The Kullback–Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus on the (h,τ)-divergence and (h,τ)-exponential families. We present a sufficient condition for the (h,τ)-divergence to induce a Hessian structure on an (h,τ)-exponential family. We also define the (h,τ)-dependence of random variables and prove a kind of the law of large numbers.
Consider that there are $k\le n$ agents in a simple, connected, and undirected graph $G=(V,E)$ with $n$ nodes and $m$ edges. The goal of the dispersion problem is to move these $k$ agents to mutually distinct nodes. Agents can communicate only when they are at the same node, and no other communication means, such as whiteboards, are available. We assume that the agents operate synchronously. We consider two scenarios: when all agents are initially located at a single node (rooted setting) and when they are initially distributed over one or more nodes (general setting). Kshemkalyani and Sharma presented a dispersion algorithm for the general setting, which uses $O(m_k)$ time and $\log(k + \Delta)$ bits of memory per agent [OPODIS 2021], where $m_k$ is the maximum number of edges in any induced subgraph of $G$ with $k$ nodes, and $\Delta$ is the maximum degree of $G$. This algorithm is currently the fastest in the literature, as no $o(m_k)$-time algorithm has been discovered, even for the rooted setting. In this paper, we present significantly faster algorithms for both the rooted and the general settings. First, we present an algorithm for the rooted setting that solves the dispersion problem in $O(k\log \min(k,\Delta))=O(k\log k)$ time using $O(\log (k+\Delta))$ bits of memory per agent. Next, we propose an algorithm for the general setting that achieves dispersion in $O(k \log k \cdot \log \min(k,\Delta))=O(k \log^2 k)$ time using $O(\log (k+\Delta))$ bits. Finally, for the rooted setting, we give a time-optimal (i.e.,~$O(k)$-time) algorithm with $O(\Delta+\log k)$ bits of space per agent. All algorithms presented in this paper work only in the synchronous setting, while several algorithms in the literature, including the one given by Kshemkalyani and Sharma at OPODIS 2021, work in the asynchronous setting.
Three-phase induction motors are widely utilized in numerous industrial applications due to their reliability and efficiency. However, inadequate maintenance can lead to costly operational failures and downtime. Early detection of faults, especially bearing abrasion faults, is essential to maintain motor performance and reduce expenses. This study proposes a novel abrasion fault detection method utilizing load current measurements, an accessible and cost-effective diagnostic parameter. Fast Fourier Transform (FFT) analysis is applied to extract critical fault indicators from the spectral features of the motor's load current. To address the challenge of overlapping and distinguishing fault features from healthy operational conditions, Principal Component Analysis (PCA) is employed as a preprocessing step, significantly enhancing diagnostic accuracy. Subsequently, Support Vector Machines (SVM) classify the PCA-extracted features using a Support Vector Machine (SVM) model, further improving accuracy. The proposed PCA and SVM framework introduces two key innovations having automatic PCA based selection of the most discriminative minimal FFT features, and automatic optimization of SVM hyperparameters (C and gamma), enabling robust classification even under highly overlapping spectral conditions. The method improves single fault (abrasion fault) diagnostic accuracy from 79.38% (SVM only) to 92.50% by enhancing separability between healthy and faulty spectra and achieves 90.12% accuracy for more challenging multiple-fault (hole and scratch) combinations. This approach provides significant advantages supporting proactive maintenance strategies, enhancing motor reliability, and promoting cost-effectiveness in diverse industrial environments. The results underline the effectiveness and practicality of the proposed methodology, marking it as a valuable advancement in induction motor fault diagnostics.
This roadmap provides a comprehensive and forward-looking perspective on the individualized application and safety of non-ionizing radiation (NIR) dosimetry in diagnostic and therapeutic medicine. Covering a wide range of frequencies, i.e., from low-frequency to terahertz, this document provides an overview of the current state of the art and anticipates future research needs in selected key topics of NIR-based medical applications. It also emphasizes the importance of personalized dosimetry, rigorous safety evaluation, and interdisciplinary collaboration to ensure safe and effective integration of NIR technologies in modern therapy and diagnosis.
This paper presents a general framework for end-to-end mutual information maximization in communication and sensing systems represented by stochastic directed acyclic graphs (DAGs). We derive a unified formula for the (mutual) information gradient with respect to arbitrary internal parameters, utilizing marginal and conditional score functions. We demonstrate that this gradient can be efficiently computed using vector-Jacobian products (VJP) within standard automatic differentiation frameworks, enabling the optimization of complex networks under global resource constraints. Numerical experiments on both linear multipath DAGs and nonlinear channels validate the proposed framework; the results confirm that the estimator, utilizing score functions learned via denoising score matching, accurately reproduces ground-truth gradients and successfully maximizes end-to-end mutual information. Beyond maximization, we extend our score-based framework to a novel unsupervised paradigm: digital twin calibration via Fisher divergence minimization.
