Australian Mathematical Society (AustMS): E-Journals
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Challenge from Transpower: Determining the effect of the aggregated behaviour of solar photovoltaic power generation and battery energy storage systems on grid exit point load in order to maintain an accurate load forecast
Get PDFWith limited data beyond the grid exit point (GXP) or substation level, how can Transpower determine the effect of the aggregated behaviour of solar photovoltaic power generation and battery energy storage systems on GXP load in order to maintain an accurate load forecast? In this initial study it is assumed that the GXP services a residential region. An algorithm based on non-linear programming, which minimises the financial cost to the consumer, is developed to model consumer behaviour. Input data comprises forecast energy requirements (load), solar irradiance, and pricing. Output includes both the load drawn from the grid and power returned to the grid. The algorithm presented is at the household level. The next step would be to combine the load drawn from the grid and the power returned to the grid from all the households serviced by a GXP, enabling Transpower to make load predictions. Various means of load forecasting are considered including the Holt--Winters methods which perform well for out-of-sample forecasts. Linear regression, which takes into account comparable days, solar radiation, and air temperature, yields even better performance
Stochastic modelling of chlamydial infections
Get PDFChlamydia trachomatis is a bacterial pathogen that can cause serious reproductive harm. We describe a class of stochastic branching processes and their application in modelling the growth of an infection by Chlamydia. Using simulations we show that the model can reproduce biological phenomena of interest, and we show the variability in outcomes of infections under the same parameter conditions. We further speculate how this model might be used to explain long-term adverse reproductive sequelae.
References
Y. M. AbdelRahman and R. J. Belland. The chlamydial developmental cycle. FEMS Microbio. Rev., 29(5):949–959, 2005. doi:10.1016/j.femsre.2005.03.002.
T. E. Harris. Branching processes. Ann. Math. Stat., 19(4):474–494, 12 1948. doi:10.1214/aoms/1177730146.
C. Jacob. Branching processes: Their role in epidemiology. Int. J. Env. Res. Public Health, 7(3):1186–1204, 2019. doi:10.3390/ijerph7031204.
N. Low, M. Egger, J. A. C. Sterne, R. M. Harbord, F. Ibrahim, B. Lindblom, and B. Herrmann. Incidence of severe reproductive tract complications associated with diagnosed genital chlamydial infection: The Uppsala women's cohort study. Sexually Trans. Infect., 82(3):212–218, 2006. doi:10.1136/sti.2005.017186.
D. Mallet, M. Bagher-Oskouei, A. Farr, D. Simpson, and K. Sutton. A mathematical model of chlamydial infection incorporating movement of chlamydial particles. Bull. Math. Bio., 75:2257–2270, 10 2013. doi:10.1007/s11538-013-9891-9.
H. K. Maxion, W. Liu, M.-H. Chang, and K. A. Kelly. The infecting dose of chlamydia muridarum modulates the innate immune response and ascending infection. Infect. Immun., 72(11):6330–6340, 2004. doi:10.1128/IAI.72.11.6330-6340.2004.
S. Menon, P. Timms, J. A. Allan, K. Alexander, L. Rombauts, P. Horner, M. Keltz, J. Hocking, and W. M. Huston. Human and pathogen factors associated with chlamydia trachomatis-related infertility in women. Clinic. Microbio. Rev., 28(4):969–985, 2015. doi:10.1128/CMR.00035-15.
D. P. Wilson. Mathematical modelling of chlamydia. In J. Crawford and A. J. Roberts, editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, ANZIAM J., volume 45, pages C201–C214, 2004. doi:10.21914/anziamj.v45i0.883.
D. P. Wilson and D. L. S. McElwain. A model of neutralization of chlamydia trachomatis based on antibody and host cell aggregation on the elementary body surface. J. Theor. Bio., 226(3):321–330, 2004. doi:10.1016/j.jtbi.2003.09.010.
D. P. Wilson, P. Timms, and D. L. S. McElwain. A mathematical model for the investigation of the Th1 immune response to chlamydia trachomatis. Math. Biosci., 182(1):27–44, 2003. doi:10.1016/S0025-5564(02)00180-3
Ancient solutions of co-dimension two surfaces with curvature pinching
No full texthttp://dx.doi.org/10.1017/S000497272000017
Algebraic structure of the range of a trigonometric polynomial
No full texthttp://dx.doi.org/10.1017/S000497271900122
regularity of the weighted Bergman projection on the Fock-Bargmann-Hartogs domain
No full texthttp://dx.doi.org/10.1017/S000497271900142
Applications of systems of quadratic forms to generalised quadratic forms
No full text‎A system of quadratic forms is associated to every generalized quadratic form over a division algebra with involution of the first kind in characteristic two‎. ‎It is shown that this system determines the isotropy behaviour and the isometry class of generalized quadratic forms‎. An application of this construction to the Witt index of generalized quadratic forms is also given
Sequential collision-free optimal motion planning algorithms in punctured Euclidean spaces
No full texthttp://dx.doi.org/10.1017/S000497272000016
