scholarly journals Topological data analysis to uncover the shape of immune responses during co-infection

2019 ◽  
Author(s):  
Karin Sasaki ◽  
Dunja Bruder ◽  
Esteban Hernandez-Vargas
Keyword(s):  
Immune Response ◽  
Data Analysis ◽  
Bacterial Infection ◽  
Viral Infection ◽  
Topological Data Analysis ◽  
High Dimensional ◽  
Data Sets ◽  
Contributing Factors ◽  
Transition Points ◽  
Topological Data

AbstractCo-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the contributing factors of the immune response when two infections take place at the same time is largely unexplored. Using data sets of the immune response during influenza-pneumococcal co-infection in mice, we employ here topological data analysis to simplify and visualise high dimensional data sets.We identified persistent shapes of the simplicial complexes of the data in the three infection scenarios: single viral infection, single bacterial infection, and co-infection. The immune response was found to be distinct for each of the infection scenarios and we uncovered that the immune response during the co-infection has three phases and two transition points. During the first phase, its dynamics is inherited from its response to the primary (viral) infection. The immune response has an early (few hours post co-infection) and then modulates its response to finally react against the secondary (bacterial) infection. Between 18 to 26 hours post co-infection the nature of the immune response changes again and does no longer resembles either of the single infection scenarios.Author summaryThe mapper algorithm is a topological data analysis technique used for the qualitative analysis, simplification and visualisation of high dimensional data sets. It generates a low-dimensional image that captures topological and geometric information of the data set in high dimensional space, which can highlight groups of data points of interest and can guide further analysis and quantification.To understand how the immune system evolves during the co-infection between viruses and bacteria, and the role of specific cytokines as contributing factors for these severe infections, we use Topological Data Analysis (TDA) along with an extensive semi-unsupervised parameter value grid search, and k-nearest neighbour analysis.We find persistent shapes of the data in the three infection scenarios, single viral and bacterial infections and co-infection. The immune response is shown to be distinct for each of the infections scenarios and we uncover that the immune response during the co-infection has three phases and two transition points, a previously unknown property regarding the dynamics of the immune response during co-infection.

scholarly journals Topological data analysis : an overview

2021 ◽  
Author(s):  
Amy Bednar
Keyword(s):  
Data Analysis ◽  
Large Data ◽  
Large Data Sets ◽  
Topological Data Analysis ◽  
Background Information ◽  
High Dimensional ◽  
Data Sets ◽  
Complex Data ◽  
Topological Network ◽  
Topological Data

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.

scholarly journals The Application of Topological Data Analysis in Practice and Its Effectiveness

2020 ◽  
Vol 214 ◽  
pp. 03034
Author(s):  
Liang Cheng
Keyword(s):  
Data Analysis ◽  
Data Science ◽  
Topological Data Analysis ◽  
High Dimensional ◽  
Data Sets ◽  
Relevant Feature ◽  
Mathematical Algorithm ◽  
Working Efficiency ◽  
Analyze Data ◽  
Topological Data

Topological Data Analysis(TDA) is a new and fast growing field in data science. TDA provides an approach to analyze data sets and derive their relevant feature out of complex high-dimensional data, which greatly improves the working efficiency in many fields. In this paper, the author mainly discusses some mathematics concepts about topology, methods in TDA and the relation between these topological concepts and data sets (how to apply topological concepts on data). The problems of TDA, mathematical algorithm using in TDA and two application-examples are introduced in this paper. In addition, the advantages, limitations, and the direction of future development of TDA are discussed.

Topological Data Analysis with Applications

2021 ◽  
Author(s):  
Gunnar Carlsson ◽  
Mikael Vejdemo-Johansson
Keyword(s):  
Data Analysis ◽  
Data Science ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Data Sets ◽  
Advanced Learners ◽  
Computer Scientists ◽  
Dramatic Rise ◽  
Modeling Data ◽  
Topological Data

The continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.

scholarly journals Generating dynamical neuroimaging spatiotemporal representations (DyNeuSR) using topological data analysis

2019 ◽  
Vol 3 (3) ◽  
pp. 763-778 ◽  
Author(s):  
Caleb Geniesse ◽  
Olaf Sporns ◽  
Giovanni Petri ◽  
Manish Saggar
Keyword(s):  
Data Analysis ◽  
Mental Disorders ◽  
Open Source ◽  
Topological Data Analysis ◽  
High Dimensional ◽  
Graphical Representations ◽  
Neuroimaging Data ◽  
Open Datasets ◽  
Topological Data

In this article, we present an open source neuroinformatics platform for exploring, analyzing, and validating distilled graphical representations of high-dimensional neuroimaging data extracted using topological data analysis (TDA). TDA techniques like Mapper have been recently applied to examine the brain’s dynamical organization during ongoing cognition without averaging data in space, in time, or across participants at the outset. Such TDA-based approaches mark an important deviation from standard neuroimaging analyses by distilling complex high-dimensional neuroimaging data into simple—yet neurophysiologically valid and behaviorally relevant—representations that can be interactively explored at the single-participant level. To facilitate wider use of such techniques within neuroimaging and general neuroscience communities, our work provides several tools for visualizing, interacting with, and grounding TDA-generated graphical representations in neurophysiology. Through Python-based Jupyter notebooks and open datasets, we provide a platform to assess and visualize different intermittent stages of Mapper and examine the influence of Mapper parameters on the generated representations. We hope this platform could enable researchers and clinicians alike to explore topological representations of neuroimaging data and generate biological insights underlying complex mental disorders.

scholarly journals When remote sensing meets topological data analysis

2018 ◽  
Author(s):  
Ludovic Duponchel
Keyword(s):  
Remote Sensing ◽  
Data Analysis ◽  
Oil Spills ◽  
Point Of View ◽  
Topological Data Analysis ◽  
Data Sets ◽  
Data Set ◽  
Environmental Preservation ◽  
Life Problems ◽  
Topological Data

Hyperspectral remote sensing plays an increasingly important role in many scientific domains and everyday life problems. Indeed, this imaging concept ends up in applications as varied as catching tax-evaders red-handed by locating new construction and building alterations, searching for aircraft and saving lives after fatal crashes, detecting oil spills for marine life and environmental preservation, spying on enemies with reconnaissance satellites, watching algae grow as an indicator of environmental health, forecasting weather to warn about natural disasters and much more. From an instrumental point of view, we can say that the actual spectrometers have rather good characteristics, even if we can always increase spatial resolution and spectral range. In order to extract ever more information from such experiments and develop new applications, we must, therefore, propose multivariate data analysis tools able to capture the shape of data sets and their specific features. Nevertheless, actual methods often impose a data model which implicitly defines the geometry of the data set. The aim of the paper is thus to introduce the concept of topological data analysis in the framework of remote sensing, making no assumptions about the global shape of the data set, but also allowing the capture of its local features.

scholarly journals Topological data analysis reveals principles of chromosome structure throughout cellular differentiation

2019 ◽  
Author(s):  
Natalie Sauerwald ◽  
Yihang Shen ◽  
Carl Kingsford
Keyword(s):  
Data Analysis ◽  
Cell Lines ◽  
Cellular Differentiation ◽  
Structural Changes ◽  
Chromosome Structure ◽  
Three Dimensional ◽  
Topological Data Analysis ◽  
Data Sets ◽  
Chromosomal Architecture ◽  
Topological Data

AbstractThree-dimensional chromosome structure has a significant influence in many diverse genomic processes and has recently been shown to relate to cellular differentiation. Many methods for describing the chromosomal architecture focus on specific substructures such as topologically-associating domains (TADs) or compartments, but we are still missing a global view of all geometric features of chromosomes. Topological data analysis (TDA) is a mathematically well-founded set of methods to derive robust information about the structure and topology of data sets, making it well-suited to better understand the key features of chromosome structure. By applying TDA to the study of chromosome structure through differentiation across three cell lines, we provide insight into principles of chromosome folding generally, and observe structural changes across lineages. We identify both global and local differences in chromosome topology through differentiation, identifying trends consistent across human cell lines.AvailabilityScripts to reproduce the results from this study can be found at https://github.com/Kingsford-Group/[email protected]

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