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- Novikov D. Optimal schedule to test independent hypotheses
The first stage of any creative activity consists in generating a set of hypotheses and testing them. Generally, the time, required for testing a hypothesis is random and depends on its complexity (the prior probability of testing per unit time) and on acquired experience, determined by the set of hypotheses, successfully tested before. The problem is to choose an optimal schedule of testing, i.e. minimizing the sum of expected testing times, which are essentially nonlinear past-sequence-dependent and take into account learning and deterioration effects. For this aim, the general model of creative activity is formulated and the corresponding problem of optimal scheduling is stated; the classification of subproblems is introduced. Analysis of related works demonstrates the absence of methods to find computationally “simple” solution of the problem in hand. The used method of analytical proof of certain monotonic schedule optimality consists in reordering of two adjacent hypothesis, violating monotonicity. Main result is a set (for different subproblems) of sufficient conditions, under which the monotonic “simple-to-complex” schedule is optimal: the hypotheses are arranged in ascending order of their complexity.
- Zverkina G., Koshelev A. On simulation of random variables using intensity
As is well known, random variables are usually modelled using the inverse function of the distribution function. However, often when modelling the behaviour of complex technical models, a researcher is faced with a change in the parameters of the simulated random variables. Often in these cases, the intensity of the completion of a certain random period changes (or "failure rate", or "hazard rate"). Therefore, it is important to be able to simulate a random variable under conditions of a (random) change in the intensity of this random variable. This paper proposes a new method for modelling a random variable by its intensity. The text is provided with illustrative material of the results of numerical experiments confirming the efficiency of the proposed method. Naturally, this text is just the beginning of work. In the future, the technical details of the effectiveness of the application of the proposed method will be clarified.
- Koposov A. Robust networked iterative learning control of a variable configurationsystem under random disturbances
The paper considers the iterative learning control design problem of a system, consisting of identical subsystems (agents) under changing the information network configuration. The agents represent discrete linear dynamic plants with affine model of uncertainty operating in a repetitive mode. Each plant is under the influence of random disturbances, and the output variables of the plants are measured in the presence of noises. The configurations of the information network determine the group of functioning agents and the type of information exchange between agents. The configuration change takes place in accordance with certain external rules. The control design is based on the divergent method of the vector Lyapunov function. The results of modeling the obtained control law for a group of manipulators with flexible single-links are presented.
- Chebotarev P. Cooperation and liberalism: evolutionary scenarios in the ViSE model
Under the assumptions of the ViSE model, we consider societies consisting of a group and egoists. Scenarios of the evolution of society due to changes in its structure and voting threshold in the interests of the participants are studied, provided that a Gaussian proposal generator is used. It is shown that for non-trivial societies there are scenarios that lead to the formation of an “open” group, whose size allows it to make monopoly decisions through voting. On the other hand, there are no trajectories traversed on the initiative of the participants from societies with a non-singleton group to societies consisting of egoists. A “mafia” type group never lets go of those who want to leave it. In societies whose decision procedure is close to the majority, the mechanism of “snowball” of cooperation is implemented, while in the most liberal and most conservative societies the mechanism of consecutive atomization dominates. “Open” and “democratic” groups admit cyclic evolutionary scenarios. In unfavorable environments, it is rational to strengthen conservatism.
- Korneenko V. Method for constructing the results scale for objects in orderal scales taking into account their expert probability
When solving multi-criteria problems for the correct application of the additive integral aggregation mechanism, the problem arises of converting the initial estimates of objects in ordinal measurement scales, taking into account their expert probability, into point estimates of the resulting difference scale. The essence of the method of transition from the initial estimates of objects in ordinal scales, taking into account their expert probability, initially reduces to the transition of estimates in the point scale to interval gradations of the division of the intermediate quantitative scale. Then, taking into account the subjective probability, a transition is made to a point estimate on the interval of splitting the resulting difference scale. The article proves that the proposed approach ensures the preservation of the ordering of objects in the initial and resulting scales. The idea of the method is shown by the example of solving the problem of multi-criteria evaluation of the value of information and analytical materials, the initial estimates of which are presented in point gradations and the corresponding subjective (expert) probability.
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