Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin–Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Actualisation of interdisciplinary connections on the example of mastering the “Minimax” principle in game theory

Topicality of this work is associated with the lack of practical interaction of the studied disciplines of higher mathematics and computer science. The authors argue that in order to increase interest, it is necessary to actively use information technologies right inside the classes in higher mathematics. At the same time, the authors believe that a student must understand the theory of certain types of calculations, must be able to perform them manually and only then, must apply automated calculation methods. Examples of the implementation of game theory in the mathematical application Mathcad are given, while students themselves develop the programme according to the proposed algorithm, which undoubtedly develops logical thinking and shows students the visual use of interdisciplinary connections between two subjects studied – mathematics and computer science. The text contains examples of author's texts of mathematical problems aimed at training students of a military higher education institution. According to the authors, when studying the topic under consideration, it is possible to form the competences necessary for a modern specialist.

Robust Stop-Skipping at the Tactical Planning Stage with Evolutionary Optimization

The planning of stop-skipping strategies based on the expected travel times of bus trips has a positive effect in practice only if the traffic conditions during the daily operations do not deviate significantly from those expected. For this reason, we propose a non-deterministic approach which considers the uncertainty of trip travel times and provides stop-skipping strategies which are robust to travel-time variations. In more detail, we show how historical travel-time observations can be integrated into a Genetic Algorithm (GA) that tries to compute a robust stop-skipping strategy for all daily trips of a bus line. The proposed mathematical program of robust stop-skipping at the tactical planning stage is solved using the minimax principle, whereas the GA implementation ensures that improved solutions can be obtained even for high-dimensional problems by avoiding the exhaustive exploration of the solution space. The proposed approach is validated with the use of five months of data from a circular bus line in Singapore demonstrating an improved performance of more than 10% in worst-case scenarios which encourages further investigation of the robust stop-skipping strategy.

Optimization of gas turbine engine control using dynamic programming

The aim of engine control optimization is to derive the optimal control law for engine operation managing during the aircraft flight. For numerical modeling a continuous flight process defined by a system of differential equations is replaced by a discrete multi-step process. Values of engine control parameters in particular step uniquely identify a system transitions from one state to another. The algorithm is based on the numerical method of dynamic programming and the Bellman optimality principle. The task is represented as a sequence of nested optimization subtasks, so that control optimization at the first step is external to all others. The optimum control function can be determined using the minimax principle of optimality. Aircraft performance calculation is performed by numerical integration of differential equations of aircraft movement.

Optimal threshold estimation for binary classifiers using game theory

Many bioinformatics algorithms can be understood as binary classifiers. They are usually compared using the area under the receiver operating characteristic (ROC) curve. On the other hand, choosing the best threshold for practical use is a complex task, due to uncertain and context-dependent skews in the abundance of positives in nature and in the yields/costs for correct/incorrect classification. We argue that considering a classifier as a player in a zero-sum game allows us to use the minimax principle from game theory to determine the optimal operating point. The proposed classifier threshold corresponds to the intersection between the ROC curve and the descending diagonal in ROC space and yields a minimax accuracy of 1-FPR. Our proposal can be readily implemented in practice, and reveals that the empirical condition for threshold estimation of “specificity equals sensitivity” maximizes robustness against uncertainties in the abundance of positives in nature and classification costs.

Optimal threshold estimation for binary classifiers using game theory

Many bioinformatics algorithms can be understood as binary classifiers. They are usually trained by maximizing the area under the receiver operating characteristic (ROC) curve. On the other hand, choosing the best threshold for practical use is a complex task, due to uncertain and context-dependent skews in the abundance of positives in nature and in the yields/costs for correct/incorrect classification. We argue that considering a classifier as a player in a zero-sum game allows us to use the minimax principle from game theory to determine the optimal operating point. The proposed classifier threshold corresponds to the intersection between the ROC curve and the descending diagonal in ROC space and yields a minimax accuracy of 1-FPR. Our proposal can be readily implemented in practice, and reveals that the empirical condition for threshold estimation of “specificity equals sensitivity” maximizes robustness against uncertainties in the abundance of positives in nature and classification costs.