Related papers: The complexity of dynamics in small neural circuit…
The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low…
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…
In neural circuits, statistical connectivity rules strongly depend on neuronal type. Here we study dynamics of neural networks with cell-type specific connectivity by extending the dynamic mean field method, and find that these networks…
The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, $N$. In this paper, we present a novel derivation of the…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that…
Mathematical modelling of the macroscopic electrical activity of the brain is highly non-trivial and requires a detailed understanding of not only the associated mathematical techniques, but also the underlying physiology and anatomy.…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…
In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
Can Spiking Neural Networks (SNNs) approximate the dynamics of Recurrent Neural Networks (RNNs)? Arguments in classical mean-field theory based on laws of large numbers provide a positive answer when each neuron in the network has many…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…