by AWSY Wickramasinghe and WMND Basnayake
Original Research
The discrete wavelet transformation (DWT) is of considerable use in the domain of time series analysis. A fundamental problem in DWT is the distortions occurring at the edges while utilizing finite-length series. Insufficient information at boundary regions can lead to questionable accuracies of the transformation at the edges which will thus make a profound effect on further applications. Since the generally used methods to handle edge distortion such as zero padding has their own drawbacks, there are studies that have been done to alleviate the problem using mathematical techniques. With the main objective of finding an evidence-based strategy to reduce the edge effect inherent to DWT using statistical terminologies, this research compares the effect of statistical and machine learning-based denoising and extrapolating techniques in reducing-edge distortion using daily catchment flow series. The most suitable mother wavelet function and the decomposition level for the given series were considered as “biorthogonal 3.1” and level 2 and the edge effect was quantified using MAPE metric. The extrapolating techniques outperformed the denoising methods resulting Vanilla LSTM model with the lowest MAPE values and according to the averaged results taken considering 10 different points of the series, the Vanilla-LSTM and the SARIMA-LSTM hybrid model convincingly alleviate the edge distortion of all coefficients in a more generalized manner.
American Journal of Applied Mathematics and Statistics. 2022, 10(3), 95-102. DOI: 10.12691/ajams-10-3-4
Pub. Date: November 27, 2022
by Tichaona Wilbert Mapuwei, Oliver Bodhlyera and Henry Mwambi
Original Research
The paper focuses on the development of a strategy to integrate forecasting using artificial neural networks (ANN), simulation and optimisation techniques for ambulance deployment to predefined locations with heterogeneous demand patterns under stochastic environments. The metropolitan city of Bulawayo was used as a case study with high variability in call inter-arrival rates, response times, service times, and proportions of severity of emergencies by geographical zones covered by sub-stations. These stochastic environments complicate the decision-making process at strategic, tactical and operational level, in pursuit to achieve high levels of equality, efficiency and effectiveness in resource allocation and utilisation. This paper proposes an integrated simulation optimisation methodology that integrates future demand and allows for simultaneous evaluation of operational performances of deployment plans using multiple performance indicators such as average response time, total duration of a call-in system, number of calls in response queue, average queuing time, throughput ratios and ambulance utilisation levels. Increasing the number of ambulances influences the average response time below a certain threshold. Beyond this threshold, no significant changes occur in the performance measures. As the fleet size is increased, the ambulance utilisation levels decreased, hence there is always need to balance resource allocation and capacity utilisation to avoid idleness of essential equipment and human resources. Numerical experiments conducted to align the response time to international standards resulted in reduction in number of ambulances required for optimal deployment. For medical resources such as ambulances, deploying more resources do not always translate to better performance, hence there is need to simultaneously consider multiple performance measures. Decision makers in EMS must seriously consider ways of reducing the response time as it has significant bearing in reducing the required number of ambulances, a critical but scarce resource. Efforts must be directed towards digitisation of switch boards in the call center, training of the paramedics and provision of relevant modern equipment to the response teams as it will go a long way in reducing the pre-trip delay time, chute time and ultimately the response time. Based on the scientific evidence, management could lobby for de-congestion and resurfacing of old and dilapidated roads in order to increase access and speed when responding to emergency calls.
American Journal of Applied Mathematics and Statistics. 2022, 10(3), 80-94. DOI: 10.12691/ajams-10-3-3
Pub. Date: November 24, 2022
2112 Views8 Downloads
by R. Hemavathy and P. Uma Maheswari
In this paper, we introduce a notion of extended Cone Sb-metric space and prove some fixed point results with various types of contractive conditions. Our results enlarge many results in the literature.
American Journal of Applied Mathematics and Statistics. 2022, 10(3), 76-79. DOI: 10.12691/ajams-10-3-2
Pub. Date: November 03, 2022
1239 Views
by R. Hemavathy and R. Om Gayathri
Original Research
In this paper, a new approach has been discussed to define the graph associated with the metric space and the iteration function is used to define its sub-graph. Subsequently, the fixed point theorems by Banach, Kannan, Chatterjea and Ciric are obtained using this new approach.
American Journal of Applied Mathematics and Statistics. 2022, 10(3), 69-75. DOI: 10.12691/ajams-10-3-1
Pub. Date: October 30, 2022
1399 Views1 Downloads