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Due to event-triggered sampling in a system, or maybe with the aim of reducing data storage, tracking many applications will encounter irregular sampling time. By calculating the matrix exponential using an inverse Laplace transform, this paper transforms the irregular sampling tracking problem to the problem of tracking with time-varying parameters of a system. Using the common Kalman filter, the developed method is used to track a target for the simulated trajectory and video tracking. The results of simulation experiments have shown that it can obtain good estimation performance even at a very high irregular rate of measurement sampling time.

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large data sets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of data sets with which accurate space-use assessments can be made.

Time‐series data missing is a common problem, which often happens with irregular sampling in sensor device failure in human‐cyber‐physical systems (HCPSs). The generation of networked time‐series data is conducive to achieving real‐time perception in HCPSs. Many methods exist for imputing random or non‐random missing data, but their accuracy is often inadequate at high missing rates. We propose a cross‐modality approach using dense spatio‐temporal transformer networks (DSTTN) to impute high‐rate missing data in time series. The DSTTN merges the spatio‐temporal modal data by cross‐modality data fusion technique, and then constructs an end‐to‐end transformer pipeline with dense skip connections to recover the corrupted data accurately. We have conducted many comparative experiments to assess DSTTN imputation performance in the MAR and missing not at random (MNAR). Cross‐modality data fusion offers a new solution for complete data missing, a specific case of MNAR. Furthermore, we also compare and analyse the various recent models, and the particularities between them. Based on the comparative analysis, the application value and working conditions of the DSTTN are demonstrated in detail by the results of rich experiments. We propose a cross‐modality approach using dense spatio‐temporal transformer networks (DSTTN) to impute high‐rate missing data in time series. The DSTTN merges the spatio‐temporal modal data by cross‐modality data fusion technique, and construct an end‐to‐end transformer pipeline with dense skip connections to recover the corrupted data accurately.

To address the challenges of irregular sampling and insufficient spatial sampling in field seismic data, this study proposed a deep learning-based interpolation method incorporating dual channel spatial attention mechanisms (CSAM). The proposed model establishes a collaborative framework of channel and spatial attention, enhancing feature representation by establishing connections between local reflection characteristics and global structural features. The performance of the method was evaluated through synthetic data experiments, including sparsity sensitivity tests, noise sensitivity tests, and field data validation, using metrics such as signal to noise ratio (SNR), mean absolute error (MAE), and structural similarity index (SSIM). Comparative analyses were conducted with Fourier projection onto convex sets (Fourierpocs), the classic U-net, and the efficient channel attention U-net (ECAUnet). Results demonstrate that the proposed method outperforms existing methods in reconstructing seismic reflection events and preserving amplitude fidelity, particularly in scenarios with extensive random data missing.

Abstract In seismic exploration, the acquisition of ideal seismic data is often hindered by various constraints such as high costs and environmental limitations, leading to compromised imaging quality. Compressive sensing (CS) offers novel theories and tools to analyze and guide the acquisition and processing of seismic data. This paper explores the technical advantages and physical mechanisms of CS seismic exploration techniques in direct imaging of irregularly acquired data and imaging of reconstructed data compared to traditional acquisition methods. Our research findings demonstrate that irregular acquired data based on CS acquisition inherently possesses anti-aliasing capabilities in migration imaging, converting strong regular migration noise generated by regular sampling into noise with a random distribution, and through stacking processes suppress migration noise, thereby effectively enhancing the signal-to-noise ratio of imaging. Furthermore, irregularly acquired data exhibits reconstruction advantages, enabling the reconstruction of regular high-density seismic data that yields superior imaging effects. Hence, CS seismic exploration technology is conducive to improving the imaging quality of seismic data.

The hot metal silicon content is a key indicator of the thermal state in the blast furnace and it needs to be kept within a pre-defined range in order to ensure efficient operations. Effective monitoring of silicon content is challenging due to the harsh environment in the furnace and irregularly sampled measurements. Data-driven approaches have been proposed in the literature to predict silicon content using process data and overcome the sparsity of silicon content measurements. However, these approaches rely on the selection of hand-crafted features and ad hoc interpolation methods to deal with irregular sampling of the process variables, adding complexity to model training and optimisation, and requiring significant effort when tuning the model over time to keep it to the required level of accuracy. This paper proposes an improved framework for the prediction of silicon content using a novel deep learning approach based on Phased LSTM. The model has been trained using 3 years of data and validated over a 1-year period using a robust walk-forward validation method, therefore providing confidence in the model performance over time. The Phased LSTM model outperforms competing approaches due to its in-built ability to learn from event-based sequences and scalability for real-world deployments. This is the first time that Phased LSTM has been applied to real-world datasets and results suggest that the ability to learn from event-based data can be beneficial for the process industry where event-driven signals from multiple sensors are common.

Understanding the amount of space required by animals to fulfill their biological needs is essential for comprehending their behavior, their ecological role within their community, and for effective conservation planning and resource management. The space-use patterns of habituated primates often are studied by using handheld GPS devices, which provide detailed movement information that can link patterns of ranging and space-use to the behavioral decisions that generate these patterns. However, these data may not accurately represent an animal’s total movements, posing challenges when the desired inference is at the home range scale. To address this problem, we used a 13-year dataset from 11 groups of white-faced capuchins (Cebus capucinus imitator) to examine the impact of sampling elements, such as sample size, regularity, and temporal coverage, on home range estimation accuracy. We found that accurate home range estimation is feasible with relatively small absolute sample sizes and irregular sampling, as long as the data are collected over extended time periods. Also, concentrated sampling can lead to bias and overconfidence due to uncaptured variations in space use and underlying movement behaviors. Sampling protocols relying on handheld GPS for home range estimation are improved by maximizing independent location data distributed across time periods much longer than the target species’ home range crossing timescale.

Small-scale district heating systems often rely on sensor networks that generate incomplete and irregular time-series data, presenting a significant challenge for reliable modelling and control. This study explores how artificial intelligence (AI) and explainable AI (XAI) methods can be applied directly to such real-world data to support decision-making and enhance system performance. Unlike conventional approaches, we emphasize working directly with irregular time-series data to preserve the fidelity of real-world operating conditions. We compare the predictive accuracy of models trained on raw versus preprocessed datasets, examining how different approaches to interpolation and synthetic data generation affect forecast error. Using XAI, we provide interpretable insights into the influence of environmental and operational variables-such as temperature, flow rate, and perceived temperature-on energy consumption and delivery. In addition, we investigate the timing of heating system activation, aiming to identify which features most strongly impact control decisions under irregular sampling conditions. The findings highlight the trade-offs between data regularization and model transparency and demonstrate the value of interpretable AI in real-world energy system applications.

1. Many animals undertake movements that are longer scaled and more directed than their typical home ranging behaviour. These movements include seasonal migrations (e.g. between breeding and feeding grounds), natal dispersal, nomadic range shifts and responses to local environmental disruptions. While various heuristic tools exist for identifying range shifts and migrations, none explicitly model the movement of the animals within a statistical framework that facilitates quantitative comparisons. 2. We present the mechanistic range shift analysis (MRSA), a method to estimate a suite of range shift parameters: times of initiation, duration of transitions, centroids and areas of respective ranges. The method can take the autocorrelation and irregular sampling that is characteristic of much movement data into account. The mechanistic parameters suggest an intuitive measure, the range shift index, for the extent of a range shift. The likelihood based estimation further allows for statistical tests of several relevant hypotheses, including a range shift test, a stopover test and a site fidelity test. The analysis tools are provided in an R package (MARCHER). 3. We applied the MRSA to a population of GPS tracked roe deer (Capreolus capreolus) in the Italian Alps between 2005 and 2008. With respect to seasonal migration, this population is extremely variable and difficult to classify. Using the MRSA, we were able to quantify the behaviours across the population and among individuals across years, identifying extents, durations and locations of seasonal range shifts, including cases that would have been ambiguous to detect using existing tools. 4. The strongest patterns were differences across years: many animals simply did not perform a seasonal migration to wintering grounds during the mild winter of 2006-2007, even though some of these same animals did move extensively in other, harsher winters. For seasonal migrants, however, site fidelity across years was extremely high, even after skipping an entire seasonal migration. These results suggest that for roe deer behavioural plasticity and tactical responses to immediate environmental cues are reflected in the decision of whether rather than where to migrate. The MRSA also revealed a trade-off between the probability of migrating and the size of a home range.

Verrill's modern Mussismilia (the ‘brain corals’) were described in the 19th century, being hitherto considered endemic reef-building species to Brazil. Contrasting with the original diagnoses, highly variable morphological patterns have been observed among the congeners. Interspecific overlapping of major taxonomical characters has resulted in quite inconclusive use of the skeleton macromorphology for the genus. Intending to corroborate the Mussismilia taxonomy, a comparative morphological approach was developed, combining skeleton macro- and micromorphology. A total of 132 colonies was collected between 13°S and 17°S latitude (Mussismilia hispida = 53, Mussismilia harttii = 41, and Mussismilia braziliensis = 38). Qualitative (n = 9) and quantitative characters (n = 7) were selected (the latter was analysed with Kruskal–Wallis and a principal component analysis). A non-parametric test was adopted due to heteroscedasticity and the irregular sampling among populations. As a result, the corallite diameter and number of septa were significantly distinct among the species (α = 0.05). Micromorphology also differs interspecifically, being distribution and size of septal spines diagnostic for the congeners. Intraspecific variation and morphs are approached, ensuring the relevance of the skeleton for the interspecific delimitation and the species identities. Finally, field identification and/or methods based on image analyses from video transects should be adopted with caution. These practices may provide unreliable data, once the information is restricted to the view of the colony top, resulting in biased identification – majorly if the morphotypes of M. harttii and M. hispida share closely spaced corallites.