MapperEEG: A topological approach to brain state clustering in EEG recordings.

BackgroundInterpretation of high-throughput gene expression data continues to require mathematical tools in data analysis that recognizes the shape of the data in high dimensions. Topological data analysis (TDA) has recently been successful in extracting robust features in several applications dealing with high dimensional constructs. In this work, we utilize some recent developments in TDA to curate gene expression data. Our work differs from the predecessors in two aspects: (1) Traditional TDA pipelines use topological signatures called barcodes to enhance feature vectors which are used for classification. In contrast, this work involves curating relevant features to obtain somewhat better representatives with the help of TDA. This representatives of the entire data facilitates better comprehension of the phenotype labels. (2) Most of the earlier works employ barcodes obtained using topological summaries as fingerprints for the data. Even though they are stable signatures, there exists no direct mapping between the data and said barcodes.ResultsThe topology relevant curated data that we obtain provides an improvement in shallow learning as well as deep learning based supervised classifications. We further show that the representative cycles we compute have an unsupervised inclination towards phenotype labels. This work thus shows that topological signatures are able to comprehend gene expression levels and classify cohorts accordingly.ConclusionsIn this work, we engender representative persistent cycles to discern the gene expression data. These cycles allow us to directly procure genes entailed in similar processes.

A growing area of mathematics topological data analysis (TDA) uses fundamental concepts of topology to analyze complex, high-dimensional data. A topological network represents the data, and the TDA uses the network to analyze the shape of the data and identify features in the network that correspond to patterns in the data. These patterns extract knowledge from the data. TDA provides a framework to advance machine learning’s ability to understand and analyze large, complex data. This paper provides background information about TDA, TDA applications for large data sets, and details related to the investigation and implementation of existing tools and environments.

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.

BOLD-based fMRI is the most widely used method for studying brain function. The BOLD signal while valuable, is beset with unique vulnerabilities. The most notable of these is the modest signal to noise ratio, and the relatively low temporal and spatial resolution. However, the high dimensional complexity of the BOLD signal also presents unique opportunities for functional discovery. Topological Data Analyses (TDA), a branch of mathematics optimized to search for specific classes of structure within high dimensional data may provide particularly valuable applications. In this investigation, we acquired fMRI data in the anterior cingulate cortex (ACC) using a basic motor control paradigm. Then, for each participant and each of three task conditions, fMRI signals in the ACC were summarized using two methods: a) TDA based methods of persistent homology and persistence landscapes and b) non-TDA based methods using a standard vectorization scheme. Finally, using machine learning (with support vector classifiers), classification accuracy of TDA and non-TDA vectorized data was tested across participants. In each participant, TDA-based classification out-performed the non-TDA based counterpart, suggesting that our TDA analytic pipeline better characterized task- and condition-induced structure in fMRI data in the ACC. Our results emphasize the value of TDA in characterizing task- and condition-induced structure in regional fMRI signals. In addition to providing our analytical tools for other users to emulate, we also discuss the unique role that TDA-based methods can play in the study of individual differences in the structure of functional brain signals in the healthy and the clinical brain.

Topological Data Analysis (TDA) and its mainstay computational device, persistent homology (PH), has established a strong track record of providing researchers across the data-driven sciences with new insights and methodologies by characterizing low-dimensional geometric structures in high-dimensional data. When combined with machine learning (ML) methods, PH is valued as a discriminating-feature extraction tool. This work highlights many of the recent successes at the intersection of TDA and ML, introduces some of the foundational mathematics underpinning TDA, and summarizes the efforts to strengthen the bridge between TDA and ML. Thus, this document is a launching point for experimentalists and theoreticians to consider what can be learned from the shape of their data.

Single-cell technologies have revolutionized our ability to interrogate biological systems at unprecedented resolution, revealing complex cellular heterogeneity and dynamic processes that underlie development, disease, and immune responses. However, the high dimensionality and nonlinear structure of single-cell data present substantial analytical challenges. Topological data analysis offers a powerful mathematical framework for capturing the intrinsic shape of data, providing novel insights that complement and extend traditional statistical and machine learning methods. By leveraging tools such as persistent homology and the Mapper algorithm, TDA enables the detection of subtle, multiscale patterns – including rare cell populations, transitional states, and branching trajectories – that are often obscured by conventional approaches. In this review, we explore the theoretical foundations of topological data analysis and examine its emerging applications across single-cell transcriptomics, proteomics, and spatial biology. We highlight how this approach can unveil previously unrecognized biological phenomena, from alternative differentiation paths to complex tissue architectures, and discuss the growing ecosystem of computational tools that support its use. As single-cell datasets become increasingly large and multimodal, topological data analysis stands out as a uniquely robust and interpretable approach, with the potential to deepen our understanding of cellular identity and function in health and disease. TDA is specially suited for fields such as systems immunology since it can capture the complex, nonlinear structures inherent in high-dimensional immune data helping to identify distinct immune cell states, differentiation pathways, and dynamic responses to infection or therapy. This topological perspective complements traditional statistical approaches, providing a robust, scale-invariant framework for uncovering hidden organization within the immune system’s complexity.

Abstract: Neurodegenerative diseases, such as Alzheimer's and Parkinson's, are characterized by progressive neuronal deterioration, leading to cognitive and motor impairments. Early detection is crucial for effective intervention and management. This study proposes a novel framework utilizing Topological Data Analysis (TDA), particularly persistent homology, to identify early biomarkers from neuroimaging and physiological data. This study explores the application of TDA techniques—specifically persistent homology and topological invariants—for the early detection of neurodegenerative diseases such as Alzheimer's. By analyzing functional brain connectivity, gait dynamics, and molecular structures associated with disease progression, the research demonstrates that TDA can capture subtle, yet critical, topological signatures indicative of early neurodegenerative changes. Layer-wise topological complexity in neural networks and persistent homology in clinical datasets reveal distinct structural degradation patterns. The integration of TDA with machine learning models enhances diagnostic accuracy, interpretability, and generalization, offering a promising direction for non-invasive, data-driven diagnostics in neurology.By capturing the intrinsic topological features of brain networks, the framework aims to distinguish between healthy and early-stage neurodegenerative conditions, offering a robust tool for early diagnosis.Topological Data Analysis (TDA) offers a robust mathematical framework for extracting shape-based features from high-dimensional and noisy biomedical data. Keywords: Topological Data Analysis, Persistent Homology, Neurodegenerative Disease, Alzheimer's, Brain Connectivity, Early Diagnosis, Betti Numbers, Gait Analysis, Functional Networks, Machine Learning, Biomedical Data

An approach to extract topological information from Intuitionistic Fuzzy Sets and their application in obtaining a Natural Hierarchical Clustering Algorithm

Rumination—repetitive, negatively valenced, self-focused thought—is a maladaptive cognitive style linked to emotional dysregulation and psychiatric risk. To investigate its neural underpinnings in a naturalistic context, we developed an fMRI paradigm in which participants observed and reflected on videos of their own past group-based problem-solving sessions, a naturalistic self-relevant context rarely examined in fMRI studies. Thirty-two adults (mean age = 30.4 ± 5.4 years; 13 F) were recorded during collaborative design-thinking tasks in triads. In a subsequent scanning session, each participant viewed two self-relevant team videos and one control team video, followed by a structured reflection period. We assessed trait rumination using the Rumination–Reflection Questionnaire (RRQ) and applied Topological Data Analysis (TDA) via the Mapper algorithm to model individual-level whole-brain dynamics during the task. Mapper shape graphs captured temporal transitions between brain states, allowing us to quantify the similarity of timepoints across the session. Individuals with higher trait rumination showed significantly higher temporal similarity, indicating reduced brain-state variability, during self-relevant conditions (r = 0.46, p = 0.018). This effect was not observed during the control condition. These findings suggest that rumination is associated with rigid brain dynamics during self-observation and evaluative processing. Traditional GLM and inter-subject correlation (ISC) analyses confirmed task engagement of key self-referential and social-evaluative regions, while Mapper revealed dynamic features not captured by static or group-averaged methods. Together, these findings demonstrate that trait rumination is associated with rigid large-scale brain dynamics during self-relevant cognition and highlight the value of combining naturalistic paradigms with topological approaches to capture behaviorally meaningful signatures.

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques with applicability on shape analysis, recognition and classification. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.

BackgroundMigraine is a common neurological disorder involving network-level dysfunction. Increasing evidence suggests that migraine involves network-level dysfunction and is associated with altered resting-state functional connectivity. Traditional static functional connectivity analyses are limited in capturing the temporal dynamics of large-scale brain networks. The Hidden Markov Model (HMM) provides an advanced analytical framework to identify discrete, recurrent brain states and characterize their temporal properties without the constraints of arbitrary windowing assumptions.ObjectiveTo characterize dynamic functional connectivity alterations in young patients with migraine without aura (MWoA) using HMM and examine associations between dynamic state metrics and clinical disability.MethodsResting-state fMRI data were obtained from 200 participants (100 young MWoA patients and 100 matched healthy controls). Using the Dosenbach 160 ROI template (cerebellum excluded; N = 142), HMM identified recurring brain states. Group differences in fractional occupancy (FO), mean dwell time (MDT), and state transition probabilities were assessed. State-specific functional connectivity patterns were compared, and correlations with clinical indices (MIDAS, VAS, HIT-6) were evaluated.ResultsEleven robust dynamic brain states were identified. Compared with controls, migraine patients demonstrated increased FO and MDT in States 7 (dorsal attention network–dominant) and 9 (multisensory integration), alongside reduced values in sensorimotor states (States 3, 4, 8, 11). State 9 exhibited significant abnormalities in DMN–SC and DMN–VAN connectivity (FDR-corrected q < 0.05). Transition analyses revealed enhanced self-transitions and increased incoming transitions to States 7 and 9, whereas transitions among sensorimotor states were diminished. MDT in State 9 was positively correlated with MIDAS scores (r = 0.38, p < 0.05), indicating its association with functional disability.ConclusionsYoung MWoA patients exhibit a dual-mode dysfunction in brain dynamics: heightened external vigilance (State 7) and impaired segregation of internal–external processing (State 9), accompanied by instability in baseline sensorimotor configurations. Prolonged dwelling in State 9 and its correlation with disability highlight this multisensory integration state as a potential biomarker of migraine-related functional impairment. These findings provide new insights into neurobiological mechanisms and support dynamic network–based therapeutic strategies.

Insomnia disorder is the most common sleep disorder affecting millions of people. Brain research has linked insomnia to dysfunction in large-scale brain networks, not only during sleep but also in wakeful rest. Yet, the underlying brain dynamics remain little understood. In the present study, we directly addressed this using a data-driven framework for evaluating time-varying large-scale brain activity. We used functional magnetic imaging to compare participants with insomnia disorder to matched controls with no sleep complaints. Using Hidden Markov modeling (HMM) for a completely data-driven characterization of the brain dynamics of whole-brain activity, we found that insomnia disorder is characterized by significantly reduced switching rates between large-scale brain states. In particular, HMM was used to compare insomnia patients to controls, which showed that their brains spent significantly less time in two whole-brain states-the default mode network and a fronto-parietal network-complemented by increased time spent in a global activation state. Overall, the findings reveal the brain dynamics of insomnia to show that insomnia disorder is characterized by less flexible transitions between brain states at wakeful rest. This highlights the importance of evaluating the spatiotemporal dynamics of brain activity to advance the understanding of the neural underpinnings of insomnia disorder.

Sensitisation to recombinant Aspergillus fumigatus allergens and clinical outcomes in COPD

Magnetic resonance spectroscopy (MRS) has been shown to have great clinical potential as a supplement to magnetic resonance imaging in the detection of prostate cancer (CaP). MRS provides functional information in the form of changes in the relative concentration of specific metabolites including choline, creatine, and citrate which can be used to identify potential areas of CaP. With a view to assisting radiologists in interpretation and analysis of MRS data, some researchers have begun to develop computer-aided detection (CAD) schemes for CaP identification from spectroscopy. Most of these schemes have been centered on identifying and integrating the area under metabolite peaks which is then used to compute relative metabolite ratios. However, manual identification of metabolite peaks on the MR spectra, and especially via CAD, is a challenging problem due to low signal-to-noise ratio, baseline irregularity, peak overlap, and peak distortion. In this article the authors present a novel CAD scheme that integrates nonlinear dimensionality reduction (NLDR) with an unsupervised hierarchical clustering algorithm to automatically identify suspicious regions on the prostate using MRS and hence avoids the need to explicitly identify metabolite peaks. The methodology comprises two stages. In stage 1, a hierarchical spectral clustering algorithm is used to distinguish between extracapsular and prostatic spectra in order to localize the region of interest (ROI) corresponding to the prostate. Once the prostate ROI is localized, in stage 2, a NLDR scheme, in conjunction with a replicated clustering algorithm, is used to automatically discriminate between three classes of spectra (normal appearing, suspicious appearing, and indeterminate). The methodology was quantitatively and qualitatively evaluated on a total of 18 1.5 T in vivo prostate T2-weighted (w) and MRS studies obtained from the multisite, multi-institutional American College of Radiology (ACRIN) trial. In the absence of the precise ground truth for CaP extent on the MR imaging for most of the ACRIN studies, probabilistic quantitative metrics were defined based on partial knowledge on the quadrant location and size of the tumor. The scheme, when evaluated against this partial ground truth, was found to have a CaP detection sensitivity of 89.33% and specificity of 79.79%. The results obtained from randomized threefold and fivefold cross validation suggest that the NLDR based clustering scheme has a higher CaP detection accuracy compared to such commonly used MRS analysis schemes as z score and PCA. In addition, the scheme was found to be robust to changes in system parameters. For 6 of the 18 studies an expert radiologist laboriously labeled each of the individual spectra according to a five point scale, with 1/2 representing spectra that the expert considered normal and 3/4/5 being spectra the expert deemed suspicious. When evaluated on these expert annotated datasets, the CAD system yielded an average sensitivity (cluster corresponding to suspicious spectra being identified as the CaP class) and specificity of 81.39% and 64.71%, respectively.

Because of the poor performance of the Random Forest algorithm in processing the classification of high-dimensional unbalanced data, a Hybrid Samping&Feature Selection Random Forest optimization strategy (Hybrid Samping&Feature Selection Random Forest (HF_RF) is proposed in this paper. First, from the data level, the high-dimensional unbalanced data set is preprocessed by SMOTE algorithm combined with random undersampling to achieve balanced unbalanced data. At the same time, the clustering algorithm is combined with SMOTE algorithm to improve the processing ability of the algorithm for negative samples; On the algorithm level, through the Relief F algorithm, different weight values are given to the preprocessed high-dimensional data, irrelevant and redundant features are eliminated, and high-dimensional data is reduced for dimensionality; Finally, the weighted voting principle is used to further elevate the predictive performance of HF_RF. The experimental results show that compared with the traditional algorithm, the proposed algorithm has higher indicators when dealing with high-dimensional unbalanced data, which proves that the HF_RF proposed in this paper is The correctness of the algorithm and its effectiveness in improving the classification performance of high-dimensional unbalanced data.