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We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this…
In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying…
Understanding the complexity of biological neural networks like the human brain is one of the scientific challenges of our century. The organization of the brain can be described at different levels, ranging from small neural networks to…
In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measurements, typically assumed to be reflective of either functional or structural relationships between regions…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…
Artificial and natural neural network models are a new toolkit which could be potentially have been used for clarifying of complex brain functions. To attend this goal, such models need to be neurobiologically realistic. However, although…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
From interacting cellular components to networks of neurons and neural systems, interconnected units comprise a fundamental organizing principle of the nervous system. Understanding how their patterns of connections and interactions give…
Functions of brain areas in complex animals are believed to rely on the dynamics of networks of neurons rather than on single neurons. On the other hand, the network dynamics reflect and arise from the integration and coordination of the…
If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…
Experimental fMRI studies have shown that spontaneous brain activity i.e. in the absence of any external input, exhibit complex spatial and temporal patterns of co-activity between segregated brain regions. These so-called large-scale…
Identifying the spatio-temporal network structure of brain activity from multi-neuronal data streams is one of the biggest challenges in neuroscience. Repeating patterns of precisely timed activity across a group of neurons is potentially…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
Realistic modeling of brain involves large number of neurons. The important question is how this size affects transmission efficiency? Here, these issue is studied in terms of Shannon's Theory. Mutual Information between input and output…
Previous work has shown that it is possible to train neuronal cultures on Multi-Electrode Arrays (MEAs), to recognize very simple patterns. However, this work was mainly focused to demonstrate that it is possible to induce plasticity in…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
Complex functional brain network analyses have exploded over the last eight years, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has…