Related papers: Limits and dynamics of randomly connected neuronal…
We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…
Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…
The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the…
Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neurons in an increasing number of organisms. Here, we model and quantify the complexity of the resulting…
We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…
A major challenge in neuroscience is posed by the need for relating the emerging dynamical features of brain activity with the underlying modular structure of neural connections, hierarchically organized throughout several scales. The…
We systematically study and compare damage spreading for random Boolean and threshold networks under small external perturbations (damage), a problem which is relevant to many biological networks. We identify a new characteristic…
Coordination is a desirable feature in many multi-agent systems such as robotic and socioeconomic networks. We consider a task allocation problem as a binary networked coordination game over an undirected regular graph. Each agent in the…
We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…
A fundamental understanding of the network architecture of the brain is necessary for the further development of theories explicating circuit function. Perhaps as a derivative of its initial application to abstract informational systems,…
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…
The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…
Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a…
Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. Our approach allows to derive a continuous limit for the macroscopic behavior of the system, the…