The problem of embedding a set of objects into a low-dimensional Euclidean space based on a matrix of pairwise dissimilarities is fundamental in data analysis, machine learning, and statistics. However, the assumptions of many standard analytical methods are violated when the input dissimilarities fail to satisfy metric or Euclidean axioms. We present the mathematical and statistical foundations of Topolow, a physics-inspired, gradient-free optimization framework for such embedding problems. Topolow is conceptually related to force-directed graph drawing algorithms but is fundamentally distinguished by its goal of quantitative metric reconstruction. It models objects as particles in a physical system, and its novel optimization scheme proceeds through sequential, stochastic pairwise interactions, which circumvents the need to compute a global gradient and provides robustness against convergence to local optima, especially for sparse data. Topolow maximizes the likelihood under a Laplace error model, robust to outliers and heterogeneous errors, and properly handles censored data. Crucially, Topolow does not require the input dissimilarities to be metric, making it a robust solution for embedding non-metric measurements into a valid Euclidean space, thereby enabling the use of standard analytical tools. We demonstrate the superior performance of Topolow compared to standard Multidimensional Scaling (MDS) methods in reconstructing the geometry of sparse and non-Euclidean data. This paper formalizes the algorithm, first introduced as Topolow in the context of antigenic mapping in (Arhami and Rohani, 2025) (open access), with emphasis on its metric embedding and mathematical properties for a broader audience. The general-purpose function Euclidify is available in the R package topolow.

--Despite extensive developments in motion planning of autonomous aerial vehicles (AA Vs), existing frameworks faces the challenges of local minima and deadlock in complex dynamic environments, leading to increased collision risks. T o address these challenges, we present TRUST -Planner, a topology-guided hierarchical planning framework for robust spatial-temporal obstacle avoidance. In the frontend, a dynamic enhanced visible probabilistic roadmap (DEV-PRM) is proposed to rapidly explore topological paths for global guidance. The backend utilizes a uniform terminal-free minimum control polynomial (UTF-MINCO) and dynamic distance field (DDF) to enable efficient predictive obstacle avoidance and fast parallel computation. Furthermore, an incremental multi-branch trajectory management framework is introduced to enable spatio-temporal topological decision-making, while efficiently leveraging historical information to reduce replanning time. Simulation results show that TRUST - Planner outperforms baseline competitors, achieving a 96% success rate and millisecond-level computation efficiency in tested complex environments. Real-world experiments further validate the feasibility and practicality of the proposed method. URRENTL Y, autonomous aerial vehicles (AA Vs) play an increasingly crucial role in widespread areas, e.g., transportation, search and rescue, and sightseeing [1]. With the deepening of these applications, AA Vs are required to operate in increasingly complex and dynamic flight environments, where moving obstacles, such as pedestrians, vehicles, and other AA Vs, present growing risks of collision [2].

-- T o address the challenges of localization drift and perception-planning coupling in unmanned aerial vehicles (UA Vs) operating in open-top scenarios (e.g., collapsed buildings, roofless mazes), this paper proposes EAROL, a novel framework with a downward-mounted tilted LiDAR configuration (20 inclination), integrating a LiDAR-Inertial Odometry (LIO) system and a hierarchical trajectory-yaw optimization algorithm. The hardware innovation enables constraint enhancement via dense ground point cloud acquisition and forward environmental awareness for dynamic obstacle detection. A tightly-coupled LIO system, empowered by an Iterative Error-State Kalman Filter (IESKF) with dynamic motion compensation, achieves high level 6-DoF localization accuracy in feature-sparse environments. Physical experiments demonstrate 81% tracking error reduction, 22% improvement in perceptual coverage, and near-zero vertical drift across indoor maze and 60-meter-scale outdoor scenarios. This work proposes a hardware-algorithm co-design paradigm, offering a robust solution for UA V autonomy in post-disaster search and rescue missions. I. INTRODUCTION Unmanned Aerial V ehicles (UA Vs) are currently widely used in various fields such as industry, agriculture, rescue operations, and photography [1]-[3].

Graph diffusion generative models (GDGMs) have emerged as powerful tools for generating high-quality graphs. However, their broader adoption faces challenges in \emph{scalability and size generalization}. GDGMs struggle to scale to large graphs due to their high memory requirements, as they typically operate in the full graph space, requiring the entire graph to be stored in memory during training and inference. This constraint limits their feasibility for large-scale real-world graphs. GDGMs also exhibit poor size generalization, with limited ability to generate graphs of sizes different from those in the training data, restricting their adaptability across diverse applications. To address these challenges, we propose the stochastic block graph diffusion (SBGD) model, which refines graph representations into a block graph space. This space incorporates structural priors based on real-world graph patterns, significantly reducing memory complexity and enabling scalability to large graphs. The block representation also improves size generalization by capturing fundamental graph structures. Empirical results show that SBGD achieves significant memory improvements (up to 6$\times$) while maintaining comparable or even superior graph generation performance relative to state-of-the-art methods. Furthermore, experiments demonstrate that SBGD better generalizes to unseen graph sizes. The significance of SBGD extends beyond being a scalable and effective GDGM; it also exemplifies the principle of modularization in generative modeling, offering a new avenue for exploring generative models by decomposing complex tasks into more manageable components.

Robotic arms mounted on spacecraft, known as space manipulator systems (SMSs), are critical for enabling on-orbit assembly, satellite servicing, and debris removal. However, controlling these systems in microgravity remains a significant challenge due to the dynamic coupling between the manipulator and the spacecraft base. This study explores the potential of using biological inspiration to address this issue, focusing on animals, particularly lizards, that exhibit mid-air righting reflexes. Based on similarities between SMSs and these animals in terms of behavior, morphology, and environment, their air-righting motion trajectories are extracted from high-speed video recordings using computer vision techniques. These trajectories are analyzed within a multi-objective optimization framework to identify the key behavioral goals and assess their relative importance. The resulting motion profiles are then applied as reference trajectories for SMS control, with baseline controllers used to track them. The findings provide a step toward translating evolved animal behaviors into interpretable, adaptive control strategies for space robotics, with implications for improving maneuverability and robustness in future missions.

Designing shape memory alloys (SMAs) that meet performance targets while remaining affordable and sustainable is a complex challenge. In this work, we focus on optimizing SMA compositions to achieve a desired martensitic start temperature (Ms) while minimizing cost. To do this, we use machine learning models as surrogate predictors and apply numerical optimization methods to search for suitable alloy combinations. We trained two types of machine learning models, a tree-based ensemble and a neural network, using a dataset of experimentally characterized alloys and physics-informed features. The tree-based model was used with a derivative-free optimizer (COBYLA), while the neural network, which provides gradient information, was paired with a gradient-based optimizer (TRUST-CONSTR). Our results show that while both models predict Ms with similar accuracy, the optimizer paired with the neural network finds better solutions more consistently. COBYLA often converged to suboptimal results, especially when the starting guess was far from the target. The TRUST-CONSTR method showed more stable behavior and was better at reaching alloy compositions that met both objectives. This study demonstrates a practical approach to exploring new SMA compositions by combining physics-informed data, machine learning models, and optimization algorithms. Although the scale of our dataset is smaller than simulation-based efforts, the use of experimental data improves the reliability of the predictions. The approach can be extended to other materials where design trade-offs must be made with limited data.

Trust region-based optimization methods have become foundational reinforcement learning algorithms that offer stability and strong empirical performance in continuous control tasks. Growing interest in scalable and reusable control policies translate also in a demand for morphological generalization, the ability of control policies to cope with different kinematic structures. Graph-based policy architectures provide a natural and effective mechanism to encode such structural differences. However, while these architectures accommodate variable morphologies, the behavior of trust region methods under varying action space dimensionality remains poorly understood. To this end, we conduct a theoretical analysis of trust region-based policy optimization methods, focusing on both Trust Region Policy Optimization (TRPO) and its widely used first-order approximation, Proximal Policy Optimization (PPO). The goal is to demonstrate how varying action space dimensionality influence the optimization landscape, particularly under the constraints imposed by KL-divergence or policy clipping penalties. Complementing the theoretical insights, an empirical evaluation under morphological variation is carried out using the Gymnasium Swimmer environment. This benchmark offers a systematically controlled setting for varying the kinematic structure without altering the underlying task, making it particularly well-suited to study morphological generalization.

This study investigates the application of unmanned aerial vehicles (UAVs) in public management, focusing on optimizing path planning to address challenges such as energy consumption, obstacle avoidance, and airspace constraints. As UAVs transition from 'technical tools' to 'governance infrastructure', driven by advancements in low-altitude economy policies and smart city demands, efficient path planning becomes critical. The research proposes an enhanced Rapidly-exploring Random Tree algorithm (dRRT), incorporating four strategies: Target Bias (to accelerate convergence), Dynamic Step Size (to balance exploration and obstacle navigation), Detour Priority (to prioritize horizontal detours over vertical ascents), and B-spline smoothing (to enhance path smoothness). Simulations in a 500 m3 urban environment with randomized buildings demonstrate dRRT's superiority over traditional RRT, A*, and Ant Colony Optimization (ACO). Results show dRRT achieves a 100\% success rate with an average runtime of 0.01468s, shorter path lengths, fewer waypoints, and smoother trajectories (maximum yaw angles <45°). Despite improvements, limitations include increased computational overhead from added mechanisms and potential local optima due to goal biasing. The study highlights dRRT's potential for efficient UAV deployment in public management scenarios like emergency response and traffic monitoring, while underscoring the need for integration with real-time obstacle avoidance frameworks. This work contributes to interdisciplinary advancements in urban governance, robotics, and computational optimization.

--Choice network construction is a critical technique for alleviating structural bias issues in Boolean optimization, equivalence checking, and technology mapping. Previous works on lossless synthesis utilize independent optimization to generate multiple snapshots, and use simulation and SA T solvers to identify functionally equivalent nodes. These nodes are then merged into a subject graph with choice nodes. However, such methods often neglect the quality of these choices--raising the question of whether they truly contribute to effective technology mapping. This paper introduces CRISTAL, a novel methodology and framework to constructing Boolean choice networks. Specifically, CRISTAL introduces a novel flow of choice network-based synthesis and mapping, includes representative logic cone search, structural mutation for generating diverse choice structures via equality saturation, and priority-ranking choice selection along with choice network construction and validation. Our experimental results demonstrate that CRISTAL outperforms the state-of-the-art Boolean choice network construction implemented in ABC in the post-mapping stage, achieving average reductions of 3.85%/8.35% The concept of choice network was pioneered to address optimization limitations in Electronic Design Automation (EDA).

We introduce PLUME search, a data-driven framework that enhances search efficiency in combinatorial optimization through unsupervised learning. Unlike supervised or reinforcement learning, PLUME search learns directly from problem instances using a permutation-based loss with a non-autoregressive approach. We evaluate its performance on the quadratic assignment problem, a fundamental NP-hard problem that encompasses various combinatorial optimization problems. Experimental results demonstrate that PLUME search consistently improves solution quality. Furthermore, we study the generalization behavior and show that the learned model generalizes across different densities and sizes.