Related papers: Laplacian networks: growth, local symmetry and sha…

We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically,…

Power minimisation in branched fluidic networks has gained significant attention in biology and engineering. The optimal network is defined by channel radii that minimise the sum of viscous dissipation and the volumetric energetic cost of…

We consider a growing planar network where a tip grows at constant speed, branches at constant rate and inactivates when it meets a branch already created. We only consider here orthogonal branching occurring always in the same direction.…

Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the…

Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…

We consider Hamiltonian diffeomorphisms $\phi$ of the unit cotangent bundle over a closed Riemannian manifold $(M,g)$ which extend to Hamiltonian diffeomorphisms of $T^*M$ equal to the time-1-map of the geodesic flow for $|p| \ge 1$. For…

It had been conjectured that Diffusion Limited Aggregates and Laplacian Growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a 1-parameter family of fractal growth…

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…

What are the general principles that allow proper growth of a tissue or an organ? A growing leaf is an example of such a system: it increases its area by orders of magnitude, maintaining a proper (usually flat) shape. How can this be…

The growth of laminar-turbulent band patterns in plane Couette flow is studied in the vicinity of the global stability threshold R_g below which laminar flow ultimately prevails. Appropriately tailored direct numerical simulations are…

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth…

We study the dynamics of "finger" formation in Laplacian growth without surface tension in a channel geometry (the Saffman-Taylor problem). Carefully determining the role of boundary geometry, we construct field equations of motion, these…

Adaptive networks are well-suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature. Adaptive networks consist of a collection of…

In this paper, we investigate how local rules enforced at every node can influence the topology of a network. More precisely, we establish several results on the diameter of trees as a function of the number of nodes, as listed below. These…

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…

We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is…

We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of…

We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner…

Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However,…

We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical…