Global network properties

The degree distribution P(k) is the probability that a node is linked to k other nodes. The P(k) of random networks exhibits a Poisson distribution, whereas that of scale-free networks approximates a power law of the form m An interesting suggestion is that most cellular networks approximate a scale-free topology with an exponent y between 2 and The 

The path length distribution of a network tells us how far nodes are from each other. Scale-free networks are ultra-small because they have an average path length of the order log(log N), where N is the number of nodes. Random networks are small because their mean path length is of the order logN.  

---

Equation (99) implies that it is often possible to specify intervals or approximate values for the scaled elasticities in terms of relative saturation, even when detailed kinetic information is not available. For example, as a rule of thumb, the substrate concentration can often be considered to be on the order of the Km value. As the scaled elasticities, by means of the control coefficients, can be directly translated into a systemic response, it is possible to utilize such heuristic arguments to acquire an initial approximation of global network properties. 

R. Steuer and G. Zamora Lopez, Global network properties. Analysis of Biological Networks, Wiley Series on Bioinformatics Computational Techniques and Engineering. B. H. Junker and F. Schreiber, eds., John Wiley Sons, Inc. 2008. 

MCA distinguishes between local and global (systemic) properties of a reaction network. Local properties are characterized by sensitivity coefficients, denoted as elasticities, of a reaction rate v,(S,p) toward a perturbation in substrate concentrations (e-elasticities) or kinetic parameters ( -elasticities). The elasticities measure the local response of a reaction in isolation and are defined as the partial derivatives at a reference state S°... 

The statistical approach to chemical kinetics was developed by Li et al. (2001, 2002), and high-dimensional model representations (HDMR) were proposed as efficient tools to provide a fully global statistical analysis of a model. The work of Feng et al. (2004) was focused on how the network properties are affected by random rate constant changes. The rate constants were transformed to a logarithmic scale to ensure an even distribution over the large space. 

Due to the complexity of the formation of interphases, a completely satisfying microscopic interpretation of these effects cannot be given today, especially since the process of the interphase formation is not yet understood in detail. Therefore, a micromechanical model cannot be devised for calculating the global effective properties of a thin polymer film including the above-mentioned size effects governed by the interphases. On the other hand, a classical continuum-based model is not able to include any kind of size effect. An alternative to the above-mentioned classical continuum or the microscopical model is the formulation of an extended continuum mechanical model which, on the one hand, makes it possible to capture the size effect but, on the other hand, does not need all the complex details of the underlying microstmcture of the polymer network. 

Globally, the properties of CH/NFC nanocomposite films were better than those displayed by similar chitosan films reinforced with BC Nano fibrils. This behavior could be due to the better dispersion of NFC into the chitosan matrices, related to the individual fiber morphology, contrasting with the tridimensional network fibers strac-ture of BC, as well as to the higher aspect ratio of the NFC compared withBC. 

To understand the global mechanical and statistical properties of polymeric systems as well as studying the conformational relaxation of melts and amorphous systems, it is important to go beyond the atomistic level. One of the central questions of the physics of polymer melts and networks throughout the last 20 years or so dealt with the role of chain topology for melt dynamics and the elastic modulus of polymer networks. The fact that the different polymer strands cannot cut through each other in the... 

The utility and success of Metabolic Control Analysis is mostly due to a number of simple relationships that interconnect the various coefficients and that bridge between local and global properties of the network. First, the summation theorems relate to the structural properties of the network and are independent of kinetic parameters [96]. Using Eq. (90) and (91), it is straightforward to verify that... 

Baltensperger U. Barrie L. and Wehrli C. (eds.) (2005). WMO/GA W Experts Workshop on a Global Surface-Based Network for Long Term Observations of Column Aerosol Optical Properties (Davos, Switzerland, March 8-10, 2004). WMO Publ., Davos, Switzerland, 148 pp. 

The aim of the paper was to demonstrate the current state of research and development in the field of nanocelluloses on the basis of selected examples. The extraordinary supramolecular nanofiber network structure and the resulting valuable properties have led to a real challenge and extensive global activity. It is the intention of this work to broaden knowledge in this subject area... 

Rahman SA, Schomburg D (2006) Observing local and global properties of metabolic pathways load points and choke points in the metabolic networks. Bioinformatics 22 1767-1774... 

Since the stiffness of the bonds transfers to the stiffness of the whole filler network, the small strain elastic modulus of highly filled composites is expected to reflect the specific properties of the filler-filler bonds. In particular, the small strain modulus increases with decreasing gap size during heat treatment as observed in Fig. 32a. Furthermore, it exhibits the same temperature dependence as that of the bonds, i.e., the characteristic Arrhenius behavior typical for glassy polymers. Note however that the stiffness of the filler network is also strongly affected by its global structure on mesoscopic length scales. This will be considered in more detail in the next section. 

---