Fair clustering is crucial for mitigating bias in unsupervised learning, yet existing algorithms often suffer from quadratic or super-quadratic computational complexity, rendering them impractical for large-scale datasets. To bridge this gap, we introduce the Anchor-based Fair Clustering Framework (AFCF), a novel, general, and plug-and-play framework that empowers arbitrary fair clustering algorithms with linear-time scalability. Our approach first selects a small but representative set of anchors using a novel fair sampling strategy. Then, any off-the-shelf fair clustering algorithm can be applied to this small anchor set. The core of our framework lies in a novel anchor graph construction module, where we formulate an optimization problem to propagate labels while preserving fairness. This is achieved through a carefully designed group-label joint constraint, which we prove theoretically ensures that the fairness of the final clustering on the entire dataset matches that of the anchor clustering. We solve this optimization efficiently using an ADMM-based algorithm. Extensive experiments on multiple large-scale benchmarks demonstrate that AFCF drastically accelerates state-of-the-art methods, which reduces computational time by orders of magnitude while maintaining strong clustering performance and fairness guarantees.

Neurodevelopmental disorders such as Fragile X Syndrome (FXS) and Autism Spectrum Disorder (ASD) are characterized by disrupted cortical oscillatory activity, particularly in the alpha and gamma frequency bands. These abnormalities are linked to deficits in attention, sensory processing, and cognitive function. In this work, we present an adaptive machine learning-based brain-computer interface (BCI) system designed to modulate neural oscillations through frequency-specific auditory stimulation to enhance cognitive readiness in individuals with FXS. EEG data were recorded from 38 participants using a 128-channel system under a stimulation paradigm consisting of a 30-second baseline (no stimulus) followed by 60-second auditory entrainment episodes at 7Hz, 9Hz, 11Hz, and 13Hz. A comprehensive analysis of power spectral features (Alpha, Gamma, Delta, Theta, Beta) and cross-frequency coupling metrics (Alpha-Gamma, Alpha-Beta, etc.) was conducted. The results identified Peak Alpha Power, Peak Gamma Power, and Alpha Power per second per channel as the most discriminative biomarkers. The 13Hz stimulation condition consistently elicited a significant increase in Alpha activity and suppression of Gamma activity, aligning with our optimization objective. A supervised machine learning framework was developed to predict EEG responses and dynamically adjust stimulation parameters, enabling real-time, subject-specific adaptation. This work establishes a novel EEG-driven optimization framework for cognitive neuromodulation, providing a foundational model for next-generation AI-integrated BCI systems aimed at personalized neurorehabilitation in FXS and related disorders.

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.