arXiv subjects

Junyan Xu

Publications and source records attributed to Junyan Xu.

14 recordsLinked to original sources

arXiv2026

DynaMOMA: Instantaneous Prediction of Grasp Poses for Mobile Manipulation of Dynamic Objects

Mobile manipulation is a fundamental robotics task and has advanced rapidly in recent years, enabling robots to navigate, reach, and interact with objects in complex environments. However, mobile manipulation of dynamic objects remains highly challenging, as robots must coordinate the mobile base and arm while adapting to continuously evolving target poses. A key challenge lies in predicting temporally consistent short-horizon grasp trajectories from dynamic observations. In this work, we propose \ours{}, a dynamic mobile manipulation framework that couples instantaneous grasp trajectory prediction with whole-body control policy. Our predictor uses an anchor-based diffusion model to generate temporally consistent short-horizon grasp trajectories conditioned on historical observations. The predicted trajectories are then encoded as compact features and fed to a whole-body reinforcement learning policy, which controls the mobile manipulator for dynamic grasping. We further introduce a anticipation-guided reward that equips the policy with an anticipatory grasping horizon by adaptively shifting the target from the current grasp observation to the instantaneously predicted grasp trajectory. Through extensive experiments in Isaac Gym simulation, we show that our method achieves strong performance in mobile manipulation of dynamic objects across diverse settings and grasping metrics. Furthermore, our predictor and policy demonstrate strong generalizability in real-world experiments.

cs.RO↗

arXiv2026

PAIWorld: A 3D-Consistent World Foundation Model for Robotic Manipulation

World foundation models (WFMs) are powerful simulators, yet they predominantly operate in a single-view setting and lack the multi-view 3D consistency required for robotic manipulation. While robotic systems rely on multiple cameras (egocentric, eye-to-hand, and wrist-mounted) for policy learning, current multi-view world models simply concatenate view tokens without explicit geometric reasoning. This causes cross-view object drift, depth inconsistency, and texture misalignment. We trace these failures to two deficiencies: the absence of an explicit inter-view communication mechanism and the lack of a 3D geometric prior. We argue that resolving both simultaneously is necessary and sufficient. To address this, we present PAIWorld, a framework that augments diffusion-transformer world models via three core components: (1) Geometry-Aware Cross-View Attention blocks that establish an explicit pathway across views, (2) Geometric Rotary Position Embedding that encodes camera ray directions and extrinsic poses into the attention mechanism, and (3) Latent 3D-REPA, which distills 3D-aware features from frozen 3D foundation models to ensure 3D consistency. Built upon a DiT-based world foundation model, PAIWorld achieves state-of-the-art multi-view 3D consistency on robotic manipulation benchmarks, ranking 1st on the WorldArena leaderboard and 2nd on the AgiBot-Challenge2026 leaderboard, while enabling downstream applications such as model-based planning, world action models, and multi-view policy post-training.

cs.RO↗

arXiv2026

On Elliptic Sequences over Commutative Rings

We define elliptic sequences over a commutative ring as sequences indexed by the (positive) integers satisfying a 4-parameter, highly symmetric family of homogeneous quartic relations among terms which we call elliptic relations. We classify elliptic sequences over a field into three types, and show that most of them are dilated multiples of standard elliptic divisibility sequences (EDSs) which form countably many 4-dimensional families. In particular, we show standard EDSs are elliptic in a purely algebraic way using intricate implications among elliptic relations, without relying on complex analytic theory of Weierstrass functions. We shall use results presented here to give a purely algebraic treatment of division polynomials in a follow-up paper.

math.NT↗

arXiv2025

Galaxy Protoclusters as Drivers of Cosmic Reionization: I. Bubble Overlap at Redshift z ~ 7 in LAGER-z7OD1

Since the launch of JWST, the sample size of reionization-era Lyman-alpha-emitters (LAEs) has been steadily growing; yet inferences about the neutral hydrogen fraction in the intergalactic medium exhibit increasing variance at redshift z ~ 7, possibly indicating significant field-to-field fluctuations in the progression of cosmic reionization. In this paper, we present new JWST/NIRSpec and Keck/LRIS spectra of nine LAEs in the redshift z ~ 7 protocluster, LAGER-z7OD1. Measurements of Lyman-alpha-transmission and Lyman-alpha velocity offset along multiple sightlines map the Lyman-alpha damping wing optical depth across the galaxy overdensity. In the standard context of inside-out ionization, we estimate radii of ionized bubbles (R(min) = 0.07 - 0.69 Mpc) based on the distance from each LAE to the first neutral patch along the sightline. The resulting 3D topology reveals three distinct sub-clusters where the ionized bubbles are approaching overlap. Five of the nine LAEs plausibly ionized their bubbles, a few bursts of star formation and a modest escape fraction are sufficient. We demonstrate, however, that the actual ionized volumes are likely larger, at least R(ism) = 0.42 - 1.29 Mpc, based on an empirical model for interstellar attenuation of Lyman-alpha. Modeling galactic attenuation of Lyman-alpha significantly increases the inferred intergalactic transmission (thus enlarging the ionized pathlength). The errorbars on the reddening correction allow fully overlapping bubbles, and our results are consistent with accelerated reionization in the protocluster.

astro-ph.GA↗

arXiv2025

Automated CAD Modeling Sequence Generation from Text Descriptions via Transformer-Based Large Language Models

Designing complex computer-aided design (CAD) models is often time-consuming due to challenges such as computational inefficiency and the difficulty of generating precise models. We propose a novel language-guided framework for industrial design automation to address these issues, integrating large language models (LLMs) with computer-automated design (CAutoD).Through this framework, CAD models are automatically generated from parameters and appearance descriptions, supporting the automation of design tasks during the detailed CAD design phase. Our approach introduces three key innovations: (1) a semi-automated data annotation pipeline that leverages LLMs and vision-language large models (VLLMs) to generate high-quality parameters and appearance descriptions; (2) a Transformer-based CAD generator (TCADGen) that predicts modeling sequences via dual-channel feature aggregation; (3) an enhanced CAD modeling generation model, called CADLLM, that is designed to refine the generated sequences by incorporating the confidence scores from TCADGen. Experimental results demonstrate that the proposed approach outperforms traditional methods in both accuracy and efficiency, providing a powerful tool for automating industrial workflows and generating complex CAD models from textual prompts. The code is available at https://jianxliao.github.io/cadllm-page/

cs.AI↗

arXiv2023

An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in any Characteristic

Elliptic curves are fundamental objects in number theory and algebraic geometry, whose points over a field form an abelian group under a geometric addition law. Any elliptic curve over a field admits a Weierstrass model, but prior formal proofs that the addition law is associative in this model involve either advanced algebraic geometry or tedious computation, especially in characteristic two. We formalise in the Lean theorem prover, the type of nonsingular points of a Weierstrass curve over a field of any characteristic and a purely algebraic proof that it forms an abelian group.

cs.LO↗

arXiv2022

Fusible numbers and Peano Arithmetic

Inspired by a mathematical riddle involving fuses, we define the "fusible numbers" as follows: $0$ is fusible, and whenever $x,y$ are fusible with $|y-x|<1$, the number $(x+y+1)/2$ is also fusible. We prove that the set of fusible numbers, ordered by the usual order on $\mathbb R$, is well-ordered, with order type $\varepsilon_0$. Furthermore, we prove that the density of the fusible numbers along the real line grows at an incredibly fast rate: Letting $g(n)$ be the largest gap between consecutive fusible numbers in the interval $[n,\infty)$, we have $g(n)^{-1} \ge F_{\varepsilon_0}(n-c)$ for some constant $c$, where $F_α$ denotes the fast-growing hierarchy. Finally, we derive some true statements that can be formulated but not proven in Peano Arithmetic, of a different flavor than previously known such statements: PA cannot prove the true statement "For every natural number $n$ there exists a smallest fusible number larger than $n$." Also, consider the algorithm "$M(x)$: if $x<0$ return $-x$, else return $M(x-M(x-1))/2$." Then $M$ terminates on real inputs, although PA cannot prove the statement "$M$ terminates on all natural inputs."

cs.LO↗

arXiv2020

On cyclic strong exceptional collections of line bundles on surfaces

We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation in the sense of L.Hille and M.Perling. We find simple geometric criteria of exceptionality (strong exceptionality, cyclic strong exceptionality) for collections of line bundles on weak del Pezzo surfaces. As a result, we classify smooth projective surfaces admitting a full cyclic strong exceptional collection of line bundles. Also, we provide an example of a weak del Pezzo surface of degree 2 and a full strong exceptional collection of line bundles on it which does not come from augmentations, thus answering a question by Hille and Perling.

math.AG↗

arXiv2019

Burgess bounds for short character sums evaluated at forms

In this work we establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to a very general class of "admissible" forms. This $n$-dimensional Burgess bound is nontrivial for sums over boxes of sidelength at least $q^β$, with $β> 1/2 - 1/(2(n+1))$. This is the first Burgess bound that applies in all dimensions to generic forms of arbitrary degree. Our approach capitalizes on a recent stratification result for complete multiplicative character sums evaluated at rational functions, due to the second author.

math.NT↗

arXiv2018

Optimal Two-impulse Space Interception with Multi-constraints

We consider optimal two-impulse space interception problems with multi-constraints. The multi-constraints are imposed on the terminal position of an interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. We formulate these optimization problems as multi-point boundary value problems and the calculus of variations is used to solve them. All inequality constraints are converted into equality constraints by using slackness variable methods in order to use Lagrange multiplier method. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is established for two-impulse space interception problems with multi-constraints. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions have been established based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur, and also if two impulse instants are free, then two-impulse space interception problems with velocity impulse constraints may degenerate to the one-impulse case.

math.OC↗

arXiv2017

Hohmann Transfer via Constrained Optimization

In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the Kuhn-Tucker theorem, we analytically prove the global optimality of the Hohmann transfer. Two sets of feasible solutions are found, one of which corresponding to the Hohmann transfer is the global minimum, and the other is a local minimum. In the second part, we formulate the Hohmann transfer problem as two-point and multi-point boundary-value problems by using the calculus of variations. With the help of the Matlab solver bvp4c, two numerical examples are solved successfully, which verifies that the Hohmann transfer is indeed the solution of these boundary-value problems. Via static and dynamic constrained optimization, the solution to the orbit transfer problem proposed by W. Hohmann ninety-two years ago and its global optimality are re-discovered.

eess.SY↗

arXiv2017

On exceptional collections of line bundles on weak del Pezzo surfaces

We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3$ is an augmentation in the sense of L.Hille and M.Perling, while for some weak del Pezzo surfaces of degree $2$ the above is not true. We classify smooth projective surfaces possessing a cyclic strong exceptional collection of line bundles of maximal length: we prove that they are weak del Pezzo surfaces and find all types of weak del Pezzo surfaces admitting such a collection. We find simple criteria of exceptionality/strong exceptionality for collections of line bundles on weak del Pezzo surfaces.

math.AG↗

arXiv2017

Stratification for multiplicative character sums

We prove a stratification result for certain families of $n$-dimensional (complete algebraic) multiplicative character sums. The character sums we consider are sums of products of $r$ multiplicative characters evaluated at rational functions, and the families (with $nr$ parameters) are obtained by allowing each of the $r$ rational functions to be replaced by an "offset", i.e. a translate, of itself. For very general such families, we show that the stratum of the parameter space on which the character sum has maximum weight $n+j$ has codimension at least $j\lfloor(r-1)/2(n-1)\rfloor$ for $1\le j\le n-1$ and $\lceil nr/2\rceil$ for $j=n$.

math.NT↗

arXiv2012

Survey on fusible numbers

We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties of fusible numbers. We suggest some possible approaches to the conjecture, and list further problems in the final chapter.

math.CO↗