The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena

The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex System

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\alpha= 1+ 1/d$. In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.Comment: 19 pages, 13 figure

MOx/CNTs Hetero-Structures for Gas Sensing Applications: Role of CNTs Defects

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In Situ Graphene Growth Dynamics on Polycrystalline Catalyst Foils

The dynamics of graphene growth on polycrystalline Pt foils during chemical vapor deposition (CVD) are investigated using in situ scanning electron microscopy and complementary structural characterization of the catalyst with electron backscatter diffraction. A general growth model is outlined that considers precursor dissociation, mass transport, and attachment to the edge of a growing domain. We thereby analyze graphene growth dynamics at different length scales and reveal that the rate-limiting step varies throughout the process and across different regions of the catalyst surface, including different facets of an individual graphene domain. The facets that define the domain shapes lie normal to slow growth directions, which are determined by the interfacial mobility when attachment to domain edges is rate-limiting, as well as anisotropy in surface diffusion as diffusion becomes rate-limiting. Our observations and analysis thus reveal that the structure of CVD graphene films is intimately linked to that of the underlying polycrystalline catalyst, with both interfacial mobility and diffusional anisotropy depending on the presence of step edges and grain boundaries. The growth model developed serves as a general framework for understanding and optimizing the growth of 2D materials on polycrystalline catalysts.St. John’s College, Cambridge (Research Fellowship), European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie Individual Fellowship (Global) under Grant ID: ARTIST (no. 656870)), National Science Foundation (graduate research fellowship (DGE-1324585)), European Research Council (Grant ID: InsituNANO (no. 279342)), EUFP7 Work Programme (Grant ID: GRAFOL (project reference 285275)) , Engineering and Physical Sciences Research Council (Grant ID: GRAPHTED (project reference EP/K016636/1)), Strategic Capability programme of the National Measurement System of the U.K. Department of Business, Innovation, and Skills (project no. 119376

The influence of intercalated oxygen on the properties of graphene on polycrystalline Cu under various environmental conditions.

Intercalation of oxygen at the interface of graphene grown by chemical vapour deposition and its polycrystalline copper catalyst can have a strong impact on the electronic, chemical and structural properties of both the graphene and the Cu. This can affect the oxidation resistance of the metal as well as subsequent graphene transfer. Here, we show, using near ambient pressure X-ray photoelectron spectroscopy (NAP-XPS), X-ray absorption near edge spectroscopy (XANES), energy dispersive X-ray spectroscopy (EDX) and (environmental) scanning electron microscopy (ESEM) that both the oxygen intercalation and de-intercalation are kinetically driven and can be clearly distinguished from carbon etching. The obtained results reveal that a charge transfer between as grown graphene and Cu can be annulled by intercalating oxygen creating quasi-free-standing graphene. This effect is found to be reversible on vacuum annealing proceeding via graphene grain boundaries and defects within the graphene but not without loss of graphene by oxidative etching for repeated (de-)intercalation cycles.P.R.K. acknowledges the Lindemann Trust Fellowship. R.S.W. acknowledges a Research Fellowship from St. John’s College, Cambridge. S.H. acknowledges funding from ERC grant InsituNANO (No. 279342) and EPSRC under grant GRAPHTED (Ref. EP/K016636/1). R.B. and A.K.-G. acknowledge funding from EU project GRAFOL, grant 285275.This is the final published version. It first appeared at http://pubs.rsc.org/en/Content/ArticleLanding/2014/CP/c4cp04025b#!divAbstract

Large Scale Cross-Correlations in Internet Traffic

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio

Management of late-onset fetal growth restriction: pragmatic approach

OBJECTIVES: International guidelines recommend delivery from 37 weeks in small for gestational age (SGA) fetuses mostly because of stillbirth concerns. Differentiating SGA from late-onset fetal growth restriction (FGR) is challenged by the limited prospective evidence to guide management. We prospectively assessed a novel protocol that used ultrasound criteria to classify women with suspected late FGR into two groups: low-risk with expectant management until the expected date of delivery and high-risk with delivery soon after 37 weeks. Furthermore, we compared the outcome of this prospective cohort with a historical cohort of women similarly presenting with suspected late FGR, to evaluate the impact of implementation of the new protocol. METHODS: This was a prospective study in women with a singleton non-anomalous fetus at ≥32 weeks with any of the following inclusion criteria: estimated fetal weight (EFW) ≤10th centile, ≥50 centiles decrease of the abdominal circumference (AC) from previous scans, umbilical artery Doppler pulsatility index >95th centile or cerebroplacental ratio <5th centile. Women were stratified into low- or high-risk late FGR. Women in the low-risk group were delivered by 41 weeks unless meeting high-risk criteria for delivery later on, whereas women in the high-risk group (PAPP-A <0.4MoM, EFW <3rd centile, or EFW ≥3rd and ≤10th centile with AC drop or abnormal Dopplers) were delivered at 37 weeks. The primary outcome was adverse neonatal outcome including hypothermia, hypoglycemia, neonatal unit admission, jaundice requiring treatment, suspected infection, feeding difficulties, Apgar score <7 at 1 minute, hospital readmission and any of the severe adverse neonatal outcome (perinatal death, resuscitation using inotropes or mechanical ventilation, Apgar score <7 at 5 minutes, metabolic acidosis, sepsis, cerebral, cardiac or respiratory morbidity). Secondary outcomes were adverse maternal outcome (operative delivery for abnormal fetal heart rate) and severe adverse neonatal outcome. Women managed according with the new protocol were compared with a historical cohort where management was guided by individual clinician's expertise. RESULTS: Over 18 months (2018-2019), 321 women were included. Adverse neonatal outcome was significantly less common in low- (n=156) compared with high-risk fetus (n=165): 45 vs 57%; aOR, 0.6; 95% CI, 0.4-0.9; P=0.022. There was no significant difference in adverse maternal outcome (18% vs 24%; aOR, 0.7; 95% CI, 0.4-1.2; P=0.142) and severe adverse neonatal outcome (3.8% vs 8.5%; aOR: 0.5; 95% CI, 0.2-1.3; P=0.153) between low and high-risk group. Compared to women delivered prior to the implementation of the new protocol and classified retrospectively into low- and high-risk late FGR (n=323), there was a lower adverse neonatal outcome (45% vs 58%; aOR, 0.6; 95% CI, 0.4-0.9; P=0.026) in the low-risk late FGR clinic group. CONCLUSIONS: Appropriate risk classification to define management in low- and high-risk FGR groups was associated with reduced adverse neonatal outcome in the low-risk group. In clinical practice a policy of expectantly managing women with late-onset low-risk FGR pregnancies at term could improve neonatal and long-term development. Randomized controlled trials are needed to assess the effect of an evidence based conservative management protocol of late FGR on perinatal morbidity, mortality and long-term neurodevelopment

Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.

Estimation of traffic matrices for LRD traffic

The estimation of traffic matrices in a communications network on the basis of a set of traffic measurements on the network links is a well known problem, for which a number of solutions have been proposed when the traffic does not show dependence over time, as in the case of the Poisson process. However, extensive measurements campaigns conducted on IP networks have shown that the traffic exhibits long range dependence. Here two methods are proposed for the estimation of traffic matrices in the case of long range dependence, their asymptotic properties are studied, and their relative merits are compared