Australian Mathematical Society (AustMS): E-Journals
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On fine Selmer groups and signed Selmer groups of elliptic modular forms
No full texthttp://dx.doi.org/10.1017/S000497271200033
Adversarial risk analysis for first-price sealed-bid auctions
No full texthttp://dx.doi.org/10.1017/S000497271200033
Non divisibility among irreducible character co-degrees
No full texthttp://dx.doi.org/10.1017/S000497271200033
Extending results of Morgan and Parker about commuting graphs
No full texthttp://dx.doi.org/10.1017/S0004972712000330
On the regular graph related to the -conjugacy classes
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the connectedness of the Chabauty space of a locally compact pronilpotent group: On the connectedness of the Chabauty space
No full texthttp://dx.doi.org/10.1017/S000497271200033
Concrush: Understanding fugitive dust production and potential emission at a recycled concrete manufacturing facility
Get PDFThe production and emission of fugitive dust is a topic ofconcern that Concrush brought to the MISG, 2020. Concrushis recycled concrete manufacturing company in the Hunterregion of New South Wales. Concrush's operations producefugitive dust, fine particles that can escape the site. Fugitive dust can travel long distances from the site ofemission, and can have negative health impacts includingrespiratory illnesses. Presently, concrete recyclingfacilities are managed by the Environmental ProtectionAgency using guidelines initially developed for the coalindustry. Concrush seeks to understand the appropriatenessof these guidelines, and how they can reduce and managefugitive dust on their Teralba site. Mathematical modellingof dust emission and transport, together with a review ofsimilar processes in the literature, identified a number ofpractical options for Concrush to reduce their dustemissions. In addition, opportunities for improved datacollection are identified
An efficient Bayesian neural network surrogate algorithm for shape detection
Get PDFWe present an efficient Bayesian algorithm for identifying the shape of an object from noisy far field data. The data is obtained by illuminating the object with one or more incident waves. Bayes' theorem provides a framework to find a posterior distribution of the parameters that determine the shape of the scatterer. We compute the distribution using the Markov Chain Monte Carlo (MCMC) method with a Gibbs sampler. The principal novelty of this work is to replace the forward far-field-ansatz wave model (in an unbounded region) in the MCMC sampling with a neural-network-based surrogate that is hundreds of times faster to evaluate. We demonstrate the accuracy and efficiency of our algorithm by constructing the distributions, medians and confidence intervals of non-convex shapes using a Gaussian random circle prior.
References
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D. Colton and R. Kress. Inverse acoustic and electromagnetic scattering theory. 4th Edition. Vol. 93. Applied Mathematical Sciences. References C112 Springer, 2019. doi: 10.1007/978-3-030-30351-8
R. DeVore, B. Hanin, and G. Petrova. Neural Network Approximation. Acta Num. 30 (2021), pp. 327–444. doi: 10.1017/S0962492921000052
M. Ganesh and S. C. Hawkins. A reduced-order-model Bayesian obstacle detection algorithm. 2018 MATRIX Annals. Ed. by J. de Gier et al. Springer, 2020, pp. 17–27. doi: 10.1007/978-3-030-38230-8_2
M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM—A T-matrix reduced order model software. ACM Trans. Math. Softw. 44.9 (2017), pp. 1–18. doi: 10.1145/3054945
M. Ganesh and S. C. Hawkins. Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms. ANZIAM J. 56 (2016), pp. C312–C338. doi: 10.21914/anziamj.v56i0.9313
M. Ganesh, S. C. Hawkins, and D. Volkov. An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R3. J. Comput. Phys. 398 (2019), p. 108881. doi: 10.1016/j.jcp.2019.108881
L. Lamberg, K. Muinonen, J. Ylönen, and K. Lumme. Spectral estimation of Gaussian random circles and spheres. J. Comput. Appl. Math. 136 (2001), pp. 109–121. doi: 10.1016/S0377-0427(00)00578-1
T. Nousiainen and G. M. McFarquhar. Light scattering by quasi-spherical ice crystals. J. Atmos. Sci. 61 (2004), pp. 2229–2248. doi: 10.1175/1520-0469(2004)061<2229:LSBQIC>2.0.CO;2
A. Palafox, M. A. Capistrán, and J. A. Christen. Point cloud-based scatterer approximation and affine invariant sampling in the inverse scattering problem. Math. Meth. Appl. Sci. 40 (2017), pp. 3393–3403. doi: 10.1002/mma.4056
M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045
A. C. Stuart. Inverse problems: A Bayesian perspective. Acta Numer. 19 (2010), pp. 451–559. doi: 10.1017/S0962492910000061
B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande. Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry. J. Quant. Spectro. Rad. Trans. 100 (2006), pp. 393–405. doi: 10.1016/j.jqsrt.2005.11.05
Fitting a superposition of Ornstein–Uhlenbeck process to time series of discharge in a perennial river environment
Get PDFClassical Ornstein–Uhlenbeck (ou) processes are Lévy-driven linear stochastic models with exponentially decaying autocorrelation functions which do not always fit more slowly decaying real time series data. A superposition of ou processes (known as a supou process) is proposed to overcome this issue for application to river discharge time series data. The discharge data has a sub-exponential autocorrelation function and this is captured by the supou process based on the mean reversion speed generated by a Gamma distribution. All the parameters of the supou process are identified by matching the autocorrelation and the first to fourth statistical moments of the discharge data. The empirical and modelled histograms of the discharge data are comparable with each other.
References
O. E. Barndorff-Nielsen. Superposition of Ornstein–Uhlenbeck type processes. Theory Prob. Appl. 45.2 (2001), pp. 175–194. doi: 10.1137/S0040585X97978166
O. E. Barndorff-Nielsen, F. E. Benth, and A. E. D. Veraart. Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19.3 (2013), pp. 803–845. doi: 10.3150/12-BEJ476
O. E. Barndorff-Nielsen and N. N. Leonenko. Burgers’ turbulence problem with linear or quadratic external potential. J. Appl. Prob. 42.2 (2001), pp. 550–565. url: http://www.jstor.org/stable/30040809
J. Beran, Y. Feng, S. Ghosh, and R. Kulik. Long-Memory Processes. Springer-Verlag, Berlin, Heidelberg, 2016. doi: 10.1007/978-3-642-35512-7
F. Fuchs and R. Stelzer. Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM: Prob. Stat. 17 (2013), pp. 455–471. doi: 10.1051/ps/2011158
Y. Kabanov and S. Pergamenshchikov. Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process. Fin. Stoch. 24.1 (2020), pp. 39–69. doi: 10.1007/s00780-019-00413-3
R. Kawai and H. Masuda. On simulation of tempered stable random variates. J. Comput. Appl. Math. 235.8 (2011), pp. 2873–2887. doi: 10.1016/j.cam.2010.12.014
S. Pelacani and F. G. Schmitt. Scaling properties of the turbidity and streamflow time series at two different locations of an intra-Apennine stream: Case study. J. Hydro. 603.B (2021), p. 126943. doi: 10.1016/j.jhydrol.2021.126943
R. Stelzer, T. Tosstorff, and M. Wittlinger. Moment based estimation of supOU processes and a related stochastic volatility model. Stat. Risk Model. 32.1 (2015), pp. 1–24. doi: 10.1515/strm-2012-1152
S. Suweis, E. Bertuzzo, G. Botter, A. Porporato, I. Rodriguez-Iturbe, and A. Rinaldo. Impact of stochastic fluctuations in storage-discharge relations on streamflow distributions. Water Resource. Res. 46.3 (2010), W03517. doi: 10.1029/2009WR008038
M. Tamborrino and P. Lansky. Shot noise, weak convergence and diffusion approximations. Physica D: Nonlinear Phenomena 418 (2021), p. 132845. doi: 10.1016/j.physd.2021.132845
E. Taufer and N. Leonenko. Simulation of Lévy-driven Ornstein–Uhlenbeck processes with given marginal distribution. In: Comput. Stat. Data Anal. 53.6 (2009), pp. 2427–2437. doi: 10.1016/j.csda.2008.02.026
C. Van Den Broeck. On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process. J. Stat. Phys. 31 (1983), pp. 467–483. doi: 10.1007/BF01019494
H. Yoshioka and Y. Yoshioka. Designing cost-efficient inspection schemes for stochastic streamflow environment using an effective Hamiltonian approach. Opt. Eng. (2021), pp. 1–33. doi: 10.1007/s11081-021-09655-