On the discrete time dynamics of a self-stabilizing MCA learning algorithm

The stability of minor component analysis (MCA) learning algorithms is an important problem in many signal processing applications. In this paper, we propose an effective MCA learning algorithm that can offer better stability. The dynamics of the proposed algorithm are analyzed via a corresponding deterministic discrete time (DDT) system. It is proven that if the learning rate satisfies some mild conditions, almost all trajectories of the DDT system starting from points in an invariant set are bounded, and will converge to the minor component of the autocorrelation matrix of the input data. Simulation results will be furnished to illustrate the theoretical results achieved.

Trajectory characterizations for a discrete-time bearing-only navigation strategy

In this paper we explore the geometry of a particular navigation scheme which guides a pursuer from a fixed initial position to a given fixed final position using a one-step look ahead strategy and using only bearing measurements. We explicitly characterize the optimal trajectories for the problem in terms of the Cramer-Rao bound such that the derived trajectories permit a minimization in the error of an unbiased estimate of the target position.

Robust filtering for uncertain discrete-time systems with uncertain noise covariance and uncertain observations

The use of Kalman filtering is very common in state estimation problems. The problem with Kalman filters is that they require full prior knowledge about the system modeling. It is also assumed that all the observations are fully received. In real applications, the previous assumptions are not true all the time. It is hard to obtain the exact system model and the observations may be lost due to communication problems. In this paper, we consider the design of a robust Kalman filter for systems subject to uncertainties in the state and white noise covariances. The systems under consideration suffer from random interruptions in the measurements process. An upper bound for the estimation error covariance is proposed. The proposed upper bound is further minimized by selection of optimal filter parameters. Simulation example shows the effectiveness of the proposed filter.

Optimising discrete event simulation models using a reinforcement learning agent

A reinforcement learning agent has been developed to determine optimal operating policies in a multi-part serial line. The agent interacts with a discrete event simulation model of a stochastic production facility. This study identifies issues important to the simulation developer who wishes to optimise a complex simulation or develop a robust operating policy. Critical parameters pertinent to 'tuning' an agent quickly and enabling it to rapidly learn the system were investigated.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

Making a difference with a discrete course on accounting ethics

Calls for the expansion of ethics education in the business and accounting curricula have resulted in a variety of interventions including additional material on ethical cases, the code of conduct, and the development of new courses devoted to ethical development [Lampe, J.: 1996]. The issue of whether ethics should be taught has been addressed by many authors [see for example: Hanson, K. O.: 1987; Huss, H. F. and D. M. Patterson: 1993; Jones, T. M.: 1988–1989; Kerr, D. S. and L. M. Smith: 1995; Loeb, S. E.: 1988; McDonald, G. M. and G. D. Donleavy: 1995]. The question addressed in this paper is not whether ethics should be taught but whether accounting students can reason more ethically after an intervention based on a discrete and dedicated course on accounting ethics. The findings in this paper indicate that a discrete intervention emphasising dilemma discussion has a positive and significant effect on students’ moral reasoning and development. The data collected from interviews suggest that the salient influences on moral judgement development include: learning theories of ethics particularly Kohlberg’s theory of cognitive moral reasoning and development; peer learning; and moral discourse. The implications from the findings in this study suggest that moral reasoning is responsive to particular types of ethics intervention and educators should carefully plan their attempts to foster moral judgement development.

Managing realtime information flow between distributed discrete event simulation models

Investigates the creation of a method for the connection and communication of commercial off the shelf discrete-event simulation packages for simulation models of manufacturing systems. Through this research a method to connect different commercial off the shelf discrete-event simulation packages was successfully developed facilitating parallel development of models and the creation of extremely large models.

Spatial discretization of discrete dynamical systems

Investigates what can go wrong when dynamical systems are modelled with a computer. Number theoretic techniques were used to detail the effects "discretization" errors caused by computer round-off had on characteristics of a system. In particular, a relationship was established between the occurrence of long cycles in a system and the classical result known as Artin's conjecture. Algorithms were then developed which eliminated discretization errors.

Potential applications of discrete-event simulation and fuzzy rule-based systems to structural reliability and availability

This chapter discusses and illustrates some potential applications of discrete-event simulation (DES) techniques in structural reliability and availability analysis, emphasizing the convenience of using probabilistic approaches in modern building and civil engineering practices. After reviewing existing literature on the topic, some advantages of probabilistic techniques over analytical ones are highlighted. Then, we introduce a general framework for performing structural reliability and availability analysis through DES. Our methodology proposes the use of statistical distributions and techniques – such as survival analysis – to model component-level reliability. Then, using failure- and repair-time distributions and information about the structural logical topology (which allows determination of the structural state from their components’ state), structural reliability, and availability information can be inferred. Two numerical examples illustrate some potential applications of the proposed methodology to achieving more reliable and structural designs. Finally, an alternative approach to model uncertainty at component level is also introduced as ongoing work. This new approach is based on the use of fuzzy rule-based systems and it allows the introduction of experts’ opinions and evaluations in our methodology.

Means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties. We also discuss which of them coincide with the Cartesian product of the standard mean and median.

Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Image reduction using means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

Improving casthouse throughput using discrete-event modeling

The scheduling of metal to different casters in a casthouse is a complicated problem, attempting to find the balance between pot-line, crucible carrier, furnace and casting machine capacity. in this paper, a description will be given of a casthouse modelling system designed to test different scenarios for casthouse design and operation. Using discrete-event simulation, the casthouse model incorporates variable arrival times of metal carriers, crucible movements, caster operation and furnace conditions. Each part of the system is individually modelled and synchronised using a series of signals or semaphores. in addition, an easy to operate user interface allows for the modification of key parameters, and analysis of model output. Results from the model will be presented for a case study, which highlights the effect different parameters have on overall casthouse performance. The case study uses past production data from a casthouse to validate the model outputs, with the aim to perform a sensitivity analysis on the overall system. Along with metal preparation times and caster strip-down/setup, the temperature evolution within the furnaces is one key parameter in determining casthouse performance.