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All of arXiv

Thursday 17 September

Differential Geometry

Deformations of harmonic maps with conical singularities

Dominik Gutwein and Thibault Langlais

We study the deformation theory of harmonic maps with isolated singularities between compact Riemannian manifolds, in the case where all the tangent maps are smooth (away from the origin) and the decay to the tangents is polynomial. We will refer to these as conically singular harmonic maps. Under certain conditions on the Morse index and the nullity of the tangent maps and a non-degeneracy assumption on a weighted kernel of the Jacobi operator, we prove that such harmonic maps persist under a small $C^2$-perturbation of the background metric. In the second part of the paper, we construct examples of conically singular harmonic maps satisfying the assumptions of our deformation theorem. We first prove that the desired conditions on the tangent maps are satisfied by the radial projections $\mathbb{R}^m \setminus \{0\} \to \mathbb{S}^{m-1}$ ($m \geq 4$) and the complex Hopf fibrations $\mathbb{C}^{n+1} \setminus \{0\} \to \mathbb{CP}^{n}$ ($n \geq 1$). We then construct explicit examples of conically singular maps $\mathbb{S}^{m} \setminus \{N,S\} \to \mathbb{S}^{m-1}$, $\mathbb{S}^{4} \setminus \{N,S\} \to \mathbb{S}^2$ and $\mathbb{CP}^2 \setminus \{[0:0:1]\} \to \mathbb{CP}^1$ which are harmonic and satisfy the assumptions of the deformation theorem with respect to an appropriate metric on the domain and the round metric on the target.
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Biological Physics

The Motile-Units model: Interacting spins model of cell polarization and motility

Jonathan E. Ron and Nir S. Gov

We introduce a coarse-grained interacting-spin model for two-dimensional cell motility, in which the cell perimeter is discretized into stochastic binary spins that switch between active and inactive states. Each perimeter spin represents a "motile-unit" that is a source of protrusive force and retrograde flow when active. Long-range interactions between the motile-units arise through a polarity cue advected by the collective actin retrograde flow, providing a minimal realization of spontaneous symmetry breaking and self-propulsion. The model exhibits three dynamical phases, a random walk phase, persistent random walk phase, and an intermittent bistable phase characterized by run-and-tumble migration. Additional nearest-neighbor interactions modulate speed and persistence without altering the overall phase structure. Owing to its simplicity, the framework naturally incorporates external cues, reproducing chemotactic migration, steering by localized optogenetic activation, and directional decision-making (symmetry breaking) under competing stimuli. The model introduces a new class of active-particle model in which both speed and polarity emerge from internal stochastic spin dynamics, rather than being imposed as particle-level variables, offering a framework for the study of cell migration and extends the scope of active-matter physics.
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Robotics

CoRef-GS: Cooperative Referring Gaussian Splatting for Multi-Agent Scene Understanding

Zhikun Zhou, Kunyu Peng, Runyi Yang et al. (+7 more)

Referring scene understanding for embodied robots requires grounding object- and relation-centric language queries from a designated viewpoint. While a local semantic Gaussian map can support such grounding within one agent's observations, cooperative settings require this ability to remain effective after independently reconstructed maps are aligned and fused. In this setting, the referred target or its contextual landmark may come from another agent's observations, while spatial relations must still be interpreted from the querying robot's viewpoint. We formulate this problem as cooperative referring Gaussian grounding over fused maps, which requires geometric alignability, instance-level semantic comparability, and view-conditioned relation reasoning. Existing language-aware Gaussian methods mainly focus on single-map querying, whereas Gaussian registration methods optimize geometric or photometric alignment without preserving language-grounding-oriented semantic compatibility. We propose CoRef-GS, a cooperative referring Gaussian splatting framework. CoRef-GS constructs local open-vocabulary instance-aware Gaussian maps, then aligns partially overlapping maps with a cross-agent alignment module by geometric and semantic consistency, and grounds queries using a view-conditioned mask relation graph. We further introduce CoQuad-Ref, a dual-quadruped benchmark spanning both real-world and simulated indoor scenes. Experiments show that, on simulated scenes, CoRef-GS reduces the rotation error from 2.58{\deg} after coarse initialization to 0.15{\deg} after refinement, and improves real-world referring mIoU over ReferSplat from 52.6% to 68.8%. The established benchmark and source code will be publicly released at https://github.com/ruojiruoli17/CoRef-GS.git.
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All authors Zhikun Zhou, Kunyu Peng, Runyi Yang, Junhao Cai, Di Wen, Ruiping Liu, Danda Pani Paudel, Yi Zhou, Luc Van Gool, Kailun Yang

Algebraic Geometry

Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II

Connor Stewart

Let $K$ be a Henselian discretely valued field with excellent ring of integers $\mathcal{O}_K$ and algebraically closed residue field $k$. Let $X\to\mathbb{P}^1_K$ be a cyclic cover of degree $n$ prime to the characteristic of $k$. In joint work with Obus and Srinivasan (arXiv:2609.20553), we define an integer called the conductor-discriminant contribution $\text{cdc}(y)$ associated to a multiplicity $2$ point $y$ of the branch divisor of the normalization in $K(X)$ of a regular $\mathcal{O}_K$-model $\mathcal{Y}$ of $\mathbb{P}^1_{K}$; modulo several key results about $\text{cdc}(y)$, we prove a conductor-discriminant inequality for $X$, extending previous work of Ogg, Saito, Liu, Srinivasan, and Obus$-$Srinivasan. In this companion paper, we supply the necessary technical results for $\text{cdc}(y)$. In particular, we show $\text{cdc}(y)$ is non-negative except under highly restrictive conditions on $n$ and the structure of the branch divisor at $y$. Moreover, if $\text{cdc}(y)$ is negative, we show the spectrum of the complete local ring of any point lying over $y$ under the normalization of $\mathcal{Y}$ in $K(X)$ is a rational double point. Along the way, we show the non-negativity of a related quantity, the conductor exponent-discriminant contribution $\text{cedc}(y)$, which is used in our joint work with Obus and Srinivasan to give a new proof of a result of Kohls.
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Computation and Language

SAFARI: An Industrial Benchmark for LLM-Assisted Hazard Analysis and Risk Assessment

Chenxi Wu, Zimu Wang, Haiyang Zhang et al. (+2 more)

Large language models (LLMs) are increasingly considered for safety-critical engineering, yet their reliability in regulated functional-safety workflows remains underexplored. We introduce SAFARI (Safety-Aware Functional Automotive Risk Inference), the first industrial benchmark for LLM-assisted automotive Hazard Analysis and Risk Assessment (HARA) under ISO 26262. It contains 3,000 de-identified industrial HARA cases and evaluates two coupled tasks: open-ended hazard analysis and standards-grounded risk assessment. To evaluate open-ended HARA artifacts, we propose the first reference-anchored LLM-as-a-judge protocol with high expert correlation. Experiments with nine frontier LLMs show that models often produce plausible hazard narratives but remain weak at ISO 26262 risk classification, with the best ASIL macro-F1 reaching only 0.261. Chain-of-Thought prompting provides limited benefit and often degrades categorical risk assessment. Error analysis further localizes major failures to scenario-critical context omissions during hazard generation and to controllability misjudgments during risk assessment, indicating where expert oversight should be concentrated. The dataset can be obtained from https://github.com/xixi47520-hash/HARA.
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All authors Chenxi Wu, Zimu Wang, Haiyang Zhang, Wei Wang, Zhijie Xu

Statistical Methodology

Sampling-Based Batch Sequential Design by Stein Variational Gradient Descent

Penghui Fu, Xiaoxian Ding, Chunlin Ji et al. (+2 more)

Many real-world experimental design problems require a batch of experimental runs across stages, in which multiple points are selected and evaluated at each stage. However, most work in the design literature is focused on fully sequential (point-by-point) methods. This paper proposes a sampling-based framework to systematically convert a fully sequential method to a batch sequential method. In particular, Stein variational gradient descent (SVGD) is adapted to efficiently sample a batch of points from a properly constructed target distribution while balancing the individual utility and the batch diversity. We address challenges that arise in using SVGD for experimental designs, including constrained design regions and near-uniform target distributions. We apply the proposed method to obtain batch versions of the state-of-the-art fully sequential methods, and demonstrate their performance through extensive numerical studies.
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All authors Penghui Fu, Xiaoxian Ding, Chunlin Ji, Jianhua Z. Huang, C. F. Jeff Wu

Robotics

V2-STRep: VLM-Grounded Structured Task Representations for Reusable Robot Skills Acquired from Generated Videos

Yexin Hu and Dongheui Lee

Human manipulation videos provide rich motion and interaction cues for acquiring robot skills without robot demonstrations. Video generation models synthesize such demonstrations from an initial scene image and task instruction, avoiding the need to record demonstrations for each task. However, the recovered motion captures only one scene-specific realization, leaving task structure, geometric relations, and constraints implicit. We present V2-STRep, a zero-shot framework that converts generated video motion into reusable robot skills through VLM-grounded structured task representations. The representation specifies motion phases, references, and task-relevant constraints, with targets described by minimal geometric structures: points, point-normals, axes, planes, and full 6D poses. VLM-provided 2D image-space cues are lifted into 3D using RGB-D observations to reconstruct task geometry and candidate grasp poses. Geometry-specific rules transfer motion to new scenes, while task-constrained trajectory optimization couples grasp selection with complete robot motion planning. It preserves task requirements while using remaining rotational freedom to accommodate joint limits. Updating deployment grounding and constraints enables reuse under new compatible instructions without generating another video. Experiments on six real-world manipulation tasks demonstrate improved execution success over baselines, reliable cross-scene transfer of successfully acquired skills, and adaptation to changed deployment instructions. Details are available on the project website: https://tuwien-asl.github.io/V2-STRep/.
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Artificial Intelligence

Limits of Confidence in Diffusion

Russ Webb, Amitis Shidani, Alice Bizeul et al. (+1 more)

Discrete diffusion, including remasking and uniform-state samplers, generate a sequence by writing multiple token positions per step, drawing each from a per-position distribution and choosing which positions to write from those same distributions. For domains of general interest (pixels, phonemes, or words) there are inherent dependencies between tokens. We show that a step matches the training distribution only when the positions it writes are conditionally independent given the tokens already fixed, that no product of per-position distributions can match a dependent group, and that per-position distributions do not determine whether a group is dependent: two joint distributions can have identical per-position marginals while differing in which combinations of values occur. On ScanAndAdd, a synthetic task whose joint distribution is available in closed form, we verify that every group of two or more undetermined positions a confidence ranking writes is dependent, and measure the generated distribution to be $29\times$ the sampling-noise floor total variation while per-sample metrics are $1.0$.
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All authors Russ Webb, Amitis Shidani, Alice Bizeul, Dan Busbridge

Dynamical Systems

Degree Growth of Iterates of Curves and Likely Intersections

Sina Saleh and Jit Wu Yap

We study the growth of the bidegree of an ample irreducible curve in $\mathbb{P}^1 \times \mathbb{P}^1$ under a product polynomial endomorphism $\varphi=(f,g)$, where at least one of $f$ and $g$ is non-exceptional. We prove that, if the curve $C$ is not preperiodic under $(f^a,g^b)$ for any $a,b\geq 1$, then the bidegree of $\varphi^n(C)$ is asymptotic to $(\text{deg}(g)^n,\text{deg}(f)^n)$. As an application of this exponential growth, we prove a geometric analogue of Silverman's theorem on the finiteness of $S$-integral points in orbits. Namely if $C$ is not $(f^a,g^b)$-preperiodic and $C'$ is not totally invariant for $\varphi$, then for any infinite sequence ${n_i}$ of positive integers, the union of the intersections $$ \bigcup_{i \geq 1} \left( \varphi^{n_i}(C)\cap C' \right) $$ is Zariski dense in $C'$.
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Game Theory

Faster Verification of PJR$^+$ via Mincuts

Drew Springham

PJR$^+$ is a polynomial-time verifiable proportionality axiom for approval-based committee elections, but its known polynomial-time verification procedure relies on general submodular-function minimisation. We show that its objective is a maximum-closure problem and give a direct mincut formulation of the problem on a bipartite graph. Using an almost-linear-time maximum-flow algorithm, this yields an $\mathcal{O}(m(nk)^{1+o(1)})$-time verifier, where $n$, $m$, and $k$ are the numbers of voters, candidates, and committee members, respectively. The dependence of this bound on each parameter separately is almost linear: it is linear in $m$, and almost linear in $n$ and $k$. The verifier also returns an explicit group witnessing a violation and admits a slower but immediately implementable variant based on the preflow–push mincut algorithm. Finally, for the parameterised axiom $\alpha$-PJR$^+$, where $\alpha$ is used as a multiplier in the group size, we demonstrate how to compute the largest value of $\alpha$ for which a committee still fails the axiom using this mincut formulation.
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Networking

NS3Learn: Transferring 5G NR Mode-2 Reception Realism from ns-3 to the Veins/SUMO Stack for Connected-Vehicle Safety Assessment

Rasheed Bello, Arthur Mukwaya, Gurcan Comert et al. (+5 more)

Connected-vehicle safety evaluations rely on coupled traffic and network simulations, but standard channel models ignore radio resource competition in 5G NR sidelink Mode-2, reporting unrealistically high message delivery in dense traffic. This study introduces resource-competition losses without requiring full protocol reimplementation. We labeled 10.5 million reception outcomes from ns-3 5G-LENA traces (calibrated on 3GPP scenarios and driven by SUMO trajectories) to fit NS3Learn - a closed-form model capturing half-duplex loss, scheduling collisions, receiver capture, and decoding. Evaluation spanned two signalized urban networks, six penetration levels (1-100%), and five random seeds per condition. NS3Learn achieved a mean absolute deviation of 0.06 in per-instant delivery compared to ns-3 5G-LENA, outperforming alternative models (0.44 and 0.55 deviation). Fitted parameters transferred to a distinct intersection with only 20% additional error. Crucially, using realistic communication models reversed simulated traffic speed trends and more than doubled predicted hard-braking events. The framework transfers reception realism between simulators via model distillation instead of full reimplementation. Every stage maps directly to an explicit physical mechanism. Researchers and transportation agencies can maintain existing simulation pipelines while accurately accounting for dense-traffic packet loss and denial-of-service impacts. Adapting to new radio configurations requires only offline refitting rather than code modification.
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All authors Rasheed Bello, Arthur Mukwaya, Gurcan Comert, Varghese Vaidyan, Vijay Bendigeri, Anthony Dontoh, Jagruti Sahoo, Judith Mwakalonge

Machine Learning (Statistics)

TAP Accuracy Below the Fluctuation Scale and Universal Posterior Geometry in Spherical Linear Models

Jingbo Liu and Zhiyuan Yu

We study the Bayes-optimal spherical linear model as the ambient dimension and sample size grow proportionally, under a quantitative Marchenko–Pastur spectral-regularity condition on the design. This condition is satisfied by normalized i.i.d. designs with standardized entries of finite fourth moment, but does not require entrywise independence or impose conditions on the singular vectors. Under this condition, we prove a quantitative all-temperature TAP approximation and characterize the posterior geometry. For the natural finite-aspect-ratio TAP functional, the normalized spherical free energy and the TAP optimum differ by $O_P(p^{-1})$. Each is within $O_P(p^{-1/2})$ of its explicit deterministic equivalent, and this fluctuation scale is sharp. Uniformly over all global TAP maximizers, the normalized squared Euclidean distance to the spherical posterior mean is $O_P(p^{-1})$. We also prove that the posterior mass outside a data-dependent band determined by the ridge estimator has sharp exponential order. More precisely, uniformly over sufficiently small band widths $\varepsilon$, the logarithm of this mass is at most $-cp\varepsilon^2+O_P(1)$. For every fixed geometrically admissible width, a spherical-cap construction gives a matching exponential-order lower bound on this mass. For every deterministic sequence of widths $\varepsilon_p\gg p^{-1/2}$, the corresponding bands capture asymptotically all posterior mass.
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Probability

Limit shape for domain-wall six-vertex model

Alexey Bufetov

In this note we announce limit shape theorems for the height function of the six-vertex model in the antiferroelectric (for arbitrary $\Delta <-1$) and disordered (in a restricted range $-1 < \Delta \le 1/2$) regimes under domain-wall boundary conditions.

Robotics

Accelerating Visual Policy Learning with Sampling-Based Model Predictive Control

Yilang Liu, Haoxiang You, Qian Wang et al. (+2 more)

Learning visual policies for locomotion and manipulation requires coordinating contact with the environment and can incur substantial computation and GPU memory costs. First-order policy gradients (FoPG) reduce training cost through differentiable simulation, but local optimization can converge to unintended contact patterns. To address this shortfall, we propose Sampling-Guided Policy Search (SGPS), which couples recurring action-target refinement by sampling-based model-predictive control with first-order policy optimization. Behavior cloning initializes the policy from sampled actions; training then alternates sampling-based refinement with short-horizon FoPG updates under perturbed initial states and randomized dynamics. For visual policy training, we use a decoupled FoPG formulation that excludes rendering from the computation graph, enabling direct learning from depth observations without a state-policy teacher. On a single GPU, SGPS learns policies for locomotion, obstacle traversal, crate pushing, and bimanual carrying on simulated Unitree Go2 and G1 robots. Our experiments further show that refinement improves policy learning beyond initialization and tracking alone. For hardware deployment, the distilled policy transfers zero-shot to a real Go2 and uses onboard depth to autonomously trot, crawl, clear hurdles, and switch between these behaviors.
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All authors Yilang Liu, Haoxiang You, Qian Wang, Daniel Rakita, Ian Abraham

Computer Vision

DocAttriBench: Benchmarking Answer Grounding in Document Visual Question Answering

Luca De Grandis, Silvia Cappelletti, William Raccagni et al. (+3 more)

Answer grounding in document visual question answering remains an open challenge: most benchmarks lack grounding annotations or provide limited-quality labels, while constructing grounded datasets still requires costly manual effort. We introduce DocAttriBench (DAB), a large-scale benchmark for fine-grained, element-level source attribution in Document VQA, grounding answers to specific layout elements such as text blocks, tables, and images. To build DAB, we propose a Mask-based Perplexity-Derived Attribution method (MAPPET) that combines document layout and language modeling to identify the most informative element for each answer. MAPPET measures the increase in perplexity after masking candidate elements and attributes the answer to the element contributing most to model confidence. Applying MAPPET to multiple existing Document VQA datasets yields DAB, with 237k documents and 296k question-answer pairs with element-level grounding. We benchmark grounding-capable multimodal LLMs on DAB, evaluating answer accuracy, attribution accuracy, and overall answer quality. Results show that while larger models generally achieve higher answer accuracy, even the strongest models often fail to localize the supporting elements. DAB provides a scalable benchmark for developing grounded, verifiable, and trustworthy Document VQA models. Dataset and code are available at https://aimagelab.github.io/DocAttriBench/.
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All authors Luca De Grandis, Silvia Cappelletti, William Raccagni, Marcella Cornia, Lorenzo Baraldi, Rita Cucchiara

Quantum Physics

FT-Weave: Real-Time Compilation Framework for Reconfigurable Fault-Tolerant Quantum Architectures

Wan-Hsuan Lin, Milan Kornjača, Chen Zhao et al. (+2 more)

Fault-tolerant quantum computing (FTQC) is essential for large-scale quantum computation, but realizing useful application throughput requires coordinating resource preparation, assignment, routing, and logical execution under strict hardware and timing constraints. Many FTQC compilation approaches construct offline schedules using nominal or fixed magic-state factory throughput. Such schedules cannot respond to stochastic resource-preparation and teleportation outcomes, leading to execution stalls and hardware underutilization. In this work, we introduce FT-Weave, a stage-aware real-time FTQC compilation framework that jointly coordinates resource preparation, resource assignment, teleportation routing, and correction handling. By adapting to runtime resource availability and hardware constraints, FT-Weave allows preparation, communication, and logical execution to overlap. We instantiate FT-Weave on two representative neutral-atom, early FTQC architectures: transversal STAR and a T-state cultivation architecture. Under the evaluated hardware and latency model, FT-Weave achieves a speedup of up to 3X over a baseline compilation flow for simulations of the two-dimensional transverse-field Ising model. In the case study, we further find that maximizing exposed concurrency does not necessarily minimize execution time. Although fine-grained asynchronous execution can reduce local idle time, its smaller optimization windows and increased routing contention can outweigh these gains. Together, these results show that effective runtime coordination, rather then exposed parallelism alone, determines how efficiently FTQC resources translate into application throughput:FT-Weave provides a blueprint for solving this real-time orchestration problem across resource protocols and architectures.
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All authors Wan-Hsuan Lin, Milan Kornjača, Chen Zhao, Sheng-Tao Wang, Jason Cong

Algebraic Geometry

The Hurwitz existence problem in prime degree

Jijian Song, Hailin Wen and Zebao Zhang

Let $p$ be a prime. We prove that every compatible branch datum of degree $p$ over the sphere is realizable by a connected branched cover. The three-point case is constructed in residue characteristic $p$. Henrio's moment theorem supplies the distinct-point moment solutions from which we construct a special primitive tail for each prescribed partition; a second application underlies the new tail required by a positive source genus. These tails are joined by a logarithmic deformation datum and embedded in one subgroup of $S_p$ containing a common regular subgroup of order $p$. Wewers's lifting theorem produces a three-point Galois cover in characteristic zero. The quotient by a point stabilizer has degree $p$ and the prescribed three ramification profiles. The fusion and realization results of Edmonds–Kulkarni–Stong then give the assertion for an arbitrary number of branch values. As consequences, the connected prime-degree Hurwitz potential has full support on the Riemann–Hurwitz locus, every corresponding connected relative Gromov–Witten invariant of $\mathbf P^1$ is nonzero, the two-relative-point disconnected sector with even completed-cycle orders at most $p$ is strictly positive subject to the dimension constraint, and the connected transposition sector is strictly positive.
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Cosmology and Nongalactic Astrophysics

Euclid: Galaxy cluster detection through the weak lensing effect - algorithm assessment and selection

A. Manjón-García, G. Leroy, S. Pires et al. (+164 more)

Weak gravitational lensing offers a powerful way to detect galaxy clusters by directly tracing their total matter content. Its effectiveness increases with the density of background galaxies, a requirement that is now being met by the high sensitivity and wide coverage of current large-area surveys. A prime example is the Euclid telescope, which will map approximately 14 000 deg2 of the sky, measuring the shapes of billions of galaxies and opening a meaningful window for detecting galaxy clusters uniquely through their weak lensing signal. We present the results of nine galaxy cluster detection algorithms in a blind challenge, using 1200 deg2 of Euclid-like weak lensing observations from the DEMNUni-Cov simulations. The performance of these methods was assessed by matching their detections to known synthetic clusters with signal-to-noise ratios greater than 2, satisfying the z-M selection cut, and adopting two different matching procedures. The purpose of the challenge was to identify and improve strategies for galaxy cluster detection via weak lensing for the upcoming Euclid data releases. We pre-selected four methods based on their individual performance and complementarity. Each pre-selected method adopts a distinct approach: AMICO-WL uses an optimal filtering technique, DoG employs Gaussian filtering, O21 relies on aperture-mass filtering, and W234 applies multi-scale wavelet filtering. Together, the results of these methods can be merged to enhance the processing of Euclid data. Individually, these algorithms reach approximately 10% completeness for a mean purity of 90%, while their combination leads to roughly a two-fold improvement in overall performance, exceeding 70% completeness for low-redshift, high-mass clusters. When extrapolating the results of this work to Euclid Data Release 1, we expect to detect approximately 2500 galaxy clusters via weak gravitational lensing.
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All authors A. Manjón-García, G. Leroy, S. Pires, J. M. Diego, C. Giocoli, L. Trobbiani, A. Díaz-Sánchez, M. Maturi, M. Oguri, G. Panebianco, G. W. Pratt, S. Andreon, L. Moscardini, M. Sereno, C. Carbone, A. M. C. Le Brun, M. Lieu, L. Chappuis, B. Altieri, T. Castro, M. Douspis, D. Eckert, S. Farrens, R. Gavazzi, A. H. Gonzalez, L. Ingoglia, E. Jullo, S. Maurogordato, J.-B. Melin, N. Okabe, F. Pacaud, M. Radovich, Z. Sakr, L. Salvati, B. Sartoris, S. A. Stanford, J. E. Taylor, J. Weller, C. Wood, C. Baccigalupi, M. Baldi, S. Bardelli, P. Battaglia, A. Biviano, E. Branchini, M. Brescia, S. Camera, V. Capobianco, V. F. Cardone, J. Carretero, M. Castellano, G. Castignani, S. Cavuoti, A. Cimatti, C. Colodro-Conde, G. Congedo, L. Conversi, Y. Copin, F. Courbin, H. M. Courtois, H. Degaudenzi, S. de la Torre, G. De Lucia, H. Dole, F. Dubath, X. Dupac, S. Escoffier, M. Farina, R. Farinelli, S. Ferriol, F. Finelli, P. Fosalba, S. Fotopoulou, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, K. George, B. Gillis, P. Gómez-Alvarez, J. Gracia-Carpio, A. Grazian, F. Grupp, S. V. H. Haugan, H. Hoekstra, M. S. Holliman, W. Holmes, F. Hormuth, A. Hornstrup, K. Jahnke, M. Jhabvala, B. Joachimi, S. Kermiche, A. Kiessling, B. Kubik, M. Kunz, H. Kurki-Suonio, S. Ligori, P. B. Lilje, V. Lindholm, I. Lloro, G. Mainetti, O. Mansutti, O. Marggraf, M. Martinelli, N. Martinet, F. Marulli, R. J. Massey, E. Medinaceli, M. Meneghetti, E. Merlin, G. Meylan, A. Mora, M. Moresco, E. Munari, R. Nakajima, C. Neissner, S.-M. Niemi, J. W. Nightingale, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, V. Pettorino, G. Polenta, M. Poncet, L. A. Popa, L. Pozzetti, F. Raison, A. Renzi, J. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, C. Rosset, R. Saglia, A. G. Sánchez, D. Sapone, M. Schirmer, P. Schneider, A. Secroun, G. Seidel, E. Sihvola, P. Simon, C. Sirignano, G. Sirri, L. Stanco, P. Tallada-Crespí, A. N. Taylor, I. Tereno, N. Tessore, S. Toft, R. Toledo-Moreo, F. Torradeflot, I. Tutusaus, J. Valiviita, T. Vassallo, G. Verdoes Kleijn, Y. Wang, A. Zacchei, G. Zamorani, F. M. Zerbi, E. Zucca, J. García-Bellido, J. Martín-Fleitas, V. Scottez, M. Viel

Robotics

Walking on the Slope: Stable Bipedal Gaits with Genetic-Algorithm-Optimized Trajectories

Madhav Rijal

This paper presents the kinematic and dynamic modeling, trajectory generation, and stability analysis of an 8-degree-of-freedom (DOF) biped robot walking on flat and inclined terrain. Denavit-Hartenberg (DH) parameters and homogeneous transformations are used to derive the forward kinematics, while closed-form inverse kinematics maps the desired hip and swing-foot Cartesian trajectories, generated with cubic splines, to joint angles. Joint torques are computed using the Newton-Euler iterative algorithm, and dynamic stability is evaluated using the zero moment point (ZMP) criterion. A genetic algorithm (GA) optimizes the hip height, maximum swing-foot lift, and frontal-plane tilt angle by minimizing the work done by the joints subject to a ZMP feasibility penalty. Simulation results in MATLAB show that the nominal 8-DOF model remains ZMP-stable for step completion times down to 0.5 s and for slope inclinations up to 22.5 degrees with the given foot geometry. Beyond these limits, the ZMP leaves the support polygon, and either the foot dimensions or the trajectory parameters must be modified. The results also show that ZMP stability is governed by the mass distribution among the links rather than the total mass of the robot.
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Networking

Value-Based Massive Access through Goal-Oriented Irregular Repetition Slotted ALOHA

Pietro Talli, Andrea Munari, Federico Mason et al. (+2 more)

The goal-oriented communication paradigm is poised to enable novel real-time applications by easing the burden on communication networks while still delivering task-relevant information. However, efforts so far have focused on the encoding problem, while the design of medium access schemes is still in the early stages of development, especially when connectivity is to be provided to a massive number of devices, e.g., for remote monitoring. In this respect, existing goal-oriented approaches are often centralized or based on simplified underlying mechanisms, requiring unrealistic assumptions. In this work, we present the Goal-oriented Irregular Repetition Slotted ALOHA (GO-IRSA) scheme, which combines modern random access techniques with belief-based policies. GO-IRSA does not impose significant computing loads on the sensors or require frequent feedback, and it can reduce the average and worst-case error of the estimate of a distributed Wiener process by over 30% with respect to the optimal centralized solution in a network with thousands of sensors, and is robust to imperfect interference cancellation and inaccurate process knowledge.
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All authors Pietro Talli, Andrea Munari, Federico Mason, Federico Chiariotti, Andrea Zanella

Group Theory

The variety generated by all additively idempotent semirings of order four

Mengya Yue and Xiaolei Shao

We prove that the variety generated by all four-element additively idempotent semirings has no finite basis for its identities.

Number Theory

Rogers–Ramanujan identities from the geometry of $X^a=Y^b$

Yifeng Huang, Kenny Lau and Ken Ono

We prove the conjecture of Huang, Jiang, and Oblomkov (HJO) giving a geometric extension of the Rogers–Ramanujan and Andrews–Gordon identities for every torus-knot singularity $X^a=Y^b$ with coprime $1<a<b.$ For a prime power $q$, let $\mathcal{NC}_n^{a,b}(\mathbb F_q)$ denote the set of pairs of commuting nilpotent $n\times n$ matrices $(A,B)$ over $\mathbb F_q$ satisfying $A^a=B^b$. We establish the threefold equality between their normalized counts, the HJO $q$-series $Z_{a,b}$, and the explicit infinite product $P_{a,b}$: \[ \underbrace{\vphantom{\Bigg|} \prod_{m\geq1}(1-q^{-m}) \Biggl(\sum_{n=0}^{\infty} \frac{\lvert\mathcal{NC}_n^{a,b}(\mathbb F_q)\rvert} {\lvert\operatorname{GL}_n(\mathbb F_q)\rvert}\Biggr) }_{\text{point count}} = \underbrace{\vphantom{\Bigg|}Z_{a,b}(q^{-1}) }_{\text{\(q\)-series}} = \underbrace{\vphantom{\Bigg|}P_{a,b}(q^{-1}) }_{\text{infinite product}}. \] Our main result is a stronger finite identity: the rank $N$ HJO sum equals $(q;q)_N$ times the generating function for balanced cylindric partitions with entries bounded by $N$. Taking $N\to\infty$ yields the HJO conjecture. The proof combines the compositional rational shuffle theorem of Bergeron–Garsia–Leven–Xin and Mellit with a multiplicativity theorem for slope operators and a determinantal model for bounded cylindric partitions, linked by a common $q$-difference equation. The finite identity and the HJO conjecture have been formalized unconditionally in Lean by AxiomProver.
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Robotics

OmniMimic: Dynamics-completed Motion Augmentation for Multi-style Omnidirectional Quadruped Locomotion

Sheng Wu, Guoqiang Zhao, Zhe Yang et al. (+7 more)

Animal demonstrations provide quadruped robots with natural and distinctive gait styles that are difficult to specify through hand-crafted rewards. However, their narrow directional coverage leaves little style-consistent supervision for backward, lateral, and turning commands. We present OmniMimic, a training framework that turns directionally limited animal demonstrations into a single multi-gait policy over target per-axis velocity ranges. OmniMimic first combines temporal reversal, constrained dynamics completion, and sagittal reflection to construct robot-specific kinematic and physical supervision beyond the observed directions. It then expands commands progressively from the demonstrated velocity distribution toward the target per-axis bounds, and uses a shared actor with soft-gated, gait-specialized residual experts to balance reusable locomotion skills with gait-specific corrections. Across four gaits in simulation, OmniMimic reduces mean foot-position RMSE at forward and backward reference velocities by 12.9% and velocity-tracking RMSE on a uniform Cartesian command grid by 63.1%, compared with the matched APEX baseline. The project page is at https://OmniMimic.github.io.
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All authors Sheng Wu, Guoqiang Zhao, Zhe Yang, Fei Teng, Zhikun Zhou, Yanlin Yang, Zheng Fang, Hong Zheng, Yaonan Wang, Kailun Yang

Computation and Language

Steering the Compass: Aligning Dynamic Psychological Counseling Conversations with Cognitive Behavioral Therapy Strategies

Zimu Wang, Yiwen Jiang, Xiangyu Zhao et al. (+10 more)

Recent advancements in large language models have revolutionized the field of psychological counseling, especially in the context of Cognitive Behavioral Therapy (CBT). While the success of CBT relies heavily on dynamic decision-making informed by the client's real-time mental state, this aspect has often been overlooked in current research, limiting both flexibility and therapeutic outcomes. In this paper, we introduce StratCBT, a dataset specifically designed for psychological counseling conversations with CBT Strategies, consisting of 9,688 sessions and around 256K utterances, with each counselor's response aligned with one of eight distinct strategies. The creation of StratCBT involves modeling clients based on their negative thoughts and generating high-quality counseling conversations through self-chat, incorporating realistic sessions as guidance, thereby significantly surpassing existing datasets in both general counseling and CBT-specific skills. We conduct extensive experiments to demonstrate the effectiveness of strategy-aligned generation and evaluate its efficacy in delivering professional and effective counseling with LLM-simulated clients to reflect real-world scenarios. The dataset can be obtained from https://github.com/zimuwangnlp/StratCBT.
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All authors Zimu Wang, Yiwen Jiang, Xiangyu Zhao, Yaling Shen, Jiahe Liu, Stephanie Fong, Maxmartwell H Cheng, Guilherme C Oliveira, Anh Nguyen, Robert Desimone, Barnaby Nelson, Dominic Dwyer, Zongyuan Ge

Geophysics

Multi-Track Time-Series Burst-Overlap Interferometry for Resolving Horizontal Deformation in Earthquake-Cycle Studies

Xing Li, Zhuang Gao, Han Chen et al. (+3 more)

Interferometric Synthetic Aperture Radar (InSAR) is intrinsically insensitive to the north-south component of crustal motion because of its near-polar geometry, which makes accurate quantification of this deformation a persistent limitation of InSAR. We introduce a Multi-track Time-Series Burst-Overlap Interferometry (MTSB) framework that delivers absolute, ITRF-referenced deformation fields across representative interseismic, coseismic, and postseismic applications by combining optimized phase linking, a unified time-series framework for separating deformation and residual misregistration, and block-wise spectral analysis. Case studies spanning co-, inter-, and postseismic phases demonstrate that MTSB accurately resolves along-track horizontal deformation, with primary sensitivity to north-south motion, while substantially reducing orbit-related artifacts. Independent comparisons with GNSS indicate centimeter-level agreement for postseismic and coseismic displacement estimates and millimeter-per-year agreement for interseismic velocities. The resulting deformation fields improve constraints on regional plate kinematics and fault kinematics, facilitate more reliable Euler-pole estimation, and provide by-product orbital corrections for conventional InSAR processing.
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All authors Xing Li, Zhuang Gao, Han Chen, Zhangfeng Ma, Yangkang Chen, Alexandros Savvaidis

Information Retrieval

Reasoning Quality Matters: Combating Reasoning Collapse in LLM-based Embedding Learning

Zihan Gong, Xiaohan Ye, Jiangchao Yao et al. (+3 more)

Large Language Models (LLMs) have recently shown strong potential for producing context-rich text embeddings for retrieval. Most existing methods either treat embedding learning as passive feature extraction or exploit LLM reasoning through instruction following for better embedding optimization. However, specialization toward embedding objectives can suppress useful reasoning generation or produce retrieval-irrelevant text. We refer to these two forms of degradation as reasoning collapse. To address this issue, we propose CoFree (Collapse-Free Reasoning Embedding), a two-stage framework that progressively integrates LLM reasoning into query and document embedding optimization while preserving reasoning quality. At the first stage, CoFree applies reference-guided supervised fine-tuning to restore the reasoning ability and retain representational strength of the foundation embedding model. At the second stage, we introduce dual rewards, an embedding-oriented reward and a reasoning-oriented reward, to guarantee fine-grained reasoning of the relevance toward the embedding goal in reinforcement learning. This endpoint-coupled optimization transforms embedding learning from static alignment into a high-quality reasoning-guided search process for retrieval. Extensive experiments demonstrate the effectiveness of CoFree, with CoFree-4B achieving an average absolute improvement of 2.8 nDCG@10 points over Qwen3-Embedding-4B across 22 datasets from MTEB and BRIGHT. Online experiments in a real-world retrieval system further show consistent gains. Code, RTED, and model checkpoints will be made publicly available.
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All authors Zihan Gong, Xiaohan Ye, Jiangchao Yao, Jinsong Lan, Xiaoyong Zhu, Xu Chen

Computer Vision

A Dual-Stream Regulated Reconstruction and Segmentation Network with Hierarchical Artifact-Prior Modeling for Ultra-Low-Field Pediatric Neuroimaging

Bahram Jafrasteh, Leo Milecki and Qingyu Zhao

Automated quality assessment, enhancement, and segmentation of multiple structures in $0.064\,\mathrm{T}$ ultra-low-field pediatric MRI are limited by a low signal-to-noise ratio, weak anatomical boundaries, and frequent artifacts. We present a unified framework for the LISA 2026 Challenge that performs all three tasks together within one inference pipeline. A network with two coupled streams, built on a 3D U-Net, first reconstructs an enhanced uLF volume and then combines the original and enhanced images for subcortical segmentation. To improve boundary stability, we add an auxiliary class covering brain tissue outside the target structures, derived from whole brain masks. A head conditioned on an artifact graph predicts the seven artifact ratings from reconstruction residuals and frozen segmentation features. We address the scarcity of dense annotations using diffeomorphic registration from atlas to target for label propagation and to regularize anatomical reconstruction. We report validation results across all three tasks.
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Cryptography and Security

Empirical Analysis of Randomness Quality in Differential Privacy Mechanisms

Cesare Gerolimetto Fabrello, Valeria Rossi, Alberto Trombetta et al. (+1 more)

Differential Privacy (DP) relies on carefully calibrated random noise to protect individual privacy in statistical analyses. While theoretical work has analyzed DP under weakened randomness assumptions, the practical consequences of entropy degradation remain poorly understood. We present a systematic empirical investigation of how randomness quality affects differential privacy mechanisms using IBM's DiffPrivLib. We introduce progressively degraded entropy sources characterized by established test suites, starting from high-quality quantum True Random Number Generators (TRNGs) and cryptographically secure Pseudo-Random Number Generators (PRNGs) down to systematically manipulated sources with controlled entropy degradation. Through repeated experiments over one million queries on a reference database and complementary statistical tests, we directly analyze empirical Privacy Loss Random Variable distributions. Our results demonstrate that DP mechanisms reliably detect deviations when approximately 1 bit in every 8 to 16 is manipulated, with detection sensitivity varying significantly between bit-level biases and temporal correlations. We demonstrate that statistical detection of distributional anomalies does not necessarily correspond to actual privacy guarantee violations.
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All authors Cesare Gerolimetto Fabrello, Valeria Rossi, Alberto Trombetta, Massimo Caccia

Astrophysics of Galaxies

Intracluster light in the infall region of simulated protoclusters of galaxies

S. V. Werner, M. Jauzac, M. Montes et al. (+4 more)

Intracluster light (ICL) is a diffuse stellar component in galaxy clusters, made of stars following the potential of the cluster. Despite its potential to unveil the accretion history of clusters, the ICL in protoclusters remains poorly understood in simulations and observations. We analyse protoclusters in TNG-Cluster and Manhattan Suite simulations to investigate when ICL forms, its host progenitors, and environments where it forms. We find a considerable amount of ICL in the infall region of protoclusters at 2<z<4, ranging from $\rm 0.1\times10^{11}$<$M_{*}/M_{\odot}$<$3\times10^{11}$. ICL star formation in protoclusters peaks at 3<z<4, with stars formed in the main halo forming earlier than those born in the infall regions. We find that $74.2_{-1.7}^{+1.7}\%$ of ICL stars in TNG-Cluster and $69.2_{-3.7}^{+3.6}\%$ in Manhattan Suite were stripped from galaxies within the main halo. However, most ICL stars in protoclusters at z=2 formed in the infall region, accounting for $57.6_{-1.6}^{+1.7}\%$ and $55.6_{-2.3}^{+2.3}\%$ in TNG-Cluster and Manhattan Suite, respectively. By the time the ICL stars are stripped, their host galaxies are 3-4 times more massive than the galaxies in which the stars originally formed, implying growth of the progenitor galaxies and/or accretion of the stars onto more massive galaxies prior to stripping. The ICL stellar masses measured in simulations agree with observations at z$\leq$2. Our findings highlight the importance of investigating the diffuse light in the outer regions of protoclusters to constrain the formation and assembly of the ICL and galaxy clusters.
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All authors S. V. Werner, M. Jauzac, M. Montes, D. Rennehan, G. Mahler, A. Niemiec, Y. Jiménez-Teja

Optics

High-order correlations and ultrafast Wigner negativities in bright-squeezed-vacuum-driven high-harmonic generation

Sebastián de-la-Peña, Heiko Appel, Marcelo F. Ciappina et al. (+2 more)

High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.
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All authors Sebastián de-la-Peña, Heiko Appel, Marcelo F. Ciappina, Ofer Neufeld, Angel Rubio