Measured impact of crooked traceroute

Data collected using traceroute-based algorithms underpins research into the Internet’s router-level topology, though it is possible to infer false links from this data. One source of false inference is the combination of per-flow load-balancing, in which more than one path is active from a given source to destination, and classic traceroute, which varies the UDP destination port number or ICMP checksum of successive probe packets, which can cause per-flow load-balancers to treat successive packets as distinct flows and forward them along different paths. Consequently, successive probe packets can solicit responses from unconnected routers, leading to the inference of false links. This paper examines the inaccuracies induced from such false inferences, both on macroscopic and ISP topology mapping. We collected macroscopic topology data to 365k destinations, with techniques that both do and do not try to capture load balancing phenomena.We then use alias resolution techniques to infer if a measurement artifact of classic traceroute induces a false router-level link. This technique detected that 2.71% and 0.76% of the links in our UDP and ICMP graphs were falsely inferred due to the presence of load-balancing. We conclude that most per-flow load-balancing does not induce false links when macroscopic topology is inferred using classic traceroute. The effect of false links on ISP topology mapping is possibly much worse, because the degrees of a tier-1 ISP’s routers derived from classic traceroute were inflated by a median factor of 2.9 as compared to those inferred with Paris traceroute

Metric embeddings with relaxed guarantees

We consider the problem of embedding finite metrics with slack: We seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004], we show that provable guarantees of this type can in fact be achieved in general: Any finite metric space can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into l 1 which exhibit gracefully degrading distortion: There is a single embedding into l 1 that achieves distortion at most O (log 1/∈) on all but at most an ∈ fraction of distances simultaneously for all ∈ > 0. We extend this with distortion O (log 1/∈) 1/p to maps into general l p, p ≥ 1, for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight and give a general technique to obtain lower bounds for ∈-slack embeddings from lower bounds for low-distortion embeddings. © 2009 Society for Industrial and Applied Mathematics.published_or_final_versio

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

Applications of in-line fiber optic raman spectroscopy to polymer processes

Process monitoring is an essential part of ensuring the final product quality in a manufacturing process. In-line monitoring is developing at a fast pace as the method of choice as compared to the off-line monitoring techniques due to its advantages such as lower cost and lower waste. It also eliminates the sample preparation and handling concerns associated with the polymeric processes. In this research, in-line monitoring techniques were developed for emulsion polymerization and extrusion processes using fiber-optic Raman spectroscopy. Varying product quality from batch to batch and the residual monomer content are important concerns in the emulsion polymerization reactions. The kinetics of the batch emulsion polymerization were studied for the methyl methacrylate (MMA) and vinyl acetate (VA) polymerization. The Raman spectroscopy was also used to monitor changes in the reaction rate due to varying comonomer content (AA) for copolymerization of 2-ethylhexyl acrylate (2-EHA) with acrylic acid (AA). For the extrusion processes, a thorough study of the poly(ethylene vinyl acetate) (EVA) random copolymers was performed. Rigorous multivariate analysis was used to develop robust calibration models for quantification of VA concentrations. Rheological properties, such as melt index (MI) and complex viscosity (|η*(ω)|) of the EVA and polypropylene (PP) samples were monitored in real time using polarized Raman spectroscopy