The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series

Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords representing major consumer categories. Our results show that while SAX and eSAX offer fast and interpretable clustering for stable time series, they struggle with volatility and complexity, often producing ambiguous ``catch-all'' clusters. TDA, by contrast, captures global structural features through persistent homology and achieves more balanced and meaningful groupings. We conclude with practical guidance for using symbolic and topological methods in consumer analytics and suggest that hybrid approaches combining both perspectives hold strong potential for future applications.

Process mining-driven modeling and simulation to enhance fault diagnosis in cyber-physical systems

Fault diagnosis in Cyber-Physical Systems (CPSs) is essential for ensuring system dependability and operational efficiency by accurately detecting anomalies and identifying their root causes. However, the manual modeling of faulty behaviors often demands extensive domain expertise and produces models that are complex, error-prone, and difficult to interpret. To address this challenge, we present a novel unsupervised fault diagnosis methodology that integrates collective anomaly detection in multivariate time series, process mining, and stochastic simulation. Initially, collective anomalies are detected from low-level sensor data using multivariate time-series analysis. These anomalies are then transformed into structured event logs, enabling the discovery of interpretable process models through process mining. By incorporating timing distributions into the extracted Petri nets, the approach supports stochastic simulation of faulty behaviors, thereby enhancing root cause analysis and behavioral understanding. The methodology is validated using the Robotic Arm Dataset (RoAD), a widely recognized benchmark in smart manufacturing. Experimental results demonstrate its effectiveness in modeling, simulating, and classifying faulty behaviors in CPSs. This enables the creation of comprehensive fault dictionaries that support predictive maintenance and the development of digital twins for industrial environments.

Multiresolution local smoothness detection in non-uniformly sampled multivariate signals

Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity within the framework of microlocal spaces introduced by Jaffard. The central tool in our analysis is the fast samplet transform, a distributional wavelet transform tailored to scattered data. We establish a connection between the decay of samplet coefficients and the pointwise regularity of multivariate signals. As a by product, we derive decay estimates for functions belonging to classical H\"older spaces and Sobolev-Slobodeckij spaces. While traditional wavelets are effective for regularity detection in low-dimensional structured data, samplets demonstrate robust performance even for higher dimensional and scattered data. To illustrate our theoretical findings, we present extensive numerical studies detecting local regularity of one-, two- and three-dimensional signals, ranging from non-uniformly sampled time series over image segmentation to edge detection in point clouds.

A Practical Analysis: Understanding Phase Noise Modelling in Time and Frequency Domain for Phase-Locked Loops

In MIMO systems, the presence of phase noise is a significant factor that can degrade performance. For MIMO testbeds build from SDR devices, phase noise cannot be ignored, particular in applications that require phase synchronization. This is especially relevant in MIMO systems that employ digital beamforming, where precise phase alignment is crucial. Accordingly, accurate phase noise modelling of SDR devices is essential. However, the information provided in data sheets for different SDR models varies widely and is often insufficient for comprehensive characterization of their phase noise performance. While numerical simulations of PLL phase noise behavior are documented in the literature, there is a lack of extensive measurements supported by appropriate system modelling. In this work, we present a practical phase noise modeling methodology applied to an SDR from the USRP X310 series. Based on measurement data, we derive estimates of key PLL performance indicators such as cycle-to-cycle jitter, oscillator constants, and PLL bandwidth. Furthermore, we propose a parametric model for the phase noise PSD of the PLL circuit and provide corresponding parameter estimates. This model can be used for further investigation into the impact of phase noise on MIMO system performance implemented by similar SDR devices.

TAMMs: Temporal-Aware Multimodal Model for Satellite Image Change Understanding and Forecasting

Satellite image time-series analysis demands fine-grained spatial-temporal reasoning, which remains a challenge for existing multimodal large language models (MLLMs). In this work, we study the capabilities of MLLMs on a novel task that jointly targets temporal change understanding and future scene generation, aiming to assess their potential for modeling complex multimodal dynamics over time. We propose TAMMs, a Temporal-Aware Multimodal Model for satellite image change understanding and forecasting, which enhances frozen MLLMs with lightweight temporal modules for structured sequence encoding and contextual prompting. To guide future image generation, TAMMs introduces a Semantic-Fused Control Injection (SFCI) mechanism that adaptively combines high-level semantic reasoning and structural priors within an enhanced ControlNet. This dual-path conditioning enables temporally consistent and semantically grounded image synthesis. Experiments demonstrate that TAMMs outperforms strong MLLM baselines in both temporal change understanding and future image forecasting tasks, highlighting how carefully designed temporal reasoning and semantic fusion can unlock the full potential of MLLMs for spatio-temporal understanding.

A Review of the Long Horizon Forecasting Problem in Time Series Analysis

The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo

Forecasting Time Series with LLMs via Patch-Based Prompting and Decomposition

Recent advances in Large Language Models (LLMs) have demonstrated new possibilities for accurate and efficient time series analysis, but prior work often required heavy fine-tuning and/or ignored inter-series correlations. In this work, we explore simple and flexible prompt-based strategies that enable LLMs to perform time series forecasting without extensive retraining or the use of a complex external architecture. Through the exploration of specialized prompting methods that leverage time series decomposition, patch-based tokenization, and similarity-based neighbor augmentation, we find that it is possible to enhance LLM forecasting quality while maintaining simplicity and requiring minimal preprocessing of data. To this end, we propose our own method, PatchInstruct, which enables LLMs to make precise and effective predictions.

FINN-GL: Generalized Mixed-Precision Extensions for FPGA-Accelerated LSTMs

Recurrent neural networks (RNNs), particularly LSTMs, are effective for time-series tasks like sentiment analysis and short-term stock prediction. However, their computational complexity poses challenges for real-time deployment in resource constrained environments. While FPGAs offer a promising platform for energy-efficient AI acceleration, existing tools mainly target feed-forward networks, and LSTM acceleration typically requires full custom implementation. In this paper, we address this gap by leveraging the open-source and extensible FINN framework to enable the generalized deployment of LSTMs on FPGAs. Specifically, we leverage the Scan operator from the Open Neural Network Exchange (ONNX) specification to model the recurrent nature of LSTM computations, enabling support for mixed quantisation within them and functional verification of LSTM-based models. Furthermore, we introduce custom transformations within the FINN compiler to map the quantised ONNX computation graph to hardware blocks from the HLS kernel library of the FINN compiler and Vitis HLS. We validate the proposed tool-flow by training a quantised ConvLSTM model for a mid-price stock prediction task using the widely used dataset and generating a corresponding hardware IP of the model using our flow, targeting the XCZU7EV device. We show that the generated quantised ConvLSTM accelerator through our flow achieves a balance between performance (latency) and resource consumption, while matching (or bettering) inference accuracy of state-of-the-art models with reduced precision. We believe that the generalisable nature of the proposed flow will pave the way for resource-efficient RNN accelerator designs on FPGAs.

The interplay of robustness and generalization in quantum machine learning

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.

SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance.