Theories of initial segments of standard models of arithmetics and their complete extensions

We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.We also estimate the complexity of complete extensions of the arithmetic with addition and multiplication.     

Functional Differentiation of Computer Programs

We present a purely functional implementation of the computational differentiation tools—the well known numeric (i.e., not symbolic) techniques which permit one to compute point-wise derivatives of functions defined by computer programs economically and exactly (with machine precision). We show how the use of lazy evaluation permits a transparent and elegant construction of the entire infinite tower of derivatives of higher order for any expressions present in the program. The formalism may be useful in various problems of scientific computing which often demand a hard and ungracious human preprocessing before writing the final code. Some concrete examples are given.     

ELECTROCHEMICAL MACHINING OF CURVILINEAR SURFACES

In this work a theoretical analysis of the ECM process of curvilinear surfaces has been presented. The purpose of this analysis is to predict the shape evolution of the machined object using: a shaping surface of small thickness (flat issue) and a blade of hydrodynamic machine (quasi-three dimensional issue). ECM modeling involves prediction of the machined surface shape evolution and distribution of physical-chemical parameters inside the interelectrode gap. The problem has been solved with the use of an equation of the electrolyte and hydrogen mixture (liquid and gas) flat flow inside the interelectrode gap. After introducing simplifying assumptions for the flow, void fraction distribution and the gap thickness, the equations were solved partly analytically, partly numerically. The obtained solutions for assigned parameters of the machining process are presented graphically in the form of distributions of: static pressure, the mixture flow rate, temperature, void fraction and evolution of the machined surface shape evolution.     

An empirical analysis of heuristics for solving the two-machine flow shop problem with job release times

The theoretical analysis of heuristics for solving intractable optimization problems has many well-known drawbacks. Constructed instances demonstrating an exceptionally poor worst-case performance of heuristics are typically too peculiar to occur in practice. Theoretical results on the average-case performance of most heuristics could not be established due to the difficulty with the use of probabilistic analysis. Moreover, the heuristics for which some type of asymptotic optimality has been proven are likely to perform questionably in practice. The purpose of this paper is to confront known theoretical results with our empirical results concerning heuristics for solving the strongly NP-hard problem of minimizing the makespan in a two-machine flow shop with job release times. The heuristics' performance is examined with respect to their average and maximum relative errors, as well as their optimality rate, that is, the probability of being optimal. In particular, this allows us to observe that the asymptotic optimality rate of so called “almost surely asymptotically optimal” heuristic can be zero. We also present a new heuristic with short worst-case running time and statistically prove that it outperforms all heuristics known so far. However, our empirical experiments reveal that the heuristic is on average slower that its competitors with much longer worst-case running times.     

Incompetence and impact of training in bimatrix games

The concept of games with incompetence has been introduced to better represent games where players may not be capable of executing strategies that they select. In particular this paper introduces incompetence into bimatrix games and investigates the properties of such games. The results obtained describe both the general dependence of “extreme Nash equilibrium payoffs” on incompetence and special behaviour arising in particular cases. The dependence of the payoffs can be complex and include non-linearities and transition points. Transition points occur when kernels change and may result in the number of “extreme Nash equilibria” changing. Understanding these changes allows the determination of the benefits of regimes that seek to decrease a player’s incompetence. While the games we consider are normally static, in our context there is a hidden dynamics resulting from the fact that players will strive to improve their equilibrium payoffs by changing their incompetence levels. This might require training, in the case of games like tennis, or it might require the purchase of new equipment costing billions of dollars, in the case of military applications.     

A new generation of power supplies for electron beam welding machines

Widely used electron beam welding machines are equipped with heavy power supplies, located in a special oil tank and connected with an electron gun to a high-voltage cable. A special system detects electric discharges in the electron gun space, which may arise during welding and then it tries to switch off the high voltage to interrupt an electric arc. Such disadvantages have been eliminated with the novel power supply described here. The Q of resonance circuit of this supply is stabilized and as a result circulating power appears. During an electric discharge in the gun, power is not sent to the electron gun but circulates between the electronic parts of the resonance circuit without losses and “waits” for the break in the short circuit. The power supply is much smaller and lighter than supplies of similar rating used nowadays. It is connected directly to the electron gun chamber without a high-voltage cable. The first construction of the supply was designed for electron beam welding machine of 5 kW power and 60 kV accelerating voltage. Tests of the new power supply in laboratory and industrial conditions have shown its usefulness for electron beam welding.     

Automating test generation for discrete event oriented embedded systems

A method for the automatic generation of test scenarios from the behavioral requirements of a system is presented in this paper. The generated suite of test scenarios validates the system design or implementation against the requirements. The approach proposed here uses a requirements model and a set of four algorithms. The requirements model is an executable model of the proposed system defined in a deterministic state-based modeling formalism. Each action in the requirements model that changes the state of the model is identified with a unique requirement identifier. The scenario generation algorithms perform controlled simulations of the requirements model in order to generate a suite of test scenarios applicable for black box testing. Measurements of several metrics on the scenario generation algorithms have been collected using prototype tools.     

A comparison of two MLEM2 rule induction algorithms extended to probabilistic approximations

A probabilistic approximation is a generalization of the standard idea of lower and upper approximations, defined for equivalence relations. Recently probabilistic approximations were additionally generalized to an arbitrary binary relation so that probabilistic approximations may be applied for incomplete data. We discuss two ways to induce rules from incomplete data using probabilistic approximations, by applying true MLEM2 algorithm and an emulated MLEM2 algorithm. In this paper we report novel research on a comparison of both approaches: new results of experiments on incomplete data with three interpretations of missing attribute values. Our results show that both approaches do not differ much.