9 research outputs found
Emergence of slow-switching assemblies in structured neuronal networks
Unraveling the interplay between connectivity and spatio-temporal dynamics in
neuronal networks is a key step to advance our understanding of neuronal
information processing. Here we investigate how particular features of network
connectivity underpin the propensity of neural networks to generate
slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased
firing within assemblies of neurons which transition slowly between different
assemblies throughout the network. We show that the emergence of SSA activity
is linked to spectral properties of the asymmetric synaptic weight matrix. In
particular, the leading eigenvalues that dictate the slow dynamics exhibit a
gap with respect to the bulk of the spectrum, and the associated Schur vectors
exhibit a measure of block-localization on groups of neurons, thus resulting in
coherent dynamical activity on those groups. Through simple rate models, we
gain analytical understanding of the origin and importance of the spectral gap,
and use these insights to develop new network topologies with alternative
connectivity paradigms which also display SSA activity. Specifically, SSA
dynamics involving excitatory and inhibitory neurons can be achieved by
modifying the connectivity patterns between both types of neurons. We also show
that SSA activity can occur at multiple timescales reflecting a hierarchy in
the connectivity, and demonstrate the emergence of SSA in small-world like
networks. Our work provides a step towards understanding how network structure
(uncovered through advancements in neuroanatomy and connectomics) can impact on
spatio-temporal neural activity and constrain the resulting dynamics.Comment: The first two authors contributed equally -- 18 pages, including
supplementary material, 10 Figures + 2 SI Figure
Spectral identification of networks using sparse measurements
We propose a new method to recover global information about a network of
interconnected dynamical systems based on observations made at a small number
(possibly one) of its nodes. In contrast to classical identification of full
graph topology, we focus on the identification of the spectral graph-theoretic
properties of the network, a framework that we call spectral network
identification.
The main theoretical results connect the spectral properties of the network
to the spectral properties of the dynamics, which are well-defined in the
context of the so-called Koopman operator and can be extracted from data
through the Dynamic Mode Decomposition algorithm. These results are obtained
for networks of diffusively-coupled units that admit a stable equilibrium
state. For large networks, a statistical approach is considered, which focuses
on spectral moments of the network and is well-suited to the case of
heterogeneous populations.
Our framework provides efficient numerical methods to infer global
information on the network from sparse local measurements at a few nodes.
Numerical simulations show for instance the possibility of detecting the mean
number of connections or the addition of a new vertex using measurements made
at one single node, that need not be representative of the other nodes'
properties.Comment: 3
Graph partitions and cluster synchronization in networks of oscillators
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators
Stochastic dynamics and delta-band oscillations in clustered spiking networks
Following experimental measurements of clustered connectivity in the cortex, recent studies have found that clustering connections in simulated spiking networks causes transitions between high and low firing-rate states in subgroups of neurons. An open question is to what extent the sequence of transitions in such networks can be related to existing statistical and mechanical models of sequence generation. In this thesis we present several studies of the relationship between connection structure and network dynamics in balanced spiking networks. We investigate which qualities of the network connection matrix support the generation of state sequences, and which properties determine the specific structure of transitions between states. We find that adding densely overlapping clusters with equal levels of recurrent connectivity to a network with dense inhibition can produce sequential winner-takes-all dynamics in which high-activity states pass between correlated clusters. This activity is reflected in the power spectrum of spiking activity as a peak in the low-frequency delta range. We describe and verify sequence dynamics with a Markov chain framework, and compare them mechanically to “latching” models of sequence generation. Additionally we quantify the chaos of clustered networks and find that minimally separated states diverge in distinct stages. The results clarify the computational capabilities of clustered spiking networks and their relationship to experimental findings. We conclude that the results provide a supporting intermediate link between abstract models and biological instances of sequence generation