The ever increasing use of computer systems in society brings emergent challenges to companies and system designers. The reliability of software and hardware can be financially critical, and lives can depend on it. The growth in size and complexity of software, and increasing concurrency, compounds the problem. The potential for errors is greater than ever before, and the stakes are higher than ever before. Formal methods, particularly model checking, is an approach that attempts to prove mathematically that a model of the behaviour of a product is correct with respect to certain properties. Certain errors can therefore be proven never to occur in the model. This approach has tremendous potential in system development to provide guarantees of correctness. Unfortunately, in practice, model checking cannot handle the enormous sizes of the models of real-world systems. The reason is that the approach requires an exhaustive search of the model to be conducted. While there are exceptions, in general model checkers are said not to scale well. In this thesis, we deal with this scaling issue by using a guiding technique that avoids searching areas of the model, which are unlikely to contain errors. This technique is based on a process of model abstraction in which a new, much smaller model is generated that retains certain important model information but discards the rest. This new model is called a heuristic. While model checking using a heuristic as a guide can be extremely effective, in the worst case (when the guide is of no help), it performs the same as exhaustive search, and hence it also does not scale well in all cases. A second technique is employed to deal with the scaling issue. This technique is based on the concept of random walks. A random walk is simply a `walk' through the model of the system, carried out by selecting states in the model randomly. Such a walk may encounter an error, or it may not. It is a non-exhaustive technique in the sense that only a manageable number of walks are carried out before the search is terminated. This technique cannot replace the conventional model checking as it can never guarantee the correctness of a model. It can however, be a very useful debugging tool because it scales well. From this point of view, it relieves the system designer from the difficult task of dealing with the problem of size in model checking. Using random walks, the effort goes instead into looking for errors. The effectiveness of model checking can be greatly enhanced if the above two techniques are combined: a random walk is used to search for errors, but the walk is guided by a heuristic. This in a nutshell is the focus of this work. We should emphasise that the random walk approach uses the same formal model as model checking. Furthermore, the same heuristic technique is used to guide the random walk as a guided model checker. Together, guidance and random walks are shown in this work to result in vastly improved performance over conventional model checking. Verification has been sacrificed of course, but the new technique is able to find errors far more quickly, and deal with much larger models.

The ever increasing use of computer systems in society brings emergent challenges to companies and system designers. The reliability of software and hardware can be financially critical, and lives can depend on it. The growth in size and complexity of software, and increasing concurrency, compounds the problem. The potential for errors is greater than ever before, and the stakes are higher than ever before. Formal methods, particularly model checking, is an approach that attempts to prove mathematically that a model of the behaviour of a product is correct with respect to certain properties. Certain errors can therefore be proven never to occur in the model. This approach has tremendous potential in system development to provide guarantees of correctness. Unfortunately, in practice, model checking cannot handle the enormous sizes of the models of real-world systems. The reason is that the approach requires an exhaustive search of the model to be conducted. While there are exceptions, in general model checkers are said not to scale well. In this thesis, we deal with this scaling issue by using a guiding technique that avoids searching areas of the model, which are unlikely to contain errors. This technique is based on a process of model abstraction in which a new, much smaller model is generated that retains certain important model information but discards the rest. This new model is called a heuristic. While model checking using a heuristic as a guide can be extremely effective, in the worst case (when the guide is of no help), it performs the same as exhaustive search, and hence it also does not scale well in all cases. A second technique is employed to deal with the scaling issue. This technique is based on the concept of random walks. A random walk is simply a `walk' through the model of the system, carried out by selecting states in the model randomly. Such a walk may encounter an error, or it may not. It is a non-exhaustive technique in the sense that only a manageable number of walks are carried out before the search is terminated. This technique cannot replace the conventional model checking as it can never guarantee the correctness of a model. It can however, be a very useful debugging tool because it scales well. From this point of view, it relieves the system designer from the difficult task of dealing with the problem of size in model checking. Using random walks, the effort goes instead into looking for errors. The effectiveness of model checking can be greatly enhanced if the above two techniques are combined: a random walk is used to search for errors, but the walk is guided by a heuristic. This in a nutshell is the focus of this work. We should emphasise that the random walk approach uses the same formal model as model checking. Furthermore, the same heuristic technique is used to guide the random walk as a guided model checker. Together, guidance and random walks are shown in this work to result in vastly improved performance over conventional model checking. Verification has been sacrificed of course, but the new technique is able to find errors far more quickly, and deal with much larger models.

In this expository paper we study the stationary measures of a stochastic process called nearest neighbor random walk on Z, and further we describe conditions for these measures to have the stronger property of reversibility. We consider both the cases of symmetric and non-symmetric random walk.

Sammanfattning Syfte och frågeställningar Syftet var att studera sambandet mellan GIH:s Gångtest och bestämd maximal syreupptagningsförmåga (VO2max). En av frågeställningarna var om GIH:s Gångtest är ett alternativt test för att försöka predicera maximal syreupptagningsförmåga hos friska fysiskt aktiva unga vuxna. Metod I studien ingick 45 fysiskt aktiva personer (26 kvinnor och 19 män) i åldrarna 19-28 år. De två genomförda testerna är GIH:s Gångtest (ett 6-minuters gångtest) och bestämning av maximal syreupptagningsförmåga med löpning på ett motordrivet rullband. GIH:s gångtest är ett shytteltest där testpersonen (Tp) går fram och tillbaka på en 50 meter lång sträcka och runda två koner. Tp får gå denna sträcka så många gånger som möjligt under 6 minuter. Vid testets slut mättes maximal gångsträcka, puls och ansträngningsgrad. Testet för att bestämma maximal syreupptagningsförmåga utfördes med löpning på ett motordrivet rullband. Under testets första 2 minuter var lutningen på bandet 1 grad. Därefter höjdes lutningen med 1 grad per minut till dess att testpersonen nått sin maximala syreupptagningförmåga, varpå testet avbryts. Var 15 sekund registrerades testpersonens hjärtfrekvens, VO2 (l/min), VCO2 (l/min), kroppsvikt/min (ml/kg/min) med hjälp av ett syreupptagningsmätningssystem. Resultat Korrelationen mellan gångsträcka och VO2max för samtliga 45st testpersoner i studien visade r = 0.16. Detta innebär att korrelationen mellan GIH:s Gångtest och maximal syreupptagningsförmåga inte är nämnvärd för detta material på friska fysiskt aktiva unga vuxna mellan 19-28 år. GIH:s Gångtest är således inte ett alternativ för att predicera syreupptagningsförmågan hos denna målgrupp. Slutsats GIH:s Gångtest uppvisar en mycket svag korrelation med bestämd maximal syreupptagningsförmåga, för friska fysiskt aktiva unga vuxna. / Abstract Aim The aim was to correlate the result on GIH:s walk test with the determined maximum oxygen uptake (VO2max). The question was if GIH:s walk test can be used as an alternative to estimate maximum oxygen uptake in healthy physical active young adults? Methods In this study 45 physical active persons (26 women and 19 men) at the age of 19-28 years participated. The two tests that have been carried out are GIH:s walk test ( a 6-minute walk test) and determined maximum oxygen uptake during running on a treadmill. GIH:s walk test is a shuttle test in which the participant (P) walks a 50 meters long distance back and forth between two cones. P shall walk this distance as many times as possible during 6 minutes. At the end of the test, maximum walk distance, pulse and rank of effort were measured. The test to determine maximum oxygen uptake was performed running on a treadmill. During the first 2 minutes the treadmill was elevated 1 degree. The elevation increased 1 degree every minute until the participant reached her maximum oxygen uptake, whereupon the test was interrupted. Every 15 second the participants heart rate, VO2 (l/min), VCO2 (l/min), bodyweight/min (ml/kg/min) was registered by means of an online system. Results The correlation coefficient between walked distance and VO2max for all 45 participants in this study was 0.16. This means that the correlation between GIH:s walk test and maximum oxygen uptake is very weak in the present material of healthy physical active young adults between 19-28 years. Thus GIH:s walk test is not an alternative to use for determination of maximum oxygen uptake capacity in this group of persons.  Conclusion GIH:s walk test prove to have a weak correlation with maximum oxygen uptake, for healthy physical active younger adults.

The diploma thesis is focused on the comparison of goodwill values of two construction companies. The theoretical part describes the basic knowledge and principles they are required to terminated the value of goodwill. Furthermore, terms such as marketing planning and questionnaire creation are explained. In the practical part, selected methods are used to terminate the value of goodwill. Subsequently, five questions are set and the questions are tested. Based on the analysis results is proposed marketing strategy at the end of the thesis.

Diffusion and random walks have been studied for more than 100 years. However, there are still details in the methodology that are overlooked, and more information can be extracted from the typical data that is studied. In this thesis, I simulate random walks on two dimensional lattices with immobile obstacles configured in a variety of ways: periodic, random, and "Fuzzy" (a cross intermediate state of disorder between periodic and random). The primary goal is to develop a deeper understanding of "Fuzzy" systems by designing different ways of generating tunable disorder. An example of this is the universal Fz parameter that we developed to unify the natural disorder parameters of the various disorder generation methods we developed. Often times the importance of analysing the transient/anomalous regime with more precision and consistency is overlooked. In our work, we expand on random walk dynamics by applying non-standard probabilities, and justify our choice analytically and through a comparison of results. Furthermore we discuss how the transient regime should be analyzed so that there is consistency in the field. Other than discussing semantics of algorithms and analysis, we study the connection between the transient regime and the steady-state. We introduce two measures of the width of the transient/anomalous regime, and compare them to the crossover time. Using the width of the transient/anomalous regime we are able to provide an estimate of the steady-state diffusion coefficient without access to the steady-state simulation data.

Part I: The Theory of Brownian Vacancy Driven Walk We analyze the lattice walk performed by a tagged member of an infinite 'sea' of particles filling a d-dimensional lattice, in the presence of a single vacancy. The vacancy is allowed to be occupied with probability 1/2d by any of its 2d nearest neighbors, so that it executes a Brownian walk. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. Thus, the tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a random walk "driven" by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after n-steps of the vacancy, are derived. Neither is a Gaussian! We also show that the only nontrivial dimension where the walk is recurrent is d=2. As an application, we compute the expected energy shift caused by a Brownian vacancy in a model for an extreme anisotropic binary alloy. In the last chapter we present a Monte-Carlo study and a mean-field analysis for interface erosion caused by mobile vacancies. Part II: One-Dimensional Periodic Hopping Models with Broken Translational Invariance.Case of a Mobile Directional Impurity We study a random walk on a one-dimensional periodic lattice with arbitrary hopping rates. Further, the lattice contains a single mobile, directional impurity (defect bond), across which the rate is fixed at another arbitrary value. Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. Analytic solution for the distributions in the steady state limit is obtained. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. As an application, we extend the Duke-Rubinstein reputation model of gel electrophoresis to include polymers with impurities and give the exact distribution of the steady state. / Ph. D.

Rugged terrains, including much of the earth's surface, other planets, and many man-made structures, are inaccessible to wheeled and tracked vehicles. This has inspired research into legged vehicles. Prior to the research described here, virtually all legged vehicle designs relied on the concept of mounting actuated leg-type mechanisms onto a single rigid frame or chassis. This dissertation research explores and advances a novel vehicle concept that uses passive legs attached to an actuated multibody structure. This new vehicle moves only its actuated body trunk to achieve locomotion; thus moving in a manner similar to that used by insect larvae known as caterpillars. The passive-legged design is termed a "crawling" vehicle, to differentiate it from "walking" vehicles, which have powered legs. A conceptual design for the proposed vehicle was developed using insights from observations of caterpillar specimen geometry, gaits, leg trajectories, and ranges of motion. The flexible, segmented body of the robot is realized using a series of actuated truss-like mechanisms, resulting in a configuration similar to the body structure of caterpillars. A computer simulation was developed to verify the concept and to assist in creating future designs. This simulation includes a parametric model of the robot structure, an efficient kinematics model, a motion programming method based on six-dimensional parametric cubic trajectories, static stability analysis, actuator velocity and acceleration analysis, wire-frame animations, and rendering, thus providing synthesis and analysis tools for this new class of vehicle. Results of this work show that by using properly designed Stewart-Gough platform mechanisms for the vehicle multibody structure, a range of motion very similar to that of caterpillars is achievable. Simulation tests showed that imitating the caterpillars" primary gait (or stepping sequence) yields superior speed and efficiency, with little reduction of stability, when compared to a simpler, more obvious gait. With proper controls, this crawling vehicle will, like its biological counterpart, be intrinsically stable and have excellent maneuverability over rough terrain. The crawling vehicle is shown to be a viable legged locomotion system that may prove to have superior rough terrain mobility to all previous types of man-made land vehicles. / Ph. D.

Organisms have movements that are usually modeled by particles’ random walks. Under some mathematical technical assumptions the movements are described by diffusion equations. However, empirical data often show that the movements are not simple random walks. Instead, they are correlated random walks and are described by telegraph equations. This thesis considers telegraph equations with and without bias corresponding to correlated random walks with and without bias. Analytical solutions to the equations with absorbing boundary conditions and their mean passage times are obtained. Numerical simulations of the corresponding correlated random walks are also performed. The simulation results show that the solutions are approximated very well by the corresponding correlated random walks and the mean first passage times are highly consistent with those from simulations on the corresponding random walks. This suggests that telegraph equations can be a good model for organisms with the movement pattern of correlated random walks. Furthermore, utilizing the consistency of mean first passage times, we can estimate the parameters of telegraph equations through the mean first passage time, which can be estimated through experimental observation. This provides biologists an easy way to obtain parameter values. Finally, this thesis analyzes the velocity distribution and correlations of movement steps of amoebas, leaving fitting the movement data to telegraph equations as future work.

Today, there is a large amount of assets which are offered to investors, and if we consider the possibility of relocating the investor's funds, we come to a very complicated problem, which this thesis aims to cover. The main objective is to explore the basics of the portfolio theory and its real usage in practice. Emphasis is put on the periodic re-optimizing of the investor's portfolio and getting the answer to the question of whether such conduct is more successful than the standard and investment in equity indices. The theoretical part summarizes the currently used approaches to optimization which are tested in the practical part on real data and evaluated.