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Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
A brain microstate is characterized by a unique, fixed spatial distribution of electrically active neurons with time varying amplitude. It is hypothesized that a microstate implements a functional/physiological state of the brain during…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
An approach to nonlinear dynamical modeling of interaction between conscious and automatic processes in the brain is proposed. Illustration of this approach on the nonlinear equation for the current density in the cortex is presented.…
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 net of N ``physical'' neurons is considered as a dynamical system. These neurons form a complete graph. The state of any neuron is its electric potential. The potential linearly increases until reaches its maximal value. Then it falls…
This paper develops a mathematical framework to study signal networks, in which nodes can be active or inactive, and their activation or deactivation is driven by external signals and the states of the nodes to which they are connected via…
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…
Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…
Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific…
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbour. The symmetry…
Biological nervous systems consist of networks of diverse, sophisticated information processors in the form of neurons of different classes. In most artificial neural networks (ANNs), neural computation is abstracted to an activation…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
Activity in neocortex exhibits a range of behaviors, from irregular to temporally precise, and from weakly to strongly correlated. So far there has been no single theoretical framework that could explain all these behaviors, leaving open…
We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…