各位老师：
现有我校药学院外籍专家吉尔伯特教授团队寻求数学教师进行合作研究，详情附后，望有兴趣的老师自行与其联系。
数学与统计学院
2014/3/12
The area of application is the relations between biosynthesis, degradation, structure and properties of starch and glycogen. These are hyperbranched polymers of glycogen, and these relations are very important for three major public health problems: diabetes, obesity and colo-rectal cancers. Our previous mathematical development in this field has led to extensive new experimental results from our world-leading new lab in Wuhan. It is apparent that new knowledge and methods of considerable benefit to public health in China and the world will flow from much more extensive and sophisticated mathematical developments.
The complete mathematical description of these hyperbranched polymers is an infinite-dimensioned hierarchical distribution function with an infinite number of independent variables.
We have succeeded in obtaining and solving this equation for a simple but very important low-order subset, a one-dimensional projection of the full problem: the distribution of individual branches. The result is an infinite set of homogenous ordinary differential equations which can be expressed in terms of an appropriate matrix, and solved by eigenanalysis. This has proved very useful in practical applications such as analyzing data by reducing to a few simple variables, and in developing conditions for creating new botanical varieties which promise improved nutritional properties. There are indications that a number of important inferences can be obtained by examining the analytical eigenanalysis structure of the matrix describing this subset, for which some elegant results have already been obtained.
A major challenge is understanding higher-order subsets. The infinitely hierarchical nature of the problem makes this conceptually difficult but tractable eigenfunction problem. Considerable guidance can be obtained by carrying out inverse Monte Carlo simulations.
Some key theoretical papers:
A parameterized model of amylopectin synthesis provides key insights into the synthesis of granular starch. AC Wu, MK Morell, RG Gilbert. PLoS ONE 8 e65768 (2013)
Molecular weight distributions of starch branches reveal genetic constraints on biosynthesis. AC Wu, RG Gilbert. Biomacromolecules, 11 3539-47 (2010).
General description of the structure of branched polymers. A Gray-Weale, RG Gilbert, J. Polym. Sci. Part A Polymer Chem. Ed. 49 3914–30 (2009).
Randomly hyperbranched polymers. D Konkolewicz, RG Gilbert, AA Gray-Weale, Phys. Rev. Letters, 98, 238301-1–4 (2007).
Professor Robert G (Bob) Gilbert (F.A.A.)
University of Queensland,
Brisbane, Queensland 4072, Australia.
+61 41 2215 144 (mobile/cell); +61 7 3365 4809 (office)
b.gilbert@uq.edu.au robert_gilbert@icloud.com
www.uq.edu.au/gilbertgroup
and
Huazhong University of Science and Technology, Wuhan, China, 430030
+86 186-7145-9682 (mobile/cell)
