Recent advancements in machine learning-based signal analysis, coupled with open data initiatives, have fuelled efforts in automatic sleep stage classification. Despite the proliferation of classification models, few have prioritised reducing model complexity, which is a crucial factor for practical applications. In this work, we introduce Multi-Scale and Attention Convolutional Neural Network (MSA-CNN), a lightweight architecture featuring as few as similar to 10,000 parameters. MSA-CNN leverages a novel multi-scale module employing complementary pooling to eliminate redundant filter parameters and dense convolutions. Model complexity is further reduced by separating temporal and spatial feature extraction and using cost-effective global spatial convolutions. This separation of tasks not only reduces model complexity but also mirrors the approach used by human experts in sleep stage scoring. We evaluated both small and large configurations of MSA-CNN against nine state-of-the-art baseline models across three public datasets, treating univariate and multivariate models separately. Our evaluation, based on repeated cross-validation and re-evaluation of all baseline models, demonstrated that the large MSA-CNN outperformed all baseline models on all three datasets in terms of accuracy and Cohen's kappa, despite its significantly reduced parameter count. Lastly, we explored various model variants and conducted an in-depth analysis of the key modules and techniques, providing deeper insights into the underlying mechanisms. The code for our models, baselines, and evaluation procedures is available at https://github.com/sgoerttler/MSA-CNN.

Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is essential for understanding its role in processes such as memory and attention. However, this remains a significant challenge. Most existing methods rely on variations in the temporal profile to detect PAC, but they often suffer from key limitations, most notably, their sensitivity to filter bandwidth selection and their susceptibility to detecting spurious couplings. Previous studies have suggested that approaches grounded in the actual generative dynamics of PAC may offer improved accuracy. In this study, we adopt a dynamical systems perspective and propose a novel method for PAC detection and characterisation based on nonlinear system identification. This approach involves identifying a nonlinear dynamical model that captures the temporal dynamics underlying PAC. The resulting generative model enables noise-free simulation of estimated PAC signals, facilitating detailed analysis of modulation strength and the low-frequency phase at which the high-frequency bursts occur. The proposed method accounts for harmonic-induced spurious couplings through empirically derived criteria and remains robust to high noise levels and variations in slow-frequency power, offering an accurate and interpretable framework for PAC analysis. The performance of the proposed approach is illustrated using several simulated examples and a real case using local field potentials (LFP) data. The results are compared with several popular methods.

A growing number of techniques leverage the spatial structures that underlie many real-world datasets. Despite these advances, the complementary task of estimating spatial structures and understanding their role within these techniques has often been overlooked. In neurophysiological data analysis specifically, numerous methods exist to estimate brain connectivity, but most are not explicitly model-based, dynamic, multivariate, or directed. To address these limitations, we previously introduced noise-driven heat modelling on graphs for neurophysiological connectivity estimation. In this study, we extend this framework by relaxing earlier noise assumptions and adding regularisation to improve robustness. We also develop a simulation procedure to characterise and evaluate our technique in a controlled setting. Finally, we demonstrate that the technique is able to capture meaningful spatial structure across two experiments, each using two real-world datasets. The explicit model formulation of our connectivity estimator has the potential to improve the interpretability of graph-based techniques across a wide range of applications. The code implementing our method is available at https://github.com/sgoerttler/Heat_Connectivity.

In multi-carrier wireless systems, dynamic channel conditions significantly affect reliable data transmission. Traditional power allocation strategies, like water-filling, prioritize channels with the highest gains, often overlooking fairness among users or subcarriers. However, fairness-oriented allocation is challenging when discrete constellations lack closed-form expressions for channel capacity. Furthermore, computing such information can be challenging for Internet of Things (IoT) devices due to their limited resources. To address these issues, we propose a power allocation strategy that leverages a lower bound on mutual information and its relationship with minimum mean squared error to approximate channel capacity. This approximation is combined with Gaussianinput capacity estimates to improve accuracy. Experimental results show that, unlike water-filling, our approach allocates more power to weaker channels, enhancing fairness without sacrificing efficiency. In certain SNR ranges, the proposed method achieves performance comparable to exact capacity-based allocation, offering a practical solution for fairness-aware resource management in next-generation networks.

Despite significant advances in deep learningbased sleep stage classification, the clinical adoption of automatic classification models remains slow. One key challenge is the lack of explainability, as many models function as black boxes with millions of parameters. In response, recent work has increasingly focussed on enhancing model explainability. This study contributes to these efforts by introducing an explainability tool for spectral processing of individual EEG channels. Specifically, this tools retrieves the filter spectrum of low-level convolutional feature extraction and compares it with the classificationrelevant spectral information in the data. We apply our tool on the EEGNet and MSA-CNN models using the ISRUC-S3 and Sleep-EDF-20 datasets. The tool reveals that spectral processing plays a significant role in the lower frequency bands. In addition, comparing the correlation between filter spectrum and data-derived spectral information with univariate performance indicates that the model naturally prioritises the most informative channels in a multimodal setting. We specify how these insights can be leveraged to enhance model performance.

Dementia, including Alzheimer’s disease and frontotemporal dementia, is a progressive brain disorder that disrupts memory, thinking, and behavior, with early diagnosis being critical for effective intervention. This study examines the alteration of brain activity caused by dementia by analyzing electroencephalogram (EEG) signals using an information geometry method known as information rate, which captures the evolving patterns of brain signals over time rather than relying on static averages. This method is applied across standard EEG frequency bands – delta, theta, alpha, beta, and gamma – in participants with dementia and healthy controls. The characteristics of the distribution of information rate are studied through the statistical moments (such as mean, variance, skewness, and kurtosis) and Shannon entropy. The statistical comparisons are accessed using the Kruskal-Wallis test with Dunn’s post-hoc analysis, and results are compared against a conventional average-base method using Jensen-Shannon distance. The results show that dynamic features of EEG signals – particularly in the theta, alpha, and beta bands – effectively distinguish Alzheimer’s patients from healthy individuals, while the Shannon entropy of signal dynamics in frontal region differentiates frontotemporal dementia patients across the theta to gamma bands. Moreover, changes in the occipital region detected by information rate, but not by traditional method, further highlight the importance of capturing temporal variability. The method also successfully distinguishes individuals with Mild Cognitive Impairment from healthy controls, which conventional analysis failed to achieve. These results suggest that analyzing the dynamics properties of the brain signals provides a more sensitive and informative approach for identifying and distinguishing various forms of dementia.

Electroencephalography (EEG), as a well-established, non-invasive tool, has been successfully applied to a wide range of conditions due to its many evident advantages, such as economy, portability, easy operation, easy accessibility, and widespread availability in hospitals [...]

Accurate characterization of functional connectivity (FC) in neural signals is critical for investigating a wide range of brain disorders and cognitive processes. Conventional approaches typically rely on correlation-based metrics to capture pairwise interactions; however, such measures may fail to capture more global patterns of connectivity. Pairwise Maximum Entropy Models (pMEM) a complementary global perspective by jointly modeling all pairwise interactions, but they can diverge significantly from traditional linear FC measures and are often prone to numerical instability. In this study, we propose a penalized pMEM framework that incorporates correlation-based FC into pMEM as a prior constraint, aiming to balance the global coupling captured by pMEM with the interpretability and simplicity of correlation-based approaches. By regulating the adherence of pMEM parameters to traditional FC, our method achieves more stable learning and better preserves key linear relationships. We evaluate the proposed framework using a public available EEG dataset comprising individuals with Alzheimer’s disease and healthy controls. The proposed hybrid modelling of FC achieves a classification accuracy of 83.13%, outperforming both standalone pMEM and correlation-based classifiers. Furthermore, the penalized pMEM reveals more pronounced group difference in network small-worldness, offering improved interpretability alongside enhanced classification performance.

Heat diffusion describes the process by which heat flows from areas with higher temperatures to ones with lower temperatures. This concept was previously adapted to graph structures, whereby heat flows between nodes of a graph depending on the graph topology. Here, we combine the graph heat equation with the stochastic heat equation, which ultimately yields a model for multivariate time signals on a graph. We show theoretically how the model can be used to directly compute the diffusion-based connectivity structure from multivariate signals. Unlike other connectivity measures, our heat model-based approach is inherently multivariate and yields an absolute scaling factor, namely the graph thermal diffusivity, which captures the extent of heat-like graph propagation in the data. On two datasets, we show how the graph thermal diffusivity can be used to characterise Alzheimer's disease. We find that the graph thermal diffusivity is lower for Alzheimer's patients than healthy controls and correlates with dementia scores, suggesting structural impairment in patients in line with previous findings.

Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these multivariate signals, while at the same time taking the spatial structure between the time signals into account. A central idea in GSP is the graph Fourier transform, which projects a multivariate signal onto frequency-ordered graph Fourier modes, and can therefore be regarded as a spatial analog of the temporal Fourier transform. This chapter derives and discusses key concepts in GSP, with a specific focus on how the various concepts relate to one another. The experimental section focuses on the role of graph frequency in data classification, with applications to neuroimaging. To address the limited sample size of neurophysiological datasets, we introduce a minimalist simulation framework that can generate arbitrary amounts of data. Using this artificial data, we find that lower graph frequency signals are less suitable for classifying neurophysiological data as compared to higher graph frequency signals. Finally, we introduce a baseline testing framework for GSP. Employing this framework, our results suggest that GSP applications may attenuate spectral characteristics in the signals, highlighting current limitations of GSP for neuroimaging.

In smart greenhouse farming, the impact of light qualities on plant growth and development is crucial but lacks systematic identification of optimal combinations. This study addresses this gap by analysing various light properties' effects (photoperiod, intensity, ratio, light-dark order) on Arabidopsis thaliana growth using days-to-flower (DTF) and hypocotyl length as proxies to measure plant growth and development. After establishing suitable ranges through a comprehensive literature review, these properties varied within those ranges. Compared to white light, a 16-h cycle of blue light reduces DTF and hypocotyl length by 12 % and 3 %, respectively. Interestingly, similar results can be achieved using a shorter photoperiod of 14-h light (composed of 8 h of a mixture of 66.7 mu mol m-2s-1 red and 800 mu mol m-2s-1 blue lights (i.e. blue:red ratio of 12:1) followed by 6 h of monochromatic red light and 10-h dark. These findings offer potential for efficient growth light recipes in smart greenhouse farming, optimizing productivity while minimizing energy consumption.

In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer’s disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to quantify the time evolution of probability density functions of simulated EEG signals, and employ causal information rates to quantify one signal’s instantaneous influence on another signal’s information rate. These two measures help us find significant and interesting distinctions between healthy subjects and AD patients when they open or close their eyes. These distinctions may be further related to differences in neural information processing activities of the corresponding brain regions, and to differences in connectivities among these brain regions. Our results show that information rate and causal information rate are superior to their more traditional or established information-theoretic counterparts, i.e., differential entropy and transfer entropy, respectively. Since these novel, information geometry theoretic measures can be applied to experimental EEG signals in a model-free manner, and they are capable of quantifying non-stationary time-varying effects, nonlinearity, and non-Gaussian stochasticity presented in real-world EEG signals, we believe that they can form an important and powerful tool-set for both understanding neural information processing in the brain and the diagnosis of neurological disorders, such as Alzheimer’s disease as presented in this work.

Graph neural networks (GNN) are increasingly used to classify EEG for tasks such as emotion recognition, motor imagery and neurological diseases and disorders. A wide range of methods have been proposed to design GNN-based classifiers. Therefore, there is a need for a systematic review and categorisation of these approaches. We exhaustively search the published literature on this topic and derive several categories for comparison. These categories highlight the similarities and differences among the methods. The results suggest a prevalence of spectral graph convolutional layers over spatial. Additionally, we identify standard forms of node features, with the most popular being the raw EEG signal and differential entropy. Our results summarise the emerging trends in GNN-based approaches for EEG classification. Finally, we discuss several promising research directions, such as exploring the potential of transfer learning methods and appropriate modelling of cross-frequency interactions.

The prospect of future treatment warrants the development of cost-effective screening for Alzheimer’s disease (AD). A promising candidate in this regard is electroencephalography (EEG), as it is one of the most economic imaging modalities. Recent efforts in EEG analysis have shifted towards leveraging spatial information, employing novel frameworks such as graph signal processing or graph neural networks. Here, we investigate the importance of spatial information relative to spectral or temporal information by varying the proportion of each dimension for AD classification. To do so, we systematically test various dimension resolution configurations on two routine EEG datasets. Our findings show that spatial information is more important than temporal information and equally valuable as spectral information. On the larger second dataset, substituting spectral with spatial information even led to an increase of 1.1% in accuracy, which emphasises the importance of spatial information for EEG-based AD classification. We argue that our resolution-based feature extraction has the potential to improve AD classification specifically, and multivariate signal classification generally.Clinical relevance— This study proposes balancing the spectral, temporal and spatial feature resolution to improve EEGbased diagnosis of neurodegenerative diseases.

Electroencephalogram (EEG) is a valuable technique to record brain electrical activity through electrodes placed on the scalp. Analyzing EEG signals contributes to the understanding of neurological conditions and developing brain-computer interface. Graph Signal Processing (GSP) has emerged as a promising method for EEG spatial-temporal analysis, by further considering the topological relationships between electrodes. However, existing GSP studies lack interpretability of electrode importance and the credibility of prediction confidence. This work proposes an EEG Graph Mutual Attention Convolutional Network (EEG-GMACN), by introducing an ’Inverse Graph Weight Module’ to output interpretable electrode graph weights, enhancing the clinical credibility and interpretability of EEG classification results. Additionally, we incorporate a mutual attention mechanism module into the model to improve its capability to distinguish critical electrodes and introduce credibility calibration to assess the uncertainty of prediction results. This study enhances the transparency and effectiveness of EEG analysis, paving the way for its widespread use in clinical and neuroscience research.

System identification involves constructing mathematical models of dynamic systems using input-output data, enabling analysis and prediction of system behaviour in both time and frequency domains. This approach can model the entire system or capture specific dynamics within it. For meaningful analysis, it is essential for the model to accurately reflect the underlying system's behaviour. This paper introduces NonSysId, an open-sourced MATLAB software package designed for nonlinear system identification, specifically focusing on NARMAX models. The software incorporates an advanced term selection methodology that prioritises on simulation (free-run) accuracy while preserving model parsimony. A key feature is the integration of iterative Orthogonal Forward Regression (iOFR) with Predicted Residual Sum of Squares (PRESS) statistic-based term selection, facilitating robust model generalisation without the need for a separate validation dataset. Furthermore, techniques for reducing computational overheads are implemented. These features make NonSysId particularly suitable for real-time applications such as structural health monitoring, fault diagnosis, and biomedical signal processing, where it is a challenge to capture the signals under consistent conditions, resulting in limited or no validation data.

Signals measured with multiple sensors simultaneously in time form multivariate signals and are commonly acquired in biomedical imaging. These temporal signals are generally not independent of each other, but exhibit a rich spatial structure. Graph filtering, either spatial or spectral, is a method that can leverage this spatial structure for various preprocessing tasks, such as graph denoising. Previous studies have focused on learning the parameters of spatial graph impulse response (GIR) filters, while neglecting spectral graph frequency response (GFR) filters, even though GFR filters offer unique advantages in terms of regularisation and interpretation. In this study, we therefore compare learning GIR filters and GFR filters as a trainable preprocessing step for two different neural networks on an Alzheimer’s classification task. We tested both a functional connectivity graph as well as a geometric graph as the base of each filter type, and varied the localisation of the spatial filter. As expected, the retrieved shapes of the trained filters suggest that GFR filters can be interpreted in terms of their graph structure, while the same does not hold for GIR filters. Contrarily, however, we found that only the geometric, highly localised GIR filter outperforms the baseline significantly, surpassing it by 3.8 percentage points. These findings suggest that the observed performance boost of a trained localised GIR filter may in fact not be due to the graph structure. Instead, we hypothesise that this boost is caused by favourable algebraic properties of the filter matrix.

The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction of one process based on the knowledge of another process at an earlier time. However, they have their own limitations, e.g., in applications to nonlinear, non-stationary data, or non-parametric models. In this study, we propose an alternative approach to quantify causality through information geometry that overcomes such limitations. Specifically, based on the information rate that measures the rate of change of the time-dependent distribution, we develop a model-free approach called information rate causality that captures the occurrence of the causality based on the change in the distribution of one process caused by another. This measurement is suitable for analyzing numerically generated non-stationary, nonlinear data. The latter are generated by simulating different types of discrete autoregressive models which contain linear and nonlinear interactions in unidirectional and bidirectional time-series signals. Our results show that information rate causalitycan capture the coupling of both linear and nonlinear data better than GC and TE in the several examples explored in the paper.

Graph neural network (GNN) models are increasingly being used for the classification of electroencephalography (EEG) data. However, GNN-based diagnosis of neurological disorders, such as Alzheimer's disease (AD), remains a relatively unexplored area of research. Previous studies have relied on functional connectivity methods to infer brain graph structures and used simple GNN architectures for the diagnosis of AD. In this work, we propose a novel adaptive gated graph convolutional network (AGGCN) that can provide explainable predictions. AGGCN adaptively learns graph structures by combining convolution-based node feature enhancement with a correlation-based measure of power spectral density similarity. Furthermore, the gated graph convolution can dynamically weigh the contribution of various spatial scales. The proposed model achieves high accuracy in both eyes-closed and eyes-open conditions, indicating the stability of learned representations. Finally, we demonstrate that the proposed AGGCN model generates consistent explanations of its predictions that might be relevant for further study of AD-related alterations of brain networks.