Related papers: Moving bumps in theta neuron networks
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe…
The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic…
Large ensembles of globally coupled chaotic neural networks undergo a transition to complete synchronization for high coupling intensities. The onset of this fully coherent behavior is preceded by a regime where clusters of networks with…
We study a model of networked atoms or molecules oscillating around their equilibrium positions. The model assumes the harmonic approximation of the interactions. We provide bounds for the total number of phonons, and for the specific heat,…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
We have investigated the evolution of the neutrino asymmetry in active-sterile neutrino oscillations in the early universe. We find that there are large regions of parameter space where the asymmetry is extremely sensitive to variations in…
We re-examine neutrino oscillations in the early universe. Contrary to previous studies, we show that large neutrino asymmetries can arise due to oscillations between ordinary neutrinos and sterile neutrinos. This means that the Big Bang…
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…
For more than half a century, nucleons are considered to move continuously in the nuclei. Recent electron-scattering experiments indicate about 20$\sim$25\% nucleons in heavier nuclei are involved in the neutron-proton short-range…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive…
We discuss a specific circumstance in which the topology of the communication network of a robotic swarm has to change during the movement. The variation is caused by a topological obstruction which emerges from certain geometric…
Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
Red giants undergo dramatic and complex structural transformations as they evolve. Angular momentum is transported between the core and envelope during this epoch, a poorly understood process. Here, we infer envelope and core rotation rates…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
Dynamic instability in the cytoskeleton underlies a great many vital cellular processes. In neurons, it is thought to play a role in information processing and the establishment of synaptic connections. It is from this interneuronal…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…
Functional oscillator networks, such as neuronal networks in the brain, exhibit switching between metastable states involving many oscillators. We give exact results how such global dynamics can arise in paradigmatic phase oscillator…