This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation -- high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.

The rise of 3D generative models has enabled automatic 3D geometry and texture synthesis from multimodal inputs (e.g., text or images). However, these methods often ignore physical constraints and manufacturability considerations. In this work, we address the challenge of producing 3D designs that are both lightweight and self-supporting. We present DensiCrafter, a framework for generating lightweight, self-supporting 3D hollow structures by optimizing the density field. Starting from coarse voxel grids produced by Trellis, we interpret these as continuous density fields to optimize and introduce three differentiable, physically constrained, and simulation-free loss terms. Additionally, a mass regularization penalizes unnecessary material, while a restricted optimization domain preserves the outer surface. Our method seamlessly integrates with pretrained Trellis-based models (e.g., Trellis, DSO) without any architectural changes. In extensive evaluations, we achieve up to 43% reduction in material mass on the text-to-3D task. Compared to state-of-the-art baselines, our method could improve the stability and maintain high geometric fidelity. Real-world 3D-printing experiments confirm that our hollow designs can be reliably fabricated and could be self-supporting.

Figure 7: Jet images averaged over 10000 jet samples.

Abstract--Dynamic modeling and control are critical for unleashing soft robots' potential, yet remain challenging due to their complex constitutive behaviors and real-world operating conditions. Bio-inspired musculoskeletal robots, which integrate rigid skeletons with soft actuators, combine high load-bearing capacity with inherent flexibility. Although actuation dynamics have been studied through experimental methods and surrogate models, accurate and effective modeling and simulation remain a significant challenge, especially for large-scale hybrid rigid-soft robots with continuously distributed mass, kinematic loops, and diverse motion modes. T o address these challenges, we propose EquiMus, an energy-equivalent dynamic modeling framework and MuJoCo-based simulation for musculoskeletal rigid-soft hybrid robots with linear elastic actuators. The equivalence and effectiveness of the proposed approach are validated and examined through both simulations and real-world experiments on a bionic robotic leg. EquiMus further demonstrates its utility for downstream tasks, including controller design and learning-based control strategies.

Aerosol-cloud--radiation interactions remain among the most uncertain components of the Earth's climate system, in partdue to the high dimensionality of aerosol state representations and the difficulty of obtaining complete \textit{in situ} measurements. Addressing these challenges requires methods that distill complex aerosol properties into compact yet physically meaningful forms. Generative autoencoder models provide such a pathway. We present a framework for learning deep variational autoencoder (VAE) models of speciated mass and number concentration distributions, which capture detailed aerosol size-composition characteristics. By compressing hundreds of original dimensions into ten latent variables, the approach enables efficient storage and processing while preserving the fidelity of key diagnostics, including cloud condensation nuclei (CCN) spectra, optical scattering and absorption coefficients, and ice nucleation properties. Results show that CCN spectra are easiest to reconstruct accurately, optical properties are moderately difficult, and ice nucleation properties are the most challenging. To improve performance, we introduce a preprocessing optimization strategy that avoids repeated retraining and yields latent representations resilient to high-magnitude Gaussian noise, boosting accuracy for CCN spectra, optical coefficients, and frozen fraction spectra. Finally, we propose a novel realism metric -- based on the sliced Wasserstein distance between generated samples and a held-out test set -- for optimizing the KL divergence weight in VAEs. Together, these contributions enable compact, robust, and physically meaningful representations of aerosol states for large-scale climate applications.

Figure 7: Jet images averaged over 10000 jet samples.

The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from critical limitations: spherical harmonics diverge within the Brillouin sphere where spacecraft typically operate, polyhedral models assume unrealistic homogeneous density distributions, and existing machine learning methods like GeodesyNets and Physics-Informed Neural Networks (PINN-GM) require extensive computational resources and training time. This work introduces Mascon-Cubes, a novel self-supervised learning approach that formulates gravity inversion as a direct optimization problem over a regular 3D grid of point masses (mascons). Unlike implicit neural representations, MasconCubes explicitly model mass distributions while leveraging known asteroid shape information to constrain the solution space. Comprehensive evaluation on diverse asteroid models including Bennu, Eros, Itokawa, and synthetic planetesimals demonstrates that MasconCubes achieve superior performance across multiple metrics. Most notably, MasconCubes demonstrate computational efficiency advantages with training times approximately 40 times faster than GeodesyNets while maintaining physical interpretability through explicit mass distributions. These results establish MasconCubes as a promising approach for mission-critical gravitational modeling applications requiring high accuracy, computational efficiency, and physical insight into internal mass distributions of irregular celestial bodies.

We present a Reinforcement Learning (RL)-based locomotion system for Cosmo, a custom-built humanoid robot designed for entertainment applications. Unlike traditional humanoids, entertainment robots present unique challenges due to aesthetic-driven design choices. Cosmo embodies these with a disproportionately large head (16% of total mass), limited sensing, and protective shells that considerably restrict movement. To address these challenges, we apply Adversarial Motion Priors (AMP) to enable the robot to learn natural-looking movements while maintaining physical stability. We develop tailored domain randomization techniques and specialized reward structures to ensure safe sim-to-real, protecting valuable hardware components during deployment. Our experiments demonstrate that AMP generates stable standing and walking behaviors despite Cosmo's extreme mass distribution and movement constraints. These results establish a promising direction for robots that balance aesthetic appeal with functional performance, suggesting that learning-based methods can effectively adapt to aesthetic-driven design constraints.

This study presents a grasping method for objects with uneven mass distribution by leveraging diffusion models to localize the center of gravity (CoG) on unknown objects. In robotic grasping, CoG deviation often leads to postural instability, where existing keypoint-based or affordance-driven methods exhibit limitations. We constructed a dataset of 790 images featuring unevenly distributed objects with keypoint annotations for CoG localization. A vision-driven framework based on foundation models was developed to achieve CoG-aware grasping. Experimental evaluations across real-world scenarios demonstrate that our method achieves a 49\% higher success rate compared to conventional keypoint-based approaches and an 11\% improvement over state-of-the-art affordance-driven methods. The system exhibits strong generalization with a 76\% CoG localization accuracy on unseen objects, providing a novel solution for precise and stable grasping tasks.

--Underactuated wheeled vehicles are commonly studied as nonholonomic systems with periodic actuation. Twistcar is a classical example inspired by a riding toy, which has been analyzed using a planar model of a dynamical system with nonholonomic constraints. Most of the previous analyses did not account for energy dissipation due to frictional resistance. In this work, we study a theoretical two-link model of the Twistcar while incorporating dissipation due to rolling resistance. We obtain asymptotic expressions for the system's small-amplitude steady-state periodic dynamics, which reveals the possibility of reversing the direction of motion upon varying the geometric and mass properties of the vehicle. Next, we design and construct a robotic prototype of the Twistcar whose center-of-mass position can be shifted by adding and removing a massive block, enabling experimental demonstration of the Twistcar's direction reversal phenomenon. We also conduct parameter fitting for the frictional resistance in order to improve agreement with experiments.