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In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and…
Here, the general design and properties of new multiple network elastomers with an exceptional combination of stiffness, toughness, and elasticity are reported. In this paper, it is reported in more detail how the increase in strain at…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow…
Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of…
The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density $\rho(\lambda)$ of this matrix reveals important network…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
Elastic netwok models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks,…
We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on $X$ which is either observed directly or derived from a data set. For an electrical network there are two…