Development of Variational Thinking Skills in Programming Teaching

The paper presents an example of methodological approach to the development of variational thinking skills in teaching programming. Various ways in solving a given task are implemented for the purpose. One of the forms, through which the variational thinking is manifested, is related to trail practical actions. In the process of comprehension of the properties thus acquired, students are doing their own (correct or incorrect) conclusions for other, hidden properties and at the same time they discover possibilities for new ways of action and acquiring of new effects. The variability and the generalizing function of thinking are in a close interrelation, and their interaction to a great extend determines the dynamics of the cognitive activity of the student.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.