FaultXformer: A Transformer-Encoder Based Fault Classification and Location Identification model in PMU-Integrated Active Electrical Distribution System

Accurate fault detection and localization in electrical distribution systems is crucial, especially with the increasing integration of distributed energy resources (DERs), which inject greater variability and complexity into grid operations. In this study, FaultXformer is proposed, a Transformer encoder-based architecture developed for automatic fault analysis using real-time current data obtained from phasor measurement unit (PMU). The approach utilizes time-series current data to initially extract rich temporal information in stage 1, which is crucial for identifying the fault type and precisely determining its location across multiple nodes. In Stage 2, these extracted features are processed to differentiate among distinct fault types and identify the respective fault location within the distribution system. Thus, this dual-stage transformer encoder pipeline enables high-fidelity representation learning, considerably boosting the performance of the work. The model was validated on a dataset generated from the IEEE 13-node test feeder, simulated with 20 separate fault locations and several DER integration scenarios, utilizing current measurements from four strategically located PMUs. To demonstrate robust performance evaluation, stratified 10-fold cross-validation is performed. FaultXformer achieved average accuracies of 98.76% in fault type classification and 98.92% in fault location identification across cross-validation, consistently surpassing conventional deep learning baselines convolutional neural network (CNN), recurrent neural network (RNN). long short-term memory (LSTM) by 1.70%, 34.95%, and 2.04% in classification accuracy and by 10.82%, 40.89%, and 6.27% in location accuracy, respectively. These results demonstrate the efficacy of the proposed model with significant DER penetration.

GNNs for Time Series Anomaly Detection: An Open-Source Framework and a Critical Evaluation

There is growing interest in applying graph-based methods to Time Series Anomaly Detection (TSAD), particularly Graph Neural Networks (GNNs), as they naturally model dependencies among multivariate signals. GNNs are typically used as backbones in score-based TSAD pipelines, where anomalies are identified through reconstruction or prediction errors followed by thresholding. However, and despite promising results, the field still lacks standardized frameworks for evaluation and suffers from persistent issues with metric design and interpretation. We thus present an open-source framework for TSAD using GNNs, designed to support reproducible experimentation across datasets, graph structures, and evaluation strategies. Built with flexibility and extensibility in mind, the framework facilitates systematic comparisons between TSAD models and enables in-depth analysis of performance and interpretability. Using this tool, we evaluate several GNN-based architectures alongside baseline models across two real-world datasets with contrasting structural characteristics. Our results show that GNNs not only improve detection performance but also offer significant gains in interpretability, an especially valuable feature for practical diagnosis. We also find that attention-based GNNs offer robustness when graph structure is uncertain or inferred. In addition, we reflect on common evaluation practices in TSAD, showing how certain metrics and thresholding strategies can obscure meaningful comparisons. Overall, this work contributes both practical tools and critical insights to advance the development and evaluation of graph-based TSAD systems.

Ill-Conditioning in Dictionary-Based Dynamic-Equation Learning: A Systems Biology Case Study

Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown considerable promise, but they face a critical challenge when candidate functions become strongly correlated: numerical ill-conditioning. Poor or restricted sampling, together with particular choices of candidate libraries, can produce strong multicollinearity and numerical instability. In such cases, measurement noise may lead to widely different recovered models, obscuring the true underlying dynamics and hindering accurate system identification. Although sparse regularization promotes parsimonious solutions and can partially mitigate conditioning issues, strong correlations may persist, regularization may bias the recovered models, and the regression problem may remain highly sensitive to small perturbations in the data. We present a systematic analysis of how ill-conditioning affects sparse identification of biological dynamics using benchmark models from systems biology. We show that combinations involving as few as two or three terms can already exhibit strong multicollinearity and extremely large condition numbers. We further show that orthogonal polynomial bases do not consistently resolve ill-conditioning and can perform worse than monomial libraries when the data distribution deviates from the weight function associated with the orthogonal basis. Finally, we demonstrate that when data are sampled from distributions aligned with the appropriate weight functions corresponding to the orthogonal basis, numerical conditioning improves, and orthogonal polynomial bases can yield improved model recovery accuracy across two baseline models.

A Data-Driven Approach to Support Clinical Renal Replacement Therapy

This study investigates a data-driven machine learning approach to predict membrane fouling in critically ill patients undergoing Continuous Renal Replacement Therapy (CRRT). Using time-series data from an ICU, 16 clinically selected features were identified to train predictive models. To ensure interpretability and enable reliable counterfactual analysis, the researchers adopted a tabular data approach rather than modeling temporal dependencies directly. Given the imbalance between fouling and non-fouling cases, the ADASYN oversampling technique was applied to improve minority class representation. Random Forest, XGBoost, and LightGBM models were tested, achieving balanced performance with 77.6% sensitivity and 96.3% specificity at a 10% rebalancing rate. Results remained robust across different forecasting horizons. Notably, the tabular approach outperformed LSTM recurrent neural networks, suggesting that explicit temporal modeling was not necessary for strong predictive performance. Feature selection further reduced the model to five key variables, improving simplicity and interpretability with minimal loss of accuracy. A Shapley value-based counterfactual analysis was applied to the best-performing model, successfully identifying minimal input changes capable of reversing fouling predictions. Overall, the findings support the viability of interpretable machine learning models for predicting membrane fouling during CRRT. The integration of prediction and counterfactual analysis offers practical clinical value, potentially guiding therapeutic adjustments to reduce fouling risk and improve patient management.

The Chebyshev Polynomial Series Frequency Modulation Model for Waveform Design and Analysis

Polynomial phase signals (PPS) are a staple of waveform design and analysis in sonar, radar, and communications fields. They also find application in the modeling of bioacoustic emissions, especially those of echolocating animals such as bats and odontocetes. This work presents a novel PPS waveform formulation that exploits some special properties of Chebyshev polynomials, such as orthogonality, recurrence relations, and equivalence to trigonometric functions. The result is the Chebyshev Polynomial Frequency Modulation (CPSFM) family of waveforms, which prove useful in the modeling of bioacoustic signals and the approximation of non-polynomial-phase signals such as hyperbolic chirps. We demonstrate that the CPSFM model admits compact analytic expressions for fundamental continuous-time signal processing functions such as the Fourier transform, the convolution and correlation operations, and the ambiguity function. Derivations for these expressions using CPSFM are presented, along with their application to the analysis of biosonar emissions of Mexican free-tailed bats.

Adjacency Spectral Embeddings of Correlation Networks

In many applications, weighted networks are constructed based on time series data: each time series is associated to a vertex and edge weights are given by pairwise correlations. The result is a network whose edge dependency structure violates the assumptions of most common network models. Nonetheless, it is common to analyze these "correlation networks" using embedding methods derived from edge-independent network models, based on a belief that the edges are approximately independent. In this work, we put this modeling choice on firm theoretical ground. We show that when the time series are expressible in terms of a small number of Fourier basis elements (or in some other suitably-chosen basis), correlation networks correspond to latent space networks with dependent edge noise in which the vertex-level latent variables encode the basis coefficients. Further, we show that when time series are observed subject to noise, spectral embedding of the resulting noisy correlation network still recovers these true vertex-level latent representations under suitable assumptions. This characterization of embeddings as learning Fourier coefficients appears to be folklore in the signal processing community in the context of principal component analysis, but is, to the best of our knowledge, new to the statistical network analysis literature.

Augmenting representations with scientific papers

Astronomers have acquired vast repositories of multimodal data, including images, spectra, and time series, complemented by decades of literature that analyzes astrophysical sources. Still, these data sources are rarely systematically integrated. This work introduces a contrastive learning framework designed to align X-ray spectra with domain knowledge extracted from scientific literature, facilitating the development of shared multimodal representations. Establishing this connection is inherently complex, as scientific texts encompass a broader and more diverse physical context than spectra. We propose a contrastive pipeline that achieves a 20% Recall@1% when retrieving texts from spectra, proving that a meaningful alignment between these modalities is not only possible but capable of accelerating the interpretation of rare or poorly understood sources. Furthermore, the resulting shared latent space effectively encodes physically significant information. By fusing spectral and textual data, we improve the estimation of 20 physical variables by 16-18% over unimodal spectral baselines. Our results indicate that a Mixture of Experts (MoE) strategy, which leverages both unimodal and shared representations, yields superior performance. Finally, outlier analysis within the multimodal latent space identifies high-priority targets for follow-up investigation, including a candidate pulsating ULX (PULX) and a gravitational lens system. Importantly, this framework can be extended to other scientific domains where aligning observational data with existing literature is possible.

Stringology-Based Motif Discovery from EEG Signals: an ADHD Case Study

We propose a novel computational framework for analyzing electroencephalography (EEG) time series using methods from stringology, the study of efficient algorithms for string processing, to systematically identify and characterize recurrent temporal patterns in neural signals. The primary aim is to introduce quantitative measures to understand neural signal dynamics, with the present findings serving as a proof-of-concept. The framework adapts order-preserving matching (OPM) and Cartesian tree matching (CTM) to detect temporal motifs that preserve relative ordering and hierarchical structure while remaining invariant to amplitude scaling. This approach provides a temporally precise representation of EEG dynamics that complements traditional spectral and global complexity analyses. To evaluate its utility, we applied the framework to multichannel EEG recordings from individuals with attention-deficit/hyperactivity disorder (ADHD) and matched controls using a publicly available dataset. Highly recurrent, group-specific motifs were extracted and quantified using both OPM and CTM. The ADHD group exhibited significantly higher motif frequencies, suggesting increased repetitiveness in neural activity. OPM analysis revealed shorter motif lengths and greater gradient instability in ADHD, reflected in larger mean and maximal inter-sample amplitude changes. CTM analysis further demonstrated reduced hierarchical complexity in ADHD, characterized by shallower tree structures and fewer hierarchical levels despite comparable motif lengths. These findings suggest that ADHD-related EEG alterations involve systematic differences in the structure, stability, and hierarchical organization of recurrent temporal patterns. The proposed stringology-based motif framework provides a complementary computational tool with potential applications for objective biomarker development in neurodevelopmental disorders.

Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems

Root cause analysis (RCA) in networked industrial systems, such as supply chains and power networks, is notoriously difficult due to unknown and dynamically evolving interdependencies among geographically distributed clients. These clients represent heterogeneous physical processes and industrial assets equipped with sensors that generate large volumes of nonlinear, high-dimensional, and heterogeneous IoT data. Classical RCA methods require partial or full knowledge of the system's dependency graph, which is rarely available in these complex networks. While federated learning (FL) offers a natural framework for decentralized settings, most existing FL methods assume homogeneous feature spaces and retrainable client models. These assumptions are not compatible with our problem setting. Different clients have different data features and often run fixed, proprietary models that cannot be modified. This paper presents a federated cross-client interdependency learning methodology for feature-partitioned, nonlinear time-series data, without requiring access to raw sensor streams or modifying proprietary client models. Each proprietary local client model is augmented with a Machine Learning (ML) model that encodes cross-client interdependencies. These ML models are coordinated via a global server that enforces representation consistency while preserving privacy through calibrated differential privacy noise. RCA is performed using model residuals and anomaly flags. We establish theoretical convergence guarantees and validate our approach on extensive simulations and a real-world industrial cybersecurity dataset.

From Signals to Causes: A Causal Signal Processing Framework for Robust and Interpretable Clinical Risk Prediction

Learning-based signal processing systems increasingly support high-stakes medical decisions using heterogeneous biomedical signals, including medical images, physiological time series, and clinical records. Despite strong predictive performance, many models rely on statistical correlations that are unstable across acquisition settings, patient populations, and institutional practices, limiting robustness, interpretability, and clinical trust. We advocate a causal signal processing perspective in which biomedical signals are treated as effects of latent generative mechanisms rather than as isolated predictive inputs. Using clinical risk prediction as a motivating example, we show how disease-related factors generate observable biomarkers, while acquisition processes act as confounders influencing signal appearance. In clinical disease risk prediction from chest CT scans and patient risk factors, correlational models may fail under scanner changes, whereas causal abstractions remain invariant. Building on this view, we propose a unifying conceptual framework integrating causal modeling with learning-based signal processing and neuro-symbolic reasoning. Statistical models extract multimodal representations that are mapped to interpretable causal abstractions and combined with symbolic knowledge encoding clinical risk factors and guidelines. This structure enables clinically grounded explanations, counterfactual reasoning about hypothetical interventions, and improved robustness to distribution shifts arising from changes in acquisition conditions or screening policies. Rather than introducing a specific algorithm, this article presents schematic causal structures and a comparative analysis of correlation-based, causal, and neuro-symbolic approaches to guide the design of robust and interpretable medical decision-support systems.