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Demystifying effective connectivity among neuronal populations has become the trend to understand the brain mechanisms of Parkinson's disease, schizophrenia, mild traumatic brain injury, and many other unlisted neurological diseases.…
Objective: Brain is a fantastic organ that helps creature adapting to the environment. Network is the most essential structure of brain, but the capability of a simple network is still not very clear. In this study, we try to expound some…
On the basis of the tight-binding formalism and Green function technique we obtain all the Green functions matrix elements for a biased chain with a linear variation of the electron on-site energy. Their dependence on the system parameters…
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties…
The network paradigm is increasingly used to describe the topology and dynamics of complex systems. Here we review the results of the topological analysis of protein structures as molecular networks describing their small-world character,…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
Molecular dynamics (MD) simulation, which is considered an important tool for studying physical and chemical processes at the atomic scale, requires accurate calculations of energies and forces. Although reliable energies and forces can be…
Unraveling the structural factors influencing the dynamics of amorphous solids is crucial. While deep learning aids in navigating these complexities, transparency issues persist. Inspired by the successful application of prototype neural…
It has become increasingly popular to study the brain as a network due to the realization that functionality cannot be explained exclusively by independent activation of specialized regions. Instead, across a large spectrum of behaviors,…
Structured prediction in natural language processing (NLP) has a long history. The complex models of structured application come at the difficulty of learning and inference. These difficulties lead researchers to focus more on models with…
Key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures.…
An exchange correlation energy functional involving fractional power of the one-body reduced density matrix [Phys. Rev. B {\bf 78}, 201103 (2008)] is applied to finite systems and to the homogeneous electron gas. The performance of the…
The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed-points are determined and the renormalization-group flow for certain initial conditions is…
Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity, related to the…
To the reduct problems of decision system, the paper proposes the notion of dynamic core according to the dynamic reduct model. It describes various formal definitions of dynamic core, and discusses some properties about dynamic core. All…
A system of $N$ interacting objects with internal degrees of freedom is considered. Derivation of system of equations for the description of two interacting objects with spin is given. Relations between the parameters describing subsystems…
This paper provides the analysis for functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced. The concepts of strength, power, domain and…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…
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…