相关论文: A comparison of Euclidean metrics and their applic…
Multi-electrode arrays (MEAs) can record extracellular action potentials (also known as 'spikes') from hundreds or thousands of neurons simultaneously. Inference of a functional network from a spike train is a fundamental and formidable…
Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the…
Quantification of neuronal correlations in neuron populations helps us to understand neural coding rules. Such quantification could also reveal how neurons encode information in normal and disease conditions like Alzheimer's and…
I provide a convolution metric which takes neural membrane potential recordings as arguments and compares their subthreshold features along with the timing and number of spikes within them--summarizing differences in these with a single…
Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
Given a set of points in the Euclidean space $\mathbb{R}^\ell$ with $\ell>1$, the pairwise distances between the points are determined by their spatial location and the metric $d$ that we endow $\mathbb{R}^\ell$ with. Hence, the distance…
In this paper we investigate the metric properties of quadrics and cones of the $n$-dimensional Euclidean space. As applications of our formulas we give a more detailed description of the construction of Chasles and the wire model of…
Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…
In this article, our wish is to demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding. The goal is to help better understanding to which extend computing and…
Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes generated by many neurons. Unfortunately these ''many neurons''…
Clustering, as an unsupervised technique, plays a pivotal role in various data analysis applications. Among clustering algorithms, Spectral Clustering on Euclidean Spaces has been extensively studied. However, with the rapid evolution of…
Categorical attributes with qualitative values are ubiquitous in cluster analysis of real datasets. Unlike the Euclidean distance of numerical attributes, the categorical attributes lack well-defined relationships of their possible values…
Neuromorphic computing has recently gained momentum with the emergence of various neuromorphic processors. As the field advances, there is an increasing focus on developing training methods that can effectively leverage the unique…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…
Encoding the distance between locations in space is essential for accurate navigation. Grid cells, a functional class of neurons in medial entorhinal cortex, are believed to support this computation. However, existing theories of how…
Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.
Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…
Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…