Distribution efficiency and structure of complex networks

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g. the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states. The combination of flow resistance, fluid inertia, and elasticity of the vessel walls causes the flow and pressure of the fluid t...

Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures in the framework of percolation theory, and in particular the key role of edge interfaces bridging the communication between core and periphery, allow us to shed light on the structural properties of real and theoretical flow networks, and t...

We introduce a mesoscopic model for natural network formation processes, acting as a bridge between the discrete and continuous network approach proposed by Hu and Cai. The models are based on a common approach where the dynamics of the conductance network is subject to pressure force effects. We first study topological properties of the discrete model and we prove that if the metabolic energy consumption term is concave with respect to the conductivities, the optimal network...

The identification of vascular networks is an important topic in the medical image analysis community. While most methods focus on single vessel tracking, the few solutions that exist for tracking complete vascular networks are usually computationally intensive and require a lot of user interaction. In this paper we present a method to track full vascular networks iteratively using a single starting point. Our approach is based on a cloud of sampling points distributed over c...

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges, organisms can robustly control the propagation of inputs to perform specific tasks. However, a fundamental disconnect exists between the structure and function of these networks: networks with different local architectures can perform the ...

Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to capillaries and uses scaling exponents to quantify these changes. Prominent scaling theories predict that combinations of these exponents explain how metabolic, growth, and other biological rates vary with body size. Nevertheless, direct mea...

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is stil...

A model is proposed to minimize the total volume of the main distribution networks of fluids in relation to the organ form. The minimization analysis shows that the overall exterior form of distribution networks is a modified ellipsoid, a geometric form that is a good approximation to the external anatomy of the kidney and lung. The variational procedure implementing this minimization is similar to the traditional isoperimetric theorems of geometry. A revised version of thi...

The design of efficient transportation networks is an important challenge in many research areas. Among the most promising recent methods, biological routing mimic local rules found in nature. However comparisons with other methods are rare. In this paper we define a common framework to compare network design method. We use it to compare biological and a shortest-path routing approaches. We find that biological routing explore a more efficient set of solution when looking to ...

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in p...