Probabilistic Inductive Classes of Graphs

Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive classes of graphs - for formalizing and studying evolution of complex networks. Our definition of probabilistic inductive class of graphs (PICG) extends the standard notion of inductive class of graphs (ICG) by imposing a probability space. A PICG is given by: (1) class B of initial graphs, the basis of PICG, (2) class R of generating rules, each with distinguished left element to which the rule is applied to obtain the right element, (3) probability distribution specifying how the initial graph is chosen from class B, (4) probability distribution specifying how the rules from class R are applied, and, finally, (5) probability distribution specifying how the left elements for every rule in class R are chosen. We point out that many of the existing models of growing networks can be cast as PICGs. We present how the well known model of growing networks - the preferential attachment model - can be studied as PICG. As an illustration we present results regarding the size, order, and degree sequence for PICG models of connected and 2-connected graphs.Comment: 15 pages, 6 figure

A study on wear failure analysis of tungsten carbide hardfacing on carbon steel blade in a digester tank

This paper addresses wear failure analysis of tungsten carbide (WC) hardfacing on a carbon steel blade known as the continuous digester blade (CD blade). The CD blade was placed in a digester tank to mix ilmenite ore with sulphuric acid as part of a production process. Tungsten carbide hardfacing was applied on the CD blade to improve its wear resistance while the CD blade was exposed to an abrasive and acidic environment. Failure analysis was car-ried out on the hardfaced CD blade in order to improve its wear resistance and lifetime. A thickness and hardness comparison study was conducted on worn and unworn specimens from the CD blades. The carbide distribution along with elemental composition analysis of the hardfaced CD blade specimens was examined using scanning electron microscopy and energy-dispersive spectroscopy. The investigation revealed that an inconsistent hardfacing thickness was welded around the CD blade. Minimum coating thickness was found at the edges of the blade surfaces causing failure to the blades as the bare carbon steel blades were exposed to the mixed environment. The wear resistance of the CD blade can be improved by distributing the carbide uniformly on the hardfaced coating. Applying extra coating coverage at the critical edge will prevent the exposure of bare carbon steel blade, thus increasing the CD blade lifetime

2007. “Oscillatory dynamics of city-size distributions in world historical systems

(proof corrections; variables not italicized) Globalization, world-system, and historical dynamic theory offer complementary perspectives for the study of city systems as the politico-economic engine of interstate networks. Here we combine these perspectives to examine a dynamical perspective on systems of cities. Globalization theory applied to Eurasia in the last millennium (e.g. Modelski and Thompson, 1996) focuses on centers of economic innovation and political power and their successive periods of rise and fall in dominance. Units of larger scale, as for example polities, are shown to operate at successively longer time-scales in their rise and fall than the economic innovation centers within those polities. Worldsystem theory for similar regions and processes (e.g. Chase-Dunn and Hall, 1997) differs in the way in which it also focuses on innovation at the peripheries of states and empires, that is, on the marcher or boundary polities that resist the encroachment of expanding empires. Marcher states that amalgamate to defeat the spread of an empire often defeat polities formally organized on

City-system dynamics in world history studied by change in city-size distributions 1

Abstract. Oscillatory patterns of expansion/contraction have long characterized the dynamics of demographic, economic, and political processes of human societies, including those of exchange economies and globalization. Major perturbations in city-size distributions are shown to exist for major regions in Eurasia in the last millennium and to exhibit some of the characteristics of cyclical oscillations on the scale of 100s of years as well as longer fluctuations, from 400 up to 800 years, between periods of major collapse, often punctuated by lesser collapse. Variations in timing, irregularities in amplitudes, and ups and downs in our measures appear to correlate with some of the peaks and troughs in urban population growth and show long-cycle correlations with J.S. Lee’s (1931) sociopolitical instability (SPI) data on the durations of internecine wars for China. We focus here on central civilization within the world cities database, including China and Europe, and the Mid-Asian region between. These data are likely to reflect changes in the macro regions connected by trade networks, where we would expect synchronization. Our interpretation of city-size distribution oscillations is that they follow, with generational time lags, rises and falls in the expansion/contraction of multi-connected trade network macro zones, with Zipfian city-size hierarchies tending to rise with trade network expansions and fall with contractions. City system rise and fall also tend to couple with oscillations of population relative to resources interacting with SPI in total cycles that average about 220 years. Time-lagged synchronies in the dating of phase