Contrasting Views of Complexity and Their Implications For Network-Centric Infrastructures

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design

Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type

Regulated mitochondrial DNA replication during oocyte maturation is essential for successful porcine embryonic development.

Cellular ATP is mainly generated through mitochondrial oxidative phosphorylation, which is dependent on mitochondrial DNA (mtDNA). We have previously demonstrated the importance of oocyte mtDNA for porcine and human fertilization. However, the role of nuclear-encoded mitochondrial replication factors during oocyte and embryo development is not yet understood. We have analyzed two key factors, mitochondrial transcription factor A (TFAM) and polymerase gamma (POLG), to determine their role in oocyte and early embryo development. Competent and incompetent oocytes, as determined by brilliant cresyl blue (BCB) dye, were assessed intermittently during the maturation process for TFAM and POLG mRNA using real-time RT-PCR, for TFAM and POLG protein using immunocytochemistry, and for mtDNA copy number using real-time PCR. Analysis was also carried out following treatment of maturing oocytes with the mtDNA replication inhibitor, 2',3'-dideoxycytidine (ddC). Following in vitro fertilization, preimplantation embryos were also analyzed. Despite increased levels of TFAM and POLG mRNA and protein at the four-cell stage, no increase in mtDNA copy number was observed in early preimplantation development. To compensate for this, mtDNA appeared to be replicated during oocyte maturation. However, significant differences in nuclear-encoded regulatory protein expression were observed between BCB(+) and BCB(-) oocytes and between untreated oocytes and those treated with ddC. These changes resulted in delayed mtDNA replication, which correlated to reduced fertilization and embryonic development. We therefore conclude that adherence to the regulation of the timing of mtDNA replication during oocyte maturation is essential for successful embryonic development

More "normal" than normal: scaling distributions and complex systems

One feature of many naturally occurring or engineered complex systems is tremendous variability in event sizes. To account for it, the behavior of these systems is often described using power law relationships or scaling distributions, which tend to be viewed as "exotic" because of their unusual properties (e.g., infinite moments). An alternate view is based on mathematical, statistical, and data-analytic arguments and suggests that scaling distributions should be viewed as "more normal than normal". In support of this latter view that has been advocated by Mandelbrot for the last 40 years, we review in this paper some relevant results from probability theory and illustrate a powerful statistical approach for deciding whether the variability associated with observed event sizes is consistent with an underlying Gaussian-type (finite variance) or scaling-type (infinite variance) distribution. We contrast this approach with traditional model fitting techniques and discuss its implications for future modeling of complex systems

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

Optimal vaccination in a stochastic epidemic model of two non-interacting populations

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional, deterministic SIR model. For intermediate quantities of vaccine, the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case.Comment: 21 pages, 7 figure

Understanding Internet topology: principles, models, and validation

Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet

Towards a theory of diagnosis in second and foreign language assessment:insights from professional practice across diverse fields

Diagnostic language assessment has received increased research interest in recent years, with particular attention on methods through which diagnostic information can be gleaned from standardized proficiency tests. However, diagnostic procedures in the broader sense have been inadequately theorized to date, with the result that there is still little agreement on precisely what diagnosis in second and foreign language learning actually entails. In order to address this problem, this article investigated how diagnosis is theorized and carried out in a diverse range of professions with a view to finding commonalities that can be applied to the context of language assessment. Ten semi-structured interviews were conducted with professionals from the fields of car mechanics, IT systems support, medicine, psychology and education. Data were then coded, yielding five macro-categories that fit the entire data set: (i) definitions of diagnosis, (ii) means of diagnosis, (iii) key players, (iv) diagnostic procedures, (v) treatment/follow-up. Based on findings within these categories, a set of five tentative principles of diagnostic language assessment is drawn-up, as well as a list of implications for future research

Phonons in honeycomb and auxetic two-dimensional lattices

The modes of vibrations in honeycomb and auxetic structures are studied, with models in which the lattice is represented by a planar network where sites are connected by strings and rigid rods. The auxetic network is obtained modifying a model proposed by Evans et al. in 1991, and used to explain the negative Poisson's ratio of auxetic materials. This relevant property means that the materials have a lateral extension, instead to shrink, when they are stretched. For what concerns the acoustic properties of these structures, they absorb noise and vibrations more efficiently than non-auxetic equivalents. The acoustic and optical dispersions obtained in the case of the auxetic model are compared with the dispersions displayed by a conventional honeycomb network. It is possible to see that the phonon dispersions of the auxetic model possess a complete bandgap and that the Goldstone mode group velocity is strongly dependent on the direction of propagation. The presence of a complete bandgap can explain some experimental observations on the sound propagation properties of the auxetic materials.Comment: 12 pages, 6 figure