arXiv subjects

Lucas Chen

Publications and source records attributed to Lucas Chen.

6 recordsLinked to original sources

arXiv2026

Bounding The Number of Zeros Near the Central Point in Families of Cuspidal Newforms

We study low-lying zeros in families of even holomorphic cuspidal newforms of fixed weight and prime level, with particular emphasis on the number of forms having a zero in a prescribed normalized window about the central point and on the distribution of the number of such zeros among the forms. We quantify the number of forms having at least one zero in the window and study the distribution of the number of zeros in that window among the forms. Assuming the Generalized Riemann Hypothesis, we obtain new lower bounds for the number of forms having a low-lying zero. We first prove that, along an infinite sequence of prime levels $N$, the number of such forms is $\gg N^{7/8}\log N$. We then use higher centered moments and an appropriate test function to show that a positive proportion of the family has a zero in a prescribed window. Finally, we obtain polynomial upper-tail bounds for the number of zeros occurring there and show that a positive proportion of forms have a bounded, nonzero number of low-lying zeros.

math.NT↗

arXiv2026

On the Existence of Hyperelliptic Curves over $\mathbb{Q}(T)$ with Certain Jacobian Ranks

Let $y^2 = f(x,T)$ be a hyperelliptic curve of genus $g\geq 1$, defined over $\mathbb{Q}(T)$. We prove the existence of infinitely many imaginary hyperelliptic curves with a fixed genus $g$ having a certain rank for $5\leq r\leq 4g+2$, and a similar result for real hyperelliptic curves with a fixed genus $g$ having a certain rank for $6\leq r\leq 4g+4$. We begin by constructing such curves and prove the rank using two methods. First, we apply the generalized Nagao's conjecture, which relates the first moment and the rank of the Jacobian variety $J_\mathcal{X}(\mathbb{Q}(T))$, and that the conjecture holds for our curves, making the result unconditional. Furthermore, we explicitly construct rational points in the Mordell-Weil group and use Shioda-Tate to prove that the rank is equal to $r$.

math.NT↗

arXiv2025

Differentiable Particle Optimization for Fast Sequential Manipulation

Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time and at large scales has remained out of reach due to computational requirements. Recently, GPU-based acceleration has shown promising results, but prior methods achieve limited performance due to CPU-GPU data transfer overhead and complex logic that prevents full hardware utilization. To this end, we present SPaSM (Sampling Particle optimization for Sequential Manipulation), a fully GPU-parallelized framework that compiles constraint evaluation, sampling, and gradient-based optimization into optimized CUDA kernels for end-to-end trajectory optimization without CPU coordination. The method consists of a two-stage particle optimization strategy: first solving placement constraints through massively parallel sampling, then lifting solutions to full trajectory optimization in joint space. Unlike hierarchical approaches, SPaSM jointly optimizes object placements and robot trajectories to handle scenarios where motion feasibility constrains placement options. Experimental evaluation on challenging benchmarks demonstrates solution times in the realm of $\textbf{milliseconds}$ with a 100% success rate; a $4000\times$ speedup compared to existing approaches. Code and examples are available at $\href{https://commalab.org/papers/spasm}{commalab.org/papers/spasm}$.

cs.RO↗

arXiv2025

Parallel Simulation of Contact and Actuation for Soft Growing Robots

Soft growing robots, commonly referred to as vine robots, have demonstrated remarkable ability to interact safely and robustly with unstructured and dynamic environments. It is therefore natural to exploit contact with the environment for planning and design optimization tasks. Previous research has focused on planning under contact for passively deforming robots with pre-formed bends. However, adding active steering to these soft growing robots is necessary for successful navigation in more complex environments. To this end, we develop a unified modeling framework that integrates vine robot growth, bending, actuation, and obstacle contact. We extend the beam moment model to include the effects of actuation on kinematics under growth and then use these models to develop a fast parallel simulation framework. We validate our model and simulator with real robot experiments. To showcase the capabilities of our framework, we apply our model in a design optimization task to find designs for vine robots navigating through cluttered environments, identifying designs that minimize the number of required actuators by exploiting environmental contacts. We show the robustness of the designs to environmental and manufacturing uncertainties. Finally, we fabricate an optimized design and successfully deploy it in an obstacle-rich environment.

cs.RO↗

arXiv2025

Multimodal Human-Intent Modeling for Contextual Robot-to-Human Handovers of Arbitrary Objects

Human-robot object handover is a crucial element for assistive robots that aim to help people in their daily lives, including elderly care, hospitals, and factory floors. The existing approaches to solving these tasks rely on pre-selected target objects and do not contextualize human implicit and explicit preferences for handover, limiting natural and smooth interaction between humans and robots. These preferences can be related to the target object selection from the cluttered environment and to the way the robot should grasp the selected object to facilitate desirable human grasping during handovers. Therefore, this paper presents a unified approach that selects target distant objects using human verbal and non-verbal commands and performs the handover operation by contextualizing human implicit and explicit preferences to generate robot grasps and compliant handover motion sequences. We evaluate our integrated framework and its components through real-world experiments and user studies with arbitrary daily-life objects. The results of these evaluations demonstrate the effectiveness of our proposed pipeline in handling object handover tasks by understanding human preferences. Our demonstration videos can be found at https://youtu.be/6z27B2INl-s.

cs.RO↗

arXiv2025

Physics-Grounded Differentiable Simulation for Soft Growing Robots

Soft-growing robots (i.e., vine robots) are a promising class of soft robots that allow for navigation and growth in tightly confined environments. However, these robots remain challenging to model and control due to the complex interplay of the inflated structure and inextensible materials, which leads to obstacles for autonomous operation and design optimization. Although there exist simulators for these systems that have achieved qualitative and quantitative success in matching high-level behavior, they still often fail to capture realistic vine robot shapes using simplified parameter models and have difficulties in high-throughput simulation necessary for planning and parameter optimization. We propose a differentiable simulator for these systems, enabling the use of the simulator "in-the-loop" of gradient-based optimization approaches to address the issues listed above. With the more complex parameter fitting made possible by this approach, we experimentally validate and integrate a closed-form nonlinear stiffness model for thin-walled inflated tubes based on a first-principles approach to local material wrinkling. Our simulator also takes advantage of data-parallel operations by leveraging existing differentiable computation frameworks, allowing multiple simultaneous rollouts. We demonstrate the feasibility of using a physics-grounded nonlinear stiffness model within our simulator, and how it can be an effective tool in sim-to-real transfer. We provide our implementation open source.

cs.RO↗