Scale-free

Acrylic esters can be polymerized by a number of routes. Anionic polymerization gives the narrow standards used primarily for calibration, but is not used on an industrial/commercial scale. Free-radical polymerization is the dominant mode of polymerization for making these polymers on an industrial scale. Significant volumes of polymer are made by both solution polymerization... 

Improved processes and quality control have helped to establish these new coating materials but the care necessary for successful use has to be appreciated. Sections 11.1 and 11.2 have shown how necessary it is to remove millscale before coating and how scale-free surfaces may still retain seeds of further corrosion even when apparently cleaned well. The percentage of premature failures with sophisticated systems is still high, even on apparently well-prepared surfaces and there is a strong case for effective inspection at each stage of coating operations. 

This is an indication of the collective nature of the effect. Although collisions between hard spheres are instantaneous the model itself is not binary. Very careful analysis of the free-path distribution has been undertaken in an excellent old work [74], It showed quite definite although small deviations from Poissonian statistics not only in solids, but also in a liquid hard-sphere system. The mean free-path X is used as a scaling length to make a dimensionless free-path distribution, Xp, as a function of a free-path length r/X. In the zero-density limit this is an ideal exponential function (Ap)o- In a one-dimensional system this is an exact result, i.e., Xp/(Xp)0 = 1 at any density. In two dimensions the dense-fluid scaled free-path distributions agree quite well with each other, but not so well with the zero-density scaled distribution, which is represented by a horizontal line (Fig. 1.21(a)). The maximum deviation is about... 

The /1CDM paradigm for structure formation in the Universe, described in many hundreds of published papers, is very effective at reproducing observed large scale structure, based on a boundary condition of a scale-free Gaussian random power spectrum. Yet ACDM contains no information on the physics of whatever makes up CDM, and remains deficient in its description of galaxies and small-scale structures thus it is on galaxy scales and smaller where we can still learn the most, and hopefully attach some (astro-)physics to an ab initio power spectrum. 

There are two detection sensitivities that are of interest for characterizing the BioCD performance. The first is a metrology sensitivity that includes experimental noise sources such as the laser intensity fluctuations and detector noise, but does not include variability of the protein spots on the disc. The second detection sensitivity is under actual assay conditions in which antibody spot variability plays a dominant role. For both of these sensitivities, it is important to define a scale-free sensitivity that is an intrinsic property of the detection platform. 

In experiments23, we have observed a metrology-limited height of 20 pm per pixel, and an assay-limited height of 75 pm per protein spot. Based on these values, the scale-free minimum detectable height... 

In the past decade, a large number of studies emphasized the heterogeneous scale-free degree distribution of metabolic networks Most substrates participate in only a few reactions, whereas a small number of metabolites ( hubs ) participate in a very large number of reactions [19,45,52]. Not surprisingly, the list of highly connected metabolites is headed by the ubiquitous cofactors, such as adenosine triphosphate (ATP), adenosine diphosphate (ADP), and nicotinamide adenine dinucleotide (NAD) in its various forms, as well as by intermediates of glycolysis and the tricarboxylic acid (TCA) cycle. 

Some factors do make the process easier. Several studies suggest that metabolic networks are scale-free. There are also important stoichiometric constraints and elementary nodes... 

The emergence of slow kinetics with its typical slowly decaying memory effects is tightly connected to a scale-free waiting time pdf that is, the temporal occurrence of the motion events performed by the random walking particle is broadly distributed such that no characteristic waiting time exists. It has been demonstrated that it is the assumption of the power-law form for the waiting time pdf which leads to the explanation of the kinetics of a broad diversity of systems such as the examples quoted above. 

Keywords Scale-free networks Internet structure quantum key... 

Barabasi and his collaborators [2]-[3] researched and established foundations for the real large random networks called scale-free. 

One of the key discoveries was the realization that very many real networks in nature, technology (e.g., the Internet and WWW) and human relations have similar structure and growth patterns, and can be described by the same mathematical formulas. All of them share similar properties and behavior. This discovery and the new theory have created an unprecedented opportunity for investigating resilience and vulnerabilities of the Internet and the WWW. For this reason we consider the scale-free network theory and related empirical results as being a significant development in the Cyberspace Security and Defense. 

Random networks were a significant contribution to the future theory of large real networks but the most dramatic and useful development took place about forty years later when A-L Barabasi and his collaborators made empirical mapping of the Internet and using different growth principles created the theory of nets called scale-free networks. 

The scale-free networks investigated by A-L Barabasi and his collaborators follow a different growth rule than the rules for creating random networks. All scale-free networks are characterized by distribution functions P(k) which are powers of k. 

The pattern of growth for scale-free networks follows the rule of preferential attachment [7]. According to this rule a new node prefers attaching itself to the highly connected nodes. For example a simple linear version of this rule can be expressed formally as... 

The most dramatic result of the preferential attachment growth rule is the appearance of highly connected nodes called hubs. The scale-free networks do not have typical nodes with average number of edges. The concept of average connectivity does not have meaning for these nets. 

Scale-free networks have few very highly connected hubs and most of the nodes have only few edges. This difference in the structure between the... 

Scale free networks are common in nature, human relations, economy and technology. The Internet and WWW are important examples of scale-free networks. A possible reason for popularity of scale-free nets in nature may be their robustness in the presence of random node failures. Computer experiments have shown that Internet would not fall apart even if 80% of all routers fail [7]. 

This structural robustness could be attributed to the existence of hubs in scale-free networks. Similar experiments indicate that by removing a few hubs the Internet would disintegrate into disjoint components. 

Both developments, scale-free network theory and quantum key distribution offer new opportunities for Cyberspace Security and Defense. In... 

Barabasi, A-L., Albert Reka, and Jeong Hawoong, Mean-Field Theory for Scale-Free Random Networks, Physics A, 272, (1999) 173-187. 

Dezso, Zoltan and A-L. Barabasi, Halting viruses in scale- free networks, Phys Rev. E, 65, 055103(R)... 

Bollt EM, ben-Avraham D (2005) What is special about diffusion on scale-free nets New J Phys 7 26... 

Montgomery E. B. Dynamically Coupled, High-Frequency Reentrant, Non-linear Oscillators Embedded in Scale-Free Basal Ganglia-Thalamic-Cortical Networks Mediating Function and Deep Brain Stimulation Effects. Nonlinear Stud, 2004, 22, 385-421. 

Following the considerable recent interest in scale-free networks, Jeong et al. [145] have shown that the metabolic networks of extant living systems are scale-free networks sharing the same metabolite hubs over evolutionary time. Wagner and Fell [146] suggest that there are three reasons why metabolic networks may be scale free. 

Metabolism may be scale-free because of chemical constraints of the underlying chemical network. They dismiss this possibility, claiming as evidence the fact that in different organisms the metabolic network takes many different forms. However, this does not rule out the existence of more general chemical constraints that may produce the scale-free network. For example, it is generally the case that small molecules have more possible synthesis routes than large molecules and so we expect connectivity to scale as a function of size. 

In the long run, it is likely that some combination of quantum mechanical calculations (which tend to build up the enzyme around the reaction) and large-scale free energy calculations (which make predictions regarding the whole enzyme and then endeavor to decompose them into chemically meaningful parts) will play a key role in unraveling the mystery of ODCase. 

Tobita H (2004) Scale-free power-law distribution of emulsion-polymerized nonlinear polymers Free-radical polymerization with chain transfer to polymer. Macromolecules... 

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