Gaining insight through case-based explanation

Traditional explanation strategies in machine learning have been dominated by rule and decision tree based approaches. Case-based explanations represent an alternative approach which has inherent advantages in terms of transparency and user acceptability. Case-based explanations are based on a strategy of presenting similar past examples in support of and as justification for recommendations made. The traditional approach to such explanations, of simply supplying the nearest neighbour as an explanation, has been found to have shortcomings. Cases should be selected based on their utility in forming useful explanations. However, the relevance of the explanation case may not be clear to the end user as it is retrieved using domain knowledge which they themselves may not have. In this paper the focus is on a knowledge-light approach to case-based explanations that works by selecting cases based on explanation utility and offering insights into the effects of feature-value differences. In this paper we examine to two such a knowledge-light frameworks for case-based explanation. We look at explanation oriented retrieval (EOR) a strategy which explicitly models explanation utility and also at the knowledge-light explanation framework (KLEF) that uses local logistic regression to support case-based explanation.

A note on application of the method of supplementary variables to the analysis of a processor sharing system

We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author’s monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author’s work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.     

On instability of control systems for a certain class of objects and methods of its elimination

In practice of design of control systems, the cases occur when some of the roots of the transfer function of a controllable object are disposed on the imaginary axis of the complex plane. The optimal controller constructed for such objects, despite its realizability, will not afford the robustness properties in the system. The methods of removal of this phenomenon are given. The comparative estimate of the solution of this problem is provided both in the space of states and in the input-output relations (in the space of operators).     

Development and application of the theory of parametric regulation of evolution of economic systems based on a neoclassical model of optimal growth

Presented were some results on roughness of the mathematical model of the neoclassical theory of optimal growth with and without parametric regulation, selection of the optimal law of parametric regulation, and the optimal law of parametric regulation vs. the uncontrollable parameters of this mathematical model based on the parametric regulation theory.     

Problem of optimal oscillator control for nulling its energy under bounded control action

Consideration was given to the problem of optimal control based on two performance criteria with the aim of full oscillator stopping from the initial state.     

Comparison of the quantile and guaranteeing approaches to system analysis

The worst value of the quantile of the distribution of the linear loss function which depends on the uncertain stochastic parameters was compared with the maximum value of this function. The stochastic uncertainty is modelled by distributions from the Barmish class.     

Dynamic features of flexible spacecraft control in process of its transformation into a large space structure

Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( $ \tilde f Consideration was given to dynamics of angular motion control of the flexible spacecraft reconstructed into a large space structure. In formal terms, this transformation lies in gradual reduction of the constructive rigidity to small values giving rise to low-frequency ( ≤ 0.05 Hz) oscillations which represent one of the attributes of the class of large space structures. The existing quantitative definition of the large space structure was specified. It was demonstrated that as the frequencies of structure’s elastic oscillations approach those of the control of object “rigid” motion, a new kind of interrelations between the motions of both types, the so-called “capture” of the controller frequency by that of the elastic oscillations, arises which impairs control efficiency to the point of losing system stability. Analytical (for the linear control systems) and computer-aided (for the discrete systems) methods for determination of the boundaries separating the two qualitatively different forms of existence of the transformed elastic object were proposed. Some results of computer simulation of the orientation control of variable objects such as flexible spacecraft and large space structure were presented. Original Russian Text ? I.N. Krutova, V.M. Sukhanov, 2008, published in Avtomatika i Telemekhanika, 2008, No. 5, pp. 41–56. This work was supported by the Russian Foundation for Basic Research, project no. 05-08-18175.     

Algorithms to construct suboptimal organization hierarchies

The problem of controlling an organization structure (hierarchy of organization control) was considered as that of discrete optimization, that is, minimization by selecting the permissible hierarchy of total costs of maintaining its managers. For the case of the so-called uniform functions of manager costs, the lower estimate of the costs of the optimal hierarchy was obtained allowing one, besides all other things, to determine approximately the main characteristics of the optimal hierarchy such as the number of managers, their norm of controllability, and so on. Quality of this lower estimate was studied, and effective algorithms to construct suboptimal hierarchies with costs slightly exceeding the optimal ones were proposed for some important cases.     

Equipment life time optimization with respect to operational expenses

The subject of investigations is the equipment operational model, where the operational expenses are represented by planned replacement expenses and losses due to failures. The two replacement strategies are considered: “planned replacement at the end of predetermined life time or after a failure” and “planned replacement at the end of predetermined life time.” In the second case only working capacity is restored after failure. The optimal lifetime value is shown to depend on the ratio of planned replacement expenses and losses due to failure. The rated conditions for the optimal equipment lifetime and for the gamma-percentile life are obtained providing the distribution of time to failure is determined by the Weibull law. The expediency of the equipment group replacement is discussed.     

Universal software packages to model the distributed-parameter systems

Consideration was given to the universal software packages for modeling objects and distributed-parameter systems obeying the partial differential equations. The packages may serve as important tools for industrial automation because the majority of industrial objects have distributed parameters. The review presented the results of comparing a number of commercial packages against a set of user-defined criteria. Its final part was devoted to some freeware packages. Conclusions were drawn, and recommendations for using the considered packages were given.     

Operating ratio of the technical systems,subjected to failures

The original way of definition of operating ratio in view of reliability of the equipment of the control, time of the control over periodic checks and time of restoration is offered. The received results allow to define the best value of operating ratio of system both in view of, and without taking into account operational expenses.     

Application of the finite difference method to the problem of pursuit in the distributed-parameter systems

The problem of pursuit in the controlled systems of parabolic type without mixed derivatives with variable coefficients was considered and solved using the finite difference method. Sufficient conditions for pursuit completion were established.     

Design of modified PD algorithm to control angular motion of large space structure

Consideration was given to the design of an algorithm to control orientation of the large space structure (LSS) in the presence of infralow (less than 0.01Hz) frequencies of elastic oscillations exerting considerable influence on the quality of transients due to closeness of the LSS eigenfrequencies to the frequency of control of the object’s “rigid” motion. Procedure for designing a modified PD-algorithm for orientation of the LSS with infralow frequencies of elastic structural oscillations was described. Methods were proposed for calculation of the coefficients of additional components of the modified algorithm and determination of the LSS eigenfrequency boundary to the right of which the orientation control system is robust to the deviations of the object frequencies or inaccuracy of their definition. Some examples of mathematical modeling of the processes of the relay gyroforce control of LSS orientation using the proposed algorithm were given.     

Organization of the remote access to tomographic data through a slow communications link

Consideration is given to the problem of organization of the remote access to tomographic data obtained as a result of the investigation on the computerized tomograph through a slow communications link. The proposed access strategy together with the developed and realized method of tomographic data compression makes it possible to help users (physicians, scientists, and etc.) work with remote tomographic data, e.g., using the Internet. This, in its turn, opens up vast possibilities for using the data of tomographic investigations for conducting medical consultations “at a distance,” videoconferences, organizing network seminars for medical staff training, and etc.     

Method to determine an optimal control in the minimum of resource consumption for the nonlinear stationary systems

An iterative method to solve the nonlinear problems of minimization of resource consumption was proposed. It generalizes to a more general class of nonlinear systems the method of resource minimization for the nonlinear systems with the control-linear right-hand side separated in state and control.     

Application of the Floyd algorithm to the asymptotic analysis of networks with unreliable ribs

The problem of finding parameters of asymptotic relations for the probability of operation of a graph with unreliable ribs is solved. These parameters are expressed through minimax functions of lengths of ribs. To compute them, an economical modification of the Floyd algorithm is constructed.     

Adaptive algorithms to estimate parameters of the optimal policies of inventory control under limited stock-out

Consideration was given to the inventory control by the criterion for minimum of the cumulative mean costs over a sufficiently long planning horizon in conditions of uncertain demand characteristics. Adaptive algorithms to estimate the parameters of the optimal two-level control policies oriented to the supply systems with high level of customer servicing were constructed for the stationary mode of operation.     

Application of the method of extremal deviations to studying forced parametric bending vibrations of the pipeline

By means of a method of extremal deviations, dynamic stability of the pipeline and ensuring estimation of the amplitude of its bending vibrations and tensions caused by transported medium pressure pulsation are analyzed. The most dangerous pressure pulsations are synthesized. A criterion for dynamic stability and estimation of maximal possible amplitude of bending vibrations and tensions are obtained in analytic form.