Related papers: The Syncytial Mesh Model: A Mesoscale Control-Fiel…
Recent years have seen dramatic progress in the development of techniques for measuring the activity and connectivity of large populations of neurons in the brain. However, as these techniques grow ever more powerful---allowing us to even…
The functioning of an organ such as the brain emerges from interactions between its constituent parts. Further, this interaction is not immutable in time but rather unfolds in a succession of patterns, thereby allowing the brain to adapt to…
Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by…
Oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model was investigated by simulating coupled stochastic processes defined by stochastic differential equations. It was found, for several…
In [1], we have shown that the dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT)bifurcation point can generate the observed scale-free avalanches at the population…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
Since the earliest electroencephalography experiments, large scale oscillations have been observed in the mammalian brain. More recently, episodes of oscillation and bursting have been identified not only in the cerebral cortex and…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Understanding how internal community structure shapes the course of epidemics remains a fundamental challenge in modeling real-world populations. Standard metapopulation models often assume uniform mixing within communities, overlooking how…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
Scale-free behavior as well as oscillations are frequently observed in the activity of many natural systems. One important example is the cortical tissues of mammalian brain where both phenomena are simultaneously observed. Rhythmic…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…
Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
At rest, human brain functional networks display striking modular architecture in which coherent clusters of brain regions are activated. The modular account of brain function is pervasive, reliable, and reproducible. Yet, a complementary…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly…