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Papers

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All of arXiv

Monday 21 September

Number Theory

On the generation of multiplicative groups by small primes

Oleksiy Klurman, Igor E. Shparlinski and Joni Teräväinen

Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^\times$ when each prime may be used with exponent only $0$ or $1$. We prove that, for every fixed $\varepsilon>0$ and $A>0$, there is an absolute constant $C_*$ and a set of at most $(\log Q)^{1+\varepsilon}$ primes, all at most $(\log Q)^{C_*(A+1)}$, such that for all but $O(Q(\log Q)^{-A})$ (with the implied constant depending only on $\varepsilon$ and $A$) integers $q\leq Q$, every element of $({\mathbb Z}/q{\mathbb Z})^\times$ is a product of a subset of these primes modulo $q$. The exponent $1+\varepsilon$ in the number of primes is best possible up to the arbitrary $\varepsilon$ in the exponent.
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General Relativity and Quantum Cosmology

A Systematic Study of Resonance-Driven Flux Modifications in Extreme-Mass-Ratio Inspirals

Edoardo Levati, Lennox S. Keeble and Alejandro Cárdenas-Avendaño

Transient orbital resonances can introduce phase-dependent corrections to the evolution of extreme-mass-ratio inspirals (EMRIs), potentially altering their long-term dynamics and emitted gravitational-wave signals. In this work, we quantify the resonance-induced modifications to the energy, axial angular momentum, and Carter constant fluxes and compute the corresponding resonance coefficients across a broad region of the orbital parameter space. Using the publicly available $\texttt{pybhpt}$ code, we solve the Teukolsky equation in the frequency domain to coherently combine the degenerate radial and polar harmonics that arise at resonance. We analytically derive a selection rule governing the relative radial-polar phase dependence of the resonant flux modifications. We argue that the relative strength of the resonant flux modifications reflects a balance between symmetry-induced cancellations and the degree to which the resonant orbit samples the underlying two-dimensional orbital phase space. For the dynamically important $3{:}2$ and $2{:}1$ resonances, we also characterize how the resonance coefficients vary with the primary black-hole spin, orbital eccentricity and inclination. Our results constitute the largest set of Teukolsky-based resonance coefficients calculated to date and provide essential input for future studies of transient orbital resonances in EMRIs.
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Mathematical Physics

On soliton asymptotics for Maxwell–Lorentz equations with rotating particle

Elena Kopylova

We consider the 2D Maxwell–Lorentz equations with an extended charged rotating particle. The system admits soliton solutions corresponding to a particle moving with a constant velocity and rotating with a constant angular velocity. Our main result is the asymptotic stability of the solitons.
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Combinatorics

Asymmetric Homomorphism Thresholds for Graphs of Large Odd Girth

Romain Bourneuf, Raphael Steiner, Stéphan Thomassé et al. (+1 more)

We determine the asymmetric homomorphism threshold from graphs of odd girth at least $7$ to triangle-free graphs, showing that $\delta_{\mathrm{hom}}(\{C_3,C_5\},\{C_3\})=\frac{1}{9}$. Equivalently, for every $\varepsilon>0$, every $n$-vertex graph of odd girth at least $7$ and minimum degree at least $(1/9+\varepsilon)n$ admits a homomorphism to a triangle-free graph of size bounded by a function of $\varepsilon$, while there exist graphs of odd girth at least $7$ and minimum degree at least $(1/9-\varepsilon)n$ for which no such bounded-size triangle-free homomorphic image exists. More generally, for every $t\geq 3$, we prove $\delta_{\mathrm{hom}}(\{C_3,C_5\},\{K_t\})=\frac{1}{3t}$. In particular, for every proper monotone class $\mathcal C$ of graphs, the threshold for graphs of odd girth at least $7$ to admit a homomorphism to a bounded-size graph in $\mathcal C$ is positive. We further extend this phenomenon to arbitrary odd girth: for every $k\geq 2$ and every proper monotone subclass $\mathcal C$ of the class of graphs of odd girth at least $2k-1$, the threshold for graphs of odd girth at least $2k+3$ to admit a homomorphism to a bounded-size graph in $\mathcal C$ is positive. These results disprove conjectures of Gishboliner, Hurley and Wigderson and exhibit a sharp contrast with the corresponding zero chromatic-threshold results. Our lower-bound constructions are based on high-dimensional Borsuk graphs, while the matching upper bounds use regularity arguments to recover the structure underlying these constructions.
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All authors Romain Bourneuf, Raphael Steiner, Stéphan Thomassé, Yuval Wigderson

Cosmology and Nongalactic Astrophysics

Cross-Bispectrum Constraints from HI Intensity Mapping and Galaxy Surveys

Warren Naidoo, Moumita Aich and Kavilan Moodley

Future neutral hydrogen (HI) intensity mapping (IM) and optical surveys probe large-scale structure over unprecedented volumes, offering powerful constraints on cosmological models. We study the cross-correlation between the HI IM field and the galaxy density and cosmic shear fields from optical surveys. By formulating the HI-HI-galaxy and HI-HI-shear cross-bispectra, we recover sensitivity to long-wavelength radial modes otherwise removed by foreground subtraction in HI maps, evaluating their detectability for HIRAX and Rubin-LSST. Combining the probes breaks degeneracies in redshift-dependent quantities, including the $f$-$\sigma_8$ degeneracy. Our constraints range from $0.74\%$ to $9.8\%$ on $f$ and $0.073\%$ to $3.5\%$ on $\sigma_8$ across the six redshift bins that we consider. Our constraints on the first- and second-order HI bias parameters range from $0.42\%$ to $5.6\%$ on $b_{\rm HI}^{(1)}$ and from $2.0\%$ to $29\%$ on $b_{\rm HI}^{(2)}$, while the galaxy bias constraints range from $2.6\%$ to $11\%$ on $b_{\rm gal}.$ The HI-HI-galaxy density cross-bispectrum measurement allows us to constrain a linear scale-dependent model for the stochastic cross-correlation coefficient between HI and stars, $r_{{\rm HI \,HI\,}\delta_g} = r_0 + r_1 k,$ with a break scale of $0.14\,\mbox{Mpc}^{-1}.$ We obtain $r_0$ constraints that range from $3.8\%$ to $13.5\%$ and $r_1$ constraints that range from $7.5\%$ to $19.9\%$. For cosmology, adding cross-bispectra enhances Lambda CDM constraints, notably via the HI-HI-shear cross-bispectrum. For the $w_0\, w_a$CDM model, the power-spectrum-only constraints on $w_0$ and $w_a,$ including Planck priors, improve from $(\sigma_{w_0},\sigma_{w_a})=(0.036,0.15)$ and $(0.032,0.12)$ to $(\sigma_{w_0},\sigma_{w_a})=(0.014,0.057)$ and $(0.015,0.059)$ when adding the HI-HI-galaxy and HI-HI-shear cross-bispectra, respectively.
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Machine Learning (Statistics)

PICPIs: Prediction-Interval-Conditional Prediction Intervals

Xuelin Yang, Baihe Huang, Yilong Hou et al. (+2 more)

A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal prediction in nonparametric uncertainty quantification, standard marginal validity offers limited resolution at the prediction values on which decisions are based, and fully conditional guarantees with respect to the covariates are provably unattainable. We address this gap by introducing a prediction-based conditioning framework that we refer to as Prediction-Interval-Conditional Prediction Intervals (PICPIs). Formally, a PICPI is an interval $I$ satisfying a self-consistency condition: $$\mathbb{E} [Y \mid p(X) \in I] \in I,$$ for predictive model $p$, contextual covariate $X$, and outcome $Y$. Thus, an interval simultaneously defines a stratum of prediction values and certifies that the mean outcome in that stratum lies in the same interval. This self-consistency condition yields data-adaptive strata without altering the original prediction. Such intervals can be constructed using practical algorithms. Under regularity of the prediction distribution, the constructed intervals cover all but an arbitrarily small fraction of prediction values and have widths that decrease at rate $n^{-1/3}$, up to logarithmic factors and the prediction error. Moreover, identifying these locally calibrated intervals can, in turn, inform downstream decision-making. We derive inference procedures for PICPIs in probabilistic prediction and multi-class classification, accompanied by theoretical guarantees. Empirical results are provided that compare PICPIs with existing interval-based baselines.
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All authors Xuelin Yang, Baihe Huang, Yilong Hou, Guido Imbens, Michael I. Jordan

General Relativity and Quantum Cosmology

Cosmology in sixth-order higher-derivative theories of gravity

Carlos Aguilar, Manuel Asorey, Diego Muñoz et al. (+1 more)

We analyze the cosmological implications of theories of gravity with quadratic curvature invariants $R^2$ and $C^{\mu\nu\rho\sigma}C_{\mu\nu\rho\sigma}$, and six-derivative operators $R\Box R$ and $C^{\mu\nu\rho\sigma}\Box C_{\mu\nu\rho\sigma}$. We first analyze homogeneous and isotropic cosmological solutions, showing that the theory admits expanding, recollapsing and non-singular bouncing solutions. We clarify in the Einstein-frame formulation the mechanism that circumvents the Hawking–Penrose singularity theorems, and identify the role played by the additional higher-derivative degrees of freedom in that mechanism. We show that the complete set of linear equations governing tensor perturbations on standard backgrounds admit analytically stable solutions. The analysis reveals that the stability properties are determined by the pole structure of the propagator and by specific relations among the higher-derivative couplings, while the singularity-free backgrounds are found to be unstable against tensor perturbations. For scalar cosmological perturbations, the higher-derivative theories presents super-horizon scalar instabilities in de Sitter spacetimes for both quadratic and sixth-order gravity. To extract inflationary observables, we adopt an EFT approach to the sixth-order theory, treating these terms as perturbative corrections around the Starobinsky background. Within this framework, we compute the modification of the primordial scalar and tensor power spectra, obtaining predictions for the scalar spectral index and tensor-to-scalar ratio. We find that sixth-order operators produce controlled deviations from the Starobinsky model while preserving the EFT expansion, thereby providing a consistent phenomenological framework to probe ultraviolet gravitational corrections through cosmological observables.
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All authors Carlos Aguilar, Manuel Asorey, Diego Muñoz, Miguel Pardina

Computer Vision

Sex Estimation from Footwear Outsole Impressions Using CNN Transfer Learning and Interpretable Image Statistics

Jinyi Niu, Ziyi Song and Weining Shen

Footwear outsole impressions are a common form of forensic pattern evidence, yet quantitative methods for estimating wearer attributes from these images remain relatively underdeveloped. We investigate binary sex estimation from footwear outsole impressions by comparing convolutional neural network (CNN) transfer learning with traditional feature-based classification. Using a publicly available outsole-impression dataset, we adopt a shoe-level training and test partition that keeps replicate scans of the same physical shoe together to reduce data leakage. We evaluate pretrained CNNs through end-to-end fine-tuning, frozen feature extraction followed by support vector machine classification, and hybrid feature fusion incorporating handcrafted, geometric, and metadata-derived descriptors. Fine-tuned CNNs achieve the strongest overall predictive performance and substantially outperform traditional classifiers trained on the manually specified descriptors alone, while frozen-feature approaches offer a less computationally demanding alternative. Exploratory analysis of low-dimensional CNN representations reveals associations with frequency threshold ratio, image contrast, and wavelet-based summaries, providing a connection between learned representations and measurable properties of outsole impressions. These findings suggest that CNN transfer learning captures discriminative information beyond the descriptors considered and offers a promising approach to footwear-based forensic screening. Further validation on independently collected and casework-like impressions is needed before operational use.
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Strongly Correlated Electrons

Lattice in Line: Optimized DMRG ordering for complex lattice geometries

Roman Rausch

The density-matrix renormalization group (DMRG) is a one-dimensional tensor-network technique, but it is not limited to one-dimensional systems: it can be applied to periodic 2D and 3D clusters and molecules, provided their sites are first enumerated along a line; a step one may call "lattice compilation". This paper discusses three proxy loss functions for finding this optimal enumeration: the graph bandwidth $B$ (maximum interaction range), the cutwidth $C$ (maximum number of bonds crossing a cut), and the average interaction range $R$. Constructing the Hamiltonian MPO (matrix-product operator) for a large set of clusters that are of interest in frustrated magnetism, I find that $C$ determines the peak SU(2) Heisenberg MPO bond dimension and $R$ the average one. Targeting $(C,R)$ lexicographically yields the best energies. Targeting $B$ indirectly reduces $C$, but not as efficiently as targeting $C$ directly. Otherwise, the value of $B$ itself is largely irrelevant in the sense that good DMRG energies can have large $B$. To perform the optimization, classic heuristics (e.g. reverse Cuthill–McKee) prove unreliable even for small clusters, and I find that a QUBO formulation improves them only marginally. Instead I propose a staged optimization built on Boolean satisfiability (SAT) and constraint-programming (CP) solvers, chiefly CP-SAT of Google's OR-Tools, a hybrid of CP propagation and SAT clause learning. This approach yields significantly better orderings together with rigorous bounds. The corresponding Lattice in Line code is available at https://github.com/spinflip/lattice_in_line and was designed with extensive use of the Fable 5 large language model.
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High Energy Physics (Experiment)

Spin-spin correlations in $\Lambda\bar{\Lambda}$ pair production at the SPD experiment at NICA

D. Gubachev and A. Guskov

Recent measurements by the STAR collaboration have demonstrated that spin correlations of $\Lambda\bar{\Lambda}$ pairs provide sensitivity to the spin structure of $s\bar{s}$ pairs and to spin transfer during hadronization.These results, together with recent CMS measurements at higher energies, open a new avenue for studying spin dynamics in the transition from partons to hadrons. A feasibility study of spin-spin correlations in $\Lambda\bar{\Lambda}$ pairs at the SPD experiment at NICA is presented for $pp$ and $dd$ collisions at $\sqrt{s_{NN}}\leq27$~GeV. The expected correlation $P_{\Lambda\bar{\Lambda}}$ is estimated within the SU(6) and Burkardt–Jaffe models for a spin-triplet $s\bar{s}$ pair. The kinematic properties of the process are analysed, and the suitability of the detector for such measurements is evaluated using a full simulation. The SPD experiment provides an opportunity to investigate the relative contributions of non-perturbative and perturbative $s\bar{s}$-production mechanisms and, with polarized beams, to study the role of initial-state polarization in spin-dependent partonic dynamics.
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Quantum Physics

Complementarity Test with Unmeasured, Permanently Inaccessible Path Markers

Paul Gauthier, Sahil Patel, Sean Doan et al. (+1 more)

In prior complementarity tests, path markers were measured and remained causally accessible, leaving the collapse-locality loophole open. We address this loophole using a quantum eraser that isolates the encoding of path information in the joint quantum state from its later measurement and causal accessibility. We launch idler photons – the sole path markers for entangled signal photons in an interferometer – on outgoing null trajectories while the joint state remains in a coherent superposition of both interferometer path alternatives. Our flat $\Lambda$CDM transmission model predicts that 73-82% of launched idlers will propagate forever without absorption, scattering, or environmental path-record formation. For these modeled survivors, each path marker remains perpetually unmeasured, and propagation along its outgoing trajectory precludes later causal contact with its interferometric record. Unconditioned signal detections show no statistically significant launch-induced change in interference, as standard quantum theory predicts. Normalized to the modeled survivors, the 95% confidence upper bound on any launch-induced fringe is 0.16 of full restoration.
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All authors Paul Gauthier, Sahil Patel, Sean Doan, Galan Moody

Machine Learning (Statistics)

Penalized Nonreversible Langevin for Constrained Sampling

Pervez Ali, Weihao Dong and Xiaoyu Wang

We propose penalized nonreversible Langevin algorithms for sampling from $\pi(x)\propto e^{-f(x)}\mathbf 1_{\mathcal C}(x)$, where $\mathcal C\subset\mathbb R^d$ is a compact convex set. The algorithms combine a squared distance penalty with constant or compatible state dependent skew symmetric perturbations that preserve the penalized Gibbs distribution. For smooth, possibly nonconvex $f$, we derive nonasymptotic total variation bounds for the full gradient algorithm under a log Sobolev inequality. When unbiased stochastic gradients are available, we establish $2$-Wasserstein bounds under global contraction and Lipschitz conditions on the full drift in an adapted quadratic metric. For a fixed penalty parameter, the error relative to the penalized Gibbs distribution decays exponentially to an $\mathcal{O}(\sqrt{\eta})$ neighborhood, where $\eta$ is the stepsize. We also bound the discrepancy between the penalized Gibbs distribution and the constrained target. In a two dimensional quadratic model, we establish nonreversible acceleration by tuning the skew perturbation to the curvature imbalance induced by penalization. With the target accuracy and smaller curvature fixed and initial Wasserstein distances uniformly bounded, tuning the skew perturbation improves the sufficient Euler iteration bound from linear to logarithmic in the curvature ratio. Numerical experiments evaluate the algorithms on constrained Bayesian regression, classification, neural networks, and truncated sampling, and examine the acceleration mechanism in a stochastic quadratic model.
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Probability

Stein Solution Factors via Mills Ratios: Affine Birth Rates and Symmetric Potential Distributions

Peter Eichelsbacher

We study Stein solution factors for indicator test functions by a common Mills-ratio method in discrete and continuous settings. In the discrete case, a general birth–death formulation gives exact solution envelopes and recovers the first-increment theory of Brown and Xia. For binomial and Poisson targets, and for negative binomial targets with shape parameter $r\ge1$, the additional algebraic structure of affine birth rates yields improved uniform bounds for the Stein solution. In the continuous case, we consider symmetric densities proportional to $e^{-V}$. Under natural structural assumptions on the potential $V$, Mills ratios yield explicit finite bounds for the indicator Stein solution and show that the uniform derivative and drift Stein factors have the sharp value $1$. Under an additional one-crossing condition, the solution-factor optimization can be carried out exactly and gives the optimal value $1/(4p(0))$. The even-power targets arising in statistical mechanics, including the quartic critical Curie–Weiss law, provide the original examples, and the calculation extends to the wider Subbotin family. For $1<\beta<2$ in the Subbotin family, the exact envelope has two off-center maximizers characterized by a unique incomplete-gamma equation, while the two first-order factors remain equal to $1$. The results exhibit a common discrete–continuous mechanism behind improved and, in the continuous sharp regime, optimal Stein solution factors.
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Sound

Narrowband Voice Communication Using Streaming Neural Compression

Dahong Luo, Anannya Trehan, Aritrik Ghosh et al. (+1 more)

Low-bitrate speech communication on resource-constrained edge devices remains challenging due to stringent computational, memory, and bandwidth constraints. We present TinyCall, a lightweight neural audio codec designed for real-time speech communication on low-power platforms such as the ESP32 microcontroller and Raspberry Pi. The proposed system targets emergency communication and other bandwidth-limited scenarios while preserving speech intelligibility, speaker identity, and vocal expressiveness. To enable efficient deployment, we propose a minimal neural audio codec architecture together with a framework for converting a causally trained codec into a truly streamable codec through pseudo-lookahead decoding and decoder-input caching. We further replace conventional residual vector quantization (RVQ) with Residual Finite Scalar Quantization (RFSQ) to reduce inference complexity on edge processors and employ a progressive three-stage training strategy for stable optimization under latent quantization. An MFCC-based perceptual loss encourages preservation of speaker characteristics, including harmonic structure and vocal timbre. Experimental results demonstrate real-time operation on a Raspberry Pi 3 while achieving intelligible speech reconstruction at bitrates as low as 2.3 kbps. The proposed approach demonstrates that practical neural speech communication is feasible on highly resource-constrained edge devices.
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All authors Dahong Luo, Anannya Trehan, Aritrik Ghosh, Nirupam Roy

Geometric Topology

Cannon-Thurston maps and measures

Ursula Hamenstaedt

We give a short proof of the following extension of a recent result of Gadre, Maher, Pfaff and Uyanki: Consider a closed hyperbolic 3-manifold M which fibers over the circle, with fiber a closed surface S. Any measure class on the ideal boundary of hyperbolic 3-space which is invariant and totally ergodic under the action of the fundamental group of M is singular with respect to the push-forward by a Cannon-Thurston map of a stationary measure on the circle of a random walk with finite first moment on the fundamental group of S.
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Statistical Computation

Some surprising properties of essential data points visualization

Hamideh Bakhshi, Hamid Abdollahi and Róbert Rajkó

Essential Data Points (EDPs) - the vertices of the convex hull of a bilinear data matrix $\mathbf{D}$ in its row space, column space, or both - are widely used in chemometrics to reduce the size of large data sets while nominally preserving their underlying geometric structure. Using simulated three- and two-component chromatographic/spectral data sets and a real source-apportionment data set ($\mathbf{D = C\, A^\mathsf{T}}$), together with Borgen-Rajkó plots, Procrustes analysis, and variance-covariance comparisons, we show that this preservation is only partial: row-wise EDP reduction preserves the row-space geometry (inner and outer polygons) exactly while distorting the column-space geometry, and column-wise reduction shows the opposite behavior; joint row-and-column reduction distorts both. We then give a rigorous, general proof - based on the four fundamental subspaces of a matrix and its singular value decomposition $\mathbf{D = U\,S\,V^\mathsf{T}}$ - that the subspace which is not being reduced is always preserved exactly, up to an orthogonal rotation, whereas the subspace whose ambient dimension shrinks is related to the original only through a general, non-orthogonal isomorphism. This distinction is confirmed numerically to machine precision ($\sim 10^{-14}$-$10^{-16}$) on the real data set, and a deliberate negative control confirms that the "ambient-shrinking" map is genuinely non-orthogonal (residual $\approx 1$). These results demonstrate that the apparent rotation of an EDP-reduced polygon relative to the original is not, in general, a rigid rotation, and that visual or numerical comparisons between an EDP-reduced data set and the original data require an explicit, mode-dependent change-of-basis correction before any geometric or statistical conclusion can be drawn. A MATLAB implementation of this correction is provided.
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Robotics

VLAQuantBench: Closed-Loop Evaluation of Post-Training Quantization for Vision-Language-Action Models

Jiuyi Xu, Qing Jin, Meida Chen et al. (+3 more)

Post-training quantization reduces the memory requirements of vision-language-action (VLA) models, but precision selection must account for the interaction between layer scope, numerical format, and calibration. We introduce VLAQuantBench, a controlled evaluation with 409 runs and 94,574 simulation episodes: four models on LIBERO, with X-VLA additionally evaluated on three simulation benchmark families. Under uncalibrated W4A4 round-to-nearest quantization, expanding a $\pi_{0.5}$ action-head subset from 126 to 167 layers raises success from 7.0% to 70.5%. Fixed-observation replay confirms a corresponding numerical recovery. Two-episode calibration removes the severe joint failures in the tested subsets, whereas the same smoothing-and-clipping recipe lowers $\pi_0$ success and does not recover OpenVLA-OFT end-to-end. For OpenVLA-OFT, protecting one 28,672-parameter output projection instead restores near-baseline success: the remaining 441 eligible linear layers retain W3 on LIBERO-Long or eight-bit activations across all four suites. Task-clustered intervals support the large failure and recovery contrasts. These results establish recipe-dependent interactions and identify concrete precision assignments, rather than universal layer-sensitivity rules. Real-kernel and physical-robot measurements complement the accuracy analysis. Code, configurations, and episode records are publicly available at https://github.com/jiuyixu25/VLAQuantBench.
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All authors Jiuyi Xu, Qing Jin, Meida Chen, Song Wang, Yang Sui, Yangming Shi

Robotics

PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration

Abolfazl Babanazari, Carson Cramer, Tyler Summers et al. (+2 more)

Global point-cloud registration remains challenging when limited overlap, repetitive geometry, and sensor noise produce correspondence sets dominated by outliers. Planar regions are particularly difficult for conventional point descriptors and are therefore often suppressed or discarded before matching. We present PARTE (Plane-Assisted Robust Transformation Estimation), a global registration method that instead treats planar structure as complementary registration evidence. PARTE extracts planar patches and represents them using our novel Plane Context Histogram (PCH), a descriptor that encodes the geometry surrounding each patch, while a two-level matching procedure identifies reliable plane correspondences. Candidate point and plane correspondences are combined in a confidence-weighted compatibility graph for joint outlier rejection, followed by rigid transformation estimation. When no usable plane correspondences are available, PARTE naturally reduces to point-only registration. We evaluate PARTE on 8,097 registration pairs across six indoor and outdoor benchmarks spanning dense RGB-D and sparse LiDAR measurements. Evaluations show PARTE achieves the highest overall success rate against 13 standard and state-of-the-art methods while maintaining low runtime. An open-source C++ implementation with Python bindings is provided at https://ariarobotics.github.io/parte/.
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All authors Abolfazl Babanazari, Carson Cramer, Tyler Summers, Carlos Nieto, Kaveh Fathian

Robotics

Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study

Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin et al. (+1 more)

Human gait in reality extends beyond straight-line walking, with some situations even requiring drastic back-and-forth rotations. A smooth and stable execution may seem intuitive, but the underlying mechanics remains unknown. The Karate roundhouse kick may be an extreme case of exhibiting dynamic back-and-forth rotations, but investigating the angular momentum (AM) management can potentially inform stability analysis in dynamic human motions and smoother gait in robots and exoskeletons. This paper introduces two new AM-based measures and analyzes AM-related variables to study the target-less retractable back-leg Karate roundhouse kick. The purpose is to understand the underlying AM management, analyze the differences between stable and unstable kicks, and investigate how these variables and measures change over time with improvement. A one-year longitudinal study was conducted with the first author as a Karate student, and a Karate instructor was also recruited for one session as an expert, whose data is used for comparison. Results show that unstable kicks have higher peak total AM before Strike and smaller braking peak after Strike. The proposed AM-based measures are able to identify the cause of some unstable kicks, though no clear distinction could be made between stable and unstable kicks since kicks can be unstable for different reasons. Nonetheless, the proposed measures can be applied as performance measures to analyze other types of dynamic motions. To incorporate them as stability criteria, however, it is recommended to also consider their coordination with time, kinematics, and center of pressure.
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All authors Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin, Katja Mombaur

Machine Learning

Extending FunctionGemma for Practical On-Device Mobile Function Calling

Ali Rezagholizadeh and Soheila Samiee

On-device assistants require function-calling models that map natural language to local system actions, but existing resources emphasize web APIs or narrow mobile-action catalogs. We extend FunctionGemma 270M-it to practical Android workflows by introducing MOBILEACTIONSEXTENDED, a synthetic, schema-validated dataset of ~9,500 conversations covering fifteen device-control categories, including messaging, phone calls, camera/screenshot, brightness control, device-status queries, flashlight control, and application management. We fine-tune the 270M model with TRL supervised fine-tuning under completion-only loss, producing an extended specialist and a combined model trained jointly with Google's MOBILEACTIONSGOOGLE. On MOBILEACTIONSEXTENDED, end-to-end accuracy improves from 29.3% for the base model and 17.2% for Google's Mobile-Actions variant to 76.5%. The combined model retains 76.5% on MOBILEACTIONSEXTENDED and reaches 82.3% on MOBILEACTIONSGOOGLE, down from the 90.3% of Google's Mobile-Actions specialist, representing an 8.0-percentage-point trade-off in return for doubling category coverage. We release the dataset, fine-tuned models, reproducible training/evaluation pipeline, and an Android demo, highlighting compact local function calling as a practical path towards low-latency and privacy-preserving mobile assistants.
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Optimization and Control

Optimal Control of Traveler Testing in Epidemic Models

Maria Teresa Chiri, Christopher Denaro, Xiaoqian Gong et al. (+1 more)

We propose an optimal control framework for mitigating cross-border epidemic spread through testing of incoming travelers. The general model considers multiple countries with SEIR dynamics, while the explicit analysis focuses on a simplified two country SIR system without vaccination. The control variable is a time measurable function representing the testing rate. For the two country SIR case, we show the optimal control is bang bang by excluding singular arcs via Hamiltonian analysis and derive the optimal switching time. Our results offer theoretical insights and practical guidelines for designing cost effective border testing policies. We then present numerical simulations for the optimal control in the two population setting.
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All authors Maria Teresa Chiri, Christopher Denaro, Xiaoqian Gong, Benedetto Piccoli

Astrophysics of Galaxies

SALVAGE II: no systematic molecular gas depletion in the central 2 kpc of AGN hosts

Scott Wilkinson, Chiara Circosta, Toby Brown et al. (+5 more)

In cosmological simulations, active galactic nuclei (AGN) feedback is found to be necessary for the shutdown of galaxy-wide star-formation by heating and/or removing molecular gas. However, at low-redshift, there is little evidence of systematic large-scale gas depletion. Some recent observations have found molecular gas depletion in AGN hosts, but limited to the central regions of galaxies. In this work, we use the SDSS-ALMA Legacy-Value Archival Gas Exploration (SALVAGE) dataset, which provides molecular gas and stellar mass measurements from the inner (r < 0.5-2 kpc) and outer region of the galaxy. Using AGN diagnostics from optical emission lines, mid-IR colour, and X-ray luminosity, we identify 70 AGN at z < 0.07 and inspect their central molecular gas reservoirs with a suite of metrics compared to non-AGN controls. In agreement with global studies of low-z AGN hosts, we find that, compared to matched non-AGN, the central regions of AGN have equal molecular gas fractions and enhanced molecular gas surface densities. For the first time, we explore the central gas reservoirs of AGN identified with different selection criteria and find two optical AGN classes that show a tentative 1.5$\sigma$ and 1.8$\sigma$ signal of central molecular gas depletion. However, the AGN with central gas depletion do not occupy any specific region of the parameter space, such as AGN luminosity, that can provide a physical explanation for the depletion. If AGN are responsible for large-scale gas removal, the lack of systematic gas depletion in SALVAGE AGN sets an upper limit on the physical scale of the gas removal while the AGN remains observable.
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All authors Scott Wilkinson, Chiara Circosta, Toby Brown, Sara L. Ellison, Shoshannah Byrne-Mamahit, Almudena Alonso-Herrero, Santiago Garcia-Burillo, Federico Esposito

High Energy Physics (Experiment)

Measurement of the $\Omega_b^-$ baryon lifetime

LHCb collaboration: R. Aaij, M. Abdelfatah, A.S.W. Abdelmotteleb et al. (+1187 more)

The lifetime ratio ${r_{\tau}\equiv\tau_{\Omega_b^-}/\tau_{\Xi_b^-}}$ between the ${{\Omega_b^-}}$ and ${{\Xi_b^-}}$ baryons is measured using a sample of $pp$ collision data corresponding to an integrated luminosity of 6 fb$^{-1}$ and collected by the LHCb experiment during LHC Run 2 (2015$-$2018). The ratio $r_{\tau}$ is measured in two sets of decays modes, ${ {(\Omega_b^-,\Xi_b^-)\to(\Omega_c^0\pi^-,\Xi_c^0\pi^-)}}$ and ${{(\Omega_b^-,\Xi_b^-)\to(J/\psi\Omega^-, J/\psi\Xi^-)}}$, with ${{(\Omega_c^0,\Xi_c^0)\to pK^-K^-\pi^+}}$, ${{(\Omega^-,\Xi^-)\to(\Lambda^0 K^-,\Lambda^0\pi^-)}}$, ${{\Lambda^0\to p\pi^-}}$ and $J/\psi\to\mu^+\mu^-$. The measured $r_{\tau}$ values are averaged and combined with Run 1 (2011$-$2012) measurements in the same decay modes to obtain ${r_{\tau} = 1.109\pm0.055\pm0.010}$. Multiplying by the known ${{\Xi_b^-}}$ lifetime results in the ${{\Omega_b^-}}$ lifetime ${\tau_{\Omega_b^-} = 1.751\pm0.089\pm0.022~{\rm ps}}$, where the uncertainties are statistical and systematic. This measurement improves on the precision of the $\Omega_b^-$ lifetime by about a factor of two over the previous world average. The value of $r_{\tau}$ is in agreement with the most recent theoretical predictions from the heavy quark expansion framework.
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All authors LHCb collaboration: R. Aaij, M. Abdelfatah, A.S.W. Abdelmotteleb, C. Abellan Beteta, F. Abudinén, T. Ackernley, A.A. Adefisoye, B. Adeva, M. Adinolfi, P. Adlarson, C. Agapopoulou, C.A. Aidala, S. Akar, K. Akiba, H. Al Saleh, P. Albicocco, J. Albrecht, R. Aleksiejunas, F. Alessio, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, J.L. Amey, Y. Amhis, Z. Amos, L. An, L. Anderlini, P. Andreola, M. Andreotti, S. Andres Estrada, A. Anelli, D. Ao, C. Arata, F. Archilli, Z. Areg, M. Argenton, S. Arguedas Cuendis, L. Arnone, M. Artuso, E. Aslanides, R. Ataíde Da Silva, M. Atzeni, B. Audurier, J.A. Authier, D. Bacher, I. Bachiller Perea, S. Bachmann, M. Bachmayer, J.J. Back, M. Bai, Z.B. Bai, V. Balagura, A. Balboni, W. Baldini, Z. Baldwin, L. Balzani, H. Bao, J. Baptista de Souza Leite, C. Barbero Pretel, I.R. Barbosa, W. Barker, R.J. Barlow, M. Barnyakov, S. Baron, S. Barsuk, W. Barter, J. Bartz, S. Bashir, B. Batsukh, P.B. Battista, A. Bavarchee, A. Bay, A. Beck, M. Becker, F. Bedeschi, I.B. Bediaga, N.A. Behling, S. Belin, A. Bellavista, I. Belyaev, G. Bencivenni, E. Ben-Haim, J.L.M. Berkey, R. Bernet, A. Bertolin, L. Bertsch, F. Betti, J. Bex, O. Bezshyyko, S. Bhattacharya, M.S. Bieker, N.V. Biesuz, A. Biolchini, M. Birch, F.C.R. Bishop, A. Bitadze, A. Bizzeti, T. Blake, F. Blanc, J.E. Blank, S. Blusk, J.A. Boelhauve, O. Boente Garcia, T. Boettcher, A. Bohare, C. Bolognani, R.B. Bonacci, A. Bordelius, F. Borgato, S. Borghi, M. Borsato, J.T. Borsuk, E. Bottalico, S.A. Bouchiba, M. Bovill, T.J.V. Bowcock, A. Boyer, C. Bozzi, J.D. Brandenburg, A. Brea Rodriguez, N. Breer, C. Breitfeld, J. Brodzicka, J. Brown, E. Buchanan, M. Burgos Marcos, C. Burr, E. Butera, C. Buti, J.S. Butter, W. Byczynski, S. Cadeddu, H. Cai, Y. Cai, Y. Cai, A. Caillet, R. Calabrese, L. Calefice, M. Calvi, M. Calvo Gomez, P. Camargo Magalhaes, J.I. Cambon Bouzas, P. Campana, A. Campomagnani, A.C. Campos, A.F. Campoverde Quezada, Y. Cao, S. Capelli, M. Caporale, L. Capriotti, R. Caravaca-Mora, A. Carbone, L. Carcedo Salgado, R. Cardinale, A. Cardini, P. Carniti, L. Carus, R. Caspary, G. Casse, M. Cattaneo, G. Cavallero, V. Cavallini, S. Celani, I. Celestino, S. Cesare, A.J. Chadwick, M. Charles, Ph. Charpentier, E. Chatzianagnostou, R. Cheaib, M. Chefdeville, C. Chen, J. Chen, S. Chen, Z. Chen, A. Chen Hu, M. Cherif, S. Chernyshenko, X. Chiotopoulos, G. Chizhik, V. Chobanova, A. Christakakis, M. Chrzaszcz, Y. Chu, V. Chulikov, P. Ciambrone, X. Cid Vidal, P. Cifra, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, C. Cocha Toapaxi, V. Coco, A. Codovini, C.S. Codovini, J. Cogan, E. Cogneras, L. Cojocariu, S. Collaviti, P. Collins, T. Colombo, M. Colonna, A. Comerma-Montells, L. Congedo, J. Connaughton, A. Contu, N. Cooke, A. Corallo, G. Cordova, C. Coronel, I. Corredoira, A. Correia, G. Corti, G.C. Costantino, C. Cotirlan, J. Cottee Meldrum, B. Couturier, D.C. Craik, N. Crepet, M. Cruz Torres, M. Cubero Campos, E. Curras Rivera, R. Currie, C.L. Da Silva, X. 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Zheng, Y. Zheng, T. Zhou, X. Zhou, V. Zhovkovska, L.Z. Zhu, X. Zhu, X. Zhu, Y. Zhu, V. Zhukov, J. Zhuo, T. Zies, D. Zuliani, X. Zuo

Robotics

Capability-Aware Arbitration for Semantic Intent-Based Shared Control

Zhaoda Du, Michael Bowman and Xiaoli Zhang

Shared control often allocates robot authority based on confidence in inferred human intent, assuming reliable autonomous execution. When this assumption fails, high intent confidence can cause over-helping. We present a capability-aware shared-control framework in which a vision-language model (VLM) infers human intent and provides semantic-intent confidence, while a vision-language-action (VLA) policy generates autonomous actions. VLA capability confidence is estimated online from the dispersion and local instability of stochastic action trajectories. We design a nonlinear arbitration policy that combines Bayesian-filtered semantic-intent confidence with VLA capability confidence through a sigmoid mapping to adapt robot authority. Our evaluation combined VLM/VLA confidence assessment with a study involving 12 participants performing pick-and-place and bidirectional stacking under in-distribution and out-of-distribution conditions. The proposed method achieved the highest task success rate (92%), compared with manual teleoperation (83%), intent-only arbitration (44%), and fixed equal-weight blending (10%). It also achieved higher control friendliness and lower authority-weighted disagreement than both shared-control baselines. These results demonstrate the benefit of incorporating VLA capability into authority allocation to mitigate over-helping and improve shared-control performance.
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Quantum Physics

Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size

Roman Ovsiannikov, Kurt Jacobs, Andrii G. Sotnikov et al. (+1 more)

The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below $10^{-5}$, the method is up to two orders of magnitude faster than QuTiP already at $D \approx 500$, and its runtime scales nearly linearly.
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All authors Roman Ovsiannikov, Kurt Jacobs, Andrii G. Sotnikov, Denys I. Bondar

Number Theory

Irreducible polynomials with restricted digits in base $b(T)$

Juan Arévalo and Matilde Lalín

We study monic irreducible polynomials over $\mathbb{F}_q[T]$ whose non-leading digits, with respect to an arbitrary polynomial base $b(T)$, avoid a prescribed set of forbidden digits. Identifying the digit set with the ring $D=\mathbb{F}_q[T]/(b)$, we obtain an asymptotic formula for the number of such irreducible polynomials under conditions given in terms of Fourier parameters of the allowed digit set. The main term contains a singular series measuring the relative density of units among the allowed digits, while the error term is controlled by both pointwise and averaged Fourier estimates. As a consequence, we obtain a general criterion depending only on the cardinality of the forbidden set, as well as stronger results for structured restrictions, including examples in which the forbidden set contains a positive proportion of all digits. In particular, we treat additive cosets, restrictions compatible with the Chinese remainder decomposition of $D$, and coefficient-wise restrictions. The proof adapts the function field circle method for restricted coefficients to arbitrary polynomial bases.
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Artificial Intelligence

From Decorative to Load-Bearing: Task Difficulty Shapes the Causal Role of Chain-of-Thought

Renee Jia and Di Mu

Chain-of-thought (CoT) monitoring is only meaningful if written reasoning causally constrains the answer. We introduce continuation-based causal testing, an ablation-patch intervention that perturbs one reasoning step, truncates the chain, and forces the model to continue from the corrupted prefix. It measures how load-bearing a CoT is for the final answer, a behavioral notion distinct from mechanistic faithfulness. Across Gemma-2-9B-IT, Llama-3.1-8B-Instruct, and DeepSeek-R1-Distill-Qwen-7B on GSM8K, MMLU, and BIG-Bench Hard, CoT load-bearingness tracks model-relative task difficulty: on easy tasks models silently bypass their own reasoning; on hard tasks they follow corrupted steps and propagate errors. A matched 2x2 analysis shows task difficulty dominates perturbation type: error propagation rises 16x from GSM8K to BBH multistep arithmetic, and a variance partition over 28,584 continuations attributes 98.8% of explained deviance to task difficulty versus 0.8% to perturbation type. Reasoning-specific RL suppresses error propagation and compresses the gradient. A four-variant judge-sensitivity analysis and blind two-annotator study (n=500) show the error-propagation vs. non-propagation label is invariant to judge prompt, with perfect inter-annotator agreement (Cohen's kappa = 1.00). This gradient creates a structural problem for CoT-based oversight and AI safety monitoring: where the trace is easy to read it carries little signal, and where it matters errors propagate before a monitor can intervene. Linear probes on hidden states separate silent bypass, self-correction, and error propagation, but additive activation steering provides limited causal control, flipping only about 25% of error-propagation cases at best. Behavioral mode is readable but not reliably controllable.
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Cryptography and Security

Quantum ROP: Using Quantum Algorithms for ROP Chain Selection in Exploit Construction

Carlos Benitez

The quantum computing threat to cybersecurity is nowadays predominantly framed around Shor's algorithm and its eventual capacity to break asymmetric cryptography. Beyond cryptanalysis, however, quantum computing may also enable other capabilities in offensive security. This work explores one such direction: the application of quantum combinatorial optimization to Return-Oriented Programming (ROP) gadget selection for exploit construction. We formulate gadget selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem that captures individual gadget cost and inter-gadget register-clobbering interactions, and solve it using QAOA on real IBM Heron r2 hardware. Applied to a Linux kernel exploitation scenario, the QAOA-selected chain achieves privilege escalation to uid=0 with SMEP and SMAP active. Across eight Linux binaries and 16 benchmark instances, QAOA recovered the lowest-cost valid chain in 11 cases; in the remaining five, it did not recover the optimum, with the failures associated with excessive circuit depth on current limited hardware.
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