Network topologies

Well-known network topologies and their performance characteristics. The network degree is the number of links supported by each simple switch, and p is the number of processors Whop is the maximum number of switches through which data must pass, and Be and nsw represent the bisection width and the number of simple switching elements, respectively 

Wells notation takes the form (n, p)-net where n and p are integers that describe, respectively, the shortest route in terms of number of nodes to complete a circuit back to the starting place and the connectivity of a given node. Thus a (6,3)-net contains hexagonal holes (or, if irregular, holes that form a six-sided polygon a 6-gon n = 6) and each node is 3-connected (p = 3). 

Recently there have been significant advances in mathematical tiling theory which have been applied to more rigorous descriptions of complex 3D (or 3-periodic) network topologies. The reader is referred to the literature for a complete description of these powerful new methods.  

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Shen W, Zhang KC, Komfield JA et al (2006) Tuning the erosion rate of artificial protein hydrogels through control of network topology. Nat Mater 5 153-158... 

Mesostructured materials with adjustable porous networks have shown a considerable potential in heterogeneous catalysis, separation processes and novel applications in optics and electronics [1], The pore diameter (typically from 2 to 30 nm), the wall thickness and the network topology (2D hexagonal or 3D cubic symmetry) are the major parameters that will dictate the range of possible applications. Therefore, detailed information about the formation mechanism of these mesostructured phases is required to achieve a fine-tuning of the structural characteristics of the final porous samples. 

Closely related to the approach considered here are the formal frameworks of Feinberg and Clarke, briefly mentioned in Section II. A. Though mainly devised for conventional chemical kinetics, both, Chemical Reaction Network Theory (CRNT), developed by M. Feinberg and co-workers [79,80], as well as Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83], seek to relate aspects of reaction network topology to the possibility of various... 

Self-Sorting Processes Lead to Dynamic Combinatorial Libraries with New Network Topologies... 

Saur, 1. Scopelliti, R. Severin, K. Utilization of self-sorting processes to generate dynamic combinatorial hbraries with new network topologies. Chem. Ear. J. 2006,12,1058-1066. 

The solutions to Equation 9 are those values of g for which the functional f=(l- ) intersects the functional f=(l-ag), where r=fcn[CQ,k, k, nQ,eQ,k, k ] and a in general also is a function of the same variables. Actin binding protein (ABP) joins contiguous chains and a therefore depends on strand density and network topology in addition to the intrinsic rate constants for attachment of ABP to an available binding site. 

Obviously, there are many subtle differences in the structure, morphology, or network topology between radiation cured and sulfur cured elastomers, but their physical properties may be nearly equal, provided that precautions are taken to avoid the occurrence of chain scissions. A comparison of radiation cross-linked and sulfur cured natural rubber (gum and carbon-black-reinforced compounds) is in Table 5.4. ... 

Thus, the analysis of the reactivity ratios of the primary and secondary amino groups indicates that for conventional curing agents this cannot be regarded as a serious factor affecting the network topology. 

Z. Roger, R. Weber, Finding an optimal artificial neural network topology in real-life modeling, presented at the ICSC Symposium on Neural Computation, article No. 1, 1403/109, 2000. 

Jackson, J. F., and S. J. Gill Elastic properties of crosslinked poly (vinyl alcohol) gels. Network topology. J. Polymer Sci. Pt A-2, 5, 663 (1967). 

Baker, E. G., Network Topology and Cohesive Forces in Polyethylene, ... 

Remark 1 The problem statement is identical to the problem statement of section 8.5.3.1 for the synthesis of HENs without decomposition (Ciric and Floudas, 1991). Note that as in section 8.5.3.1, there is no specification of any parameters so as to simplify or decompose the original problem into subproblems. In other words, the level of energy recovery (specified by fixing H RAT), the minimum approach temperature (EM AT), and the number of matches are not specified a priori. As a result, there is no decomposition into subnetworks based on the location of the pinch point(s), but instead the pinch point(s) are optimized simultaneously with the matches and the network topology. The approach presented for this problem is from Yee and Grossmann (1990) and is an alternative approach to the one of HEN synthesis without decomposition proposed by Ciric and Floudas (1991), and which was presented in section 8.5.3. 

The heat integration alternatives consist of only the different matches that may take place and do not include structural alternatives of the heat exchanger network topology presented in the hyperstructure or superstructure sections of HEN synthesis. 

Figure 9.3 Examples of network topologies along with their Schlafli symbols. The corresponding Wells symbols are (6,3), (4,82), (4,4) and (10,3)-a.

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