To evaluate the performance of decision making units (DMUs), data envelopment analysis (DEA) was introduced. Basically, the traditional DEA scheme calculates the best relative efficiency score (i.e., the “optimistic” efficiency) of each DMU with the most favorable weights. A decision maker may be unable to compare and fully rank the efficiencies of different DMUs that are calculated using these potentially distinct sets of weights on the same basis. Based on the literature, the assignable worst relative efficiency score (i.e., the “pessimistic” efficiency) for each DMU can also be determined. In this paper, the best and the worst relative efficiencies are considered simultaneously. To measure the overall performance of the DMUs, an integration of both the best and the worst relative efficiencies is considered in the form of an interval. The advantage of this efficiency interval is that it provides all of the possible efficiency values and an expanded overview to the decision maker. The proposed method determines the lower- and upper-bounds of the interval efficiency over a common set of weights. To demonstrate the implementation of the introduced method, a numerical example is provided.
Harmful algal bloom (HAB) events have alarmed authorities of human health that have caused severe illness and fatalities, death of marine organisms, and massive fish killings. This work aimed to perform the long short-term memory (LSTM) method and convolution neural network (CNN) method to predict the HAB events in the West Coast of Sabah. The results showed that this method could be used to predict satellite time series data in which previous studies only used vector data. This paper also could identify and predict whether there is HAB occurrence in the region. A chlorophyll a concentration (Chl-a; mg/L) variable was used as an HAB indicator, where the data were obtained from MODIS and GEBCO bathymetry. The eight-day dataset interval was from January 2003 to December 2018. The results obtained showed that the LSTM model outperformed the CNN model in terms of accuracy using RMSE and the correlation coefficient r as the statistical criteria.
Abstract.Immune system plays a vital role in controlling the tumor growth. Therefore, this paper proposes a new mathematical model that describes tumor-immune interaction, focusing on the role of natural killer (NK) cell and CD8 + T cell. The tumor population is subdivided into two different phases, namely interphase and mitosis. This model used Ordinary Differential Equations (ODEs) and the functions involved in the model represents tumor-immune growth, responses and interaction between the cells. The stability and analysis of the model are carried out. From the analysis, the stability curve limits tumor growth region is shown. The curve from the model lie below the curve of the model with single immune response (CD8 + T cell). This result concluded that the proposed model with involvement of NK cell suppression will lower the tumor growth region.
Delay differential equations (DDEs), as well as neutral delay differential equations (NDDEs), are often used as a fundamental tool to model problems arising from various areas of sciences and engineering. However, NDDEs particularly the systems of these equations are special transcendental in nature; it has therefore, become a challenging task or times almost impossible to obtain a convergent approximate analytical solution of such equation. Therefore, this study introduced an analytical method to obtain solution of linear and nonlinear systems of NDDEs. The proposed technique is a combination of Homotopy analysis method (HAM) and natural transform method, and the He's polynomial is modified to compute the series of nonlinear terms. The presented technique gives solution in a series form which converges to the exact solution or approximate solution. The convergence analysis and the maximum estimated error of the approach are also given. Some illustrative examples are given, and comparison for the accuracy of the results obtained is made with the existing ones as well as the exact solutions. The results reveal the reliability and efficiency of the method in solving systems of NDDEs and can also be used in various types of linear and nonlinear problems.
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