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Statistical analysis and inference on spike trains is one of the central topics in the neural coding. It is of great interest to understand the underlying structure of given neural data. Based on the metric distances between spike trains,…
We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most…
The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the {\em spike…
Statistical similarities between neuronal spike trains could reveal significant information on complex underlying processing. In general, the similarity between synchronous spike trains is somewhat easy to identify. However, the similar…
Metric-based summary statistics such as mean and covariance have been introduced in neural spike train space. They can properly describe template and variability in spike train data, but are often sensitive to outliers and expensive to…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
Neurons in the central nervous system communicate with each other with the help of series of Action Potentials, or spike trains. Various studies have shown that neurons encode information in different features of spike trains, such as the…
Measures of spike train synchrony have become important tools in both experimental and theoretical neuroscience. Three time-resolved measures called the ISI-distance, the SPIKE-distance, and SPIKE-synchronization have already been…
Statistical properties of spike trains measured from a sensory neuron in-vivo are studied experimentally and theoretically. Experiments are performed on an identified neuron in the visual system of the blowfly. It is shown that the spike…
By introducing the twin concepts of reliability and precision along with the corresponding measures, Mainen and Sejnowski's seminal 1995 paper "Reliability of spike timing in neocortical neurons" (Mainen and Sejnowski, 1995) paved the way…
The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance, and compare them…
For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
Techniques for recording large-scale neuronal spiking activity are developing very fast. This leads to an increasing demand for algorithms capable of analyzing large amounts of experimental spike train data. One of the most crucial and…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
Background: It is commonly assumed in neuronal coding that repeated presentations of a stimulus to a coding neuron elicit similar responses. One common way to assess similarity are spike train distances. These can be divided into…
We propose a statistical method for modeling the non-Poisson variability of spike trains observed in a wide range of brain regions. Central to our approach is the assumption that the variance and the mean of interspike intervals are related…
Although perceptual (dis)similarity between sensory stimuli seems akin to distance, measuring the Euclidean distance between vector representations of auditory stimuli is a poor estimator of subjective dissimilarity. In hearing, nonlinear…
Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However,…
Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in…