Optimal Base Station Network Based on Topological Data Analysis

The decision of which base stations need to be removed due to the cost is always a difficult problem, because the influence on the cover rate of the network caused by the removal should be kept to a minimum. However, the common methods to solve this problem such as K-means Clustering show a low accuracy. Barcode, which belongs to TDA, has the possibility to show the result by identifying the Persistent Homology of base station network. This essay mainly illustrates the specific problem of optimal base station network, which applies the TDA(Topological Data Analysis) methods to find which base stations need removing due to the cost K-means Clustering and Topological Data Analysis methods were mainly used. With the simulated distribution of telecommunication users, K-means Clustering algorithm was used to locate 30 best base stations. By comparing the minimum distance between the results (K=25 and K=30), K-means Clustering was used again to decide base station points to be removed. Then TDA was used to select which 5 base stations should be removed through observing barcode. By repeating above steps five times, Finally the average and variance of cover area in original network, K-means Clustering and TDA were compared. The experiment showed that the average cover rate of original network was 81.20% while the result of TDA and K-means Clustering were 92.13% and 89.87%. It was proved by simulation that it is more efficient to use TDA methods to construct the optimal base station network.

Tracking the time evolution of soft matter systems via topological structural heterogeneity

Persistent homology is an effective topological data analysis tool to quantify the structural and morphological features of soft materials, but so far it has not been used to characterise the dynamical behaviour of complex soft matter systems. Here, we introduce structural heterogeneity, a topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder transition at the microscopic scale. We show that structural heterogeneity tracks structural changes in a liquid crystal nanocomposite, reveals the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transitions, and uncovers physical differences between these two processes. The system used in this work is representative of a class of composite nanomaterials, partially ordered and with complex structural and physical behaviour, where their precise characterisation poses significant challenges. Our developed analytic framework can provide both a qualitative and quantitative characterisation of the dynamical behaviour of a wide range of semi-ordered soft matter systems.

Toroidal topology of population activity in grid cells

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal’s allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8–11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

NeuMapper: A scalable computational framework for multiscale exploration of the brain’s dynamical organization

For better translational outcomes researchers and clinicians alike demand novel tools to distil complex neuroimaging data into simple yet behaviorally relevant representations at the single-participant level. Recently, the Mapper approach from topological data analysis (TDA) has been successfully applied on noninvasive human neuroimaging data to characterize the entire dynamical landscape of whole-brain configurations at the individual level without requiring any spatiotemporal averaging at the outset. Despite promising results, initial applications of Mapper to neuroimaging data were constrained by (1) the need for dimensionality reduction, and (2) lack of a biologically grounded heuristic for efficiently exploring the vast parameter space. Here, we present a novel computational framework for Mapper—designed specifically for neuroimaging data—that removes limitations and reduces computational costs associated with dimensionality reduction and parameter exploration. We also introduce new meta-analytic approaches to better anchor Mapper-generated representations to neuroanatomy and behavior. Our new NeuMapper framework was developed and validated using multiple fMRI datasets where participants engaged in continuous multitask experiments that mimic “ongoing” cognition. Looking forward, we hope our framework could help researchers push the boundaries of psychiatric neuroimaging towards generating insights at the single-participant level while scaling across consortium-size datasets.

Machine learning approaches in Covid-19 severity risk prediction in Morocco

The purpose of this study is to develop and test machine learning-based models for COVID-19 severity prediction. COVID-19 test samples from 337 COVID-19 positive patients at Cheikh Zaid Hospital were grouped according to the severity of their illness. Ours is the first study to estimate illness severity by combining biological and non-biological data from patients with COVID-19. Moreover the use of ML for therapeutic purposes in Morocco is currently restricted, and ours is the first study to investigate the severity of COVID-19. When data analysis approaches were used to uncover patterns and essential characteristics in the data, C-reactive protein, platelets, and D-dimers were determined to be the most associated to COVID-19 severity prediction. In this research, many data reduction algorithms were used, and Machine Learning models were trained to predict the severity of sickness using patient data. A new feature engineering method based on topological data analysis called Uniform Manifold Approximation and Projection (UMAP) shown that it achieves better results. It has 100% accuracy, specificity, sensitivity, and ROC curve in conducting a prognostic prediction using different machine learning classifiers such as X_GBoost, AdaBoost, Random Forest, and ExtraTrees. The proposed approach aims to assist hospitals and medical facilities in determining who should be seen first and who has a higher priority for admission to the hospital.

Topological data analysis identifies distinct biomarker phenotypes during the inflammatory phase of COVID-19

OBJECTIVES: The relationships between baseline clinical phenotypes and the cytokine milieu of the peak inflammatory phase of coronavirus 2019 (COVID-19) are not yet well understood. We used Topological Data Analysis (TDA), a dimensionality reduction technique to identify patterns of inflammation associated with COVID-19 severity and clinical characteristics. DESIGN: Exploratory analysis from a multi-center prospective cohort study. SETTING: Eight military hospitals across the United States between April 2020 and January 2021. PATIENTS: Adult (≥18 years of age) SARS-CoV-2 positive inpatient and outpatient participants were enrolled with plasma samples selected from the putative inflammatory phase of COVID-19, defined as 15-28 days post symptom onset. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Concentrations of 12 inflammatory protein biomarkers were measured using a broad dynamic range immunoassay. TDA identified 3 distinct inflammatory protein expression clusters. Peak severity (outpatient, hospitalized, ICU admission or death), Charlson Comorbidity Index (CCI), and body mass index (BMI) were evaluated with logistic regression for associations with each cluster. The study population (n=129, 33.3% female, median 41.3 years of age) included 77 outpatient, 31 inpatient, 16 ICU-level, and 5 fatal cases. Three distinct clusters were found that differed by peak disease severity (p <0.001), age (p <0.001), BMI (p<0.001), and CCI (p=0.001). CONCLUSIONS: Exploratory clustering methods can stratify heterogeneous patient populations and identify distinct inflammation patterns associated with comorbid disease, obesity, and severe illness due to COVID-19.

The shape of cancer relapse: Topological data analysis predicts recurrence in paediatric acute lymphoblastic leukaemia

Acute Lymphoblastic Leukaemia (ALL) is the most frequent paediatric cancer. Modern therapies have improved survival rates, but approximately 15-20 % of patients relapse. At present, patients' risk of relapse are assessed by projecting high-dimensional flow cytometry data onto a subset of biomarkers and manually estimating the shape of this reduced data. Here, we apply methods from topological data analysis (TDA), which quantify shape in data via features such as connected components and loops, to pre-treatment ALL datasets with known outcomes. We combine these fully unsupervised analyses with machine learning to identify features in the pre-treatment data that are prognostic for risk of relapse. We find significant topological differences between relapsing and non-relapsing patients and confirm the predictive power of CD10, CD20, CD38, and CD45. Further, we are able to use the TDA descriptors to predict patients who relapsed. We propose three prognostic pipelines that readily extend to other haematological malignancies.

Cubical homology-based Image Classification - A Comparative Study

Persistent homology is a powerful tool in topological data analysis (TDA) to compute, study and encode efficiently multi-scale topological features and is being increasingly used in digital image classification. The topological features represent number of connected components, cycles, and voids that describe the shape of data. Persistent homology extracts the birth and death of these topological features through a filtration process. The lifespan of these features can represented using persistent diagrams (topological signatures). Cubical homology is a more efficient method for extracting topological features from a 2D image and uses a collection of cubes to compute the homology, which fits the digital image structure of grids. In this research, we propose a cubical homology-based algorithm for extracting topological features from 2D images to generate their topological signatures. Additionally, we propose a score, which measures the significance of each of the sub-simplices in terms of persistence. Also, gray level co-occurrence matrix (GLCM) and contrast limited adapting histogram equalization (CLAHE) are used as a supplementary method for extracting features. Machine learning techniques are then employed to classify images using the topological signatures. Among the eight tested algorithms with six published image datasets with varying pixel sizes, classes, and distributions, our experiments demonstrate that cubical homology-based machine learning with deep residual network (ResNet 1D) and Light Gradient Boosting Machine (lightGBM) shows promise with the extracted topological features.