Proteins in nature fold to one dominant native structure. Despite being a heavily studied field, predicting the native structure from the amino acid sequence and modeling the folding process can still be considered unsolved problems. In this thesis I present a new approach to this problem with methods borrowed from theoretical physics. In the first part I show how it is possible to use a discrete Frenet frame to define the discrete curvature and torsion of the main chain of the protein. This method is then extended to the side chains as well. In particular I show how to use the discrete Frenet frame to produce a statistical distribution of angles that works in similar fashion as the commonly used Ramachandran plot and side chain rotamers. The discrete Frenet frame displays a gauge symmetry, in the choice of basis vectors on the normal plane, that is reminiscent of features of Abelian-Higgs theory. In the second part of the thesis I show how this similarity with Abelian-Higgs theory can be translated into an effective energy for a protein. The loops of the proteins are shown to correspond to solitons so that the whole protein can be constructed by gluing together any number of solitons. I present results of simulating proteins by minimizing the energy, starting from a real line or straight helix, where the correct native fold is attained. Finally the model is shown to display the same phase structure as real proteins.

“In many interesting papers on discrete velocity models (DVMs), authors postulate from the beginning that the finite velocity space with "good" properties is given and only after this step they study the Discrete Boltzmann Equation. Contrary to this approach, our aim is not to study the equation, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. Due to the velocity discretization it is well known that it is possible to have DVMs with "spurious" summational invariants (conservation laws which are not linear combinations of physical invariants). Our purpose is to give a method for constructing normal models (without spurious invariants) and to classify all normal plane models with small number of velocities (which usually appear in applications). On the first step we describe DKMs as algebraic systems. We introduce for this an abstract discrete model (ADM) which is defined by a matrix of reactions (the same as for the concrete model). This matrix contains as rows all vectors of reactions describing the "jump" from a pre-reaction state to a new reaction state. The conservation laws corresponding to the many-particle system are uniquely determined by the ADM and do not depend on the concrete realization. We find the restrictions on ADM and then we give a general method of constructing concrete normal models (using the results on ADMs). Having the general algorithm, we consider in more detail, the particular cases of models with mass and momentum conservation (inelastic lattice gases with pair collisions) and models with mass, momentum and energy conservation (elastic lattice gases with pair collisions).”

Classical kinetic theory of gases is based on the Boltzmann equation (BE) which describes the evolution of a system of particles undergoing collisions preserving mass, momentum and energy. Discretization methods have been developed on the idea of replacing the original BE by a finite set of nonlinear hyperbolic PDEs corresponding to the densities linked to a suitable finite set of velocities. One open problem related to the discrete BE is the construction of normal (fulfilling only physical conservation laws) discrete velocity models (DVMs). In many papers on DVMs, authors postulate from the beginning that a finite velocity space with such "good" properties is given, and after this step, they study the discrete BE. Our aim is not to study the equations for DVMs, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions. We start by introducing the most general class of discrete kinetic models (DKMs) and then, develop a general method for the construction and classification of normal DKMs. We apply this method in the particular cases of DVMs of the inelastic BE (where we show that all normal models can be explicitly described) and elastic BE (where we give a complete classification of normal models up to 9 velocities). Using our general approach to DKMs and our results on normal DVMs for a single gas, we develop a method for the construction of the most natural (from physical point of view) subclass of normal DVMs for binary gas mixtures. We call such models supernormal models (SNMs). We apply this method and obtain SNMs with up to 20 velocities and their spectrum of mass ratio. Finally, we develop a new method that can lead, by symmetric transformations, from a given normal DVM to extended normal DVMs. Many new normal models can be constructed in this way, and we give some examples to illustrate this.

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This thesis consists of the four papers listed below and a survey of the research area. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andr´en: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Papers I, III and IV are all concerned with a conjecture by Häggkvist saying that there is a constant c such that for any positive integer n, if m ≤ cn, then for every n × n array A of subsets of {1, . . . , n} such that no cell contains a set of size greater than m, and none of the elements 1, . . . , n belongs to more than m of the sets in any row or any column of A, there is a Latin square L on the symbols 1, . . . , n such that there is no cell in L that contains a symbol that belongs to the set in the corresponding cell of A. Such a Latin square is said to avoid A. In Paper I, the conjecture is proved in the special case of order n = 2k . Paper III improves on the techniques of Paper I, expanding the proof to cover all arrays of even order. Finally, in Paper IV, similar methods are used together with a recoloring theorem to prove the conjecture for all orders. Paper II considers another aspect of the problem by asking to what extent way a deterministic result concerning the existence of Latin squares that avoid certain arrays can be used when the sets in the array are assigned randomly. / Denna avhandling inehåller de fyra nedan uppräknade artiklarna, samt en översikt av forskningsområdet. I Lina J. Andrén: Avoiding (m, m, m)-arrays of order n = 2k II Lina J. Andrén: Avoidability of random arrays III Lina J. Andrén: Avoidability by Latin squares of arrays with even order IV Lina J. Andrén, Carl Johan Casselgren and Lars-Daniel Öhman: Avoiding arrays of odd order by Latin squares Artikel I, III och IV behandlar en förmodan av Häggkvist, som säger att det finns en konstant c sådan att för varje positivt heltal n gäller att om m ≤ cn så finns för varje n × n array A av delmängder till {1, . . . ,n} sådan att ingen cell i A i innehåller fler än m symboler, och ingen symbol förekommer i fler än m celler i någon av raderna eller kolumnerna, så finns en latinsk kvadrat L sådan att ingen cell i L innehåller en symbol som förekommer i motsvarande cell i A. En sådan latinsk kvadrat sägs undvika A. Artikel I innehåller ett bevis av förmodan i specialfallet n = 2k. Artikel III använder och utökar metoderna i Artikel I till ett bevis av förmodan för alla latinska kvadrater av jämn ordning. Förmodan visas slutligen för samtliga ordningar i Artikel IV, där bevismetoden liknar den som finns i i Artikel I och III tillsammans med en omfärgningssats. Artikel II behandlar en annan aspekt av problemet genom att undersöka vad ett deterministiskt resultat om existens av latinska kvadrater som undviker en viss typ av array säger om arrayer där mängderna tilldelas slumpmässigt.

In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs.

This study considered using a relatively new method to study soil-tool wear which could drastically reduce the time and associated costs of traditional wear studies. The goal was to utilize discrete element method (DEM) simulations to recreate the results of a circular soil bin test in order to develop a relationship that could be used to predict wear under different conditions. Through the application of DEM, simulations could be used to study different materials or designs intended to result in improved wear performance.<p> Three replications of aluminum cylindrical bars were worn during 400 km of travel in a circular soil bin. Wear was quantified by measuring the change in radius of the cylinders at 18-degree intervals around their circumference. Mass data were also obtained to provide an overall average of wear occurring on the bar and to validate the radii measurements.<p> The DEM simulations were executed using EDEM software. Conditions present in the physical soil bin trials were simulated by recreating components in the soil bin and incorporating soil properties that were directly measured, using representative soil samples. Forces exerted on the bar by the soil and the relative velocities between the soil and tool were used to generate a relationship to predict wear of the bar. The wear equation was verified using a portion of the experimental data from the soil bin.<p> The wear model showed promise in predicting the amount of wear recorded in the soil bin through the application of DEM-predicted compressive forces and relative velocities between the tool and soil particles. The Archard equation for wear was modified to create a non-linear equation. Plotting the measured wear against the wear predicted from the fitted equation produced a trendline with a slope of 0.65. Although a perfect correlation would have produced a slope of 1, the model was able to predict a large portion of the wear that occurred. Refinement of the model could further be achieved with changes in the design of the geometry used in the simulation and through verification of force predictions with experimental data. Because of the variable nature of wear, additional replications of tools in the soil bin would have increased the number of data points available to create the model and reduced the impact of outlying data. With these recommended improvements, the wear model has the ability to very accurately predict the wear of a cylindrical bar.

There is increasing pressure from animal rights organizations (AROs) on restaurant chains, food retailers, and meat processors to implement more stringent farm animal welfare (FAW) requirements for their suppliers. In the United States, AROs have recently initiated successful ballots to phase out confinement practices in several states. In Canada AROs have been pressuring both public and private sector stakeholders to improve FAW. Are FAW issues, however, paramount in the minds of Canadian consumers? Is the demand for more stringent FAW protocols primarily determined by a subset of consumers with very strong preferences or does it signal a more fundamental underlying change in consumer and societal preferences? Given the credence nature of FAW, who do consumers trust (i.e., government vs. private industry vs. independent third parties) in the market place for the provision of FAW quality assurances? What are the determinants of trust in these organizations for providing accurate information about animal welfare?<p> In order to answer these questions, a stated preference consumer survey encompassing FAW issues specific to the Canadian pork sector was tested on two samples of consumers in summer 2008, namely: a general population sample (GPS) across Canada and a sample of AROs members. Consumers participated in a purchase experiment where they had to chose between pork chops characterized by combinations of different levels of FAW attributes (i.e., housing system, gestation stalls, and use of antibiotics), quality verifying organization, and price. Multinomial Logit and Latent Class Logit Models were used to analyse the survey data.<p> Surprisingly, outdoor system does not seem to resonate well with Canadians, as both the GPS and the members of the AROs discounted this attribute. As expected, the AROs members have much stronger preferences for the other FAW attributes than have consumers in the GPS. Nevertheless, significant heterogeneity exists within consumer preferences. Five classes of consumers were identified in the GPS with respect to their preferences for FAW. At one end of the spectrum are the FAW sensitive consumers (12.3%) that have higher willingness-to-pay (WTP) for FAW, while at the other end of the spectrum Price Conscious consumers (18.3%) do not exhibit any WTP for FAW. The other three classes (69.4%) comprise respondents with mixed perceptions regarding FAW. Government and Third Party verification of FAW quality assurances had the strongest influence on consumers preferences in both samples. As well, scientific experts in FAW along with the above two organizations are the most credible in providing information about the welfare of pigs. The extent to which these organizations are knowledgeable about the welfare of pigs is the most important factor enhancing consumers trust. Results from this study suggest that there are potential marketing opportunities for pork chops sourced from pigs raised on farms where sows are kept in groups, and where credible quality assurances can be established, that private industry could consider. As well, the results suggest that consumers would derive benefits from the government taking a more active role with respect to validating FAW quality assurances.

Innovation diffusion models have been studied extensively to forecast and explain the adoption process for new products or services. These models are often formulated using one of two approaches: The first, and most common is a macro-level approach that aggregates much of the market behaviour. An advantage of this method is that forecasts and other analyses may be performed with the necessity of estimating few parameters. The second is a micro-level approach that aims to utilize microeconomic information pertaining to the potential market and the innovation. The advantage of this methodology is that analyses allow for a direct understanding of how potential customers view the innovation. Nevertheless, when individuals are making adoption decisions, the reality of the situation is that the process consists of at least two stages: First, a potential adopter must become aware of the innovation; and second the aware individual must decide to adopt. Researchers, have studied multi-stage diffusion processes in the past, however a majority of these works employ a macro-level approach to model market flows. As a result, a direct understanding of how individuals value the innovation is lacking, making it impossible to utilize this information to model realistic word-of-mouth behaviour and other network dynamics. Thus, we propose a two-stage integrated model that utilizes the benefits of both the macro- and micro-level approaches. In the first stage, potential customers become aware of the innovation, which requires no decision making by the individual. As a result, we employ a macro-level diffusion process to describe the first stage. However, in the second stage potential customers decide whether to adopt the innovation or not, and we utilize a micro-level methodology to model this. We further extend the application to include forward looking behaviour, heterogeneous adopters and segmented Bayesian learning, and utilize the adopter's satisfaction levels to describe biasing and word-of-mouth behaviour. We apply the proposed model to Canadian colour-TV data, and cross-validation results suggest that the new model has excellent predictive capabilities. We also apply the two-stage model to early U.S. hybrid-electric vehicle data and results provide insightful managerial observations.