585 research outputs found
Complex networks: when random walk dynamics equals synchronization
No full textSynchrony prevalently emerges from the interactions of coupled dynamical units. For simple systems such as networks of phase oscillators, the asymptotic synchronization process is assumed to be equivalent to a Markov process that models standard diffusion or random walks on the same network topology. In this paper, we analytically derive the conditions for such equivalence for networks of pulse-coupled oscillators, which serve as models for neurons and pacemaker cells interacting by exchanging electric pulses or fireflies interacting via light flashes. We find that the pulse synchronization process is less simple, but there are classes of, e. g., network topologies that ensure equivalence. In particular, local dynamical operators are required to be doubly stochastic. These results provide a natural link between stochastic processes and deterministic synchronization on networks. Tools for analyzing diffusion (or, more generally, Markov processes) may now be transferred to pin down features of synchronization in networks of pulse-coupled units such as neural circuits
Inferring Synaptic Connectivity from Spatio-Temporal Spike Patterns
No full textNetworks of well-known dynamical units but unknown interaction topology arise across various fields of biology, including genetics, ecology and neuroscience. The collective dynamics of such networks is often sensitive to the presence (or absence) of individual interactions, but there is usually no direct way to probe for their existence. Here we present an explicit method for reconstructing interaction networks of leaky integrate-and-fire neurons from the spike patterns they exhibit in response to external driving. Given the dynamical parameters are known, the approach works well for networks in simple collective states but is also applicable to networks exhibiting complex spatio-temporal spike patterns. In particular, stationarity of spiking time series is not required
Connectivity Concepts
No full textThis repository contains all code and source files to reproduce the figures of the manuscript"Connectivity Concepts in Neuronal Network Modeling"by Johanna Senk, Birgit Kriener, Mikael Djurfeldt, Nicole Voges, Han-Jia Jiang, Lisa Schüttler, Gabriele Gramelsberger, Markus Diesmann, Hans E. Plesser, Sacha J. van Albada
Correlations and population dynamics in cortical networks
No full textKriener et al. The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of exci-tatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity ma-trix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale’s principle is respected.If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale’s principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.
Mirror Landing - As Remembered by Birgit Hult
Full text linkNotes - This account, Memories Mirror Landing by Birgit Hult, was compiled by Birgit's daughter, Jean Elvira Male, it documents the Hult family's experiences in Mirror Landing from 1912 - 1916. The Hults, who were originally from Sweden, arrived in Mirror Landing with two young children, a third child was born during their stay in Mirror Landing. Upon arriving in the area, the Hults made friends with the Gauthier family. The wives became good friends and would swap piano lessons for English lessons. Details of the log home where the family lived and the surrounding landscape were recalled. A memory about a large forest fire that occurred near the family home and dances that were attended in the town are discussed. Jean recalls her mother's memories regarding the animosity towards the North West Mounted Police that was felt by the people of Mirror Landing. The Hult family retained a strong connection to the Swedish heritage and practised many Swedish traditions, such as flying the Swedish flag and eating hot cross buns stuffed with Swedish Marzipan soaked in warm milk. Photos and a postcard written in 1915 are included in this article (10 pages
How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators
No full textUnder which conditions can a network of pulse-coupled oscillators sustain stable collective activity states? Previously, it was shown that stability of the simplest pattern conceivable, i.e., global synchrony, in networks of symmetrically pulse-coupled oscillators can be decided in a rigorous mathematical fashion, if interactions either all advance or all retard oscillation phases (“mono-interaction network”). Yet, many real-world networks—for example neuronal circuits—are asymmetric and moreover crucially feature both types of interactions. Here, we study complex networks of excitatory (phase-advancing) and inhibitory (phase-retarding) leaky integrate-and-fire (LIF) oscillators. We show that for small coupling strength, previous results for mono-interaction networks also apply here: pulse time perturbations eventually decay if they are smaller than a transmission delay and if all eigenvalues of the linear stability operator have absolute value smaller or equal to one. In this case, the level of inhibition must typically be significantly stronger than that of excitation to ensure local stability of synchrony. For stronger coupling, however, network synchrony eventually becomes unstable to any finite perturbation, even if inhibition is strong and all eigenvalues of the stability operator are at most unity. This new type of instability occurs when any oscillator, inspite of receiving inhibitory input from the network on average, can by chance receive sufficient excitatory input to fire a pulse before all other pulses in the system are delivered, thus breaking the near-synchronous perturbation pattern
Knowing Through Popular Music in the Western Pacific Island World
No full textPacific Indigenous scholars have long emphasized the role of relationality for Pacific Islanders’ epistemologies. In this article, the author rethinks music in terms of the procedural knowledge inherent in and specific to popular music-making by exploring the latter as knowledge practices in Micronesia. This approach opens new vistas on the relationality at the heart of Western Pacific music-making. The author calls the musical manifestation of that relational capacity sound ties, suggesting that if, following Epeli Hau‘ofa, Oceania is “humanity rising from the depths of brine”, then it is not least the sound ties of knowing in and through music that mould that very humanity of people who are at home with the sea into aquapelagic assemblages that are, after all, so much more than water and land
The Impact of Network Structure on the Spatio-Temporal Activity Dynamics of Cortical Networks
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