Principles of statistical mechanics of random networks

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.Comment: 14 pages, an extended versio

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure

Some aspects of progeny testing Southdown rams : a thesis presented in part fulfilment of the requirements for the degree of Master of Agricultural Science in Massey University of Manawatu, New Zealand

Recent changes that have taken place in the preparation and presentation of New Zealand lamb for marketing have been discussed by Barton (1964). Probably the most important of these changes is the increasing amount of lamb that is being displayed and sold as cuts. This is to some extent, the result of, and has definitely contributed to, the growing interest shown by the consumer in meat quality over the last decade. Such interest has been further amplified by increases in the general standard of living of people in many countries, and by the growing consumer aversion to animal fats. Indications of consumer preferences in any particular area may be obtained by surveys, and although these have been carried out extensively for beef, not many have been made concerning lamb. An example however, is that conducted by Marsh (1960), who, by sending questionnaires to members of the middle and working classes of Leeds, showed that the leg was the most popular cut, and that the most favoured quality characteristics in order of popularity were: economy in price and use, leanness, and absence of bone. Results such as these give an indication of the consumers' concept of meat quality, and it is the function of a grading system to integrate this concept with the aims of the lamb producer (Kiehl, 1957; Brayshaw and DeLoach, 1963). These aims will basically be to maximize his profit per unit time, and in order to do this he must produce the greatest possible weight of top grade carcasses in the shortest possible time. Grading of lamb in New Zealand which is carried out subjectively on the whole carcass, is based mainly on conformation and fat cover (Smith-Pilling, 1959), and it has been shown that the carcasses of the top grade contain more fat and less meat or bone, than those of the lowest grade (Barton, 1960). If, as it seems, present grading standards are not a true reflection of consumer preferences, then they can offer no real guidance or incentive to farmers who are interested in planning their management and breeding policies, so as to produce the type of lamb that the consumer wants, and for which he is prepared to pay the highest price. For the same reason there would be no real incentive to improve carcass quality through progeny testing. However, considerable interest has been shown in the grading of meat in recent years, both overseas (e.g., Brayshaw and DeLoach, 1963) and in New Zealand, where the Meat Export Grades Investigation Committee of the New Zealand Meat Producers Board is currently investigating the situation. It is assumed (in order to justify the conducting of the experiment reported herein) that the findings of the above Committee will eventually result in consumer preferences being represented more effectively in lamb grading criteria; thereby providing the producer to some extent with the required guidance and incentives. It has been shown (Morley, 1952) that greater genetic gains can be made through the selection of rams than ewes, and in the case of carcass quality characteristics, where killing of the animal is often necessary for measurement, progeny testing of rams is the obvious selection aid to use

L\'evy-type diffusion on one-dimensional directed Cantor Graphs

L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity and the mean square displacement as a function of the topological parameters of the sets. Interestingly, the systems undergoes a transition from superdiffusive to diffusive behavior as a function of the filling of the fractal. The deterministic topology also allows us to discuss the importance of the choice of the initial condition. In particular, we demonstrate that local and average measurements can display different asymptotic behavior. The analytic results are compared with the numerical solution of the master equation of the process.Comment: 9 pages, 9 figure

Measuring and Understanding Throughput of Network Topologies

High throughput is of particular interest in data center and HPC networks. Although myriad network topologies have been proposed, a broad head-to-head comparison across topologies and across traffic patterns is absent, and the right way to compare worst-case throughput performance is a subtle problem. In this paper, we develop a framework to benchmark the throughput of network topologies, using a two-pronged approach. First, we study performance on a variety of synthetic and experimentally-measured traffic matrices (TMs). Second, we show how to measure worst-case throughput by generating a near-worst-case TM for any given topology. We apply the framework to study the performance of these TMs in a wide range of network topologies, revealing insights into the performance of topologies with scaling, robustness of performance across TMs, and the effect of scattered workload placement. Our evaluation code is freely available