Related Experiment Video
Updated: Aug 11, 2026

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions
Published on: March 25, 2014
Non-Euclidean properties of spike train metric spaces
Dmitriy Aronov1, Jonathan D Victor
1Department of Biological Sciences, Columbia University, 1002 Fairchild, Mail Code 2436, 1212 Amsterdam Avenue, New York, New York 10027, USA. da2006@columbia.edu
Abstract:
Quantifying the dissimilarity (or distance) between two sequences is essential to the study of action potential (spike) trains in neuroscience and genetic sequences in molecular biology. In neuroscience, traditional methods for sequence comparisons rely on techniques appropriate for multivariate data, which typically assume that the space of sequences is intrinsically Euclidean. More recently, metrics that do not make this assumption have been introduced for comparison of neural activity patterns. These metrics have a formal resemblance to those used in the comparison of genetic sequences. Yet the relationship between such metrics and the traditional Euclidean distances has remained unclear. We show, both analytically and computationally, that the geometries associated with metric spaces of event sequences are intrinsically non-Euclidean. Our results demonstrate that metric spaces enrich the study of neural activity patterns, since accounting for perceptual spaces requires a non-Euclidean geometry.
Related Concept Videos
Vector Algebra: Graphical Method
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Cartesian Vector Notation
Dot Product
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...
Dot Product of Two Vectors
The Normal and Binormal Vectors
Torsion in Vector Calculus

