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The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the importance of collective effects in populations of neurons, only in the past two decades has it become possible to record from many cells simulatenously using advanced experimental techniques with single-spike resolution, and to relate these correlations to function and behaviour. This review focuses on the modeling and inference approaches that have been recently developed to describe the correlated spiking activity of populations of neurons. We cover a variety of models describing correlations between pairs of neurons as well as between larger groups, synchronous or delayed in time, with or without the explicit influence of the stimulus, and including or not latent variables. We discuss the advantages and drawbacks or each method, as well as the computational challenges related to their application to recordings of ever larger populations.
Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase r
We investigate the possibility that narrowband oscillations may emerge from completely asynchronous, independent neural firing. We find that a population of asynchronous neurons may produce narrowband oscillations if each neuron fires quasi-periodica
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a setup wher
The ongoing exponential rise in recording capacity calls for new approaches for analysing and interpreting neural data. Effective dimensionality has emerged as an important property of neural activity across populations of neurons, yet different stud
Neural population activity is theorized to reflect an underlying dynamical structure. This structure can be accurately captured using state space models with explicit dynamics, such as those based on recurrent neural networks (RNNs). However, using r