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Honours Projects: 2012

BanksiaA list of possible honours project being offered by staff at the School of Mathematics and Statistics is given below. Additional projects can also be arranged with other staff members from the school.

For more information on Honours degrees and projects at the School, contact the Honours Co-ordinator Dr Jorge Aarao.

These projects are also available for vacation scholarship students.

Projects will continue to be added throughout the year (Last updated: 3 December 2011).

The travelling salesperson problem: what is the state of the art?

Supervisor: Kevin White

Brief Project Outline: The TSP  (Traveling Salesman Problem in much of the literature) - given a weighted complete graph, find the simple spanning cycle with minimum total length – is a well-known and much studied "hard" problem. Over the past 60 years or so, many approaches to this problem have been developed, some of them with a great deal of success. Depending on the interest and aptitude of the student, a project in this area could include:

 I am particularly interested in a contemporary study and comparison of solution methods in the literature, especially some of the more recent ones.

References: 
Applegate, DL, Bixby, RE, Chvatal, V, Cook, WJ,  The traveling salesman problem: a computational study, Princeton series in applied mathematics 2006.
Cook, WJ, Cunningham, Pulleyblank, Schrijver, Combinatorial Optimization, Chapter 7  The Traveling Salesman Problem, Wiley-Interscience 1998.
Lawler, EL, Lenstra, Rinnooy Kan, Shmoys, The traveling salesman problem, a guided tour of combinatorial optimization, Wiley 1985.

Electro-Diffusive Modelling

Supervisors: Stan Miklavcic and Lee White

Brief Project Outline: The project involves the development and analysis of a rigorous electro-diffusive model describing the transport of a concentrated solution of charged particles under an applied electric field. The model will seek to include the significant higher-order effects of finite particle and ion size and the ensuing packing constraints imposed on the forced diffusion process. The research will focus, firstly, on an accurate description of the transition from a uniform distribution of the charged particles between two electrified plates to a steady-state, packed layer adjacent to one plate.  Second, the research program will involve developing a model to represent the unpacking of the particle layer as a result of the reversal of the applied electric field.

Techniques and Skills to be gained: Mathematical modelling; numerical and analytical methods for solving partial differential equations; computational modelling; and programming using Matlab or higher more advanced computational languages.

3D modelling of wide leaf plants using Kinect sensor

Supervisor: Jinhai Cai

Brief Project Outline: Kinect is a 3D range sensor, which can provide 3D information of objects. However, there are some errors of 3D measurement caused by various sources. In this project, we will develop new method to reduce these errors using feature detection, morphological filtering and 3D surface fitting.

Techniques and Skills to be gained: 3D morphological filtering, 3D surface fitting and 3D visualisation.

Key References:
1.   J. Lee, J. F. Kiser, A. F. Bobick, and A. L. Thomaz, "Vision based contingency detection," in Proceedings of the 2011 ACM/IEEE Conference on Human-Robot Interaction (HRI), 2011.
2  . T Kühn, "The Kinect Sensor Platform", Advances In Media Technology, 2011.

An application of a linear programming approach for analysis and optimal control of Brockett integrator type systems

Supervisor: Vladimir Gaitsgory

Brief Project Outline: A nonlinear control system called Brockett integrator was introduced in [1] and proved to be important in engineering applications. The project will be devoted to a study of Brocket integrator type systems based on their description as an infinite dimensional system of linear equations and on using linear programming and global optimisation techniques as tools for analysis and numerical solution (see [2]-[4]).

Key References:
1. R.W Brockett, "Asymptotic Stability and feedback Stabilization", in Differential geometric Control Theory , R.W. Brockett, R.S. Millman, and H.J. Sussman, eds. Birkhauser, Boston, MA, 1983, pp 181-191.
2. V. Gaitsgory and S. Rossomakhine, "Linear Programming Approach to deterministic Long Run Average Problems  of Optimal Control",  SIAM J. on Control and Optimization, 44:6 (2005/2006): 2006-2037.
3. L. Finlay, V. Gaitsgory and I. Lebedev, "Duality In Linear Programming Problems Related to Long Run Average Problems of Optimal Control", SIAM J. on Control and Optimization, 47 (2008):4, pp. 1667-1700.
4. V. Gaitsgory and M. Quincampoix, "Linear Programming Problems Related to Deterministic Infinite Horizon Optimal Control Problems with Discounting", SIAM J. on Control and Optimization, 48 (2009):4, pp.2480-2512.

Numerical Efficiency of Lagrangian functions - applications to real-life problems

Supervisors:  Regina S Burachik and C Yalçın Kaya

Brief Project Outline: The Deflected subgradient method is a computational tool for solving nonsmooth and nonconvex optimization problems.  This method enjoys primal-dual convergence properties (see [1,2,3,4]).  The Deflected subgradient method is a duality scheme which uses an augmented Lagrangian function. This Lagrangian function is called augmented because it is the sum of the objective function plus two additional terms. One of these terms is an augmenting function, and the other is the linear (classical) term. The augmenting term is a penalty expression given by a general function satisfying some mild assumptions.   The question we want to answer is as follows. Given two specific NP-hard problems, such as

  1.  Kissing number problem
  2. Boolean Least Square problem  

How does the Deflected subgradient method behave when different augmenting functions are chosen in the Lagrangian?   The objective of this research is to explore the differences in the convergence rates, and numerical implementations of the resulting primal-dual strategies. Based on this experimental study, we aim to find out which choice of Lagrangian is the best one for the given problem. Besides from checking numerically the performance of these new methods, we will compare the efficiency with other techniques.  

Student Academic Background: Multidimensional Analysis (required), Linear Algebra (required), Numerical Analysis (required), Functional Analysis (desirable), Programming skills (required).

Key References:
[1] Burachik, R. S., Gasimov R., Ismayilova N. and Kaya C. Y., 2006. On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian.  Journal of Global Optimization 34(1), pp. 55 - 78.
[2] Burachik, R. S., and Kaya, C. Y. 2007. An update rule and a convergence result for a penalty function method, Journal of Industrial and Management Optimization, 3(2), 381–398.
[3] Burachik, R. S., Kaya, C. Y., and Mammadov, M., 2010. An inexact modified subgradient algorithm for nonconvex optimization, Computational Optimization and Applications (45)1: 1-24.
[4] Burachik R. S., Kaya, C. Y., 2010. A deflected subgradient method using a general augmented Lagrangian duality with implications on penalty methods. In: Variational Analysis and Generalized Differentiation in Optimization and Control, in honour of Boris Mordukhovich, Springer Optimization and Its Applications, to appear.

Image analysis for plant growth modelling, and variation of a plant's texture, colour and shape characteristics during its development

Supervisors: Mahmood Golzarian and Jinhai Cai

Group Webpage: Phenomics and Bioinformatics Research centre

Brief Project Outline: Non-destructively imaging and automatically monitoring the growth of plants is fundamental to identifying genes underlying their structure change. This is particularly important when the phenotype of the plants change under different treatments, such as salt and water stresses. In this project we will develop a non-destructive visible and NIR imaging and analysis system for automated and accurate phenotyping of wheat and barley plants. Important features of the plants are extracted from their images including colour, morphological and texture characteristics. However these characteristics can only be obtained if we have high resolution images. The NIR images will help to monitor the salt and water stresses. Moreover, the images taken in NIR will provide opportunity to produce better segmentation results.

Techniques/Skills Learnt:

Key References:
Bharati, MH, Liu, JJ & MacGregor, JF 2004, 'Image texture analysis: methods and comparisons', Chemometrics and Intelligent Laboratory Systems, vol. 72, no. 1, pp. 57-71.
Bhatt, R, Carpenter, GA & Grossberg, S 2007, 'Texture segregation by visual cortex: Perceptual grouping, attention, and learning', Vision Research, vol. 47, no. 25, pp. 3173-3211.
Davies, ER 2005, 'Texture', in Machine Vision (Third Edition), Morgan Kaufmann, Burlington, pp. 756-779.
Tang, L, Tian, L & Steward, BL 2003, 'Classification of broadleaf and grass weeds using Gabor wavelets and an artificial neural network', Transaction of ASAE, vol. 46, no. 4, pp. 1247-1254.  

ACPFG Honours Scholarships are available for this project. These scholarships are competitive and are awarded principally on academic merit.

Want to know more? Then contact mahmood.golzarian@unisa.edu.au with the subject heading 'Honours Project', so that we can have a chat about the project in more details.

The Identification of Plant Growth Stages

Supervisors: Jinhai Cai and Stan Miklavcic

Group Webpage: Phenomics and Bioinformatics Research centre

Brief Project Outline: Phenomics and bioinformatics are two indispensable aspects of molecular biology and genetics. Applied to plant biology, automated phenotypic analysis of plant images, captured as a function of growth conditions, can help us to obtain a large amount of information on the function of genes and to study the impacts of abiotic stress on plants.  In order to do this, it is desired to automatically identify the growth stages from plant images. In this project, we will develop algorithms to extract both statistical and structural features from images. We will use machine learning/pattern recognition methods to train and identify cereal plant growth stages. In this project, we will work with plant biologists as well.  

Techniques/Skills Learnt:

Key References:
A Tutorial on Support Vector Machines for Pattern Recognition by Christopher J. C. Burges. Data Mining and Knowledge Discovery 2:121-167, 1998.
Jolliffe I.T. Principal Component Analysis, Series: Springer Series in Statistics, 2nd ed., Springer, NY, 2002.
Tang, L, Tian, L & Steward, BL 2003, 'Classification of broadleaf and grass weeds using Gabor wavelets and an artificial neural network', Transaction of ASAE, vol. 46, no. 4, pp. 1247-1254. M.
Petrou, C. Petrou, Image Processing: The Fundamentals, Wiley, 2010.
Crop Monitoring and Zadoks Growth Stages for Wheat, CSIRO      

ACPFG Honours Scholarships are available for this project. These scholarships are competitive and are awarded principally on academic merit.

Image Fusion for Phenotypic Analysis of Plant Images

Supervisors: Jinhai Cai, Mahmood Golzarian and Stan Miklavcic

Group Webpage: Phenomics and Bioinformatics Research centre

Brief Project Outline: The Australian Plant Phenomics Facility (APPF) provides state-of-the-art plant growth environments and the latest technology in high throughput plant imaging for the automatic and non-destructive phenotypic experiments of plants. It can take thousands of plant images by different cameras in one day. As different sensors capture different information, it is desirable to integrate all images for the plant phenotypic analysis. The project will focus on the review of state-of-the-art image fusion techniques and the application of suitable techniques for plant image analysis.

Techniques/Skills Learnt:

Key References:
D.W. Repperger, A.R. Pinkus, K.A. Farris, R.G. Roberts, and R.D. Sorkin,  "Investigation of image fusion procedures using optimal registration and SVD algorithms," Aerospace & Electronics Conference (NAECON), Proceedings of the IEEE 2009 National, pp.231-235, 21-23 July 2009.
J. Cai and R. Walker, "Robust Motion Estimation for Camcorders Mounted in Mobile Platforms," DICTA '08,  pp.491-497, 1-3 Dec. 2008.
C. Wei, and S. B. Rick, "Theoretical analysis of correlation-based quality measures for weighted averaging image fusion," Information Fusion, vol.11, no.4, pp.301-310, October 2010.
T. Stathaki, Image fusion: Algorithms and Applications, Academic Press, 2008.
M. Petrou, C. Petrou, Image Processing: The Fundamentals, Wiley, 2010.

ACPFG Honours Scholarships are available for this project. These scholarships are competitive and are awarded principally on academic merit.

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