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 …
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
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 …
addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a …
Centralities in simplicial complexes. Applications to protein interaction networks
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 …
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 …
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 …
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
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 …
between neuronal dynamics and computation. A prime example of functional activity …
Persistent homology guided force-directed graph layouts
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 …
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 …
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
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 …
collective dynamical events such as network spikes, UP and DOWN states, global …
[HTML][HTML] Discovery of statistical equivalence classes using computer algebra
Discrete statistical models supported on labeled event trees can be specified using so-
called interpolating polynomials which are generalizations of generating functions. These …
called interpolating polynomials which are generalizations of generating functions. These …