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 …
Generative models for network neuroscience: prospects and promise
RF Betzel, DS Bassett - Journal of The Royal Society …, 2017 - royalsocietypublishing.org
Network neuroscience is the emerging discipline concerned with investigating the complex
patterns of interconnections found in neural systems, and identifying principles with which to …
patterns of interconnections found in neural systems, and identifying principles with which to …
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 …
What makes a neural code convex?
Neural codes allow the brain to represent, process, and store information about the world.
Combinatorial codes, comprised of binary patterns of neural activity, encode information via …
Combinatorial codes, comprised of binary patterns of neural activity, encode information via …
[HTML][HTML] Identification of control targets in Boolean molecular network models via computational algebra
Background Many problems in biomedicine and other areas of the life sciences can be
characterized as control problems, with the goal of finding strategies to change a disease or …
characterized as control problems, with the goal of finding strategies to change a disease or …
[HTML][HTML] Tropical coordinates on the space of persistence barcodes
S Kališnik - Foundations of Computational Mathematics, 2019 - Springer
The aim of applied topology is to use and develop topological methods for applied
mathematics, science and engineering. One of the main tools is persistent homology, an …
mathematics, science and engineering. One of the main tools is persistent homology, an …
[HTML][HTML] Obstructions to convexity in neural codes
How does the brain encode spatial structure? One way is through hippocampal neurons
called place cells, which become associated to convex regions of space known as their …
called place cells, which become associated to convex regions of space known as their …
On open and closed convex codes
Neural codes serve as a language for neurons in the brain. Open (or closed) convex codes,
which arise from the pattern of intersections of collections of open (or closed) convex sets in …
which arise from the pattern of intersections of collections of open (or closed) convex sets in …
Neural codes, decidability, and a new local obstruction to convexity
Given an intersection pattern of arbitrary sets in Euclidean space, is there an arrangement of
convex open sets in Euclidean space that exhibits the same intersections? This question is …
convex open sets in Euclidean space that exhibits the same intersections? This question is …
A no-go theorem for one-layer feedforward networks
It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain
the set of possible response patterns, thereby shaping the neural code. This implies the …
the set of possible response patterns, thereby shaping the neural code. This implies the …