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Item Metadata only 10 lessons from 10 years of measuring and modeling the internet's autonomous systems(IEEE-Inst Electrical Electronics Engineers Inc, 2011) Roughan, M.; Willinger, W.; Maennel, O.; Perouli, D.; Bush, R.Formally, the Internet inter-domain routing system is a collection of networks, their policies, peering relationships and organizational affiliations, and the addresses they advertize. It also includes components like Internet exchange points. By its very definition, each and every aspect of this system is impacted by BGP, the de-facto standard inter-domain routing protocol. The element of this inter-domain routing system that has attracted the single-most attention within the research community has been the "inter-domain topology". Unfortunately, almost from the get go, the vast majority of studies of this topology, from definition, to measurement, to modeling and analysis, have ignored the central role of BGP in this problem. The legacy is a set of specious findings, unsubstantiated claims, and ill-conceived ideas about the Internet as a whole. By presenting a BGP-focused state-of-the-art treatment of the aspects that are critical for a rigorous study of this inter-domain topology, we demystify in this paper many "controversial" observations reported in the existing literature. At the same time, we illustrate the benefits and richness of new scientific approaches to measuring, modeling, and analyzing the inter-domain topology that are faithful to the BGP-specific nature of this problem domain.Item Metadata only A 'simple' hybrid model for power derivatives(Elsevier Science BV, 2009) Lyle, M.; Elliott, R.Item Metadata only A 1000-year-old case of Klinefelter's syndrome diagnosed by integrating morphology, osteology, and genetics.(Elsevier BV, 2022) Roca-Rada, X.; Tereso, S.; Rohrlach, A.B.; Brito, A.; Williams, M.P.; Umbelino, C.; Curate, F.; Deveson, I.W.; Souilmi, Y.; Amorim, A.; Carvalho, P.C.; Llamas, B.; Teixeira, J.C.Item Metadata only A BEM for time dependent infiltration from an irrigation channel(Elsevier Sci Ltd, 2010) Clements, D.; Lobo, M.In this paper some two dimensional time dependent infiltration problems are considered. The problems involve infiltration from an irrigation channel into a homogenous soil and a soil which contains an impermeable finite inclusion. The problems are reduced to boundary integral equations which may be solved numerically using established procedures. Numerical results are obtained to provide the distribution of the matric flux potential for some particular impermeable inclusions and a particular channel shape. The results indicate how the distance from the channel influences the speed with which the matric flux potential reaches its steady state value. They also illustrate how the presence of an impermeable inclusion can increase the matric flux potential at points below the surface. © 2010 Elsevier Ltd. All rights reserved.Item Metadata only A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space)(Springer-Verlag, 2016) Roberts, D.The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown and Danesh-Naruie lifted the fundamental groupoid to a topological groupoid. For locally relatively contractible spaces the resulting topological bigroupoid is locally trivial in a way analogous to the case of the topologised fundamental groupoid.Item Metadata only A boundary element method for transient heat conduction problem of nonhomogeneous anisotropic materials(Pushpa Publishing House, 2014) Azis, M.; Clements, D.A boundary element method (BEM) is obtained for the nonlinear transient heat conduction problem of inhomogeneous anisotropic media.Item Metadata only A BSDE approach to a risk-based optimal investment of an insurer(Pergamon-Elsevier Science Ltd, 2011) Elliott, R.; Siu, T.We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer's risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. It leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases. © 2010 Elsevier Ltd. All rights reserved.Item Metadata only A BSDE approach to convex risk measures for derivative securities(Marcel Dekker Inc, 2012) Elliott, R.; Siu, T.A backward stochastic differential equation (BSDE) approach is used to evaluate convex risk measures for unhedged positions of derivative securities in a continuous-time economy. The convex risk measure is represented as the solution of a BSDE. We use the Clark-Ocone representation result together with Malliavin calculus to identify the integrand in the martingale representation associated with the BSDE. In the Markov case, we relate the BSDE solution to a partial differential equation solution for convex risk measure evaluation.Item Restricted A canonical connection on sub-Riemannian contact manifolds(Department of Mathematics, Faculty of Science of Masaryk University, Brno, 2016) Eastwood, M.; Neusser, K.We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.Item Metadata only A case study of OSPF behavior in a large enterprise network(ACM Press, 2002) Shaikh, A.; Isett, C.; Greenberg, A.; Roughan, M.; Gottlieb, J.; Internet Measurement Conference (2002 : Marseilles, France)Open Shortest Path First (OSPF) is widely deployed in IP networks to manage intra-domain routing. OSPF is a link-state protocol, in which routers reliably flood "Link State Advertisements" (LSAs), enabling each to build a consistent, global view of the routing topology. Reliable performance hinges on routing stability, yet the behavior of large operational OSPF networks is not well understood. In this paper, we provide a case study on the eharacteristics and dynamics of LSA traffic for a large enterprise network. This network consists of several hundred routers, distributed in tens of OSPF areas, and connected by LANs and private lines. For this network, we focus on LSA traffic and analyze: (a) the class of LSAs triggered by OSPF's soft-state refresh, (b) the class of LSAs triggered by events that change the status of the network, and (c) a class of "duplicate" LSAs received due to redundancy in OSPF's reliable LSA flooding mechanism. We derive the baseline rate of refresh-triggered LSAs automatically from network configuration information. We also investigate finer time scale statistical properties of this traffic, including burstiness, periodicity, and synchronization. We discuss root causes of event-triggered and duplicate LSA traffic, as well as steps identified to reduce this traffic (e.g., localizing a failing router or changing the OSPF configuration).Item Metadata only A characterisation of tangent subplanes of PG(2, q³)(Springer US, 2014) Barwick, S.; Jackson, W.In “Barwick and Jackson (Finite Fields Appl. 18:93–107 2012)”, the authors determine the representation of Order-q-subplanes s and order-q-sublines of PG(2, q³) in the Bruck–Bose representation in PG(6, q). In particular, they showed that an Order-q-subplanes of PG(2, q³) corresponds to a certain ruled surface in PG(6, q). In this article we show that the converse holds, namely that any ruled surface satisfying the required properties corresponds to a tangent Order-q-subplanes of PG(2, q³).Item Metadata only A characterisation of the lines external to a quadric cone in PG(3,q), q odd(Academia Press, 2008) Barwick, S.; Butler, D.In this article, the lines not meeting a quadric cone in PG(3, q) (q odd) are characterised by their intersection properties with points and planes.Item Metadata only A characterisation of the lines external to an oval cone in PG(3, q), q even(Birkhauser Verlag Ag, 2009) Barwick, S.; Butler, D.In this article, the lines not meeting an oval cone in PG(3, q) (q even) are characterised by their intersection properties with points and planes.Item Metadata only A characterization of the classical unital(Springer, 1994) Barwick, S.G.We define Buekenhout unitals in derivable translation planes of dimension 2 over their kernel and provide a characterization of these unitals. We use this result to improve the characterization of classical unitals given by Lefèvre-Percsy [13] and Faina and Korchmáros [7].Item Metadata only A characterization of translation ovals in finite even order planes(Academic Press Inc Elsevier Science, 2015) Barwick, S.G.; Jackson, W.A.In this article we consider a set C of points in PG(4,q), q even, satisfying certain combinatorial properties with respect to the planes of PG(4,q). We show that there is a regular spread in the hyperplane at infinity, such that in the corresponding Bruck-Bose plane PG(2,q2), the points corresponding to C form a translation hyperoval, and conversely. CrownItem Metadata only A coboundary morphism for the grothendieck spectral sequence(Springer, 2014) Baraglia, D.Given an abelian category A with enough injectives we show that a short exact sequence of chain complexes of objects in A gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Item Metadata only A coherent structure approach for parameter estimation in Lagrangian Data Assimilation(Elsevier, 2017) Maclean, J.; Santitissadeekorn, N.; Jones, C.K.We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection.Item Metadata only A comparison of Gaussian, Student-t and Vine copulas for modelling geophysical measurements along a rock drill core(Australian Mathematical Society, 2018) Addo Junior, E.; Metcalfe, A.V.; Chanda, E.; Clark, A.; Clarke, R.This case study is a based on measurements made approximately at 20cm lengths along a down-the-hole diamond drill core from a pyrite mine in South Australia. The measurements are the P-wave velocity, magnetic susceptibility and impedance. The trivariate distribution is modelled using Gaussian, Student-t and vine copulas and the results are compared in terms of goodness of fit and differences in extreme values from distributions obtained by simulation from the copulas. The vine copula provides the best fit for the variables. Trivariate linear spatial Gaussian, Student-t and vine copulas are used to predict magnetic susceptibility one step below the depth of the drill core. The vine copula allows for more detailed modelling of the error structure, and so provides more accurate 90% prediction intervals. The 90% prediction interval for the vine copula is wider than that for the Student-t copula, and both are wider than the interval obtained with the Gaussian copula. In general, copulas provides a more realistic modelling of geological variables and hence allows for accurate assessment of risk and uncertainty.Item Metadata only A comparison of information criteria for traffic model selection(IEEE, 2016) Tune, P.; Roughan, M.; Cho, K.; 10th International Conference on Signal Processing and Communication Systems (ICSPCS 2016) (19 Dec 2016 - 21 Dec 2016 : Surfers Paradise); Wysocki, T.; Wysocki, B.Traffic modelling is a core component of network planning and engineering. Although good models are approximations of reality, they are very useful in various network applications. However, traffic modelling is often done in an ad hoc manner, guided only by the experience of the model designer. In this paper, we propose the use of information criteria, such as the Akaike Information Criterion (AIC), to systematically choose models. We study these criteria on Frequency, Frequency + Spike, and Wavelet models of the network traffic to select the best of these. However, there are many alternative information criteria, which give different results. We found that the Bayesian Information Criterion (BIC), and Minimum Description Length (MDL) provided better models than the (perhaps) more commonly used AIC and corrected AIC for network traffic modelling. Interestingly, we found that fancier models, such as Wavelet models, may reduce prediction accuracy, so simple frequencybased models are preferable.Item Metadata only A comparison of models for predicting population persistence(Elsevier Science BV, 2007) Cairns, B.; Ross, J.; Taimre, T.We consider a range of models that may be used to predict the future persistence of populations, particularly those based on discrete-state Markov processes. While the mathematical theory of such processes is very well-developed, they may be difficult to work with when attempting to estimate parameters or expected times to extinction. Hence, we focus on diffusion and other approximations to these models, presenting new and recent developments in parameter estimation for density dependent processes, and the calculation of extinction times for processes subject to catastrophes. We illustrate these and other methods using data from simulated and real time series. We give particular attention to a procedure, due to Ross et al. [Ross, J.V., Taimre, T., Pollett, P.K. On parameter estimation in population models, Theor. Popul. Biol., in press], for estimating the parameters of the stochastic SIS logistic model, and demonstrate ways in which these parameters may be used to estimate expected extinction times. Although the stochastic SIS logistic model is strictly density dependent and allows only for birth and death events, it nonetheless may be used to predict extinction times with some accuracy even for populations that are only weakly density dependent, or that are subject to catastrophes.