The Joint Routing-Assignment (JRA) optimization problem simultaneously determines the assignment of items to placeholders and a Hamiltonian cycle that visits each node pair exactly once, with the objective of minimizing total travel cost. Previous studies introduced an exact mixed-integer programming (MIP) solver, along with datasets and a Gurobi implementation, showing that while the exact approach guarantees optimality, it becomes computationally inefficient for large-scale instances. To overcome this limitation, heuristic methods based on merging algorithms and shaking procedures were proposed, achieving solutions within approximately 1% deviation from the optimum. This work presents a novel and more efficient approach that attains high-accuracy, near-optimal solutions for large-scale JRA problems. The proposed method introduces a Partial Path Reconstructon (PPR) solver that first identifies key item-placeholder pairs to form a reduced subproblem, which is solved efficiently to refine the global solution. Using this PJAR framework, the initial heuristic merging solutions can be further improved, reducing the deviation by half. Moreover, the solution can be iteratively polished with PPR based solver along the optimization path to yield highly accurate tours. Additionally, a global Large-α constraint is incorporated into the JRA model to further enhance solution optimality. Experimental evaluations on benchmark datasets with n = 300, 500, and 1000 demonstrate that the proposed method consistently delivers almost optimal solutions, achieving an average deviation of 0.00% from the ground truth while maintaining high computational efficiency. Beyond the JRA problem, the proposed framework and methodologies exhibit strong potential for broader applications. The Framework can be applied to TSP and related optimization problems.

Quantum federated learning (QFL) is an emerging field that has the potential to revolutionize computation by taking advantage of quantum physics concepts in a distributed machine learning (ML) environment. However, the majority of available quantum simulators are primarily built for general quantum circuit simulation and do not include integrated support for machine learning tasks such as training, evaluation, and iterative optimization. Furthermore, designing and assessing quantum learning algorithms is still a difficult and resource-intensive task. Real-time updates are essential for observing model convergence, debugging quantum circuits, and making conscious choices during training with the use of limited resources. Furthermore, most current simulators fail to support the integration of user-specific data for training purposes, undermining the main purpose of using a simulator. In this study, we introduce SimQFL, a customized simulator that simplifies and accelerates QFL experiments in quantum network applications. SimQFL supports real-time, epoch-wise output development and visualization, allowing researchers to monitor the process of learning across each training round. Furthermore, SimQFL offers an intuitive and visually appealing interface that facilitates ease of use and seamless execution. Users can customize key variables such as the number of epochs, learning rates, number of clients, and quantum hyperparameters such as qubits and quantum layers, making the simulator suitable for various QFL applications. The system gives immediate feedback following each epoch by showing intermediate outcomes and dynamically illustrating learning curves. SimQFL is a practical and interactive platform enabling academics and developers to prototype, analyze, and tune quantum neural networks with greater transparency and control in distributed quantum networks.

Tyler's M-estimator is a well known procedure for robust and heavy-tailed covariance estimation.

Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly.

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

Four-Period Detailed Design Period 1: Topic Selection and Initial Exploration Period 2: Principle Analysis and Model Design Period 3: Model Construction and Refinement Period 4: "Historical Technology Expo" with presentations [Includes detailed student reflection prompts, extension activities, and troubleshooting guidance...] Base Model: Generic Outline Interdisciplinary Lesson Plan Design Learning Objectives: Help students understand how physics influences historical progress... Cultivate ability to analyze social factors behind technological development... Class Schedule: Four periods covering physics review, historical technologies, case study, and modern applications. Assessment: Class participation, group reports, reflection journals [Subsequent periods contain only high-level bullet points without actionable details...] 12 Qualitative Analysis This comparison reveals dramatic capability differences for complex generation tasks. The Base Model produces only a generic outline with vague bullet points--entirely insufficient for classroom use. Both AutoSynth and Expert-Designed models generate outstanding, comprehensive lesson plans with detailed objectives, granular activities, and sophisticated assessment schemes. The subtle differences reflect their optimization processes: AutoSynth emphasizes systematic difficulty coverage (likely from iterative refinement), while Expert-Designed showcases deep assessment design expertise. Both represent quantum leaps over baseline, validating that specialized workflows-- automated or manual--are essential for professional-grade content. This supports our quantitative findings (Table 1): while Au-toSynth achieves lower human preference (51 percent vs 96 percent), it produces genuinely high-quality outputs far superior to baseline capabilities.

Learning dexterous and agile policy for humanoid and dexterous hand control requires large-scale demonstrations, but collecting robot-specific data is prohibitively expensive. In contrast, abundant human motion data is readily available from motion capture, videos, and virtual reality, which could help address the data scarcity problem. However, due to the embodiment gap and missing dynamic information like force and torque, these demonstrations cannot be directly executed on robots. To bridge this gap, we propose Scalable Physics-Informed DExterous Retargeting (SPIDER), a physics-based retargeting framework to transform and augment kinematic-only human demonstrations to dynamically feasible robot trajectories at scale. Our key insight is that human demonstrations should provide global task structure and objective, while large-scale physics-based sampling with curriculum-style virtual contact guidance should refine trajectories to ensure dynamical feasibility and correct contact sequences. SPIDER scales across diverse 9 humanoid/dexterous hand embodiments and 6 datasets, improving success rates by 18% compared to standard sampling, while being 10X faster than reinforcement learning (RL) baselines, and enabling the generation of a 2.4M frames dynamic-feasible robot dataset for policy learning. As a universal physics-based retargeting method, SPIDER can work with diverse quality data and generate diverse and high-quality data to enable efficient policy learning with methods like RL.

Accurate intra-operative localization of the bronchoscope tip relative to patient anatomy remains challenging due to respiratory motion, anatomical variability, and CT-to-body divergence that cause deformation and misalignment between intra-operative views and pre-operative CT. Existing vision-based methods often fail to generalize across domains and patients, leading to residual alignment errors. This work establishes a generalizable foundation for bronchoscopy navigation through a robust vision-based framework and a new synthetic benchmark dataset that enables standardized and reproducible evaluation. We propose a vision-based pose optimization framework for frame-wise 2D-3D registration between intra-operative endoscopic views and pre-operative CT anatomy. A fine-tuned modality- and domain-invariant encoder enables direct similarity computation between real endoscopic RGB frames and CT-rendered depth maps, while a differentiable rendering module iteratively refines camera poses through depth consistency. To enhance reproducibility, we introduce the first public synthetic benchmark dataset for bronchoscopy navigation, addressing the lack of paired CT-endoscopy data. Trained exclusively on synthetic data distinct from the benchmark, our model achieves an average translational error of 2.65 mm and a rotational error of 0.19 rad, demonstrating accurate and stable localization. Qualitative results on real patient data further confirm strong cross-domain generalization, achieving consistent frame-wise 2D-3D alignment without domain-specific adaptation. Overall, the proposed framework achieves robust, domain-invariant localization through iterative vision-based optimization, while the new benchmark provides a foundation for standardized progress in vision-based bronchoscopy navigation.

We propose an optimization model where a parking lot manager (PLM) can aggregate parked EV batteries to provide virtual energy storage services that are provably robust under uncertain EV departures and state-of-charge caps. Our formulation yields a data-driven convex optimization problem where a prosumer community agrees on a contract with the PLM for the provision of storage services over a finite horizon. Leveraging recent results in the scenario approach, we certify out-of-sample constraint safety. Furthermore, we enable a tunable profit-risk trade-off through scenario relaxation and extend our model to account for robustness to adversarial perturbations and distributional shifts over Wasserstein-based ambiguity sets. All the approaches are accompanied by tight finite-sample certificates. Numerical studies demonstrate the out-of-sample and out-of-distribution constraint satisfaction of our proposed model compared to the developed theoretical guarantees, showing their effectiveness and potential in robust and efficient virtual energy services.