Topological data analysis

L Wasserman - Annual Review of Statistics and Its Application, 2018 - annualreviews.org
Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data

C Giusti, R Ghrist, DS Bassett - Journal of computational neuroscience, 2016 - Springer
The language of graph theory, or network science, has proven to be an exceptional tool for
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …

Centralities in simplicial complexes. Applications to protein interaction networks

E Estrada, GJ Ross - Journal of theoretical biology, 2018 - Elsevier
Complex networks can be used to represent complex systems which originate in the real
world. Here we study a transformation of these complex networks into simplicial complexes …

What can topology tell us about the neural code?

C Curto - Bulletin of the American Mathematical Society, 2017 - ams.org
Neuroscience is undergoing a period of rapid experimental progress and expansion. New
mathematical tools, previously unknown in the neuroscience community, are now being …

An in vitro method to manipulate the direction and functional strength between neural populations

L Pan, S Alagapan, E Franca… - Frontiers in neural …, 2015 - frontiersin.org
We report the design and application of a Micro Electro Mechanical Systems (MEMs) device
that permits investigators to create arbitrary network topologies. With this device …

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

B Pietras, V Schmutz, T Schwalger - PLoS Computational Biology, 2022 - journals.plos.org
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link
between neuronal dynamics and computation. A prime example of functional activity …

Persistent homology guided force-directed graph layouts

A Suh, M Hajij, B Wang… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
Graphs are commonly used to encode relationships among entities, yet their abstractness
makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and …

Feed-Forward Propagation of Temporal and Rate Information between Cortical Populations during Coherent Activation in Engineered In Vitro Networks

TB DeMarse, L Pan, S Alagapan, GJ Brewer… - Frontiers in neural …, 2016 - frontiersin.org
Transient propagation of information across neuronal assembles is thought to underlie many
cognitive processes. However, the nature of the neural code that is embedded within these …

Network events on multiple space and time scales in cultured neural networks and in a stochastic rate model

G Gigante, G Deco, S Marom… - PLoS computational …, 2015 - journals.plos.org
Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of
collective dynamical events such as network spikes, UP and DOWN states, global …

[HTML][HTML] Discovery of statistical equivalence classes using computer algebra

C Görgen, A Bigatti, E Riccomagno, JQ Smith - International Journal of …, 2018 - Elsevier
Discrete statistical models supported on labeled event trees can be specified using so-
called interpolating polynomials which are generalizations of generating functions. These …