First Manchester SIAM Student Chapter Conference, Monday 26th April 2010
This was a one day conference held in the Alan Turing Building, University of Manchester, aimed at those interested or working in applied or industrial mathematics, including undergraduates, postgraduates and staff. There were talks given by students, faculty members, and industry. The talks were aimed at a general applied maths background.
This is the timetable of the conference:
|1015 - 1045||Arrivals and registration|
|1045 - 1050||Welcome, Chris Munro|
|1050 - 1100||
Nick Higham (School of Mathematics, Manchester)
|1100 - 1145||
Bill Lionheart (School of Mathematics, Manchester)
The problem of finding the electrical conductivity of a body from exterior measurements of current and voltage has been studied mathematically for many decades and is in common use in geophysics. It has been under investigation as a possible method of medical imaging for 30 years but has only recently found a use in medicine in respiratory intensive care. Mathematically the problem is to find an unknown coefficient in an elliptic partial differential equation from a knowledge of the correspondence between Dirichlet and Neumann data at the boundary. I will give a brief introduction to the theory and to numerical algorithms used to solve this problem. Finally I will discuss the question "if it is so hard for us how can a fish do it with a tiny brain". Several species of weakly electric fish locate their pray using a very similar method. Do they know something we do not?
|1145 - 1215||
Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this talk, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs.
|1215 - 1245|
Houman Dallali (School of Mathematics, Manchester)
Robotics is an area of research that encompasses various disciplines including mechanics, electronics, computer science and mathematics. Robotic systems have high interaction between their mechanical structure and different actuators (electric, hydraulic, pneumatic, etc) that are used in their design. Hence various interesting problems arise in terms of their modelling, analysis of dynamics and controller synthesis. In this talk, we look at development of a high degree of freedom model for a humanoid robot with detailed models of its actuators and transmission drives as well as linear controller design for stabilization and tracking problems. The control system synthesis involves some signal processing to estimate the velocities which is addressed via linear observers. The designs in this talk are implemented on a humanoid robot "The iCub" and videos of the experiments as well as the collected data will be presented.
|1245 - 1345||Lunch, Atrium Bridge|
|1345 - 1430||
We look at the development and influence of software libraries and packages for numerical computation, with an emphasis on software for numerical linear algebra, as well as developments that have been important to the production of quality, portable software.
|1430 - 1500|| |
Wuxiang Ge, Zixu Song (School of Computer Science, Manchester)
Software engineering in computer science has been developing in terms of flexibility, modularity and performance for many years. And software has been used in multi-disciplines to improve productivity. The complexity of the infrastructures have seen speeds far outpacing our imagination, and mathematical models have been accepted as an effective way to solve these problems. In this talk, we will discuss two typical problems involving software engineering and mathematics. In the first case, stochastic models are demonstrated for future event forecasting. The second case gives an efficient implementation of general band matrix multiplication, the performance of which is on par with other implementations for matrix with fixed bandwidth.
|1500 - 1530|| |
A major enterprise in compressed sensing and sparse approximation is the design and analysis of algorithms for recovering sparse solutions of underdetermined linear systems of equations. Many such algorithms have now been proven using the Restricted Isometry Property (RIP) to have optimal-order uniform recovery guarantees. However, it is unclear when the RIP-based sufficient conditions on the algorithms are satisfied. We present a framework in which this task can be achieved; translating these conditions for Gaussian measurement matrices into requirements on the signal's sparsity level, size and number of measurements. We illustrate this approach on three of the state-of-the-art greedy algorithms: CoSaMP, Subspace Pursuit (SP) and Iterative Hard Thresholding (IHT). Designed to allow a direct comparison of existing theory, our framework implies that IHT, the lowest of the three in computational cost, also requires fewer compressed sensing measurements than CoSaMP and SP.
|1530 - 1600|| Coffee Break, Atrium Bridge|
|1600 - 1645|| |
Reservoir characterization is a classical problem in petroleum engineering, where a large variety of advanced mathematical tools is employed and needed. In this application, the goal is to estimate a spatial map of fluid flow properties for an active petroleum reservoir from just knowing few oil and water production data over production time at injection and production wells. Due to the limited amount of data available, this problem is extremely ill-posed, which means a stable and unique solution does not exist without employing additional prior information or artificial regularization tools. In the talk, we review and present some recently discussed mathematical techniques for addressing this important and difficult problem, and present some numerical results which demonstrate the performance of these techniques on realistic simulated situations in 2D. We focus in particular on shape based methods, which are of importance when the reservoir consists of different lithologies, i.e., of regions with different rock types
|1645 - 1715|| |
The standard methodology of a posteriori error estimation for finite element methods for PDEs is first reviewed in this talk. After that, we focus on the standard mixed finite element methods for steady-state incompressible flow equations. Then, a new effective a posteriori error estimator for these methods will be discussed. This error estimator provides very accurate estimation of the exact error, while it is computationally cheap.
|1715 - 1730||Presentation of NAG Prizes (Mike Dewar, NAG) and Close|
This conference was supported by