Sample entropy for graph signals: An approach to nonlinear dynamic analysis of data on networks

The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in Shannon entropy and symbol dynamics. In this paper, we explore, for the first time, whether and how a popular conditional-entropy based measure --Sample Entropy (SampEn)-- can be effectively defined for graph signals and used to characterise the nonlinear dynamics of data on complex networks. We introduce sample entropy for graph signals (SampEnG), a unified framework that generalises classical sample entropy from uni- and bi-dimensional signals, including time series and images, by building on topology-aware embeddings using multi-hop neighbourhoods and computing finite scale of correlation sums in the continuous embedding state space. Experiments on synthetic and real-world datasets, including weather station, wireless sensor monitoring, and traffic systems, verify that SampEnG recovers known nonlinear dynamical features on paths and grids. In the traffic-flow analysis, SampEnG on a directed topology (encoding causal flow constraint) is particularly sensitive to phase transitions between free-flow and congestion, offering information that is complementary to existing Shannon-entropy based approaches. We expect SampEnG to open up new ways to analyse graph signals, generalising sample entropy and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data.

Financial Anomaly Detection for the Canadian Market

In this work we evaluate the performance of three classes of methods for detecting financial anomalies: topological data analysis (TDA), principal component analyis (PCA), and Neural Network-based approaches. We apply these methods to the TSX-60 data to identify major financial stress events in the Canadian stock market. We show how neural network-based methods (such as GlocalKD and One-Shot GIN(E)) and TDA methods achieve the strongest performance. The effectiveness of TDA in detecting financial anomalies suggests that global topological properties are meaningful in distinguishing financial stress events.

Towards Intelligent Energy Security: A Unified Spatio-Temporal and Graph Learning Framework for Scalable Electricity Theft Detection in Smart Grids

Electricity theft and non-technical losses (NTLs) remain critical challenges in modern smart grids, causing significant economic losses and compromising grid reliability. This study introduces the SmartGuard Energy Intelligence System (SGEIS), an integrated artificial intelligence framework for electricity theft detection and intelligent energy monitoring. The proposed system combines supervised machine learning, deep learning-based time-series modeling, Non-Intrusive Load Monitoring (NILM), and graph-based learning to capture both temporal and spatial consumption patterns. A comprehensive data processing pipeline is developed, incorporating feature engineering, multi-scale temporal analysis, and rule-based anomaly labeling. Deep learning models, including Long Short-Term Memory (LSTM), Temporal Convolutional Networks (TCN), and Autoencoders, are employed to detect abnormal usage patterns. In parallel, ensemble learning methods such as Random Forest, Gradient Boosting, XGBoost, and LightGBM are utilized for classification. To model grid topology and spatial dependencies, Graph Neural Networks (GNNs) are applied to identify correlated anomalies across interconnected nodes. The NILM module enhances interpretability by disaggregating appliance-level consumption from aggregate signals. Experimental results demonstrate strong performance, with Gradient Boosting achieving a ROC-AUC of 0.894, while graph-based models attain over 96% accuracy in identifying high-risk nodes. The hybrid framework improves detection robustness by integrating temporal, statistical, and spatial intelligence. Overall, SGEIS provides a scalable and practical solution for electricity theft detection, offering high accuracy, improved interpretability, and strong potential for real-world smart grid deployment.

Topological Detection of Hopf Bifurcations via Persistent Homology: A Functional Criterion from Time Series

We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis. The central idea is that changes in the dynamical regime are reflected in the emergence or disappearance of a dominant one-dimensional homological features in the reconstructed attractor. To quantify this behavior, we introduce a simple and interpretable scalar topological functional defined as the maximum persistence of homology classes in dimension one. This functional is used to construct a computable criterion for identifying critical parameters in families of dynamical systems without requiring knowledge of the underlying equations. The proposed approach is validated on representative systems of increasing complexity, showing consistent detection of the bifurcation point. The results support the interpretation of dynamical transitions as topological phase transitions and demonstrate the potential of topological data analysis as a model-free tool for the quantitative analysis of nonlinear time series.

Hybrid Quantum-Classical Spatiotemporal Forecasting for 3D Cloud Fields

Accurate forecasting of three-dimensional (3D) cloud fields is important for atmospheric analysis and short-range numerical weather prediction, yet it remains challenging because cloud evolution involves cross-layer interactions, nonlocal dependencies, and multiscale spatiotemporal dynamics. Existing spatiotemporal prediction models based on convolutions, recurrence, or attention often rely on locality-biased representations and therefore struggle to preserve fine cloud structures in volumetric forecasting tasks. To address this issue, we propose QENO, a hybrid quantum-inspired spatiotemporal forecasting framework for 3D cloud fields. The proposed architecture consists of four components: a classical spatiotemporal encoder for compact latent representation, a topology-aware quantum enhancement block for modeling nonlocal couplings in latent space, a dynamic fusion temporal unit for integrating measurement-derived quantum features with recurrent memory, and a decoder for reconstructing future cloud volumes. Experiments on CMA-MESO 3D cloud fields show that QENO consistently outperforms representative baselines, including ConvLSTM, PredRNN++, Earthformer, TAU, and SimVP variants, in terms of MSE, MAE, RMSE, SSIM, and threshold-based detection metrics. In particular, QENO achieves an MSE of 0.2038, an RMSE of 0.4514, and an SSIM of 0.6291, while also maintaining a compact parameter budget. These results indicate that topology-aware hybrid quantum-classical feature modeling is a promising direction for 3D cloud structure forecasting and atmospheric Earth observation data analysis.

VIANA: character Value-enhanced Intensity Assessment via domain-informed Neural Architecture

Predicting the perceived intensity of odorants remains a fundamental challenge in sensory science due to the complex, non-linear behavior of their response, as well as the difficulty in correlating molecular structure with human perception. While traditional deep learning models, such as Graph Convolutional Networks (GCNs), excel at capturing molecular topology, they often fail to account for the biological and perceptual context of olfaction. This study introduces VIANA, a novel "tri-pillar" framework that integrates structural graph theory, character value embeddings, and phenomenological behavior. This methodology systematically evaluates knowledge transfer across three distinct domains: molecular structure via GCNs, semantic odor character values via Principal Odor Map (POM) embeddings, and biological dose-response logic via Hill's law. We demonstrate that knowledge transfer is not inherently positive; rather, a balance must be maintained in the volume of information provided to the model. While raw semantic data led to "information overload" in domain-informed models, applying Principal Component Analysis (PCA) to distill the 95% most impactful semantic variance yielded a superior "signal distillation" effect. Results indicate that the synthesis of these three knowledge transfer pillars significantly outperforms baseline structural models, with VIANA achieving a peak R^2 of 0.996 and a test Mean Squared Error (MSE) of 0.19. In this context, VIANA successfully captures the physical ceiling of saturation, the sensitivity of detection thresholds, and the nuance of odor character value expression, providing a domain grounded simulation of the human olfactory experience. This research provides a robust framework for digital olfaction, effectively bridging the gap between molecular informatics and sensory perception.

TopoPilot: Reliable Conversational Workflow Automation for Topological Data Analysis and Visualization

Recent agentic systems demonstrate that large language models can generate scientific visualizations from natural language. However, reliability remains a major limitation: systems may execute invalid operations, introduce subtle but consequential errors, or fail to request missing information when inputs are underspecified. These issues are amplified in real-world workflows, which often exceed the complexity of standard benchmarks. Ensuring reliability in autonomous visualization pipelines therefore remains an open challenge. We present TopoPilot, a reliable and extensible agentic framework for automating complex scientific visualization workflows. TopoPilot incorporates systematic guardrails and verification mechanisms to ensure reliable operation. While we focus on topological data analysis and visualization as a primary use case, the framework is designed to generalize across visualization domains. TopoPilot adopts a reliability-centered two-agent architecture. An orchestrator agent translates user prompts into workflows composed of atomic backend actions, while a verifier agent evaluates these workflows prior to execution, enforcing structural validity and semantic consistency. This separation of interpretation and verification reduces code-generation errors and enforces correctness guarantees. A modular architecture further improves robustness by isolating components and enabling seamless integration of new descriptors and domain-specific workflows without modifying the core system. To systematically address reliability, we introduce a taxonomy of failure modes and implement targeted safeguards for each class. In evaluations simulating 1,000 multi-turn conversations across 100 prompts, including adversarial and infeasible requests, TopoPilot achieves a success rate exceeding 99%, compared to under 50% for baselines without comprehensive guardrails and checks.

TMTE: Effective Multimodal Graph Learning with Task-aware Modality and Topology Co-evolution

Multimodal-attributed graphs (MAGs) are a fundamental data structure for multimodal graph learning (MGL), enabling both graph-centric and modality-centric tasks. However, our empirical analysis reveals inherent topology quality limitations in real-world MAGs, including noisy interactions, missing connections, and task-agnostic relational structures. A single graph derived from generic relationships is therefore unlikely to be universally optimal for diverse downstream tasks. To address this challenge, we propose Task-aware Modality and Topology co-Evolution (TMTE), a novel MGL framework that jointly and iteratively optimizes graph topology and multimodal representations toward the target task. TMTE is motivated by the bidirectional coupling between modality and topology: multimodal attributes induce relational structures, while graph topology shapes modality representations. Concretely, TMTE casts topology evolution as multi-perspective metric learning over modality embeddings with an anchor-based approximation, and formulates modality evolution as smoothness-regularized fusion with cross-modal alignment, yielding a closed-loop task-aware co-evolution process. Extensive experiments on 9 MAG datasets and 1 non-graph multimodal dataset across 6 graph-centric and modality-centric tasks show that TMTE consistently achieves state-of-the-art performance. Our code is available at https://anonymous.4open.science/r/TMTE-1873.

Persistence-based topological optimization: a survey

Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a way to incorporate topological priors or to regularize machine learning models. This is usually achieved by minimizing adequate, topologically-informed losses based on these descriptors, which, in turn, naturally raises theoretical and practical questions about the possibility of optimizing such loss functions using gradient-based algorithms. This has been an active research field in the topological data analysis community over the last decade, and various techniques have been developed to enable optimization of persistence-based loss functions with gradient descent schemes. This survey presents the current state of this field, covering its theoretical foundations, the algorithmic aspects, and showcasing practical uses in several applications. It includes a detailed introduction to persistence theory and, as such, aims at being accessible to mathematicians and data scientists newcomers to the field. It is accompanied by an open-source library which implements the different approaches covered in this survey, providing a convenient playground for researchers to get familiar with the field.

Causal AI For AMS Circuit Design: Interpretable Parameter Effects Analysis

Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device dimensions, bias voltages, etc.) and real-world performance, we propose a causal-inference framework that first discovers a directed-acyclic graph (DAG) from SPICE simulation data and then quantifies parameter impact through Average Treatment Effect (ATE) estimation. The approach yields human-interpretable rankings of design knobs and explicit 'what-if' predictions, enabling designers to understand trade-offs in sizing and topology. We evaluate the pipeline on three operational-amplifier families (OTA, telescopic, and folded-cascode) implemented in TSMC 65nm and benchmark it against a baseline neural-network (NN) regressor. Across all circuits the causal model reproduces simulation-based ATEs with an average absolute error of less than 25%, whereas the neural network deviates by more than 80% and frequently predicts the wrong sign. These results demonstrate that causal AI provides both higher accuracy and explainability, paving the way for more efficient, trustworthy AMS design automation.