scholarly journals Precision dynamical mapping using topological data analysis reveals a unique hub-like transition state at rest

2021 ◽  
Author(s):  
Manish Saggar ◽  
James M Shine ◽  
Raphael Liegeois ◽  
Nico U.F. Dosenbach ◽  
Damien Fair
Keyword(s):  
Data Analysis ◽  
Transition State ◽  
Brain Activity ◽  
Activity Patterns ◽  
Topological Data Analysis ◽  
Underlying Structure ◽  
Whole Brain ◽  
Continuous Evolution ◽  
External Stimuli ◽  
Topological Data

Even in the absence of external stimuli, neural activity is both highly dynamic and organized across multiple spatiotemporal scales. The continuous evolution of brain activity patterns during rest is believed to help maintain a rich repertoire of possible functional configurations that relate to typical and atypical cognitive phenomena. Whether these transitions or "explorations" follow some underlying arrangement or instead lack a predictable ordered plan remains to be determined. Here, using a precision dynamics approach, we aimed at revealing the rules that govern transitions in brain activity at rest at the single participant level. We hypothesized that by revealing and characterizing the overall landscape of whole brain configurations (or states) we could interpret the rules (if any) that govern transitions in brain activity at rest. To generate the landscape of whole-brain configurations we used Topological Data Analysis based Mapper approach. Across all participants, we consistently observed a rich topographic landscape in which the transition of activity from one state to the next involved a central hub-like "transition state." The hub topography was characterized as a shared attractor-like basin where all canonical resting-state networks were represented equally. The surrounding periphery of the landscape had distinct network configurations. The intermediate transition state and traversal through it via a topographic gradient seemed to provide the underlying structure for the continuous evolution of brain activity patterns at rest. In addition, differences in the landscape architecture were more consistent within than between subjects, providing evidence of idiosyncratic dynamics and potential utility in precision medicine.

scholarly journals An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

2021 ◽  
Vol 4 ◽  
Author(s):  
Frédéric Chazal ◽  
Bertrand Michel
Keyword(s):  
Data Analysis ◽  
Statistical Learning ◽  
Topological Data Analysis ◽  
Underlying Structure ◽  
Complex Data ◽  
Computational Tools ◽  
Fast Growing ◽  
Learning Techniques ◽  
Statistical Learning Techniques ◽  
Topological Data

With the recent explosion in the amount, the variety, and the dimensionality of available data, identifying, extracting, and exploiting their underlying structure has become a problem of fundamental importance for data analysis and statistical learning. Topological data analysis (tda) is a recent and fast-growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. It proposes new well-founded mathematical theories and computational tools that can be used independently or in combination with other data analysis and statistical learning techniques. This article is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of tda for nonexperts.

scholarly journals Topological Data Analysis Approaches to Uncovering the Timing of Ring Structure Onset in Filamentous Networks

2021 ◽  
Vol 83 (3) ◽  
Author(s):  
Maria-Veronica Ciocanel ◽  
Riley Juenemann ◽  
Adriana T. Dawes ◽  
Scott A. McKinley
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Actin Filaments ◽  
Time Series Data ◽  
Polymer Networks ◽  
Topological Data Analysis ◽  
Series Data ◽  
Topological Features ◽  
Topological Data

AbstractIn developmental biology as well as in other biological systems, emerging structure and organization can be captured using time-series data of protein locations. In analyzing this time-dependent data, it is a common challenge not only to determine whether topological features emerge, but also to identify the timing of their formation. For instance, in most cells, actin filaments interact with myosin motor proteins and organize into polymer networks and higher-order structures. Ring channels are examples of such structures that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. Given the limitations in studying interactions of actin with myosin in vivo, we generate time-series data of protein polymer interactions in cells using complex agent-based models. Since the data has a filamentous structure, we propose sampling along the actin filaments and analyzing the topological structure of the resulting point cloud at each time. Building on existing tools from persistent homology, we develop a topological data analysis (TDA) method that assesses effective ring generation in this dynamic data. This method connects topological features through time in a path that corresponds to emergence of organization in the data. In this work, we also propose methods for assessing whether the topological features of interest are significant and thus whether they contribute to the formation of an emerging hole (ring channel) in the simulated protein interactions. In particular, we use the MEDYAN simulation platform to show that this technique can distinguish between the actin cytoskeleton organization resulting from distinct motor protein binding parameters.

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

The Shape of Things: Topological Data Analysis

CHANCE ◽  
2021 ◽  
Vol 34 (2) ◽  
pp. 59-64
Author(s):  
Nicole Lazar ◽  
Hyunnam Ryu
Keyword(s):  
Data Analysis ◽  
Topological Data Analysis ◽  
Topological Data
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