MARKOV MODELS FOR THE ANALYSIS OF DYNAMICAL SYSTEMS

State-space modelling approach which is essentially time-domain developed in the late 1960s is a new approach to the analysis and design of complex control systems. Several researches have carried out modelling and analysis of mechanical systems with a number of degrees of freedom of movement using state space approach among which is the work of Sivak and Darina (2012) who modelled a system with two degrees of freedom. In this paper, therefore, we provide an extension of the work of Sivak and Darina to model and analyse a three degree of freedom translational mechanical system using state-space approach. The system was first presented in equivalent free body diagrams, then Newton's second law of motion was used to derive its equations of motion. The State-space formulation in the controllable canonical form obtained from the time-domain differential equations is adopted and the Laplace transform method was used in the analysis to determine the poles (natural frequencies) of the system using two numerical examples in MATLAB software. The software was also used to determine the controllability and observability matrices of the system. The stability, controllability and observability of the system were then discussed from the poles, controllability matrix and observability matrix respectively. Tables of numerical values and line graphs were used to present the results obtained from the analysis. Finally, in these results, the system was found to be stable, controllable and observable suggesting that a state feedback ( pole placement ) control design for the system is possible.

This paper provides exact solutions to the stationary probability distributions in some stochastic predation systems. These are derived by solving the Fokker-Planck equations for: (i) a generalized stochastic Lotka-Volterra predator-prey system, and (ii) a generalised stochastic Lotka-Volterra food chain. In all these systems the growth dynamics of all levels of species are subject to stochastic shocks. Since stationary probability distributions provide the most comprehensive characterization of a stochastic system in a steady state, system stability can be analysed accordingly

In the first part of the article is a methodology for implementing a model-driven safety analysis of dynamical technology systems. The safety analysis is performed in the development of control system, mainly aiming at critical processes of system operation. I divided my methodology into five steps. These steps of the methodology was carried out in a hierarchical sequence. The objective of the second part of the article is to demonstrate the principle of the SQMD method concept for performing safety analysis on the example of a dynamical system. By SQMD method will be developed a models of safety-critical processes by which they will be carried out on-line monitoring. The method combining qualitative and quantitative procedures of modelling and taking both methods advantages.

To design a statistical software package to provide automated calculations of normal and weighted and 3 indices.Prompted by the lack of commonly available software to compute weighted kappa and the nonproportionate workload needed to calculate our 3 variability indices manually, the new statistical software package was designed. To demonstrate the performance of the new CONQUISTADOR software, a simulation study (both intralaboratory and interlaboratory) was designed using 5,000 clinical samples randomly selected from a data file of > or = 200,000 conventional Pap smears and programmed to become "analyzed" by 12 cytologists in 5 imaginary laboratories.A representative set of both complete and partial outputs provided by the software, in Excel format (Microsoft, Redmond, Washington, U.S.A.) are shown to illustrate the different functions of the program. In the interlaboratory mode, the software calculates accuracy indicators (sensitivity, specificity, positive and negative predictive value, and their 95% CI), which are not common features of regular statistical packages; kappa and weighted kappa; and their 95% CI (comparison of single laboratories to all laboratories and pairwise comparisons between single laboratories). The 3 diagnostic variability indices can be computed separately for all samples or for only the positive samples. In the intralaboratory mode, the software calculates the same indices for individual cytologists.The CONQUISTADOR statistical package has properties that are useful in monitoring cytologic laboratory quality in both intralaboratory and interlaboratory settings. The software will be distributed by the National Institute of Health, Rome, for the delivery costs only.

Datasets are often derived by manipulating raw data with statistical software packages. The derivation of a dataset must be recorded in terms of both the raw input and the manipulations applied to it. Statistics packages typically provide limited help in documenting provenance for the resulting derived data. At best, the operations performed by the statistical package are described in a script. Disparate representations make these scripts hard to understand for users. To address these challenges, we created Continuous Capture of Metadata (C2Metadata), a system to capture data transformations in scripts for statistical packages and represent it as metadata in a standard format that is easy to understand. We do so by devising a Structured Data Transformation Algebra (SDTA), which uses a small set of algebraic operators to express a large fraction of data manipulation performed in practce. We then implement SDTA, inspired by relational algebra, in a data transformation specification language we call SDTL. In this demonstration, we showcase C2metadata's capture of data transformations from a pool of sample transformation scripts in at least two languages: SPSS and Stata (SAS and R are under development), for social science data in a large academic repository. We will allow the audience to explore C2Metadata using a web-based interface, visualize the intermediate steps and trace the provenance and changes of data at different levels for better understanding of the process.

The pulp and paper industry in Indonesia is the tenth largest producer in the world, with Acacia and Eucalyptus as the main genera used for production; however, limited publications exist related to Eucalyptus growth models in Indonesia compared with other regions. Time-based models have been developed in which height, stand density, and basal area are predicted based on initial conditions and age. In contrast, a state–space approach utilizes the rate of change of these three state variables. Previous direct comparisons of these two approaches are generally limited. Consequently, the objective of this study was to compare two stand-level growth modeling approaches for Eucalyptus hybrid species on Sumatera (Sumatra) Island using both time-based and state–space methods. Our results indicate that dynamic models using either time-based or state–space approaches are adequate for predicting stand parameters to rotation age. A modified Bazukis matrix indicated that the behavior of both methods produced reliable predictions that were biologically reasonable in terms of stand development; however, the time-based approach provided better performance than the state–space approach on a variety of equivalence tests and goodness-of-fit statistics. Overall, the analysis highlights the advantages and disadvantages of these two commonly used, yet highly contrasting, stand-level growth modeling approaches, which need further consideration and evaluation.

In control theory, models of physical processes, such as systems of differential equations, are usually checked against specifications, such as stability and set invariance. In formal methods, rich specifications, such as languages and formulae of temporal logics, are checked against models of software programs and digital circuits, such as finite transition graphs. With the development and integration of cyber physical and safety critical systems, there is an increasing need for computational tools for verification and control of complex systems from rich, temporal logic specifications. The formal verification and synthesis problems have been shown to be undecidable even for very simple classes of infinitespace continuous and hybrid systems. However, provably correct but conservative approaches, in which the satisfaction of a property by a dynamical system is implied by the satisfaction of the property by a finite over-approximation (abstraction) of the system, have received a lot of attention in recent years. Some classes of systems allowing for computationally efficient verification and control from temporal logic specifications are reviewed. For continuous and discrete-time linear systems and continuous-time multi-linear systems, it is shown that finite abstractions can be constructed through polyhedral operations only. By using techniques from model checking and automata games, this allows for verification and control from specifications given as Linear Temporal Logic (LTL) formulae over linear predicates in the state variables. A connection between the existence of Lyapunov functions and finite bisimulations is established for discrete-time linear and switched linear systems. Finally, optimality and correctness requirements are combined in a model predictive approach to generate control strategies for discrete-time linear systems. The usefulness of these computational tools is illustrated with various examples such as verification and synthesis of biological circuits in synthetic biology and motion planning and control in robotics.

The state space approach is a common method for conducting reliability assessment of protective systems. However, as more factors affecting the reliability of protective relay are considered, the system Markov model is becoming more and more complex and its solving efficiency is decreasing. To avoid this, a method to simplify the Markov model of protective system is proposed in this paper. Based on the continuous-time Markov process (CTMP), the theory underlying the state space approach, the method illustrates that the duration of the protective system in the switching states can be neglected. In other words, the protection switching state can be ignored when developing a Markov model of protective system. This method is applied to two existing models, one for a protection/component system and the other for redundant protective systems. The study results show that the method significantly reduces the complexity of the Markov model and improves the solving efficiency without reducing the capability of Markov model to describe the reliability of protective systems.

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Response to van Ginkel and Kroonenberg In our paper we indicated that “the field has not advanced to provide methods for addressing repeated measures ANOVA analysis” and cited van Ginkel and Kroonenberg (2014). It should be clarified that this refers to van Ginkel and Kroonberg (2014)’s assertion that “the implementation of the combination rules needed for ANOVA in statistical software packages has either been quite limited or very well hidden.” It should also be clarified that van Ginkel and Kroonberg (2014) have proposed methods to conduct the analyses using additional macros and explanations not integrated into major statistical software packages and argue for the inclusion in future upgrades. As van Ginkel and Kroonenberg (2014) state: “To date, the implementation of the combination rules needed for ANOVA in statistical software packages has either been quite limited or very well hidden. SPSS 19.0 does not provide any pooled results for F tests for multiply imputed data. Using an SPSS macro (Van Ginkel, 2010a) the procedure may be carried out in SPSS but this still requires substantial manual preprocessing. For repeated-measures ANOVA the procedure is even more complicated. Although SAS 9.3 and Stata 10.0 have a procedure for carrying out the combination rules for ANOVA in Multiple imputation, the manual provides no clear practical guidance in how to use them in the specific context of ANOVA. The procedure outlined in this article should also be of assistance to any SAS or Stata user who intends to use Multiple imputation in this context. In the appendix, it is explained how exactly the procedures can be carried out in SAS 9.3, Stata 10.0, and SPSS 19.0 using Van Ginkel's (2010a) macro. Considering the involved task needed to actually carry out the described procedure, its implementation in future releases of SPSS and other software packages, as well as a clear guidance with examples in the SAS and Stata manuals, seems desirable if its use is to become commonplace.”

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In this thesis, we present a dynamical systems approach to adaptive controllers for locomotion control. The approach is based on a rigorous mathematical framework using nonlinear dynamical systems and is inspired by theories of self-organization. Nonlinear dynamical systems such as coupled oscillators are an interesting approach for the on-line generation of trajectories for robots with many degrees of freedom (e.g. legged locomotion). However, designing a nonlinear dynamical system to satisfy a given specification and goal is not an easy task, and, hitherto no methodology exists to approach this problem in a unified way. Nature presents us with satisfactory solutions for the coordination of many degrees of freedom. One central feature observed in biological subjects is the ability of the neural systems to exploit natural dynamics of the body to achieve efficient locomotion. In order to be able to exploit the body properties, adaptive mechanisms must be at work. Recent work has pointed out the importance of the mechanical system for efficient locomotion. Even more interestingly, such well suited mechanical systems do not need complicated control. Yet, in robotics, in most approaches, adaptive mechanisms are either missing or they are not based on a rigorous framework, i.e. they are based on heuristics and ad-hoc approaches. Over the last three decades there has been enormous progress in describing movement coordination with the help of Synergetic approaches. This has led to the formulation of a theoretical framework: the theory of dynamic patterns. This framework is mathematically rigorous and at the same time fully operational. However, it does not provide any guidelines for synthetic approaches as needed for the engineering of robots with many degrees of freedom, nor does it directly help to explain adaptive systems. We will show how we can extend the theoretical framework to build adaptive systems. For this purpose, we propose the use of multi-scale dynamical systems. The basic idea behind multi-scale dynamical systems is that a given dynamical system gets extended by additional slow dynamics of its parameters, i.e. some of the parameters become state variables. The advantages of the framework of multi-scale dynamical systems for adaptive controllers are 1) fully dynamic description, 2) no separation of learning algorithm and learning substrate, 3) no separation of learning trials or time windows, 4) mathematically rigorous, 5) low dimensional systems. However, in order to fully exploit the framework important questions have to be solved. Most importantly, methodologies for designing the feedback loops have to be found and important theoretical questions about stability and convergence properties of the devised systems have to be answered. In order to tackle this challenge, we first introduce an engineering view on designing nonlinear dynamical systems and especially oscillators. We will highlight the important differences and freedom that this engineering view introduces as opposed to a modeling one. We then apply this approach by first proposing a very simple adaptive toy-system, consisting of a dynamical system coupled to a spring-mass system. Due to its spring-mass dynamics, this system contains clear natural dynamics in the form of resonant frequencies. We propose a prototype adaptive multi-scale system, the adaptive frequency oscillator, which is able to adapt its intrinsic frequency to the resonant frequency of the body dynamics. After a small sidetrack to show that we can use adaptive frequency oscillators also for other applications than for adaptive controllers, namely for frequency analysis, we then come back to further investigation of the adaptive controller. We apply the same controller concept to a simple spring-mass hopper system. The spring-mass system consists of a body with two legs attached by rotational joints. The legs contain spring-damper elements. Finally, we present results of the implementation of the controller on a real robot, the experimental robot PUPPY II. This robot is a under-actuated robot with spring dynamics in the knee joints. It will be shown, that due to the appropriate simplification and concentration on relevant features in the toy-system the controller concepts works without a fundamental change on all systems from the toy system up to the real robot.

In this work, an alternative model to discrete-time Markov model (DTMM) or standard continuous-time Markov model (CTMM) for analyzing ordered categorical data with Markov properties is presented: the minimal CTMM (mCTMM). Through a CTMM reparameterization and under the assumption that the transition rate between two consecutive states is independent on the state, the Markov property is expressed through a single parameter, the mean equilibration time, and the steady-state probabilities are described by a proportional odds (PO) model. The mCTMM performance was evaluated and compared to the PO model (ignoring Markov features) and to published Markov models using three real data examples: the four-state fatigue and hand-foot syndrome data in cancer patients initially described by DTMM and the 11-state Likert pain score data in diabetic patients previously analyzed with a count model including Markovian transition probability inflation. The mCTMM better described the data than the PO model, and adequately predicted the average number of transitions per patient and the maximum achieved scores in all examples. As expected, mCTMM could not describe the data as well as more flexible DTMM but required fewer estimated parameters. The mCTMM better fitted Likert data than the count model. The mCTMM enables to explore the effect of potential predictive factors such as drug exposure and covariates, on ordered categorical data, while accounting for Markov features, in cases where DTMM and/or standard CTMM is not applicable or conveniently implemented, e.g., non-uniform time intervals between observations or large number of categories.

Genome-wide linkage analysis using multiple traits and statistical software packages is a tedious process which requires a significant amount of manual file manipulation. Different linkage analysis programs require different input file formats, making the task of analyzing data with multiple methods even more time-consuming. We have developed a software tool, AUTOGSCAN, that automates file formatting, the running of statistical analyses, and the summarizing of resulting statistics for whole genome scans with a push of a button, using several independent, and often idiosyncratic, statistical software packages such as MERLIN, SOLAR and GENEHUNTER. We also describe a program, ANALYZE, designed to run qualitative linkage analysis with several different statistical strategies and programs to efficiently screen for linkage and linkage disequilibrium for a given discrete trait. The ANALYZE program can also be used by AUTOGSCAN in a genome-wide sense.

Metaanalysis of the Efficacy of Sublingual Immunotherapy in the Treatment of Allergic Asthma in Pediatric Patients, 3 to 18 Years of Age