Dynamical Systems
Angular maps for visualizing rotational dynamics
Wolf-Jürgen Beyn and Thorsten Hüls
We develop and analyze angular maps as a numerical tool for visualizing and detecting rotational dynamics in nonlinear, nonautonomous dynamical systems in discrete and continuous time. An angular map assigns to each initial point the angular spectrum of the variational equation along the corresponding trajectory. This spectrum describes the long-time average rotation of subspaces transported by the linearized dynamics, measured by maximal principal angles. Building on the theory of angular spectra, we develop efficient numerical
algorithms based on forward and backward subspace iteration. We prove that these
algorithms asymptotically provide angular spectral values for subspaces that are dominant in either forward or backward time. Applications to Hénon maps, a planar flow, and the Lorenz system illustrate how angular maps reveal rotational features across phase space. For continuous-time systems, we prove that suitably rescaled angular spectra of exact time-step maps converge to the continuous angular spectrum in the Hausdorff metric as the step size tends to zero. For autonomous systems, we also justify a simplified
algorithm that uses successive trajectory points to approximate the angular range associated with the flow direction.
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Dynamical Systems
Density of almost squares of horospherical orbits in non-uniform quotients of $\operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})$
Konstantin Andritsch
Let $\Gamma\subset\operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})$ be an irreducible, non-uniform
lattice and define the space $X = \operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})/\Gamma$. Let $U$ be the standard horospherical subgroup in $\operatorname{SL}_2(\mathbb{R})\times\operatorname{SL}_2(\mathbb{R})$. We show that for every $\delta>0$ and $x\in X$ with dense $U$-orbit, the $U$-orbit evaluated at almost squares, $\{(u_{(n^{2-\delta},m^{2-\delta})}~:~n,m\in\mathbb{N}\}\cdot x$, is dense in $X$. The main idea of the proof is to shadow large periodic $U$-orbits and reduce the statement to a density statement within the periodic $U$-orbit, i.e. a statement for the $2$-
torus $\mathbb{T}^2$. This then follows from an effective version of Weyl's inequality to deduce the result. The effective shadowing of periodic $U$-orbits is achieved using tools from homogeneous dynamics, namely quantitative non-divergence of horospherical subgroups, recurrence under the diagonal flow and effective equidistribution of expanding horospherical subgroups. Our approach follows the strategy of the work \cite{KR25} of \citeauthor{KR25} who established density of almost squares of the horocycle flow for non-uniform
lattices in $\operatorname{SL}_2(\mathbb{R})$.
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Numerical Analysis
Constraints on admissible behavior of GMRES applied to tridiagonal Toeplitz systems
Fei Chen and Kirk M. Soodhalter
The result of Greenbaum, Pták, and Strakoš that for a given set of
eigenvalues, any convergence curve is possible [SIMAX 1996] and the subsequent parameterization of such
matrix-right-hand side pairs $(A,\mathbf{b})$ of Arioli, Pták, and Strakoš [BIT 1998] demonstrated that the behavior of the GMRES could not be completely characterized by the
eigenvalues of $A$ alone. In this paper, we consider how to use this theory to understand the admissible and attainable \gmres behavior for
matrices with constrained structure, focussing on non-Hermitian (non-symmetric) tridiagonal Toeplitz
matrices. We show that Toeptliz structure necessarily constrains the how the theory from these papers can manifest but that a continuum of admissible behaviors is still attainable.
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Optimization and Control
Reinforcement Learning and Operational Research: A Review of Methodological Integration and Research Directions
Yahan Lu, Dongyang Xia, Nursen Aydin et al. (+1 more)
The growing demand for real-time, data-driven decision-making in complex and dynamic systems is placing increasing pressure on Operational Research (OR) methodologies. Sequential decision-making under uncertainty has long been studied in OR through Markov decision processes, dynamic programming, and their approximations, and reinforcement learning (RL) provides simulation-based methods for learning decision policies in such problems. Recent research shows an increasing interest in integrating RL with OR to address dynamic decision-making problems and enhance heuristic and exact methods for combinatorial optimization. The overarching goal across these efforts is to improve solution quality, computational efficiency, and robustness. Given the diversity of integration approaches and application settings, there is a clear need for a systematic and technically detailed review of how RL empowers OR methods. To address this gap, this paper presents a structured review of two methodological roles of RL in OR. The first concerns sequential decision problems in dynamic environments, where states evolve and decisions are repeated over time. The second concerns static combinatorial optimization problems, where inputs are fixed before the solution process begins and RL either constructs solutions or supports heuristic and exact
algorithms. Digital twins provide an optional deployment and evaluation layer for training, testing, and validating these methods. We critically synthesize recent advances across these roles and uses, highlighting their advantages, implementation requirements, limitations, and challenges. Finally, we consolidate guidance on when the reviewed approaches may be considered and outline directions for future research on the methodological and practical integration of RL and OR.
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All authors Yahan Lu, Dongyang Xia, Nursen Aydin, Shadi Sharif Azadeh
Robotics
D-JEPA: A Decision-Aligned Latent World Model
Shuaijun Liu, Chengyu Wu, Qifu Wen et al. (+5 more)
Latent world models predict the consequences of actions, but accurate prediction does not guarantee that latent distance reflects which candidate will execute successfully. We identify a decision-local prediction gap: among the few futures competing for execution, a candidate predicted closer to the goal can produce a worse realized outcome than an available alternative. We introduce D-JEPA, a decision-aligned latent world model that learns decision-relevant relations among candidate futures from executed outcomes. A bounded, permutation-equivariant operator jointly reasons over goal-relative predictive features and ordinal evidence, refining pretrained predictive geometry where action choices are most consequential. Restricted predictor adaptation and a shared ordinal interface extend this
alignment across complementary predictive geometries. D-JEPA further realizes the learned decision structure in JEPA-compatible future representations, enabling deployment through native latent-distance planning. Evaluations across latent control, manipulation, pretrained action-producing models, physical
robots and autonomous driving demonstrate improved action selection, including 87.89% success on PushT, a 15.04-point average gain on RoboTwin, and a 17-point gain on physical
robot tasks. These results establish decision-relevant relational structure as a direct bridge between predictive world modeling and effective control.
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All authors Shuaijun Liu, Chengyu Wu, Qifu Wen, Feiyang You, Chenglong Zhang, Shuyang Hao, Xi Lin, Ningxin Su
Statistical Mechanics
Optimal probing scale for current fluctuations in a Brownian gyrator
Badr Farih
A driven colloidal rotor sustains a circulating current whose fluctuations one would like to bound. Any such bound rests on how strongly the current responds to a perturbation and on how much extra dissipation that perturbation costs, so there is a well-posed question of where to push: the response per unit Onsager-Machlup cost depends on the radius at which the probe acts, and is maximised at a definite one. We answer this for the Brownian gyrator and a quadrupolar shear under a Gaussian envelope, a probe chosen so that linear response is exactly blind to it at every observation window, so that the entire signal is second order. The problem separates: the cost is radial and does not see the circulation, while the response lives in the $m=3$ angular sector, where the resolvent reduces to Kummer's equation with $b=4$ and the susceptibility is a hypergeometric function of the envelope width. Maximising the ratio gives the optimal probing radius in closed form. It is set by whichever of the system's two clocks is faster: for weak driving $r^*=1.1264\sqrt{D/\gamma}$, the thermal radius of the trap, and for strong driving $r^*=1.5563\sqrt{D/\Omega}$, the distance diffused in one radian of rotation, with the trap stiffness dropping out entirely. The crossover is at $\Omega=\gamma$. Both limits, and the prefactors, are confirmed against direct simulation.
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Combinatorics
Three-Layer Intersecting Temperate Families
Kada Williams
In response to a
conjecture of Petr and Turek, we prove that every largest intersecting temperate collection of sets $\mathcal{A}\subseteq [2k]^{(k)}\cup [2k]^{(k+1)}\cup [2k]^{(k+2)}$ includes all $k$-sets containing some given $a\in[2k]$, all $(k+1)$-sets, and all $(k+2)$-sets not containing $a$.
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Machine Learning
Enhancing Transformer Representations of Symbolic ODE Expressions
Xiyue Fan, Adam Prugel-Bennett and Stuart E. Middleton
Existing approaches to solving differential equations, such as symbolic regression, physics informed neural networks, and neural operators, typically focus on numerical approximations or blind symbolic search via fitting to numerical data. Less
attention has been paid to learning structured representations of mathematical expressions that preserve commutative properties and could support mathematical
reasoning in symbolic forms.
Transformer models have shown strong capabilities in solving symbolic differential equations. However, standard positional
embeddings in
transformers are designed for sequence data. Symbolic differential equations are naturally represented by expression trees, so these positional
embeddings may not efficiently capture their hierarchical structures. We investigate existing tree positional
embeddings in symbolic ordinary differential equation (ODE) tasks. We systematically study their effectiveness under different settings. Our results show that tree positional
embeddings aid learning in early epochs and continue to improve performance throughout, ultimately yielding consistent advantages across various data sizes and tasks. Based on learned structural representations, we apply contrastive learning to support the commutative property in mathematics. Ablation studies provide insight into how these methods interact in modelling symbolic mathematical structures.
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Robotics
Beyond Visual Quality: A Study of Test-Time Planning with World Action Models
Jianhao Yuan, Yu Yuan, Benjamin Ramtoula et al. (+5 more)
World action models generate actions together with visual predictions of their consequences. These paired outputs create the potential for planning by sampling multiple actions from one state, comparing their imagined outcomes, and choosing the action with the most promising predicted outcome. However, how to use imagined futures to guide action selection remains unclear. We examine this planning potential empirically. First, we estimate an oracle upper bound on selection by choosing the sampled candidate whose realised outcome is best. In a controlled same-state analysis, this choice raises success from 68.9% under uniform random selection to 79.2%. We then test selectors based on visual quality, physical consistency, and task progression as controlled interventions. Some tested selectors yield higher observed success, but the gains are uneven and the matched selectors leave much of the measured opportunity unrecovered. To investigate this gap, we examine whether sampled actions lead to different outcomes, whether these differences are visible in the predictions, and whether a score recognises them. Counterfactual branching from the same states shows that selection opportunity is concentrated in relatively few decisions in the initial candidate sets. Action spread and outcome coverage need not increase together. In a further evaluation across trajectory phases with complete action execution, the tested scores again recover little of the available improvement despite a small gain from learned value. These findings distinguish producing consequential action choices from recognising them in generated futures, motivating the evaluation of WAM predictions through their usefulness for decisions rather than visual quality alone.
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All authors Jianhao Yuan, Yu Yuan, Benjamin Ramtoula, Lukas Vierling, Paul Newman, Lars Kunze, Philip Torr, Daniele De Martini
Artificial Intelligence
World State Generator
Sungheon Jeong, Sanggeon Yun, Ryozo Masukawa et al. (+3 more)
Language agents solve complex tasks through plans and actions. A single step the world refuses puts the goal out of reach, and what the
agent does next decides the task. Prompted planners fail at exactly this point, rewriting the refused step in new words, meeting the same refusal, and burning the attempt budget without moving. They fail because the plan was never tied to the world, so a refusal has nothing in the plan to attach to. A world is where a task runs, and it has its own rules, its own admissible actions, and its own constraints. We build synthetic worlds across 7 domains and extract training data from them. A program enforces each world's rules and grades its goal, and every world is admitted only if its goal is reachable from its initial state.
Agents run inside and leave verified failures paired with repairs that carried the run to a state the world certified, a record of about 226K trajectories. On this record we train the World State Generator, a model that writes a plan as checkable states of the world and keeps that plan aligned with the world it runs in. That
alignment is what a plan written in
language lacks, since the world it runs in has physical limits, logical dependencies, and required orders the
language never states, and the plan encounters these rules only when a state fails. WSG takes that failure as the rule the world has stated and rewrites the remaining states to obey it, so the plan bends to the world as the run goes on. Across 7 public
benchmarks, WSG raises end-to-end success for two open models near 30B parameters over prompting and brings to the level of proprietary model.
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All authors Sungheon Jeong, Sanggeon Yun, Ryozo Masukawa, Haleh Alimohamadi, Mahdi Imani, Mohsen Imani
Instrumentation and Methods for Astrophysics
First Experimental Evaluation of Stray Light Noise Modeling of kilometers-long Beam Tube Arms of Gravitational Wave Detectors
Emilia Chick, Timothy O'Hanlon, Hiro Yamamoto et al. (+3 more)
We present the results of the first experimental evaluation of stray light noise models for LIGO beam tube baffles. We combine the results of a testing campaign at LIGO Livingston and SIS simulations to get a model of backscatter and diffraction noise of select mid-arm baffles. Agreement to within a factor of $3-10$ is found between models and measured gravitational waHe strain. Two distinct regions of well-propagating motion were identified, at approximately $35Hz$ and $90Hz$, and these are visible in the strain signal as broadband features. Peaks with $Q \approx 100-1000$ were also found in the strain signal between $70Hz$ and$100Hz$. These are theorized to come from diffraction noise only, and are modeled using Q-factors measured from the strain. These models are also in good agreement with the strain signal. Other findings on the effect of auxiliary arm systems on stray light noise are discussed.
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All authors Emilia Chick, Timothy O'Hanlon, Hiro Yamamoto, Denis Martynov. Valery Frolov, Anamaria Effler, Antonios Kontos
Robotics
LLM-based Conversational AI Knowledge Assistant for MyBuddy Humanoid Robot
Hanxiao Chen
Humanoid robots are increasingly being popular and developed for human-centered applications, yet their ability to provide intelligent conversations and natural interactive knowledge assistance remains constrained by traditional rule-based dialogue systems, pre-defined responses and limited knowledge repositories. Large
language models (LLMs) have emerged as a powerful foundation for enabling natural, adaptive, and context-aware Human-
Robot Interaction (HRI), which provides a significant opportunity to address such limitations by enabling
robots to understand natural
speech language, reason over complicated queries, maintain high-quality conversational context, and generate knowledge-rich responses. In this work, we originally present and implement an LLM-based versatile Conversational AI Knowledge Assistant for the Raspberry-Pi-powered 13-Axis MyBuddy
humanoid robot, which integrates LLM-driven
language understanding and AI
reasoning with real-time
speech recognition, knowledge
retrieval via extensible access of internet engines (e.g., Wikipedia, arXiv), flexible dialogue management, and natural
speech synthesis to enable much more intelligent multi-turn continuous conversations and advanced emotional-support Human-
Robot Interaction.
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Machine Learning
An Exact Junction-Tree Extended Formulation for Optimal Classification Trees
Jiancheng TU and WenqiFan
We develop an exact linear programming (LP) formulation for bounded-depth classification trees with binary features, using a junction-tree representation. The formulation is integral and supports recursive subtree optimization. Exact reductions make the model smaller while preserving the optimal value and recovery of an optimal tree. The reduced model supports two solution methods: column generation and message passing. Column generation solves integral restricted LPs and uses bounds over the full feasible domain to certify optimality. Message passing recursively combines optimal subtree costs. Both methods solve common subtree problems that, once the preceding tree decisions are fixed, can be evaluated independently and in parallel. Computational experiments show that the exact reductions substantially reduce the size of the junction-tree formulation. The resulting linear programming formulation certifies instances for which the tested mixed-integer formulation does not establish optimality within the same computational budget, while the column-generation and message-passing methods certify more instances and achieve an order-of-magnitude reduction in
geometric-mean runtime relative to an existing state-of-the-art exact method for optimal classification trees.
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Probability
Sticky Brownian Motion with a Locally Finite Atomic Sticky Measure
L.A.Jafarova
We study sticky Brownian motion on $\mathbb{R}$ with a set of sticky points $A$. In contrast to the classical case of a single sticky point, the set $A$ may have a more complicated structure and, in particular, may have accumulation points. The stickiness at the points of $A$ is described by a locally finite purely atomic measure $\nu$. We extend the classical time-change approach for sticky Brownian motion to this setting and use it to construct a weak solution of the corresponding
stochastic differential equation with a local-time condition. We then prove uniqueness in law of the solution.
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Analysis of PDEs
Counterexamples to Grad's conjecture
Javier Gómez-Serrano, Lukas Liehr and Mitchell A. Taylor
For each sufficiently large $N$, we construct smooth solutions of the magnetohydrostatic equations on embedded solid
tori whose regular pressure levels are nested
tori, whose
magnetic field vanishes exactly on a round
magnetic axis, and whose group of Euclidean
symmetries, even when isometries reversing the sign of the field are admitted, is exactly the cyclic group $C_N$ of rotations through multiples of $2\pi/N$. For each such $N$, these
equilibria form a smooth one-parameter family which is locally nontrivial in the
moduli space of embedded configurations and have none of the plane-reflection, axial, or helical
symmetries conjectured by Grad. A Lean 4 certification of the above results is also provided.
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Quantum Gases
From harmonic to sound-like oscillations in a quantum gas confined in a gravity compensated shell trap
Matthieu Cassus, Rishabh Sharma, Maxime Pesche et al. (+4 more)
We study the center of mass oscillations of a
quantum gas in a shell shaped trap in the presence of a vertical force opposed to
gravity. The measured harmonic frequency at the bottom of the shell is compared with an analytical formula for the trap potential including corrections beyond the rotating wave approximation. When
gravity is partially compensated, a quartic correction to the harmonic motion has to be included due to the shell
curvature. As
gravity is nearly canceled, the
quantum gas occupies a large fraction of the lower hemisphere. Driving the center of mass induces internal excitations in the
quantum gas, whose time
evolution is governed by the presence of sound waves. Relaxation processes induce a strong damping of the center of mass oscillation in this limit.
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All authors Matthieu Cassus, Rishabh Sharma, Maxime Pesche, Laurent Longchambon, Thomas Badr, Romain Dubessy, Hélène Perrin
Computer Vision
Ananke: Contractive Torus Attractor Networks
Zhongping Ji
We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-
torus prior, and its flagship visual backbone realization, Contractive
Torus Attractor Networks (CTAN). By factorizing high-dimensional latent spaces into an orthogonal direct sum of two-dimensional phase planes ($\bigoplus_{k=1}^K \R^2$), Ananke coordinates feature updates via a decoupled dual-phase continuous flow: skew-symmetric
Hamiltonian transport moves features tangentially along energy level sets to preserve semantic phase invariants, while signed gradient dissipation contracts transverse perturbations normally toward target invariant
manifolds. For circular potential families with frozen parameters, logarithmic radial feedback yields the Exact Log-
Symplectic Flow (ELSF), an analytical closed-form mapping with exact exponential decay of log-radius error that evaluates in a single forward pass without numerical integration. We establish local input-to-state bounds for level-set deviations and log-radius errors, and characterize the normal hyperbolicity and persistence of the ideal product
torus under bounded perturbations. We further formulate the architecture through Lie–Trotter operator splitting, unifying spatial depthwise
diffusion with local
manifold contraction, and analyze both exact trigonometric flows and hardware-friendly
symplectic dual-shear variants. Across natural image
benchmarks (CIFAR-100) and clinically challenging endoscopy
datasets (Kvasir-v2), CTAN demonstrates exceptional parameter efficiency: an ultra-compact hierarchical model with merely 0.27M parameters achieves 90.52% accuracy on Kvasir-v2, outperforming 25M+ baselines (ResNet-50, DenseNet-161) by nearly two orders of magnitude in capacity, while scaled variants attain 80.32% top-1 accuracy on CIFAR-100.
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Computer Vision
MiTHras: Task-specific Hierarchical Semi-supervised Contrastive Masked Autoencoder for Mitotic Figure Analysis
Trinh T. L. Vuong, Simon Graham, Quoc Dang Vu et al. (+5 more)
Mitotic figure (MF) analysis supports tumor grading and prognostic assessment, but automated models remain sensitive to differences in tissue type and image acquisition. We present MiTHras, a task-specific pretraining framework that combines pseudo-label-guided image- and
token-level contrastive learning with masked reconstruction. We construct TCGA-MF-Pseudo, a corpus of 1.8 million
cell-centered images from 14 TCGA cohorts spanning 11 organ sites. Comprehensive evaluation on MF classification, detection, count-based survival prediction, and subtype classification demonstrates the efficacy of MiTHras. It achieves the highest mean F1 on all three MF classification
benchmarks and both subtype
benchmarks. MiTHras also outperforms general-purpose and pathology foundation encoders by a larger margin under frozen-encoder linear probing than under full fine-tuning. Although detection gains are modest due to a shared candidate-detection stage, ablations confirm that
token-level supervision improves typical-versus-atypical classification and linear probing. These findings establish that MiTHras yields robust, transferable representations for automated mitotic activity assessment.
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All authors Trinh T. L. Vuong, Simon Graham, Quoc Dang Vu, Phat T. H. Ho, Jeewoo Lim, Mostafa Jahanifar, Nasir Rajpoot, Jin T. Kwak
High Energy Astrophysical Phenomena
Particle Acceleration in Stratified 2D MRI Turbulence: From Reconnection to First- and Second-Order Fermi and Shear Acceleration
Astor Sandoval, Mario Riquelme and Jorge Cuadra
Low-luminosity
accretion disks around black holes are weakly collisional, potentially enabling nonthermal particle acceleration. Local two-dimensional particle-in-
cell simulations of the stratified magnetorotational instability (MRI) in pair
plasmas by Sandoval et al. (2024; hereafter S24) revealed nonthermal populations with maximum energies proportional to the scale-separation ratio $\omega_{c,0}/\Omega_0$, where $\omega_{c,0}$ and $\Omega_0$ are the initial particle cyclotron and Keplerian frequencies, respectively. We identify the acceleration mechanisms involved and quantify their scale-separation dependence. Acceleration occurs primarily within large-scale current sheets associated with an MRI dynamo. Particles are initially injected by non-ideal electric fields during reconnection driven by plasmoid splitting, attaining energies independently of scale separation. They subsequently undergo rapid first-order
Fermi-like acceleration occurring within converging flows between newly formed, separating plasmoids. During this stage, energies grow at a rate proportional to the instantaneous non-relativistic cyclotron frequency, independently of $\omega_{c,0}/\Omega_0$. This fast acceleration rate implies a maximum energy proportional to $\omega_{c,0}/\Omega_0$. Particles then continue interacting repeatedly with plasmoids, undergoing slower, predominantly second-order
Fermi acceleration, with a subdominant contribution from shear acceleration. This stage increases particle energies by only a factor of a few over several orbits, regardless of $\omega_{c,0}/\Omega_0$. The combination of these three stages implies a maximum energy proportional to $\omega_{c,0}/\Omega_0$, explaining the scaling found by S24 and suggesting that the MRI may accelerate particles to ultrarelativistic energies in low-luminosity disks. Testing these results in three dimensions remains an important next step.
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Mesoscale and Nanoscale Physics
Observation of Kondo Effect in Rhombohedral Graphene Superlattices
Xin Liao, Qing Yin, Huiwen Wang et al. (+10 more)
Kondo effect in strongly correlated systems arises from the
antiferromagnetic coupling between itinerant conduction electrons and localized
magnetic moments, giving rise to a variety of exotic
quantum phenomena. Two-dimensional moiré superlattice systems provide a highly tunable platform featuring topological flat bands, where Wannier orbitals are spatially confined by the periodic moiré potential and serve as localized
magnetic moments, enabling the observable Kondo effect. Here we experimentally demonstrate Kondo interactions in hexalayer rhombohedral
graphene moiré superlattices through magneto-transport and temperature-dependent measurements. With increasing
magnetic field, the magnetoresistance exhibits an increase-decrease transition across a critical field B_c, while the
Hall resistance R_xy undergoes a sign reversal near B_c. Moreover, as temperature decreases, the longitudinal resistance R_xx first increases logarithmically and then decreases following a T^2 behavior, indicating a transition to heavy
fermion liquid. These behaviors can be consistently explained by the breakdown of Kondo singlets induced by either
magnetic field or temperature, which liberates carriers previously bound to localized moments, thereby enhancing conductivity and altering the dominant carrier type. Furthermore, our results demonstrate that the Kondo interaction can be continuously tuned by both carrier density n and displacement electric field D, and suggest the emergence of a Kondo insulating state. Our findings provide deep insight into the Kondo effect in moiré engineered flat-band systems, paving the path for exploring exotic correlated
quantum phases.
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All authors Xin Liao, Qing Yin, Huiwen Wang, Jing-Wei Dong, Jun-Xi Chen, Si-Li Wu, Cai-Zhen Li, Guowei Lyu, Kenji Watanabe, Takashi Taniguchi, Wei Jiang, Yu-Gui Yao, Zhi-Min Liao
General Relativity and Quantum Cosmology
Formalizing a unified dynamical system framework for $f(R)$ and $f(Q)$ gravity
Saikat Chakraborty
Going beyond the traditional Hubble-normalized framework, we formalize a unified dynamical system formulation for $f(R)$ and coincident gauge $f(Q)$
gravity using three distinct sets of dimensionless variables: (1) kinematical cosmographic parameters, (2) the dark energy equation of state parameter $w$ (with its $N=\ln a$ derivatives) and matter density abundance $\Omega_m$, and (3) theory space parameters $\{m_i\}$ characterizing the shape of the theory function. Our formulation is free of auxiliary variables, closing via three equivalent ways: (1) specifying a theory, (2) requiring a specific cosmological
evolution, or (3) requiring a specific dark energy equation of state
evolution. Each closure strategy is illustrated with explicit examples. The theory closure approach studies a case of Hu-Sawicki $f(R)$ and $f(Q)=-2\Lambda+Q+\beta\sqrt{-Q}$ models, where traditional formalisms fail. A heteroclinic trajectory from a GR-matter-dominated epoch to a late-time de-Sitter epoch is general for $f(Q)$, but sensitive to initial conditions for $f(R)$. The cosmographic and equation-of-state closure approaches compare $f(R)$ and $f(Q)$ gravities kinematically equivalent to $\Lambda$CDM ($j(z)=1$) and dynamically equivalent to $\Lambda$CDM ($w(z)=-1$). In both, GR acts as a cosmological past attractor for $f(Q)$
gravity, but not for $f(R)$.
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Computer Vision
GraphSVR: q-Space–Aware Graph-Based Slice-to-Volume Registration for Diffusion MRI
Noga Kertes, Daphna Link Sourani, Alex M. Bronstein et al. (+1 more)
Diffusion-weighted imaging (DWI) remains highly vulnerable to subject motion, particularly in time-efficient protocols and in motion-prone populations. While slice-to-volume registration (SVR) can mitigate inter-slice and inter-stack misalignment,
diffusion MRI introduces additional complexity due to
diffusion-direction-dependent contrast and the requirement to align dozens of measurements within a common reference frame, effectively yielding a 4D registration problem. Existing approaches rely primarily on sequential modeling or pairwise similarity and often degrade under sparse gradient sampling or severe motion. We introduce GraphSVR, a q-space-aware graph-based framework for 4D SVR registration in DWI. GraphSVR represents slice groups as nodes in an acquisition-structured graph, with edges encoding temporal proximity, spatial slice geometry and
diffusion encoding relationships. A graph neural network predicts globally consistent stack-wise rigid motion, optimized in a self-supervised, zero-shot manner using only an anatomical reference image, without requiring paired ground-truth motion. We evaluate GraphSVR using both fully synthetic
diffusion simulations and realistic recombination-based simulations from real acquisitions with controllable motion severity and gradient sparsity. Performance is quantified using grid error (mm) and rotation error relative to known ground-truth transforms. Under severe motion, GraphSVR reduces grid error and rotation error by 73% compared to FSL eddy, the standard DWI motion-correction method, with the largest gains observed in sparse-direction regimes. These results demonstrate that explicitly modeling acquisition structure through graph-based
reasoning improves robustness and global consistency in 4D DWI motion estimation. Code is available at https://github.com/nogakertes/GraphSVR.git.
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All authors Noga Kertes, Daphna Link Sourani, Alex M. Bronstein, Moti Freiman
Probability
A large deviation principle for the Gaussian beta ensemble in the high temperature regime
Helene Götz and Jan Nagel
We show a large deviation principle for the weighted spectral measure of the Gaussian beta ensemble in the high temperature regime, when $n\beta_n\to 2c \in [0,\infty)$. The resulting rate function has a novel and interesting structure: it is finite only for discrete measures and moreover, in the very high-temperature regime (when $c=0$), additional terms may arise that penalize each support point beyond the first.
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Databases
From OA colors to observable access states: A commentary on the 2026 OpenAlex proposal
Abdelghani Maddi
The OpenAlex Colors Working Group proposes replacing the familiar Gold, Green, Hybrid, Bronze and Closed taxonomy with a work-level framework based on three dimensions: access, location and license. The proposal addresses genuine weaknesses in the legacy color system, particularly its dependence on journal-level characteristics, its difficulty in describing non-article outputs, and its conflation of access conditions with venue business models. This commentary supports that general direction but argues that the proposed labels should not become the primary data model. The central technical issue is that access, location and license are not best understood as three independent attributes of a work: scholarly works commonly have several versions or copies at different locations, and access status, license and version may differ from one location to another. The analysis therefore recommends treating the location/version observation as the atomic unit of OA metadata and deriving work-level labels, legacy colors and user-facing summaries from those observations. Particular
attention is given to license semantics, version identification, the normative assumptions embedded in a “best-available” hierarchy, the coarse Publisher/Other Platform distinction, temporal change, provenance, compound works, and backward compatibility. Existing standards and infrastructure (including NISO/ALPSP Journal Article Versions, COAR controlled vocabularies, FAIR provenance principles, and OpenAlex's own current location objects) already provide many of the components needed for such an approach. The result would preserve the simplicity sought by the Working Group while making the underlying data model more extensible, auditable and suitable for funder compliance, bibliometric research and future changes in scholarly communication.
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Fluid Dynamics
High-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equationsHigh-order immersed boundary method for subsonic aeroacoustics and compressible Navier-Stokes equations
Abdoulaye Ouattara, David Marx, Christian Prax et al. (+3 more)
In computational fluid dynamics, the immersed boundary method is a classical technique to account for complex geometries when Cartesian grids are used, as is the case in finite difference methods. The present paper presents a new discrete ghost point method, which is one of the different immersed boundary methods available, for solving problems in acoustics and aeroacoustics with the linearized Euler equations or the compressible Navier-Stokes equations. This method is based on high-order schemes and a ghost point method. The flow field values at the ghost points are determined in two steps. A least-squares interpolation is first used to reconstruct the flow on a stencil of points located on the normal to the immersed boundary. Then, a 4th order Lagrangian extrapolation based on the normal stencil points adjacent to the boundary point is used to impose the boundary conditions at the immersed boundary by reconstructing the field values at the ghost points. This approach is verified and validated for the acoustical problem of a pressure pulse impinging on a cylinder. The approach is also validated for compressible flow past a circular cylinder at several Reynolds numbers.
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All authors Abdoulaye Ouattara, David Marx, Christian Prax, Véronique Fortunée, Manuel Diaz, Peter Jordan
Optics
Phase fields in momentum space of photonic crystal slabs
Chuanlin Li, Aobo Ren and Jiang Wu
Optical phase modulation is of great significant importance in fields such as optical communication, information processing, and precision measurement. Compared with real-space modulation, momentum-space phase modulation has distinct advantages: it is free from structural center constraints, supports unlimited mode capacity, and possesses intrinsic topological protection. This inherent flexibility and scalability allow practical applications systems to operate without stringent optical
alignment while providing a large number of independent control channels, thereby advancing the development of high-performance, highly integrated optical systems. Photonic
crystal slabs, with their open boundary periodicity and capabilities for momentum-space optical field manipulation, have become a crucial platform for research on momentum-space phase fields. Based on polarization orthogonal decomposition and the scattering
matrix within temporal coupled-mode theory, this paper systematically elucidates the generation mechanisms of both two-dimensional momentum-space phase fields, including phase
vortices, phase gradients, and phase difference, and multidimensional synthetic momentum-space phase fields in photonic
crystal slabs, and reviews recent research and application progress in this area. Finally, the development status, advantages, and possible breakthroughs in the field of momentum-space phase fields are summarized and prospects for future work are discussed.
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Computer Vision
ReSTI: A Source-Grounded Audit and Repair of STI-Bench
Pengzhan Sun, Ramanathan Rajaraman, Shiu-Hong Kao et al. (+2 more)
Spatial–temporal
benchmarks are valid only when their questions, source annotations, and answer options identify the same physical quantity. We audit STI-Bench against the official ScanNet, Waymo, and Omni6DPose sources and find systematic coordinate-system and timestamp errors, under-specified targets and times, and disagreements between keyed options and answer details. We introduce ReSTI, a source-backed revision that reconstructs every recoverable answer under an explicit target, time, coordinate system, physical quantity, and unit. Source reconstruction reveals task-level
geometric failures: ScanNet Grounding omits the required
alignment between annotation and raw camera coordinate systems, while Orientation measures camera rotation on the wrong plane. ReSTI replaces these labels with explicit, source-consistent
geometric definitions and corrects other source-verifiable defects, including Waymo poses evaluated at the wrong timestamp. Across 2,064 legacy questions, ReSTI retains 1,782 questions and records 282 evidence-backed exclusions. ReSTI therefore provides a conservative and source-traceable basis for evaluating precise
video spatial–temporal
reasoning. Project page: https://github.com/pengzhansun/ReSTI.
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All authors Pengzhan Sun, Ramanathan Rajaraman, Shiu-Hong Kao, Junbin Xiao, Angela Yao
Astrophysics of Galaxies
CAVITY: Calar Alto Void Integral-field Treasury surveY: II. Second public data release
B. Bidaran, A. Jiménez, R. García-Benito et al. (+30 more)
Studying
galaxy evolution under the unique environmental conditions of
cosmic voids provides an opportunity to disentangle the role of the large-scale environment in shaping mass assembly (both baryonic and dark matter), regulating
galaxy physical properties, and driving the transformation from
star-forming to quiescent systems. We present the second public data release (DR2) of the Calar Alto Void Integral-field Treasury Survey (CAVITY), an ongoing legacy programme designed to study void
galaxies (VGs) across a range of nearby ($0.005 \leq z \leq 0.050$) voids with different sizes and dynamical stages, providing 200 science-grade optical integral-field spectroscopy (IFS) data cubes. By doubling the number of
galaxies relative to DR1 while maintaining the same selection criteria, DR2 significantly increases the
dataset's statistical power, enabling more robust characterization of
galaxy properties and their correlations with environment. The observations were obtained with the PMAS/PPAK spectrograph on the 3.5-m Calar Alto
telescope using the V500 configuration, covering the optical spectral range of 3745-7500 A at a resolution of 6 A (FWHM). The DR2 VG sample spans a broad range of
stellar masses, morphologies, colours, and gas ionisation properties. We describe the sample selection, observing strategy, data reduction pipeline, quality-control procedures, and the public access to the CAVITY
datasets and associated ancillary data on the survey's database. In addition, we present a characterisation of the large- and local-scale environments of CAVITY
galaxies, showing that the 15 surveyed voids encompass a wide variety of sizes,
galaxy richness,
galaxy populations, and local structures, including
galaxy groups. This release comprises 200 IFS data cubes, publicly available together with the master catalogues at the survey's dedicated webpage: https://cavity.caha.es/data/dr2/.
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All authors B. Bidaran, A. Jiménez, R. García-Benito, M. Argudo-Fernández, M. Alcázar-Laynez, S.B. De Daniloff, S. Duarte Puertas, D. Espada, E. Florido, Y. K. González-Koda, I. Pérez, T. Ruiz-Lara, L. Sánchez-Menguiano, G. Torres-Ríos, P. Vásquez-Bustos, S. Verley, A. Zurita, M. A. Canossa-Gosteinski, A. M. Conrado, H. M. Courtois, I. del Moral-Castro, J. Falcón-Barroso, A. Ferré-Mateu, M. Hernández-Sánchez, A. Lugo-Aranda, S. Subramanian, P. Villalba-González, L. Galbany, R. M. González Delgado, R. F. Peletier, S. F. Sánchez, R. van de Weygaert, A. Fernández-Martín
Medical Physics
A digital-twin framework for forecasting treatment-day imaging with contour uncertainty in adaptive proton radiotherapy
Yizhou Wu, Jie Ding, Justin Roper et al. (+6 more)
Head-and-neck anatomy changes over a six-to-seven-week
proton course, and the anatomy of a later week cannot be imaged when the plan is made. We present a digital-twin framework that forecasts a patient's treatment-day anatomy as an ensemble of predicted CTs with propagated contours and quantifies the uncertainty of the forecast contours. The twin is a library of previously treated patients with planning and weekly quality-assurance CTs (QACTs), made patient-specific by a two-step foundation-model deformable registration: a cross-patient field carries each library patient onto the current patient, and a longitudinal field, estimated in the current patient's frame, carries that patient's planning-to-QACT change onto the current patient's own planning CT. A library of 302 observations from 88 patients yields about 300 replicates per patient, each a deformation that occurred in a treated patient. The dispersion of the propagated contours, resolved by outward normal, is six-direction contour uncertainty in millimeters. This is uncertainty in the input to the forecast, which library patient the current patient follows, rather than in model parameters, and it is unchanged when the registration engine is exchanged. On ten patients with clinician contours on two QACTs, the library alone fixes the anisotropic shape of the uncertainty (4.5 to 6.2 mm); the first QACT narrows it by a factor of 3.2 to 3.6 without a contour being drawn; an approved contour improves the center but not the width. The estimate orders directions correctly but is not Gaussian-calibrated. A clinical target volume expansion is worked out as one application.
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All authors Yizhou Wu, Jie Ding, Justin Roper, Minglei Kang, Yuheng Li, Sibo Tian, David S. Yu, Xiaofeng Yang, Chih-Wei Chang
Combinatorics
The $\mathbb{Z}$-Divisor Graph on $\mathbb{Q} \cap [1,7]$ is Planar and 3-Colorable
Michael D. Walton and Zachary D. Walton
We prove that a divisor graph on an interval of integers is a planar graph whenever the interval $[n,m]$ satisfies $m\leq 7n$, and that 7 is the greatest such real number for which we can guarantee that the graph is planar. We prove these graphs are 3-colorable.