This research presents results from evaluating a range of centroid functions for the nearest centroid classifier applied to several multivariate time series classification datasets. These are tested on seven of the largest benchmark datasets available. The centroid functions includes two proposed methods for generating centroids from time series: DTW-MP I and DTW-MP D and five state-of-art centroid functions: SoftDTW, DBA, PAM, Mean and SE. These proposed centroid algorithms use dynamic time warping to combine any number of time series together into one representative centroid. The input time series can be of different lengths and of multivariate data (n-dimensional). Centroids of time series have a wide range of uses but are often used as a nearest centroid classifier which is faster than a DTW-1NN classifier due to a much lower number of DTW comparisons being required to classify a new time series into existing classes. Therefore we utilize the task of nearest centroid classification in this research as a means to evaluate the performance of two proposed and five state-of-art centroid functions. For evaluation, six of the largest publicly available multivariate time series benchmark datasets currently available were used. These results show that the proposed DTW-MP I and DTW-MP D centroid algorithms perform comparatively with state-of-art time series centroid functions and these could have further uses in other time series applications.

TF-LLM: Enhanced time series analysis with time-frequency large language models.

• SAURL-TS is a novel framework for self-supervised time series representation learning. • SAURL-TS adaptively fits diverse temporal and spectral patterns across various time series. • SAURL-TS introduces adaptive augmentation to generate high-quality positive pairs. • SAURL-TS achieves strong performance without relying on negative samples. • SAURL-TS is validated through extensive and robust evaluation on classification and forecasting. Unsupervised time series representation learning, driven by recent advances in contrastive learning-based methods, has become a critical component for downstream tasks like forecasting and classification. However, time series data exhibit complex temporal dependencies and spectral patterns, posing challenges for existing approaches to adapt robustly. Moreover, existing contrastive learning-based approaches overlook frequency-domain information and struggle with selecting effective negative samples, further hindering model performance. To address these issues, we propose S a URL-TS, a novel self-adaptive framework for unsupervised time series representation learning. First, it dynamically learns dataset-specific augmentations to generate high-quality positive samples. Second, an adaptive self-supervised learning module with a multi-domain encoder captures both temporal and spectral patterns without relying on negative samples. Third, a representation-wise attention mechanism assigns dynamic weights to representations across domains. To the best of our knowledge, S a URL-TS is the first self-supervised learning framework to jointly model temporal and spectral patterns across both augmentation and learning stages. Extensive experiments confirm the superior performance of S a URL-TS over state-of-the-art models. Notably, its adaptive data augmentation module is plug-and-play and can be integrated into other contrastive learning frameworks, and its learning stage is capable of adapting to a wide range of time series patterns. Our codebase is available at https://github.com/YusenL/SAURL-TS .

A noise robust and distribution-adaptive framework for multivariate time series anomaly detection.

A novel anomaly detection method for concrete dam measured data based on an improved MemAE model

Stringology-based motif discovery for electrophysiological time series: A framework for temporal pattern analysis with an ADHD case study.

ZAD-ML: Dual-layer Learning for zero-Day attack detection in multivariate time series

MARINE-Transformer: A General-purpose framework for multivariate ocean time series analysis.

Abstract A theoretically operable but unvalidated method has been presented to observe the strength of the upwelling induced by global tropical cyclones (TCs); here, it is validated using observations from the daily 2-km-resolution level-3 Surface Water and Ocean Topography (SWOTl3) satellite data. The method quantifies the upwelling strength as the change of the sea surface height (SSH) extreme within a cyclonic ocean eddy (COE) or anticyclonic ocean eddy (AOE) identified from low-resolution gridded altimetry datasets. Although the artificial smoothness segment (ASS) always exists in the time series of an observed eddy SSH extreme, the method further argued that the maximum change in the ASS theoretically equals to the upwelling strength. To evidence its reliability, the time series of swath-mean SSH and the eddy extremes of three COEs and an AOE are derived from four gridded datasets. In sharp contrast to the abrupt decreases in SWOTl3-observed data, all the time series from the gridded datasets show the slow decrease near the typhoon’s passage and thus directly verify the existing ASSs. Using the method, the quantified upwelling strengths near 17°N are very consistent with the SWOTl3 observations, confirming its reliability. The quantified upwelling strengths in the Kuroshio near 27°N seem to be enhanced with the increasing quality of the gridded datasets. However, even in the Kuroshio, the upwelling strength quantified from the best available gridded dataset in recent years should still be reliable. The validated method will provide an effective tool to quantify global TC-induced upwelling. Significance Statement The upwelling induced by a tropical cyclone plays a key role in the effects of global tropical cyclones on ocean. However, a feasible method to quantify the upwelling strength is still absent for global tropical cyclones. A theoretically operable but unvalidated method has been presented. Here, this method is validated to be reliable using observations from the daily 2-km-resolution level-3 Surface Water and Ocean Topography satellite data.

FreqMLNet: Non-transformer network with frequency domain reconstruction and multi-scale representation for time series forecasting.

Aminotransferases are widely used for metabolic dysfunction-associated steatotic liver disease (MASLD) evaluation, especially in type 2 diabetes mellitus (T2DM). Whether within-person seasonal variation affects classification near commonly used thresholds or relates to long-term metabolic outcomes remains unclear. This registry-based cohort analysed monthly aspartate aminotransferase (AST) and alanine aminotransferase (ALT) measurements from 6039 adults with T2DM in the Japan Diabetes Clinical Data Management registry (2014-2020). Classification discordance across the 30 IU/L threshold was compared between winter-mean and summer-mean values. Individual seasonal amplitude was derived from seasonal-trend decomposition of multiply imputed monthly time series. Final glycated haemoglobin (HbA1c) and non-achievement of HbA1c < 7% were analysed using multivariable regression. Both AST and ALT showed significant seasonal variation, with the highest values in late autumn to early winter and the lowest in summer (p < 0.001). Approximately one in nine patients with borderline ALT values showed discordant winter-summer classification. Each 1-SD increase in AST amplitude was associated with 0.06 percentage points higher final HbA1c (95% CI, 0.04-0.08) and higher odds of not achieving HbA1c < 7% (odds ratio, 1.14; 95% CI, 1.08-1.21; p < 0.001). ALT amplitude showed a similar but weaker, less consistent association. AST and ALT exhibited reproducible seasonal variation peaking in late autumn to early winter, with approximately one in nine patients near the MASLD screening threshold reclassified depending on season. Greater seasonal amplitude, especially AST, was independently associated with poorer glycemic control, supporting season-aware interpretation in routine clinical practice.

Memory-guided mask reconstruction with central contrastive learning for robust multivariate time series anomaly detection.

Forecasting fluctuations in agricultural markets: The power of secondary decomposition and neural networks

Get over here: black capuchin monkeys use long-range vocalizations to adjust the distance between individuals.

Effects of extreme hydrological disturbances on the resilience, resistance, and functional redundancy of fish assemblages in a subtropical estuary.

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme value theory, is the asymptotic behavior of such partial sums when the subordination mechanism has a threshold depending on sample size, so as to focus on the right tail of the time series. This article substantially extends longstanding asymptotic techniques by allowing the subordination mechanism to depend on the sample size in this way and to grow at a polynomial rate, while permitting the innovation process to have infinite variance. The cornerstone of our theoretical approach is a tailored reduction principle, which enables the use of classical results on partial sums of long memory linear processes. In this way we obtain asymptotic theory for certain Peaks-over-Threshold estimators with deterministic or random thresholds. Applications cover both heavy- and light-tailed regimes, yielding unexpected results which, to the best of our knowledge, are new to the literature. A simulation study illustrates the relevance of our findings in finite samples.

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on closed-box models or require extensive user intervention for interpretability. We propose SyMPLER (Systems Modeling through Piecewise Linear Evolving Regression), an explainable model for time series forecasting in nonstationary environments based on dynamic piecewise-linear approximations. Unlike other locally linear models, SyMPLER uses generalization bounds from Statistical Learning Theory to automatically determine when to add new local models based on prediction errors, eliminating the need for explicit clustering of the data. Experiments show that SyMPLER can achieve comparable performance to both closed-box and existing explainable models while maintaining a human-interpretable structure that reveals insights about the system's behavior. In this sense, our approach conciliates accuracy and interpretability, offering a transparent and adaptive solution for forecasting nonstationary time series.

Objective. Phase gating is a critical technique to mitigate tumor motion during radiotherapy, particularly in spot-scanned particle therapy where internal motion can interfere with dynamic spot scanning patterns and, simultaneously, introducing substantial range uncertainties. However, the current commercial state of the art in real-time phase prediction is challenged by patient-specific breathing variability as well as detection and delivery system latencies. This leads to suboptimal efficiency, mis-timed radiation delivery and requires frequent manual intervention. This study aims to improve phase prediction accuracy using deep learning (DL)-based time series forecasting to enable more accurate dose delivery.Approach. Retrospective breathing waveforms from 69 proton therapy patients, sampled at 30 Hz, were labeled with inspiratory peaks and assigned subjective regularity scores (four levels). DL models with various architectures were trained using waveform amplitude to predict current or future breathing phases. Model performance was evaluated using mean squared error, phase binning accuracy, and timing deviation for radiation on/off events. Bayesian optimization was used for hyperparameter tuning. Results were compared between models and against a commercial algorithm currently in clinical use.Main Results. The curated waveform dataset included 165 242 s for training, 24 057 s for validation, and 30 322 s for testing, with an additional 40 604 s from separate patients for extended validation. The long short-term memory and temporal fusion transformer models significantly outperformed the commercial algorithm, improving phase prediction accuracy by nearly 20% and reducing timing deviations across all regularity levels.Significance. DL-based time series forecasting may substantially improve breathing phase prediction accuracy over current clinically available methods, offering a more precise and reliable approach to phase-gated radiation delivery.

A reduced order analytical model to reconstruct tower bending moments time series of onshore wind turbines validated with experimental data

Information about the spatial distribution of urban populations is highly relevant for areas such as urban planning, infrastructure services, and hazard prevention. Conventionally, census-based population maps provide a static image of population numbers. However, the distribution of urban populations is highly dynamic and changes throughout the course of a day, which can result in significant discrepancies from static maps. We therefore developed a spatio-temporal population model, which is designed to provide the relevant space- and time-dependent distribution for individual cities in Germany. Germany has been selected due to the high data availability, which allows us to base the model on public data, making it transferable to other cities. The city of Cologne serves as a case study, but the transfer of the approach to Hamburg has been successfully tested. The model is built on extensive dasymetric mapping cycles to combine extensive socio-demographic population and building data with mobility information. The results obtained are city-wide population maps for seven time sequences, which provide the total number of people, as well as the number of people for seven population subgroups (children, retired, etc.), on building level. The results are compared to three independent data sets (ENACT-POP, emergency call locations, and mobile phone location data), which show substantial improvement towards static census data and good correlation metrics. The spatio-temporal results show strong time-dependent differences in comparison to static population distribution (e.g., up to six times more people for the inner city of Cologne at midday), underlining the relevance of time-dependent data for population-based analyses. • Model to calculate spatio-temporal population maps for German cities • Uses iterative dasymetric mapping to combine geo-, demographic-, and mobility data • Produces population maps for seven time intervals of a standard working day • Results differentiate between seven population subgroups (e.g., children, elderly) • Model validation with ambulance calls, phone locations, and European day/night data