Australian Mathematical Society (AustMS): E-Journals
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Game model for online and offline retailers under buy-online and pick-up-in-store mode with delivery cost and random demand
No full textOnline retailers are increasingly adding buy-online and pick-up-in-store (BOPS) modes to order fulfilment. In this paper, we study a system of BOPS by developing a stochastic Nash equilibrium model with incentive compatibility constraints, where the online retailer seeks optimal online sale prices and an optimal delivery schedule in an order cycle, and the offline retailer pursues a maximal rate of sharing the profit owing to the consignment from the online retailer. By an expectation method and optimality conditions, the equilibrium model is first transformed into a system of constrained nonlinear equations. Then, by a case study and sensitivity analysis, the model is validated and the following practical insights are revealed. (I) Our method can reliably provide an equilibrium strategy for the online and offline retailers under BOPS mode, including the optimal online selling price, the optimal delivery schedule, the optimal inventory and the optimal allocation of profits. (II) Different model parameters, such as operational cost, price sensitivity coefficient, cross-sale factor, opportunity loss ratio and loss ratio of unsold goods, generate distinct impacts on the equilibrium solution and the profits of the BOPS system. (III) Optimization of the delivery schedule can generate greater consumer surplus, and makes the offline retailer share less sale profit from the online retailer, even if the total profit of the BOPS system becomes higher. (IV) Inventory subsidy is an indispensable factor to improve the applicability of the game model in BOPS mode.
doi:10.1017/S144618112000012
Streamlined solutions to multilevel sparse matrix problems
No full textWe define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects.
doi: 10.1017/S144618112000006
Proceedings of the 14th Engineering Mathematics and Applications Conference
No full text
EMAC 2019
UNSW Canberra, Australia
26th Nov–29th Nov 2019
This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 14th Engineering Mathematics and Applications Conference (EMAC2019), which was held at the UNSW Canberra, Australia from 26th November to 29th November 2019. EMAC is held under the auspices of the Engineering Mathematics Group (EMG), which is a special interest group of the Australian and New Zealand Industrial and Applied Mathematics division of the Australian Mathematics Society. This conference provides a forum for researchers interested in the development and use of mathematical methods in engineering and applied mathematics, and aims to foster interactions between mathematicians and engineers, from both academia and industry. A further theme of the conference is the mathematical education of applied mathematicians and engineers. The event attracted participants from around the globe, including: New Zealand, Saudi Arabia, United Kingdom, Japan and Australia.
The invited speakers at the 2019 meeting crossed the spectrum of specialities in engineering, mathematics, education and industry. They were: Alexander Kalloniatis (Defence Science and Technology Group), Robert K. Niven (UNSW Canberra), Katherine Seaton (La Trobe University) and Antoinette Tordesillas (University of Melbourne).
All of the articles included in the EMAC 2019 Proceedings have been critically peer reviewed to the usual standards of the ANZIAM Journal.
EMAC 2019 Organising Committee
The conference organising committee were Fiona Richmond, Zlatko Jovanoski (Director), Leesa Sidhu, Duncan Sutherland, Fangbao Tian, Isaac Towers, Timothy Trudgian and Simon Watt. The invited speakers were chosen by a committee of experts including Alys Clark, Jennifer Flegg, Bronwyn Hajek (EMG Chair), Zlatko Jovanoski, Dann Mallet, Robert Niven, Brandon Pincombe, Melanie Roberts (Chair) and Harvinder Sidhu
Detecting stress from imaging photoplethysmography using high frame rate video and a yellow-green filter: A pilot study
Get PDFWe investigate the use of a yellow-green filter to increase the signal-to-noise ratio (snr) in imaging photoplethysmography (iPPG) and test if high frame rate (HFR) video improves the accuracy of the derived heart rate variability (HRV). This pilot study is associated with a broader program to use iPPG to detect and monitor stress levels using HRV. To improve the snr of the iPPG signal, we employ two HFR colour video cameras of which one was fitted with a yellow-green filter (corresponding to the haemoglobin absorption peak within the visible spectrum). To our knowledge, the benefit of a yellow-green filter has never been explored. The predominant influence on HRV comes from the autonomic nervous system (ANS), which connects directly to the heart and cues the human body to relax or to stress. The linkage of HRV to the ANS makes HRV a proxy for stress levels. The HRV is derived from the iPPG signal by first using a cubic spline interpolation for more precise peak detection, and then calculating the inter-beat intervals from the peak-to-peak time differences. Instead of interpolating the signal, we hypothesise that a more accurate HRV measurement can be obtained using a HFR video camera, in our case at 200 frames per second.
References
E. B. Blackford, J. R. Estepp, and D. J. McDuff. Remote spectral measurements of the blood volume pulse with applications for imaging photoplethysmography. In G. L. Cote, editor, Optical Diagnostics and Sensing XVIII: Toward Point-of-Care Diagnostics, volume 10501, page 105010Z. International Society for Optics and Photonics, SPIE, 2018. doi:10.1117/12.2291073.
M. Brayne. Trauma and Journalism: A Guide For Journalists, Editors and Managers. DART Center for Journalism and Trauma, 2007. https://dartcenter.org/sites/default/files/DCE_JournoTraumaHandbook.pdf.
L. F. C. Martinez, G. Paez, and M. Strojnik. Optimal wavelength selection for noncontact reflection photoplethysmography. In Proceedings of the 22nd Congress of the International Commission for Optics: Light for the Development of the World, volume 8011, page 801191. International Society for Optics and Photonics, SPIE, 2011. doi:10.1117/12.903190.
Y. Sun, S. Hu, V. Azorin-Peris, R. Kalawsky, and S. E. Greenwald. Noncontact imaging photoplethysmography to effectively access pulse rate variability. J. Biomed. Optics, 18(6):061205, 2013. doi:10.1117/1.JBO.18.6.061205.
A. M. Unakafov. Pulse rate estimation using imaging photoplethysmography: generic framework and comparison of methods on a publicly available dataset. Biomed. Phys. Eng. Exp., 4(4):045001, 2018. doi:10.1088/2057-1976/aabd09
Approximate analytic solutions to a nonlinear digester problem
Get PDFBiological reactors are employed in industrial applications to break down organic waste from a range of sources into components that may be used in other applications. Such reactors may involve complex processes and many components linked by complicated interrelations. These reactions are represented mathematically as nonlinear initial value problems that must be solved numerically. Even smaller systems, more amenable to analytical analysis, require numerical solution methods due to their nonlinearity. We study a simple reactor with only two interacting components—a bacteria consuming a substrate (waste), represented by a autonomous nonlinear initial value problem not solvable analytically. We describe a process to convert this problem to an approximating linear one that can be solved exactly to provide a closed form approximate representation of the evolving system. We assess the results of this approach and show they often agree favourably with numerical computations of the original nonlinear problem, although not always.
References
J. E. Bailey and D. F. Ollis. Biochemical Engineering Fundamentals. McGraw-Hill Book Company, New York, 1966.
D. J. Batstone, J. Keller, I. Angelidaki, S. V. Kalyuzhny, S. G. Pavlostathis, A. Rozzi, W. T. M. Sanders, H. Siegrist, and V. A. Vavilin. The IWA anaerobic digestion model No 1 (ADM1). Water Sci. Tech., 45(10):65–73, 2002. doi:10.2166/wst.2002.0292.
D. T. Hill. Simplified Monod kinetics of methane fermentation of animal wastes. Agri. Wastes, 5(1):1–16, 1983. doi:10.1016/0141-4607(83)90009-4.
J. Monod. The growth of bacterial cultures. Ann. Rev. Microbio., 3(1):371–394, 1949. doi:10.1146/annurev.mi.03.100149.002103.
F. E. Mosey. Mathematical modelling of the anaerobic digestion process: Regulatory mechanisms for the formation of short-chain volatile acids from glucose. Water Sci. Tech., 15(8–9):209–232, 1983. doi:10.2166/wst.1983.0168.
J. Rodriguez, E. Roca, J. M. Lema, and O. Bernard. Determination of the adequate minimum model complexity required in anaerobic bioprocesses using experimental data. Chem. Tech. Biotech., 83(12):1694–1702, 2008. doi:10.1002/jctb.1990.
H. L. Smith and P. Waltman. The Theory of the Chemostat: Dynamics of Microbial Competition. Cambridge University Press, 1995. doi:10.1017/CBO9780511530043
Correction to: Gaps between divisible terms in
No full texthttp://dx.doi.org/10.1017/S000497271200033
Decomposition theorems for automorphism groups of trees
No full texthttp://dx.doi.org/10.1017/S000497271200033
On the difference of coefficients of OzakiI close-to-convex functions
No full texthttp://dx.doi.org/10.1017/S000497271200033
The performance of some statistical procedures used in case-control studies and methylomics
No full textDOI:
10.1017/S000497271900136
A multiphase multiscale model for nutrient-limited tissue growth, Part II: a simplified description
No full textIn this paper, we revisit our previous work in which we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. The underlying tissue dynamics is described as a multiphase mixture, thereby naturally accommodating features such as interstitial growth and active cell motion. Via a linearization of the underlying multiphase model (whose nonlinearity poses a significant challenge for such analyses), we obtain, by means of multiple-scale homogenization, a simplified macroscale model that nevertheless retains explicit dependence on both the microscale scaffold structure and the tissue dynamics, via so-called unit-cell problems that provide permeability tensors to parameterize the macroscale description. In our previous work, the cell problems retain macroscale dependence, posing significant challenges for computational implementation of the eventual macroscopic model; here, we obtain a decoupled system whereby the quasi-steady cell problems may be solved separately from the macroscale description. Moreover, we indicate how the formulation is influenced by a set of alternative microscale boundary conditions.
doi:10.1017/S144618111900013