School of Mathematical Sciences
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Comprising the disciplines of Applied Mathematics, Pure Mathematics and Statistics
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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.This paper presents a method for valuing power derivatives using a supply-demand approach. Our method extends work in the field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices written on average spot prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black-Scholes equation. The model provides a relatively simple approach to describe the complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing.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 3-D non-hydrostatic pressure model for small amplitude free surface flows(John Wiley & Sons Ltd, 2006) Lee, J.; Teubner, M.; Nixon, J.; Gill, P.A three-dimensional, non-hydrostatic pressure, numerical model with k- equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure-Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement.Item Metadata only A Bayesian approach for optimal reinsurance and investment in a diffusion model(Kluwer Academic Publ, 2012) Zhang, X.; Elliott, R.; Siu, T.A Bayesian adaptive control approach to the combined optimal investment/reinsurance problem of an insurance company is studied. The insurance company invests in a money market and a capital market index with an unknown appreciation rate, or “drift”. Using a Bayesian approach, the unknown drift is described by an unobservable random variable with a known (prior) probability distribution. We assume that the risk process of the company is governed by a diffusion approximation to the compound Poisson risk process. The company also purchases reinsurance. The combined optimal investment/reinsurance problem is formulated as a stochastic optimal control problem with partial observations. We employ filtering theory to transform the problem into one with complete observations. The control problem is then solved by the dynamic programming Hamilton–Jacobi–Bellman (HJB) approach. Semi-analytical solutions are obtained for the exponential utility case.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 a second order elliptic partial differential equation with variable coefficients(ELSEVIER SCI LTD, 1997) Ang, W.; Kusuma, J.; Clements, D.A boundary element method is derived for solving a class of boundary value problems governed by an elliptic second order linear partial differential equation with variable coefficients. Numerical results are given for a specific test problem.Item Metadata only A boundary element method for anisotropic inhomogeneous elasticity(Pergamon-Elsevier Science Ltd, 2001) Azis, M.; Clements, D.This paper is concerned with obtaining boundary integral equations for the numerical solution of the partial differential equations governing static deformations of inhomogeneous anisotropic elastic materials. The elastic parameters for the inhomogeneous materials are assumed to vary continuously with the spatial variables.Item Metadata only A boundary element method for generalized plane thermoelastic deformations of anistropic elastic media(SAGE PUBLICATIONS INC, 1999) Ang, W.; Clements, D.; Cooke, T.A boundary element method is derived for solving a class of boundary value problems governing generalized plane thermoelastic deformations of anisotropic elastic materials. The method involves boundary integrals only and provides a simple boundary element procedure for a wide class of problems which do not involve inertia or coupling effects. Numerical results are given for some specific problems in order to assess the effectiveness of the method.Item Metadata only A boundary element method for steady infiltration from periodic channels(Australian Mathematical Society, 2003) Azis, M.; Clements, D.; Lobo, M.The matric flux potential and horizontal and vertical flux distributions are obtained for periodic irrigation channels by using boundary integral equation techniques. Numerical results are given for the special cases of semicircular and rectangular channels and the results compared with those of Batu [Soil Science Society of America Journal, 42:545--549, 1978] and Warrick and Lomen [Soil Science Society of America Journal, 40:639--643, 1976] for a flat strip. The results show that the matric flux potential associated with the flat strip and semicircular channel are similar; whereas for the particular rectangular channel considered the matric flux potential is subtantially increased in the region adjacent to the channel.Item Metadata only A boundary element method for the numerical solution of a class of elliptic boundary value problems for anisotropic inhomogeneous media(Australian Mathematical Society, 2003) Azis, M.; Clements, D.; Budhi, W.A boundary element method is obtained for a class of two dimensional elliptic boundary value problems for inhomogeneous media. The method can be applied to variety of problems in such areas as antiplane strain in elastostatics, plane thermostatic problems for inhomogeneous anisotropic materials and flow through porous media.Item Metadata only A boundary element method for the solution of a class of steady-state problems for anisotropic media(American Society of Mechanical Engineers, 1999) Clements, D.; Budhi, W.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 boundary integral formulation for the indentation of an anisotropic bi-layered elastic slab(Springer, 2006) Ang, W.; Sridhar, I.; Clements, D.; First International Conference on Computational Methods. (2004 : Singapore); Liu, G.This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.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).