. Antonietti et al. (+101 more)

This paper summarizes the interest of the Italian astronomical community in the possible participation in the development of the Habitable Worlds Observatory (HWO). It is largely based on the outcome of a dedicated meeting held in Rome in July 2025, and it includes further revisions and new suggestions that have arisen in the following months. It includes a succinct description of the main scientific interests and of the key technologies that the Italian community can contribute to the development of the mission. It also includes a short section dedicated to the instrument concepts that we deem important to develop for potential adoption on HWO, and that the Italian community is interested in developing. Finally, it includes a concise presentation of the main instruments for ground-based telescopes (VLT and ELT) and space missions that will be operational before HWO and in which the Italian community has leading positions. They will be invaluable to settle the scientific landscape for the mission and to prepare the Italian scientists to make optimal use of HWO. This paper is primarily aimed at paving the way to discussions and collaborations with worldwide scientists and agencies interested in the development of the mission.
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All authors A. Fontana, F. Annibali, N. Antonietti, S. Bianchi, L. Biasiotti, K. Biazzo, E. Bisesi, A. S. Bonomo, V. Bozza, R. Briguglio, M. Brogi, D. Busonero, A. Cabras, C. Cecchi Pestellini, G. Cescutti, A. Ciaravella, G. Cresci, A. J. Corso, S. Covino, F. D'Ammando, A. De Rosa, P. D'Incecco, V. D'Odorico, V. D'Orazi, S. Desidera, P. Di Marcantonio, M. P. Di Mauro, N. Elias-Rosa, S. Fineschi, E. Fiorellino, C. Fiorini, D. Fulvio, A. Garufi, G. L. Granato, N. Greco, G. Guilluy, S. Ivanovski, L. Izzo, A. Jimenez-Escobar, N. La Rocca, M. Landoni, C. Lazzoni, E. Liistro, F. Z. Majidi, L. Mancini, A. Mangione, F. Mannucci, M. Marcellino, A. Marconi, M. Maris, D. Massari, A. Melis, D. Mesa, M. Messa, G. Micela, D. Milaković, S. Monai, M. Moresco, E. Munari, G. Murante, L. Napolitano, L. Naponiello, V. Nascimbeni, I. Pagano, M. E. Palumbo, G. Pareschi, P. Pari, F. Pedichini, M. G. Pelizzo, L. Pentericci, C. Pezzotti, F. Piazzese, M. Pilia, L. Pino, G. Piotto, S. Piranomonte, D. Polychroni, R. Ragazzoni, E. Rigliaco, F. Romanato, G. Ruffato, G. Sacco, F. Salvestrini, P. Saracco, G. Scandariato, L. Schreiber, P. Severgnini, L. Silva, P. M. Simonetti, A. Sozzetti, R. Spinelli, L. Testi, A. Tozzi, A. Traficante, M. Tsantaki, R. G. Urso, M. Uslenghi, E. Vanzella, D. Vassallo, C. Vignali, G. Vladilo, A. Vogliardi, A. Zanella, T. Zingales

Fluid Dynamics

A Reynolds-like Criterion for the Onset of Universal Active Turbulence

Kunal Kumar, Sandip Sahoo, Kirti Kashyap et al. (+4 more)

Beyond a critical Toner–Tu drive, bacterial turbulence exhibits universal statistics, including a parameter-independent energy spectrum $E(k)\sim k^{-3/2}$. We show that the same universal state can be reached not only by increasing activity, but also by strengthening nonlinear advection, weakening nonlinear saturation, or tuning the Swift–Hohenberg instability. Motivated by the competition between these processes, we identify the independent dimensionless groups governing the dynamics and construct a Reynolds-like control parameter from them. A single critical value, calibrated from the known activity-controlled transition, predicts the onset of universality along the other parameter routes and collapses them onto a common threshold. These results identify a dynamical organizing parameter for the onset of universal active turbulence and provide a Reynolds-like measure for the Toner–Tu–Swift–Hohenberg universality class.
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All authors Kunal Kumar, Sandip Sahoo, Kirti Kashyap, Amal Manoharan, Siddhartha Mukherjee, Anupam Gupta, Samriddhi Sankar Ray

High Energy Physics (Experiment)

Non-parametric and continuous extraction of amplitudes in realistic electroweak penguin decays

Tingzhen Xiao, Anja Beck and Eluned Smith

A novel approach to extract decay amplitudes in $B\to V(\to M_1M_2)\ell^+\ell^-$ processes, where $V$ represents a meson with either $J = 0$ (S-wave) or $J = 1$ (P-wave), was recently proposed. In this method, the dependence of the amplitudes on the dihadron and dimuon invariant masses is extracted model-independently through a fit to the helicity angles and a subsequent calculation of sPlot weights. In this paper, we show that this method still performs well when applied to data with experimental realism, namely in the presence of detection efficiencies and background candidates, both of which can have non-factorising dependencies between the fitted helicity angles and extracted two-particle masses. We show that a non-factorising efficiency can be accommodated with a small change to the conventional calculation of the sPlot weights, and a non-factorising background by expanding the description of the background distribution into individually factorising terms. We illustrate the method using simulated $B\to K^+\pi^-\mu^+\mu^-$ data, containing both S- and P-wave contributions to the $K^+\pi^-$ system, mixed with non-factorising background candidates and generated with a realistic function for the detection efficiency. We also show that this method can be applied over a much larger dimuon invariant-mass range than studied previously. This work suggests that the method is suitable for application to real experimental data, where it could provide model-independent decay-amplitude shapes for direct comparison with theoretical predictions. A measurement using this technique can improve sensitivity to potential new-physics effects in $b\to s\ell\ell$ transitions, as well as the understanding of hadronic form factors, particularly in the S-wave system.
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Analysis of PDEs

Global existence for Consensus-Based Kinetic Models for Image Segmentation

Abramo Agosti, Pierluigi Colli, Elisabetta Rocca et al. (+1 more)

In this article, we analyze a recently introduced kinetic model based on Hegselmann-Krause-type interaction dynamics describing consensus-based image segmentation in the mean-field regime, where particle density depends on spatial coordinates and the normalized gray level (feature) value. The model is formulated as an evolutive nonlocal partial differential equation featuring a non-local spatial drift term involving a bounded confidence interaction kernel, depending on spatial and feature proximity, and a spatial diffusion term degenerating in the feature variable representing aleatoric uncertainties. Establishing well-posedness on a bounded domain, essential for practical image processing, presents significant analytical challenges: the lack of uniform control of space derivatives due to kernels with jump discontinuities and degenerate spatial diffusion, complex non-standard boundary terms under homogeneous Neumann conditions, and a lack of compactness arising from the absence of derivatives with respect to the feature variable. To address these difficulties, we introduce a three-level regularization scheme. Specifically, we smooth the interaction kernel, apply structural boundary regularization to the non-local interaction term to simplify boundary conditions, and incorporate artificial diffusion in spatial and feature variables to resolve degeneracy. We prove the well-posedness and regularity of the regularized system via a finite difference scheme and study the asymptotic limit as regularization parameters vanish, proving the existence of weak/distributional solutions of the original model. This approach advances the mathematical theory of kinetic models for image segmentation by extending the framework of distributional solutions to bounded domains and non-smooth interaction kernels with jump discontinuities.
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All authors Abramo Agosti, Pierluigi Colli, Elisabetta Rocca, Mattia Zanella

Numerical Analysis

A Pressure-Free Virtual Element Method for the Surface Stokes Problem

Jun Hu, Shengyang Xu and Hao Zhou

We develop a pressure-free virtual element method for the surface Stokes problem on polygonal approximations of closed surfaces of arbitrary genus. The method extends the planar VEM Stokes complex to discrete surfaces, yielding a nonconforming complex with an exactly tangential, $H(\operatorname{div})$-conforming velocity space, commuting interpolation, and the correct discrete cohomology. To obtain the weak consistency needed for optimal convergence, we introduce an edge correction that preserves the complex without adding degrees of freedom; the resulting construction reduces to the original complex in the planar setting. The virtual formulation requires no penalties, and a local divergence-preserving reconstruction provides a computable pressure-robust load. We also construct explicit macroelement representatives whose energy and load induce an alternative formulation on the VEM space, algebraically equivalent to a direct macroelement Galerkin method. The original virtual formulation and the macroelement method are stable and attain optimal first-order convergence in the broken $H^1$ norm and second-order convergence in the $L^2$ norm for the velocity. Numerical experiments illustrate these convergence rates, the role of the edge correction, and pressure robustness.
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Machine Learning

Learning to Explain While Planning: Rule-Aligned Diffusion Planning for Autonomous Driving

Jiaxi Ye, Chunji Lv, Guoren Wang et al. (+1 more)

Diffusion planners exhibit strong capabilities in generating multimodal trajectories. However, existing methods primarily rely on expert demonstrations to fit trajectory distributions, learning statistical correlations among scenes, behaviors, and trajectories without explicitly modeling driving rules. In long-tail scenarios where expert data are scarce, the lack of behaviors to imitate may lead to trajectories that violate safety or compliance requirements. Moreover, their generation process lacks rule-level explanations, making it difficult to determine which rules drive trajectory adjustments, when they take effect, and how strongly they act, thereby limiting failure diagnosis, safety validation, and targeted improvement. To address these limitations, we propose the Rule-Aligned Diffusion Planner (RADP), which incorporates differentiable driving rules into the diffusion objective during training, turning rule knowledge into intrinsic behavioral principles beyond finite demonstrations. We further introduce Rule-Pressure Attribution (RPA), which constructs supervision signals from gradients of rule losses with respect to predicted trajectories and employs a lightweight attribution head to estimate the optimization pressure exerted by each rule online. To assess the closed-loop behavioral relevance of these attributions, we propose a temporal risk-alignment protocol that evaluates whether current rule pressures reflect corresponding risks during subsequent closed-loop execution. Experiments on nuPlan show that RADP improves closed-loop planning in challenging safety-critical scenarios, while RPA exhibits consistent temporal alignment with subsequent rule-specific risks, validating both intrinsic rule learning and rule-level interpretability.
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All authors Jiaxi Ye, Chunji Lv, Guoren Wang, Changsheng Li

Quantum Physics

Quantum state learning beyond approximate unitary designs

Gyungmin Cho, Changhun Oh and Dohun Kim

Approximate unitary designs reproduce the statistics of Haar-random unitaries to a given order and accuracy. Recent constructions realize such designs with logarithmic-depth circuits, enabling shallow measurement protocols for various quantum state-learning tasks while preserving performance. These results raise the question of whether approximate designs can replace exact designs more generally. We show that even exponentially small design error need not preserve the learning guarantees of exact designs. This motivates deriving learning guarantees directly from the measurement circuit structure. For observable estimation with classical shadows, we prove that logarithmic-depth two-layer Clifford circuits yield an unbiased estimator matching the global Clifford variance scaling for every state and Hermitian observable. Beyond observable estimation, this bound allows shallow measurements to retain global Clifford guarantees for other tasks, including setting-efficient tomography, mixed-state metrology, and stabilizer structure learning. We complement these statistical guarantees with a compact, exact tensor-network representation of the inverse shadow channel. When measurement bases are reused, approximate unitary designs of arbitrarily high order need not uniformly match the Haar variance in the many-shot limit. For the all-to-all random two-local circuits considered, doing so requires nearly linear depth. Together, our results reveal the capabilities and limitations of shallow quantum state learning, highlighting the distinction between approximating Haar randomness and reproducing its learning guarantees.
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Populations and Evolution

Energy, space and competition: A model of territorial organization in camelids

Tomás Ignacio González, Guillermo Abramson and María Fabiana Laguna

Ecological theory predicts that herbivores adopt behaviors that balance energetic costs and benefits, shaping both foraging and reproductive organization. In some wild ungulates, such as camelids, males defend resource-rich areas to attract females and secure their offspring, leading to the emergence of territorial systems. However, existing territorial models rarely incorporate the well-established allometric relationships between body mass and metabolic costs. In this study, we develop a spatially explicit, individual-based model of territorial organization in camelids, in which male behavior is governed by an energy balance equation that includes allometric locomotion costs, resource acquisition, and the energetic risks of aggressive encounters. We show that (i) a body-mass-dependent threshold determines which individuals can establish and maintain territories, (ii) spatial resource connectivity strongly modulates competition intensity and territorial inequality, and (iii) confrontation costs play a key stabilizing role by limiting territorial expansion and promoting coexistence. Our results provide a mechanistic link between metabolic scaling, spatial structure, and social organization, offering new insights into the ecological and evolutionary drivers of territoriality in ungulates.
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Quantum Physics

Predicting properties of Scrooge ensembles with high accuracy and low sample complexity

Yue Wu, Yuzhi Tong, Helen Propson et al. (+2 more)

The Scrooge ensemble associated with a density matrix $\rho$ is the maximally random ensemble whose average density matrix is $\rho$. It has attracted growing interest for its applications to quantum many-body dynamics and quantum information. The intrinsic statistical properties of the Scrooge ensembles are encoded in their higher-order moments, yet they are nontrivial to analyze and prepare for they feature a non-polynomial Haar integrand, blocking direct use of Haar integration machinery. Existing physical mechanisms to sample multiple copies of states from the Scrooge ensembles, meanwhile, typically require costly postselection, rendering them inefficient for large system size. In this work, we develop efficient and accurate methods for analyzing and implementing Scrooge moments. We first introduce a polynomial approximation to the Scrooge $k$-th moments whose error is tunable down to a threshold that improves from inverse polynomial to exponential in $1/||\rho||_\infty$ over previous results. Building on our approximation, we then give the first efficient quantum algorithm that estimates observable expectation values using $\widetilde{\mathcal{O}}(k^3/\epsilon^5)$ copies of $\rho$ for any target error $\epsilon$ above this threshold. We further provide a construction of a block encoding of the Scrooge $k$-th moment when the preparation circuit of $\rho$ is known. Of independent interest could be a key subroutine in our algorithms, which efficiently implements projection onto the $k$-fold symmetric subspace for $\rho^{\otimes k}$ using $\mathcal{O}(k^3/\epsilon^2)$ samples of $\rho$, avoiding the naive $k!$ postselection cost of such a projection. These results provide new tools for both the theoretical analysis and practical prediction of properties of Scrooge ensembles, with potential applications to quantum many-body dynamics and quantum information processing.
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All authors Yue Wu, Yuzhi Tong, Helen Propson, Yihui Quek, Liang Mao

Algebraic Topology

Double Steinberg coinvariants for special linear groups

Tatiana Abdelnaim, David Chan, Alexander Kupers et al. (+2 more)

For a field $F$ we study the coinvariants for the $SL_n(F)$-action on the double Steinberg module $St_n(F) \otimes St_n(F)$ and show they have a rich algebraic structure: for $n = 2$ it is the Grothendieck-Witt group of $F$, and for all $n$ they assemble to a graded nonunital $\mathbb{Z}[F^\times]$-algebra, whose rational (underived) indecomposables may be expressed in terms of the augmentation ideal of the Grothendieck-Witt group. We then explain, building on work of Galatius-Kupers-Randal-Williams, that the special linear groups $SL_n(F)$ assemble to an $E_\infty$-algebra in a suitable functor category, whose $E_2$-homology groups have a vanishing line of slope 2 and on the critical line are given by the double Steinberg coinvariants.
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All authors Tatiana Abdelnaim, David Chan, Alexander Kupers, Robin J. Sroka, Matthew Scalamandre

Statistical Mechanics

Minimizing capture time with many small traps in heterogeneous media

Denis S. Grebenkov and Theodore Kolokolnikov

We study the problem of optimally placing a large number of small absorbing traps to minimize the mean first-passage time (MFPT) of particles diffusing in a heterogeneous medium with space-dependent diffusivity $D(x)$ and prescribed initial particle distribution $\omega(x)$. In two and three dimensions we identify two distinct regimes, depending on how strongly the trap ensemble depletes the particles. In the weak trapping regime (fewer traps) the optimal trap density $\rho$ is the arithmetic average $\rho = \frac12(\mu+\omega)$ of the normalized inverse diffusivity $\mu \propto 1/D$ and the initial particle distribution $\omega$. In the strong trapping regime (more traps), it is proportional to their geometric average, $\rho \propto \sqrt{\mu \omega}$. We revisit the classical Green's function approach and show that it applies to weak trapping only; in 2D this requires the trap size to be exponentially small in the number of traps, so that most applications of interest fall in the strong trapping regime instead. We therefore develop a homogenization approach that captures both regimes. A special choice of initial particle distribution is $\omega \propto 1/D$, which corresponds to the equilibrium particle distribution in the absence of traps according to the Itô interpretation. In this case we show that the optimal trap distribution is the stationary particle distribution itself, regardless of the trapping strength, and this makes the MFPT constant throughout the domain; the same trap distribution also minimizes the worst-case capture time. Finally, in one dimension we find instead $\rho\propto\left(\mu \omega\right) ^{1/3}$, and a similar analysis covers space-dependent drift and thin domains of variable cross-section. Direct numerical optimization confirms the analytical results.
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Artificial Intelligence

Component Replacement in LLM Agents: A Critical Scoping Review of Task Benefit and Attribution

Shuyang Zhang and Jianshuo Chang

Background: Choosing an agent controller and deciding which component to improve require different evidence. A replacement can change both the decision rule and what the agent can do after that decision. Objectives: We ask what existing replacement comparisons establish about task benefit and about attribution to local decision quality. Methods: This critical scoping review maps 348 studies and applies a five-step interpretation procedure to 94 comparison and diagnostic records from 42 studies, reading every inconsistent record against its source. Eight purposively selected cases illustrate the procedure. Results: The records comprise 33 executed task-outcome contrasts, 49 comparisons with restricted endpoints, and 12 diagnostic summaries. Only 14 task contrasts report contrast-level uncertainty, and the response policy is documented as retained in nine, all rule replacements from four studies; none of the 12 necessity-decision records executes a task contrast. Source checks distinguish whole-plan correctness, correct skill loading, and choice accuracy conditional on presentation from completed workflows. In Outcome Monitors, a count-matched timing placebo detects no timing effect (+0.88 points, 95% CI -4.39 to 6.14), so the source evidence attributes the detectable package gain to recovery content; detector selection at a fixed warning quota remains untested. Conclusions: The analysis separates evidence that can inform adoption from evidence that supports component development. Recovery and disruption, intervention timing, and downstream consumption organize three candidate mechanisms, and eight conditional reporting items specify the comparisons needed to distinguish the remaining explanations.
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