Ripser.py: A Lean Persistent Homology Library for Python

Tralie, Christopher J.; Saul, Nathaniel; Bar-On, Rann

doi:10.21105/joss.00925

Cited by 174 publications

(125 citation statements)

References 11 publications

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“…In our work, we use Ripser.py [ 76 ] due to its speed and efficiency for the computation of persistent homology for the empirical networks and the null models.…”

Section: Methodsmentioning

confidence: 99%

Architecture and evolution of semantic networks in mathematics texts

2020

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Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here, we study the topological structure of semantic networks reflecting mathematical concepts and their relations in college-level linear algebra texts. We hypothesize that these networks will exhibit structural order, reflecting the logical sequence of topics that ensures accessibility. We find that the networks exhibit strong core–periphery architecture, where a dense core of concepts presented early is complemented with a sparse periphery presented evenly throughout the exposition; the latter is composed of many small modules each reflecting more narrow domains. Using tools from applied topology, we find that the expositional evolution of the semantic networks produces and subsequently fills knowledge gaps, and that the density of these gaps tracks negatively with community ratings of each textbook. Broadly, our study lays the groundwork for future efforts developing optimal design principles for textbook exposition and teaching in a classroom setting.

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“…In our work, we use Ripser.py [ 76 ] due to its speed and efficiency for the computation of persistent homology for the empirical networks and the null models.…”

Section: Methodsmentioning

confidence: 99%

Architecture and evolution of semantic networks in mathematics texts

2020

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“…Non-parametric statistics were chosen due to the uncertainty that the data were sufficiently Gaussian. Persistence homology analysis was done using the Ripser (version 0.3.2) [58] and Persim libraries (version 0.0.9) as part of the Scikit-TDA library (version 0.0.4) [53]. Other packages used include the Numpy library (version [21], iGraph (version 0.7.1) [14].…”

Section: Softwarementioning

confidence: 99%

Topological Analysis of Differential Effects of Ketamine and Propofol Anesthesia on Brain Dynamics

Varley

Denny

Sporns

et al. 2020

Preprint

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Research into the neural correlates of consciousness has found that the vividness and complexity of conscious experience is related to the structure of brain dynamics, and that alterations to consciousness track changes in temporal evolution of brain states. Despite inducing externally similar states, propofol and ketamine produce different subjective states of consciousness. Here we explore the different effects of these two anaesthetics on the structure of dynamical attractors reconstructed from brain activity recorded electrophysiologically from cerebral cortex of a non-human primate. We used two different methods of attractor reconstruction. The first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence (or absence) of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network approximation of a continuous attractor, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find significant differences between the awake, ketamine, and propofol conditions. Propofol significantly decreased the expression of higher-order structure in brain dynamics, while ketamine had the opposite effect, promoting an increase in complex dynamic features. Overall we found that ketamine produced dynamics similar to normal waking consciousness while propofol did not, and the significance of these findings is discussed. different drugs with a specific focus on how different dynamics might relate to conscious awareness [55,63]. In this paper, we take such a comparative approach to explore the differences between the effects of propofol and ketamine on multi-scale brain dynamics with an eye specifically to how these dynamics might explain the differences in consciousness induced by both drugs. Here we characterize brain dynamics by adapting two complementary models capturing the evolution of whole-brain states through time: the first plots a trajectory through a high-dimensional configuration space, while the other discretizes transitions into a Markovian state-transition network.While ketamine and propofol are both classified broadly as anesthetics, and both obliterate consciousness at high doses, it is useful to compare their different pharmacologies and the differences between the states they induce at low-to-moderate doses. By binding to GABA A receptors, propofol triggers widespread inhibition of neuronal activity and even at low doses, induces states of amnesia, sedation, atonia, and at higher doses, full anesthesia [29,23]. In contrast, ketamine acts primarily as an antagonist of glutamaterigic NMDA receptors [29,66], causing widespread, light central nervous system stimulation and a state typically referred to as "dissociative anesthesia" [16,33]. Unlike propofol, which simply ablates consciousness, an otherwise unresponsive patient anesthetized with ketamine often continues to have complex, conscious experi...

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“…Persistent homology was computed using version 0.4.1 of the Ripser package as bundled with the Scikit-TDA toolbox for python [62]. Because the computational load to calculate persistence homology increases exponentially with the homology dimension, we limit the present study to the investigation of persistence homology in dimensions 0, 1, and 2.…”

Section: Homological Graph-graph Distancementioning

confidence: 99%

Simplicial and Topological Descriptions of Human Brain Dynamics

Billings

Saggar²,

Hlinka

et al. 2020

Preprint

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Functional connectivity (FC) and its time-varying analogue (TVFC) leverage brain imaging data to interpret brain function as patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s spontaneous self-organization. One tool from TDA, “persistent homology”, observes the occurrence and the persistence of n-dimensional holes presented in the metric space over a dataset. The occurrence of n-dimensional holes within the TVFC point cloud may denote conserved and preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional TVFC metrics at the task of segmenting brain states that differ across a common time-series of experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment volunteer performance during experimentally defined tasks, and generalize better across volunteers. Finally, we present empirical and theoretical observations that interpret brain function as a topological space defined by cyclic and interlinked motifs among distributed brain regions, especially, the attention networks.

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Ripser.py: A Lean Persistent Homology Library for Python

Cited by 174 publications

References 11 publications

Architecture and evolution of semantic networks in mathematics texts

Architecture and evolution of semantic networks in mathematics texts

Topological Analysis of Differential Effects of Ketamine and Propofol Anesthesia on Brain Dynamics

Simplicial and Topological Descriptions of Human Brain Dynamics

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