Magnetism is widely used for the wireless localization and actuation of robots and devices for medical procedures. However, current static magnetic localization methods suffer from large required magnets and are limited to only five degrees of freedom due to a fundamental constraint of the rotational symmetry around the magnetic axis. We present the small-scale magneto-oscillatory localization (SMOL) method, which is capable of wirelessly localizing a millimeter-scale tracker with full six degrees of freedom in deep biological tissues. The SMOL device uses the temporal oscillation of a mechanically resonant cantilever with a magnetic dipole to break the rotational symmetry, and exploits the frequency-response to achieve a high signal-to-noise ratio with sub-millimeter accuracy over a large distance of up to 12 centimeters and quasi-continuous refresh rates up to 200 Hz. Integration into real-time closed-loop controlled robots and minimally-invasive surgical tools are demonstrated to reveal the vast potential of the SMOL method.

One of the main challenges of federated learning (FL) is handling non-independent and identically distributed (non-IID) client data, which may occur in practice due to unbalanced datasets and use of different data sources across clients. Knowledge sharing and model personalization are key strategies for addressing this issue. Clustered federated learning is a class of FL methods that groups clients that observe similarly distributed data into clusters, such that every client is typically associated with one data distribution and participates in training a model for that distribution along their cluster peers. In this paper, we present a unified Bayesian framework for clustered FL which associates clients to clusters. Then we propose several practical algorithms to handle the, otherwise growing, data associations in a way that trades off performance and computational complexity. This work provides insights on client-cluster associations and enables client knowledge sharing in new ways. The proposed framework circumvents the need for unique client-cluster associations, which is seen to increase the performance of the resulting models in a variety of experiments.

Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer linear programming network-reconfigured OPF (NR-OPF) problem, substantially increasing the computing time. Thus, a machine learning (ML)-based approach, particularly utilizing graph neural network (GNN), is proposed to accelerate the solution process. The GNN model is trained offline to predict the best topology before entering the optimization stage. In addition, this paper proposes an offline pre-ML filter layer to reduce GNN model size and training time while improving its accuracy. A fast online post-ML selection layer is also proposed to analyze GNN predictions and then select a subset of predicted NR solutions with high confidence. Case studies have demonstrated superior performance of the proposed GNN-accelerated NR-OPF method augmented with the proposed pre-ML and post-ML layers.

This book provides a comprehensive introduction to the foundational concepts of machine learning (ML) and deep learning (DL). It bridges the gap between theoretical mathematics and practical application, focusing on Python as the primary programming language for implementing key algorithms and data structures. The book covers a wide range of topics, including basic and advanced Python programming, fundamental mathematical operations, matrix operations, linear algebra, and optimization techniques crucial for training ML and DL models. Advanced subjects like neural networks, optimization algorithms, and frequency domain methods are also explored, along with real-world applications of large language models (LLMs) and artificial intelligence (AI) in big data management. Designed for both beginners and advanced learners, the book emphasizes the critical role of mathematical principles in developing scalable AI solutions. Practical examples and Python code are provided throughout, ensuring readers gain hands-on experience in applying theoretical knowledge to solve complex problems in ML, DL, and big data analytics.

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this paper, we aim to solve this problem given a minimal number of distance samples. To this end, we leverage continuous and non-convex rank minimization formulations of the problem and establish a local convergence guarantee for a variant of iteratively reweighted least squares (IRLS), which applies if a minimal random set of observed distances is provided. As a technical tool, we establish a restricted isometry property (RIP) restricted to a tangent space of the manifold of symmetric rank-$r$ matrices given random Euclidean distance measurements, which might be of independent interest for the analysis of other non-convex approaches. Furthermore, we assess data efficiency, scalability and generalizability of different reconstruction algorithms through numerical experiments with simulated data as well as real-world data, demonstrating the proposed algorithm's ability to identify the underlying geometry from fewer distance samples compared to the state-of-the-art.

The route planning problem based on the greedy algorithm represents a method of identifying the optimal or near-optimal route between a given start point and end point. In this paper, the PCA method is employed initially to downscale the city evaluation indexes, extract the key principal components, and then downscale the data using the KMO and TOPSIS algorithms, all of which are based on the MindSpore framework. Secondly, for the dataset that does not pass the KMO test, the entropy weight method and TOPSIS method will be employed for comprehensive evaluation. Finally, a route planning algorithm is proposed and optimised based on the greedy algorithm, which provides personalised route customisation according to the different needs of tourists. In addition, the local travelling efficiency, the time required to visit tourist attractions and the necessary daily breaks are considered in order to reduce the cost and avoid falling into the locally optimal solution.

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut, and various other related problems. This work potentially opens up new avenues for algorithm design in neural combinatorial optimization, bridging the gap between discrete and continuous optimization techniques.

The optimization of black-box functions with noisy observations is a fundamental problem with widespread applications, and has been widely studied under the assumption that the function lies in a reproducing kernel Hilbert space (RKHS). This problem has been studied extensively in the stationary setting, and near-optimal regret bounds are known via developments in both upper and lower bounds. In this paper, we consider non-stationary scenarios, which are crucial for certain applications but are currently less well-understood. Specifically, we provide the first algorithm-independent lower bounds, where the time variations are subject satisfying a total variation budget according to some function norm. Under $\ell_{\infty}$-norm variations, our bounds are found to be close to the state-of-the-art upper bound (Hong \emph{et al.}, 2023). Under RKHS norm variations, the upper and lower bounds are still reasonably close but with more of a gap, raising the interesting open question of whether non-minor improvements in the upper bound are possible.

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for \textit{global} acquisition function optimization. Specifically, our Piecewise-linear Kernel Mixed Integer Quadratic Programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task.

Criminal courts across the United States handle millions of cases every year, and the scheduling of those cases must accommodate a diverse set of constraints, including the preferences and availability of courts, prosecutors, and defense teams. When criminal court schedules are formed, defendants' scheduling preferences often take the least priority, although defendants may face significant consequences (including arrest or detention) for missed court dates. Additionally, studies indicate that defendants' nonappearances impose costs on the courts and other system stakeholders. To address these issues, courts and commentators have begun to recognize that pretrial outcomes for defendants and for the system would be improved with greater attention to court processes, including \emph{court scheduling practices}. There is thus a need for fair criminal court pretrial scheduling systems that account for defendants' preferences and availability, but the collection of such data poses logistical challenges. Furthermore, optimizing schedules fairly across various parties' preferences is a complex optimization problem, even when such data is available. In an effort to construct such a fair scheduling system under data uncertainty, this paper proposes a joint optimization and learning framework that combines machine learning models trained end-to-end with efficient matching algorithms. This framework aims to produce court scheduling schedules that optimize a principled measure of fairness, balancing the availability and preferences of all parties.