The higher-order interactions of complex systems, such as the brain are captured by their simplicial structure and have a significant effect on dynamics. However, existing dynamical models defined complexes make strong assumption that dynamics resides exclusively nodes. Here we formulate Kuramoto model which describes between oscillators placed not only nodes but also links, triangles, so on. We show can lead to an explosive synchronization transition using adaptive coupling dependent...

Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define ensemble correlated networks and obtain associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in case highly heterogeneous, scale-free a certain disassortativity is predicted---offering parsimonious explanation for question above....

Abstract Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from brain to social networks. Here we show that algebraic is a fundamental tool higher-order dynamics simplicial complexes. In particular consider topological signals, i.e., dynamical signals defined on simplices different dimension, here taken be nodes links for simplicity. We coupling between leads explosive synchronization in which phases synchronize simultaneously at...

Abstract Simplicial complexes constitute the underlying topology of interacting complex systems including among others brain and social interaction networks. They are generalized network structures that allow to go beyond framework pairwise interactions capture many-body between two or more nodes strongly affecting dynamical processes. In fact, simplicial allows assign a variable not only but also links, triangles, so on. Here we show evidence dynamics defined on simplices different...

Recent experiments on cortical neural networks have revealed the existence of well-defined avalanches electrical activity. Such been claimed to be generically scale invariant—i.e. power law distributed—with many exciting implications in neuroscience. Recently, a self-organized model has proposed by Levina, Herrmann and Geisel explain this empirical finding. Given that (i) dynamics is dissipative (ii) there loading mechanism progressively 'charging' background synaptic strength,...

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of neuron exhibits minimum with respect to noise. ISR has been studied individual neurons, but here, we investigate scale-free networks, where calculated over neuronal population. We use Hodgkin-Huxley model neurons channel noise (i.e., stochastic gating variable dynamics), and network connectivity implemented via electrical or chemical connections gap junctions excitatory/inhibitory synapses). find that...

Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays fundamental role establishing clear relation between topological geometrical properties its dynamics. Specifically explore determining synchronization Kuramoto model. We synchronized phase can only be thermodynamically stable for dimensions above four entrainment oscillators found greater than two. numerically test our analytical predictions on recently introduced model...

The dynamics of networks neuronal cultures has been recently shown to be strongly dependent on the network geometry and in particular their dimensionality. However, this phenomenon so far mostly unexplored from theoretical point view. Here we reveal rich interplay between synchronization coupled oscillators context a simplicial complex model manifolds called Complex Network Manifold. generated by combine small world properties (infinite Hausdorff dimension) high modular structure with finite...

Abstract Stochastic resonance is an essential phenomenon in neurobiology, it connected to the constructive role of noise signals that take place neuronal tissues, facilitating information communication, memory, etc. Memristive devices are known be cornerstone hardware neuromorphic applications since they correctly mimic biological synapses many different facets, such as short/long-term plasticity, spike-timing-dependent pair-pulse facilitation, Different types neural networks can built with...

We have examined a role of dynamic synapses in the stochastic Hopfield-like network behavior. Our results demonstrate an appearance novel phase characterized by quick transitions from one memory state to another. The is able retrieve memorized patterns corresponding classical ferromagnetic states but switches between with intermittent type This phenomenon might reflect flexibility real neural systems and their readiness receive respond changing external stimuli.

We investigate the behavior of a model neuron that receives biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from large number afferents. show that, with static synapses, such noise can give rise to inverse stochastic resonance (ISR) as function presynaptic firing rate. compare this case dynamic synapses feature short-term synaptic plasticity, and interval rate over which ISR exists be extended or diminished. consider both depression facilitation....

Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or simplicial complex. As such, topological are attracting increasing attention in theory, systems, signal processing machine learning. nodes typically studied dynamics, while much less explored. Here we investigate Dirac synchronization, describing locally coupled network, treated using operator. The dynamics is affected by phase lag depending nearby vice versa. We show that...

Abstract Triadic interactions in the brain are general mechanisms by which a node, e.g. neuron or glia cell such as astrocyte, can regulate directly link, synapse between other two nodes. The regulation takes place familiar way either depressing facilitating synaptic transmission. Such ubiquitous neural systems, accounting both for axo-axonic and tripartite synapses mediated astrocytes, instance, have been related to neuronal processes at different time-scales, including short- long-term...

Complex coherent dynamics is present in a wide variety of neural systems. A typical example the voltage transitions between up and down states observed cortical areas brain. In this work, we study phenomenon via biologically motivated stochastic model transitions. The constituted by simple bistable rate dynamics, where synaptic current modulated short-term processes which introduce stochasticity temporal correlations. complete analysis our model, both with mean-field approaches numerical...

In this work, we study, analytically and employing Monte Carlo simulations, the influence of competition between several activity-dependent synaptic processes, such as short-term facilitation depression, on maximum memory storage capacity in a neural network. contrast to case which drastically reduces network store retrieve "static" activity patterns, enhances different contexts. particular, found optimal values relevant parameters (such neurotransmitter release probability or characteristic...

We study the effect of competition between short-term synaptic depression and facilitation on dynamic properties attractor neural networks, using Monte Carlo simulation a mean-field analysis. Depending balance depression, facilitation, underlying noise, network displays different behaviors, including associative memory switching activity attractors. conclude that enhances instability in way (1) intensifies system adaptability to external stimuli, which is agreement with experiments, (2)...

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in presence certain level noisy background neural activity. Our has focused realistic assumption that synapses network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques well numerical simulations, found there are two possible noise levels which optimize signal transmission. This new finding is contrast with classical theory...

The performance of attractor neural networks has been shown to depend crucially on the heterogeneity underlying topology. We take this analysis a step further by examining effect degree-degree correlations---assortativity---on neural-network behavior. make use method recently put forward for studying correlated and dynamics thereon, both analytically computationally, which is independent how topology may have evolved. show robustness noise greatly enhanced in assortative (positively...

Abstract We present extensive simulations of a quantum version the Hopfield neural network to explore its emergent behavior. The system is N qubits oscillating at given Ω frequency and which are coupled via Lindblad jump operators built with local fields h i depending on some stored patterns. Our show emergence pattern-antipattern oscillations overlaps patterns similar (for large small temperature) those reported within recent mean-field description such system, originated deterministically...