Dynamic topological data analysis: a novel fractal dimension-based testing framework with application to brain signals.

BackgroundAttention-deficit/hyperactivity disorder (ADHD) is currently diagnosed by a diagnostic interview, mainly based on subjective reports from parents or teachers. It is necessary to develop methods that rely on objectively measureable neurobiological data to assess brain-behavior relationship in patients with ADHD. We investigated the application of a topological data analysis tool, Mapper, to analyze the brain functional connectivity data from ADHD patients.MethodsTo quantify the disease severity using the neuroimaging data, the decomposition of individual functional networks into normal and disease components by the healthy state model (HSM) was performed, and the magnitude of the disease component (MDC) was computed. Topological data analysis using Mapper was performed to distinguish children with ADHD (n = 196) from typically developing controls (TDC) (n = 214).ResultsIn the topological data analysis, the partial clustering results of patients with ADHD and normal subjects were shown in a chain-like graph. In the correlation analysis, the MDC showed a significant increase with lower intelligence scores in TDC. We also found that the rates of comorbidity in ADHD significantly increased when the deviation of the functional connectivity from HSM was large. In addition, a significant correlation between ADHD symptom severity and MDC was found in part of the dataset.ConclusionsThe application of HSM and topological data analysis methods in assessing the brain functional connectivity seem to be promising tools to quantify ADHD symptom severity and to reveal the hidden relationship between clinical phenotypic variables and brain connectivity.

EEG-based emotion recognition: A deep learning approach to brain region analysis

In this study, the Tuneable Q-factor Wavelet Transform (TQWT) method was applied to classify Attention Deficit and Hyperactivity Disorder (ADHD) diagnosis with features obtained from EEG signals. It was aimed to perform EEG-based ADHD diagnosis more objectively and reliably. EEG signals were analyzed in the prefrontal, frontal, central, parietal, temporal, and occipital regions. The importance levels of the features obtained from the four sub-bands of TQWT and the signal are determined by ANOVA test and classified by machine learning algorithms. In the evaluations made with 10-fold cross-validation, 99.34% training, and 99.41% test accuracy were obtained in the parietal region in the Ensemble Subspace k-NN model, 98.90% training accuracy and 98.53% test accuracy were obtained in the frontal region. The results show that the TQWT method successfully detects important patterns in EEG signals and reveals the cognitive and neurophysiological differences of ADHD.

During the past decade, it has been quite successful to observe how computational topology has incorporated some of the fundamental concepts and ideas from algebraic and differential topology into applications. This fusion of theories gave birth to a new field named Topological Data Analysis (TDA), which has a significant value in various fields, ranging from computational biology to personalized medicine and dynamic data analysis. Going beyond its foundational applications, TDA has enriched and complemented classical machine and deep learning frameworks in establishing what is now known as “topological machine learning.” In this paper, we review the present landscape of this emerging field, emphasizing how it merges with machine learning algorithms such as deep neural networks. Each method confers special advantages, targeting areas like machine learning integration, network reconstruction, classification of network regimes, or reduction of noisy data. We described common methodologies, discussed current implementations, and anticipate future challenges in topological machine learning.

Topological data analysis in investment decisions

• A novel foundation for topological pattern recognition of point cloud data, through persistent homology of graph approximations. • An extension of persistent homology to point cloud data of metric trees, including theoretical and experimental verification. • The first charting of cell trajectory data sets that explains some of the difficulties this field is confronted with. The rising field of Topological Data Analysis (TDA) provides a new approach to learning from data through persistence diagrams , which are topological signatures that quantify topological properties of data in a comparable manner. For point clouds, these diagrams are often derived from the Vietoris-Rips filtration—based on the metric equipped on the data—which allows one to deduce topological patterns such as components and cycles of the underlying space. In metric trees these diagrams often fail to capture other crucial topological properties, such as the present leaves and multifurcations. Prior methods and results for persistent homology attempting to overcome this issue mainly target Rips graphs, which are often unfavorable in case of non-uniform density across our point cloud. We therefore introduce a new theoretical foundation for learning a wider variety of topological patterns through any given graph . Given particular powerful functions defining persistence diagrams to summarize topological patterns, including the normalized centrality or eccentricity , we prove a new stability result, explicitly bounding the bottleneck distance between the true and empirical diagrams for metric trees. This bound is tight if the metric distortion obtained through the graph and its maximal edge-weight are small. Through a case study of gene expression data, we demonstrate that our newly introduced diagrams provide novel quality measures and insights into cell trajectory inference.

Sleep stage classification is pivotal in evaluating sleep quality and diagnosing sleep-related disorders. Recent advancements in automated single-channel electroencephalogram (EEG)--based classification have gained traction due to their cost-effectiveness and portability. However, the inherent non-stationarity of EEG signals and inter-class imbalance pose significant challenges for model design. This paper proposes MultiScaleSleepNet, an enhanced deep learning architecture that addresses these limitations through dynamic multi-scale feature fusion and residual structural optimizations. Our contributions are threefold: (1) A selective kernel convolution module (SKConv) that dynamically integrates multi-branch convolutional features (kernel sizes: 3, 5, 7) via attention mechanisms to adaptively capture frequency-specific patterns in EEG signals; (2) A residual multi-branch downsampling module that mitigates information loss while preserving high-frequency details for minority-stage classification; (3) Comprehensive experiments on the Sleep-EDF-20 dataset demonstrate superior performance, achieving a macro F1-score (MF1) of 79.6%—a 1.5% improvement over baseline models—with notable gains in classifying the N1 stage (F1-score: 47.0%, +4.4% relative improvement). Quantitative ablation studies validate the efficacy of SKConv and residual connections in enhancing feature discriminability. This study delivers a robust single-channel EEG-based sleep analysis framework, demonstrating significant clinical applicability in resource-constrained settings.

Attention-deficit hyperactivity disorder (ADHD) is a neurobiological condition that affects both children and adults. Microstate (MS) analyses, a data-driven approach that identifies stable patterns in EEG signals, offer valuable insights into the neurophysiological characteristics of ADHD. This review summarizes findings from 13 studies that applied MS analyses to resting-state and task-based brain activity in individuals with ADHD. Relevant research articles were retrieved from electronic databases, including PubMed, Google Scholar, Web of Science, PsychInfo, and Scopus. The reviewed studies applied MS analyses to explore brain activity differences in ADHD populations. Resting-state studies consistently reported alterations in MS organization, with increased duration (MS-D) and changes in temporal dynamics (MS-C), potentially reflecting executive dysfunctions and delayed maturation of the default mode network. Additionally, MS B demonstrated promise in distinguishing between ADHD subtypes based on differences in visual network function. Task-based and event-related potential (ERP) studies, using paradigms like the continuous performance task (CPT) or Go-NoGo Task, identified MS abnormalities (i.e., N2, P2, P3, CNV) linked to inhibition and attentional resource allocation. Preliminary evidence suggests that MS analyses hold potential for distinguishing individuals with ADHD from control groups. The integration of machine learning techniques holds promise for improving diagnostic accuracy and identifying ADHD subtypes, while MS analyses may also help monitor the effects of stimulant medications like methylphenidate by tracking neurophysiological changes. However, this review highlights the need for more standardized methodologies to enhance the generalizability and replicability of findings. These efforts will ultimately contribute to a deeper understanding of the neurobiological mechanisms that underlie ADHD.

Objective assessment of spatial cognitive ability is crucial for screening cognitive impairment and in neurorehabilitation. While deep learning methods for electroencephalogram (EEG) analysis show great promise, they increasingly rely on complex, parameter-heavy architectures. This complexity often leads to poor generalization due to overfitting on small datasets and hinders deployment on mobile healthcare devices. To overcome these limitations, we propose a novel lightweight multi-scale channel attention network with depthwise residual blocks. The model incorporates multi-scale convolutional layers to capture diverse temporal and spatial patterns in EEG signals. It then leverages channel attention mechanisms to dynamically prioritize informative channels, focusing on task-critical features. Furthermore, a novel depthwise separable residual block is introduced to significantly reduce computational complexity and maintain stable model performance. Evaluations on a spatial cognition EEG dataset demonstrate that our network achieves higher accuracy than baselines with only 8.453M parameters, making it an efficient and practical solution for mobile deployment. It also holds strong potential for extension to early screening and intervention in a wider range of cognitive disorders.

DGSD: Dynamical graph self-distillation for EEG-based auditory spatial attention detection

Topological data analysis (TDA) is a mathematically well-founded set of methods to derive robust information about the structure and topology of data. It has been applied successfully in several biological contexts. Derived primarily from algebraic topology, TDA rigorously identifies persistent features in complex data, making it well-suited to better understand the key features of three-dimensional chromosome structure. Chromosome structure has a significant influence in many diverse genomic processes and has recently been shown to relate to cellular differentiation. While there exist many methods to study specific substructures of chromosomes, we are still missing a global view of all geometric features of chromosomes. By applying TDA to the study of chromosome structure through differentiation across three cell lines, we provide insight into principles of chromosome folding and looping. We identify persistent connected components and one-dimensional topological features of chromosomes and characterize them across cell types and stages of differentiation. Availability: Scripts to reproduce the results from this study can be found at https://github.com/Kingsford-Group/hictda

Tactile feedback has the capability of reducing the workload on the visual channel, during visual feedback in brain-computer interfaces (BCIs). It is requisite to analyse the brain signals corresponding to the tactile stimulations. This work is aimed at analysing the brain signals while the users are vibrotactually stimulated. The brain signals are acquired non-invasively by electroencephalography (EEG), while brushless coin-type vibration motors are actuated in particular patterns to convey the object shape information on subjects' skin surface in form of vibrations. The acquired EEG signals are pre-processed to eliminate the effect of various types of noises and to extract the EEG signals corresponding to relevant frequency bands. Adaptive autoregressive (AAR) parameters are extracted from the pre-processed EEG signals and are finally classified by Naive Bayesian $(NB)$ approach, in order to recognize the vibratotactually stimulated object shapes from brain signals. In addition to the classifier output, subjects' verbal responses about the object shape they perceived are also noted for validation. Three successive sessions of shape recognition from vibrotactile pattern show an improvement in EEG classification accuracy from 63.75% to 74.37%, and also depicted learning of the stimulus from subjects' psychological response which is observed to increase from 75% to 95%. This observation substantiates the learning of vibrotactile stimulation in user over the sessions which in turn increases the system efficacy.

Asthma is a complex respiratory disease characterised by spatial ventilation heterogeneity (VH) in the lung. Multiple breath washout (MBW) and forced oscillation technique (FOT) testing has been shown to quantify VH at the mouth. Methods to provide fresh insight into the mechanisms driving VH are urgently needed to support treatment development. Computed tomography (CT) with parametric response map (PRM) analysis provides spatial and functional lung data. Integrated data sets of imaging features and VH markers present the problem of extracting meaningful information from high dimensional objects; topological data analysis (TDA) has demonstrated recent success in solving this problem. In this thesis topological methods are applied to extract information about lung anatomy and function from imaging data to study association with VH in innately high dimensional integrated data sets. It was sought to describe the spatial distributions of voxel based metrics, visualise the lungs using TDA methods, and combine PRM with simulated airway tree models to improve computational modelling of FOT. Data was obtained from a clinical trial involving 52 subjects, 41 asthmatic (11 healthy). An algorithm was developed to quantify directional Hounsfield unit change (ΔHU) gradients. TDA was applied to integrated data sets and voxel sets with measures of airway tree depth. FOT modelling was augmented with ΔHU about simulated acinar airways.Inferior-to-superior ΔHU gradient best differentiated VH markers. Visualisations of the lungs illustrated gradient reversal and increased heterogeneity in ΔHU in asthmatics. FOT modelling using ΔHU parameterisation showed increased correlation between clinically measured and simulated FOT small airway resistance (R5-R20). In this thesis additional insight is presented into mechanisms affecting VH markers derived from MBW and FOT. Topological methods to analyse imaging data were developed and implemented, including workflows to visualise the lungs and lung function. Linking simulated airway tree geometry with ΔHU showed improvement in FOT modelling.

The epilepsy is a common neurological disease caused by a neuronal electric activity imbalance in any side of the brain, named epileptic focus. The epilepsy is characterized by recurrent and sudden seizures. Recently, researchers found that approximately 50% of epileptic patients feel auras (subjective phenomenon which precedes and indicates an epileptic seizure onset) associated to a physiological anomaly. In this research, a non-invasive seizure prediction methodology is developed in order to improve the quality of life of the patients with epilepsy, alerting them about potential seizure and avoiding falls, injuries, wounds or even death. The research addresses the recognition of patterns in electroencephalographic (EEG) and electrocardiographic (ECG) signals taken from 7 patients with focal epilepsy whom are treated at the Instituto de Epilepsia y Parkinson del Eje Cafetero-NEUROCENTRO-. The biosignals were independently analyzed, at least 15 minutes before the seizure onset and in periods with no seizure were considered. The methodology considers the generation of features computed over the discrete wavelet transform of the EEG signal and others related to the heart rate variability in the ECG signal. Using feature selection techniques such as Sequential Forward Selection (SFS) with classification algorithms as cost functions (linear-Bayes and k-nearest neighbors classifier), we found which features have the most relevant information about pre-ictal state and which of them are the most appropriated for seizure forecasting, therefore we found that ECG signal could be a potential resource for predicting epileptic seizures, and we concluded that there are patterns in EEG and ECG signals that, via machine learning algorithms, can predict the epileptic seizure onset.

An Artificial Intelligence Ultrasound Platform for Screening and Staging of Thyroid Cancer