Nonionic surfactants are commonly used to stabilize proteins during upstream and downstream processing and drug formulation. Surfactants stabilize the proteins through two major mechanisms: (i) their preferential location at nearby interfaces, in this way precluding protein adsorption; and/or (ii) their association with protein into "complexes" that prevent proteins from interacting with surfaces as well as each other. In general, both mechanisms must be at play for effective protein stabilization against aggregation and activity loss, but selection of surfactants for protein stabilization currently is not made with benefit of any quantitative, predictive information to ensure that this requirement is met. In certain circumstances the kinetics of surface tension depression (by surfactant) in protein-surfactant mixtures has been observed to be greater than that recorded for surfactant alone at the same concentration. We compared surface tension depression by poloxamer 188 (Pluronic�� F68), polysorbate 80 (PS 80), and polysorbate 20 (PS 20) in the presence and absence of lysozyme and recombinant protein, at different surfactant concentrations and temperatures. The kinetic results were interpreted with reference to a mechanism for surfactant adsorption governed by the formation of a rate-limiting structural intermediate (i.e., an "activated complex") comprised of surfactant aggregates and protein. The presence of lysozyme was seen to increase the rate of surfactant adsorption in relation to surfactant acting alone at the same concentrations for the polysorbates while less of an effect was seen for Pluronic�� F68. However, the addition of salt was observed to accelerate the surface tension depression of Pluronic�� F68 in the presence of lysozyme. The addition of a more hydrophobic, surface active protein (Amgen recombinant protein) in place of lysozyme resulted in greater enhancement of surfactant adsorption than that recorded in the presence of lysozyme. A simple thermodynamic analysis indicated the presence of protein caused a reduction in ���G for the surfactant adsorption process, with this reduction deriving entirely from a reduction in ���H. We suggest that protein accelerates the adsorption of these surfactants by disrupting their self associations, increasing the concentration of surfactant monomers near the interface. Based on these air-water tensiometry results, it is fair to expect that accelerated surfactant adsorption in the presence of protein (observed with PS 20 and PS 80) will occur with surfactants that stabilize protein mainly by their own adsorption at interfaces, and that the absence of accelerated surfactant adsorption (observed with F68) will be observed with surfactants that form stable surfactant-protein associations. Optical waveguide lightmode spectroscopy was used to test this expectation. Adsorption kinetics were recorded for surfactants (PS 20, PS 80, or F68) and protein (lysozyme or Amgen recombinant protein) at a hydrophilic solid (SiO���-TiO���) surface. Experiments were performed in sequential and competitive adsorption modes, enabling the adsorption kinetic patterns to be interpreted in a fashion revealing the dominant mode of surfactant-mediated stabilization of protein in each case. Kinetic results confirmed predictions based on our earlier quantitative analysis of protein effects on surface tension depression by surfactants. In particular, PS 20 and PS 80 are able to inhibit protein adsorption only by their preferential location at the interface, and not by formation of less surface active, protein-surfactant complexes. On the other hand, F68 is able to inhibit protein adsorption by formation of protein-surfactant complexes, and not by its preferential location at the interface. / Graduation date: 2013 / Access restricted to the OSU Community at author's request from Sept. 24, 2012 - Feb. 24, 2013.

Molecular computations based on quantum mechanics and statistical mechanics have been applied to the understanding and quantification of processes leading to the degradation of therapeutic proteins. In particular, we focus on oxidation and aggregation. Specifically, two reactions, hydrogen transfer of hydrogen peroxide to form water oxide and the oxidation of dimethyl sulfide (DMS) by hydrogen peroxide to form dimethyl sulfoxide, were studied as models of these processes in general. Reaction barriers of the hydrogen transfer of H₂O₂ are in average of 10 kcal/mol or higher than the oxidation of DMS. Therefore, a two step oxidation mechanism in which the transfer of hydrogen atom occurs first to form water oxide and the transfer of oxygen to substrate occurs as the second step, is unlikely to be correct. Our proposed oxidation mechanism does not suggest a pH dependence of oxidation rate within a moderate range around neutral pH (i.e. under conditions in which hydronium and hydroxide ions do not participate directly in the reaction), and it agrees with experimental observations over moderate pH values. In the field of aggregation, we have developed a relatively simple approach for computing the change in chemical potential of a protein upon addition of an excipient (cosolute) to the protein solution. We have also developed a general approach to the design of excipients to prevent aggregation and are currently testing it experimentally. / Singapore-MIT Alliance (SMA)

In this dissertation we use Dynamic Stochastic General Equilibrium DSGE) models to explain empirical regularities and policy implications related to (1) durable goods, interest rates and small open economy business cycles, (2) Terms-of-Trade (ToT) and economic fluctuations in small open economies and (3) Budget Stabilization Funds (BSFs) and States’ business cycles. In the first essay, we document that durable spending in developed small open economies constitutes a large share of their total income. Their spending is highly procyclical, sensitive to interest rates, and leads the business cycle. We address these regularities with a RBC model with durable goods. The model successfully replicates the observed business cycle regularities and explains many anomalies not explained in the existing literature. It also emphasizes the role of interest rates uncertainty in explaining the dynamics of the small open economies. The second essay addresses the impacts of the ToT fluctuation on the business cycles of various small open economies. We argue that differences in the degree of durability in domestic production and imports may make these economies more or less sensitive to an identical ToT shock. We found that economies with higher durability usually enjoy more stable business cycle comparing with economies with lower degree of durability. Differences in the persistence of the ToT do affect the dynamic of the external accounts but it cannot explain the observed differences business cycles across small open economies. In the last essay, we evaluate the economic impacts of the Budget Stabilization Funds (BSF) on State-level business cycles. We lay out a State economy RBC model in which a State’s government applies a designated saving rule consistent with households’ optimization. Given the suggested rule we find that the BDFs become a significant automatic stabilizer. It is not only mitigates the procyclicality of the government spending but it also smooth the State’s business cycle.

Thesis (doctoral) - Freie Universität, Berlin, 2004. / "with 12 figures and tables". Includes bibliographical references ( p. [143]-155).

<p>Aim</p><p>The aim of this study was to evaluate the activity recorded with electromyography (EMG) fine-wire electrodes, in transversus abdominis (TrA) and rectus abdominis (RA) while performing various stabilization exercises, and to investigate how the level of activation was affected by specific instructions</p><p>Method</p><p>Ten physically active women (27.1 ± 5.5year, 1.74 ± 0.05 m, 67.1 ± 8.6 kg) performed six different stabilization exercises (four lying supine with bent knees and hips and two in four point kneeling). They performed two sets of exercises, the first without and the second with specific instructions. The specific instruction was “abdominal hollowing to activate” TrA. The fine-wire electrodes were inserted bilateral into TrA and RA with an injection needle with guidance from an ultrasound. EMG was recorded during the middle second (while the subjects were asked to withhold the final position) and data was normalized to maximal voluntary contraction (MVC) and value at rest.</p><p>Results</p><p>The effects from instructions were significant while looking upon muscle and exercise (p<0,05). All exercises but exercise number 4 (unilateral bridgening) were significant effected by instructions in TrA, but none of the exercises were effected in RA (p>0,05). The mean of the activity in TrA varied without instructions between 2,9% (± 4,4) to 39,5 % (± 20,0) and with instructions 15,2 % (± 14,7) to 45,6 % (± 23,5). In RA the mean of the activity varied without instructions between 0,3% (± 0,8) to 9,8 % (± 27,4) and with instructions between 2.4 % (± 2,9) to 11,3% (± 28,5).</p><p>Conclusion</p><p>It is possible to selectively increase the activity in TrA in the majority of selected stabilization exercises with supine position with bent knees and hips, and in four point kneeling.</p> / <p>Syfte</p><p>Syftet med denna studie var att med intramuskulär elektromyografi utvärdera aktiveringsgraden i transversus abdominis (TrA) och rectus abdominis (RA) vid utförandet av olika stabiliseringsövningar samt att undersöka hur graden av aktivering påverkas av specifika instruktioner.</p><p>Metod: Tio kvinnliga, fysiskt aktiva personer (27.1 ± 5.5 år, 1.74 ± 0.05 m, 67.1 ± 8.6 kg) fick utföra sex olika stabiliseringsövningar (fyra i ryggliggande och två i knäfyrfota) med tre repetitioner på varje övning. Försökspersonen (fp) fick utföra övningarna i två omgångar. Omgång ett utan och omgång två med specifik instruktion, den specifika instruktionen var; ”dra in den nedre delen av magen, den under naveln” (abdominal hollowing) för att aktivera Tr A. Intramuskulära trådelektroder fördes in bilateralt i TrA och RA med hjälp av en injektionsnål under guidning av ultraljud. Elektromyografi (EMG) mättes under den mittersta sekunden av övningen (i kvarhållen slutposition) och normaliserades mot maximal viljemässig kontraktion (MVC) och vilovärde.</p><p>Resultat: Effekten av instruktion var signifikant i betraktandet av muskel och övning (p<0,05). I samtliga övningar utom övning 4 (unilateralt bäckenlyft) påverkade instruktioner signifikant muskelaktiviteten i TrA (p<0,05), men inte i någon av övningarna i RA (p>0,05).</p><p>Medelvärdet av den normaliserade EMG-aktiviteten i TrA varierade i övning 1 till 6 utan instruktioner mellan 2,9 % (± 4,4) och 39,5 % (± 20,0). Med instruktion varierade den procentuella aktiviteten i TrA mellan 15,2 % (± 14,7) och 45,6 % (± 23,5). I RA varierade medelvärdet utan instruktioner mellan 0,3% (± 0,8) till 9.8 % (± 27,4) och med instruktioner 2.4 % (± 2,9) till 11,3% (± 28.5).</p><p>Slutsats; Det går att med hjälp av instruktioner selektivt öka aktiveringsgraden i TrA i majoriteten av valda stabiliseringsövningar i krokligg och knäfyrfota.</p>

Aim The aim of this study was to evaluate the activity recorded with electromyography (EMG) fine-wire electrodes, in transversus abdominis (TrA) and rectus abdominis (RA) while performing various stabilization exercises, and to investigate how the level of activation was affected by specific instructions Method Ten physically active women (27.1 ± 5.5year, 1.74 ± 0.05 m, 67.1 ± 8.6 kg) performed six different stabilization exercises (four lying supine with bent knees and hips and two in four point kneeling). They performed two sets of exercises, the first without and the second with specific instructions. The specific instruction was “abdominal hollowing to activate” TrA. The fine-wire electrodes were inserted bilateral into TrA and RA with an injection needle with guidance from an ultrasound. EMG was recorded during the middle second (while the subjects were asked to withhold the final position) and data was normalized to maximal voluntary contraction (MVC) and value at rest. Results The effects from instructions were significant while looking upon muscle and exercise (p&lt;0,05). All exercises but exercise number 4 (unilateral bridgening) were significant effected by instructions in TrA, but none of the exercises were effected in RA (p&gt;0,05). The mean of the activity in TrA varied without instructions between 2,9% (± 4,4) to 39,5 % (± 20,0) and with instructions 15,2 % (± 14,7) to 45,6 % (± 23,5). In RA the mean of the activity varied without instructions between 0,3% (± 0,8) to 9,8 % (± 27,4) and with instructions between 2.4 % (± 2,9) to 11,3% (± 28,5). Conclusion It is possible to selectively increase the activity in TrA in the majority of selected stabilization exercises with supine position with bent knees and hips, and in four point kneeling. / Syfte Syftet med denna studie var att med intramuskulär elektromyografi utvärdera aktiveringsgraden i transversus abdominis (TrA) och rectus abdominis (RA) vid utförandet av olika stabiliseringsövningar samt att undersöka hur graden av aktivering påverkas av specifika instruktioner. Metod: Tio kvinnliga, fysiskt aktiva personer (27.1 ± 5.5 år, 1.74 ± 0.05 m, 67.1 ± 8.6 kg) fick utföra sex olika stabiliseringsövningar (fyra i ryggliggande och två i knäfyrfota) med tre repetitioner på varje övning. Försökspersonen (fp) fick utföra övningarna i två omgångar. Omgång ett utan och omgång två med specifik instruktion, den specifika instruktionen var; ”dra in den nedre delen av magen, den under naveln” (abdominal hollowing) för att aktivera Tr A. Intramuskulära trådelektroder fördes in bilateralt i TrA och RA med hjälp av en injektionsnål under guidning av ultraljud. Elektromyografi (EMG) mättes under den mittersta sekunden av övningen (i kvarhållen slutposition) och normaliserades mot maximal viljemässig kontraktion (MVC) och vilovärde. Resultat: Effekten av instruktion var signifikant i betraktandet av muskel och övning (p&lt;0,05). I samtliga övningar utom övning 4 (unilateralt bäckenlyft) påverkade instruktioner signifikant muskelaktiviteten i TrA (p&lt;0,05), men inte i någon av övningarna i RA (p&gt;0,05). Medelvärdet av den normaliserade EMG-aktiviteten i TrA varierade i övning 1 till 6 utan instruktioner mellan 2,9 % (± 4,4) och 39,5 % (± 20,0). Med instruktion varierade den procentuella aktiviteten i TrA mellan 15,2 % (± 14,7) och 45,6 % (± 23,5). I RA varierade medelvärdet utan instruktioner mellan 0,3% (± 0,8) till 9.8 % (± 27,4) och med instruktioner 2.4 % (± 2,9) till 11,3% (± 28.5). Slutsats; Det går att med hjälp av instruktioner selektivt öka aktiveringsgraden i TrA i majoriteten av valda stabiliseringsövningar i krokligg och knäfyrfota.

Saskatchewan Ministry of Highways and Infrastructure (MHI) is responsible for maintaining approximately 26,100 km of two lane equivalent highways network. Most highways in Saskatchewan are constructed primarily of granular materials. Granular materials serve various purposes in a pavement structure. In particular, granular materials distribute stress within the road structure and reduce the stress applied to the subgrade. Granular materials also mitigate pumping of subgrade fines into surfacing materials, as well as provide drainage for the pavement structure.<p>As a result of the rapid deterioration of roadways and the increasing highway traffic, a significant portion of the Saskatchewan highway system is in need of rehabilitation in the next couple of decades. However, increasing costs associated with road construction as well as budget constraints render many conventional rehabilitation solutions untenable in many applications. In addition, the depletion of quality aggregate also exists in many areas of Saskatchewan. Given that much of Saskatchewan granular pavement system will be in need of strengthening in the next few decades, there is a need to apply new cost-effective and aggregate-preserving pavement rehabilitation technologies such as cold in-place recycling and base strengthening.<p>The goal of this research is to improve the engineering design and performance of recycled and stabilized granular base systems under Saskatchewan field state conditions. The specific objectives of this research are to characterize the conventional laboratory behaviour, moisture sensitivity, and mechanistic behaviour of various granular base strengthening systems in the laboratory, to characterize the structural responses of various granular base strengthening systems in the field, and to evaluate the pavement thickness design and responses of various granular base pavement structures.<p>This research is based on a cold in-place recycling and base stabilization project undertaken by Saskatchewan MHI in fall 2006. Control Section (C.S.) 15-11 between km 5.0 and km 8.0 was selected as a typical thin granular pavement under primary weight loadings that required strengthening. Unstabilized granular base, cement stabilized granular base, and cement with asphalt emulsion stabilized granular base were constructed and evaluated in this research. Materials employed on C.S. 15-11 were sampled and prepared for the various laboratory tests performed in this research. Conventional tests performed included sieve analysis, Atterberg limits, sand equivalent, standard proctor compaction, and California bearing ratio strength and swell test. Advanced mechanistic and moisture sensitivity testing included indirect tensile strength, moisture capillary rise and surface conductivity, unconfined compressive strength, and rapid triaxial frequency sweep testing.<p>The cement and cement with emulsion asphalt stabilization of the granular base were found to improve the conventional, mechanical and moisture susceptibility properties of in situ C.S. 15-11 granular base materials. The cement stabilization applied on C.S. 15-11 provided a high degree of improvement relative to the cement with emulsion stabilization. The cement stabilization was found to be relatively easy to apply in construction, whereas the cement with emulsion stabilization was more difficult, particularly due to the problems associated with cold temperatures during late season construction.<p>The rapid triaxial tester (RaTT) was found to be a practical and useful apparatus to characterize the mechanistic constitutive behaviours of granular materials. The C.S. 15- 11 in situ unstabilized base was found to have the poorest mechanistic behaviour among all three granular bases on C.S. 15-11, as expected. Cement stabilization improved the mechanistic behaviour of the in situ material significantly by providing the highest mean dynamic modulus, lowest mean Poissons ratio, lowest mean radial microstrain, and the lowest mean phase angle. The cement with emulsion asphalt stabilization also provided a considerable improvement on mechanistic behaviour of C.S. 15-11 granular base materials. However, the degree of improvement was less than the cement stabilization system.<p>Non-destructive falling weight deflection measurements taken across the field test sections showed that the stabilization systems yielded a significant improvement of primary structural response profiles across the C.S. 15-11 test sections after stabilization. The cement stabilization system was found to yield the most significant structural improvements among all the test sections constructed on the C.S. 15-11. The deflection measurements taken in 2007 after hot mix asphalt paving further identified that the unstabilized system is more sensitive to the freeze-thaw effects relative to cement stabilization and cement with emulsion stabilization systems.<p> This research also showed that the Saskatchewan MHI structural design system is not applicable to the design of stabilized granular base systems. Evaluation of the thickness design for C.S. 15-11 showed the unstabilized and the cement with asphalt emulsion stabilized test section met the criterion of fatigue cracking, but failed to meet the criterion of structural rutting in MHI design system. However, the cement stabilized section met both fatigue cracking and rutting criteria. The structural evaluation revealed that mechanistic pavement response analysis and validation are necessary in the thickness design of stabilized granular systems such as C.S. 15-11, where traditional MHI design system is not applicable. This research employed finite element modeling and linear elastic pavement modeling software to determine the maximum shear stresses within granular base under typical Saskatchewan stress state conditions. The maximum shear stress values were found to locate on top of granular base courses under the applied circular loading edges ranging from 177 kPa to 254 kPa. These maximum shear stresses within the C.S. 15-11 test section granular base courses under field stress states were compared to maximum shear stresses occurring within samples measured by rapid triaxial testing performed in this research. The comparison showed that the ranges of shear stresses applied in the laboratory RaTT testing were close to shear stresses of granular bases in the field computed from modeling. Therefore, this research showed a good correlation of lab RaTT testing and field results for granular pavements.<p>In summary, this research met the objectives of mechanistically evaluating various granular base stabilization systems in Saskatchewan by means of various laboratory testing, non-destructive field testing, as well as mechanistic modeling and analysis. This research provided valuable data and showed considerable potential for improving design, construction, and QA/QC of conventional and stabilized granular base systems in Saskatchewan.

Forest soils with low bulk densities are often considered less susceptible to compaction than soils with higher bulk densities. The objective of this study was to determine if soil strength controlled the compression of soils with low bulk density. Four soils were selected for this evaluation. Three of these were andic soils with low bulk density and the fourth soil was a more dense, cohesive soil. Undisturbed samples of saturated and partly saturated soil were compressed in a one-dimensional consolidation test apparatus. Measurements with separate samples were at one of 7 normal stresses between 0.033 and 1.96 MPa. Shear strength of saturated soil was measured in direct shear tests. Primary consolidation of saturated soil was completed in less than one minute at all normal stresses. Shear stress and bulk density increased continuously during shear strain. The compression index of the cohesive soil was significantly larger (p<0.05) than that of the andic soils. The shear strength of andic soils (average cohesion intercept of 0.016 MPa and friction angle of 33.3°) was significantly higher (p<0.05) than the cohesive soil (cohesion intercept of 0.028 MPa and friction angle of 28.9°). When saturated, the cohesive soil was more compressible than the andic soils because of lower soil strength. A nonlinear model of soil compression was developed that accurately predicted the compressed density of saturated and partly saturated soil as a function of normal stress, initial bulk density of undisturbed samples, and degree of saturation. As degree of saturation decreased, the compressibility of the cohesive soil decreased more rapidly than it did for the andic soils. As a result, bulk density of dry cohesive soil increased less than it did for dry andic soils. Differences in the compressibility of soils were attributed to texture and clay mineralogy. The differences in the compressibility of these soils were much smaller than were the differences in bulk density. Decreasing water content affected the compressibility of the cohesive soil more than it affected the andic soils. Because soil strength controls the compressibility of these forest soils regardless of bulk density, it will also determine the susceptibility of soils to compaction by machines. / Graduation date: 1991

In this thesis, we address a variety of challenges for analysis and enhancement of Computational Video. We present novel post-processing methods to bridge the difference between professional and casually shot videos mostly seen on online sites. Our research presents solutions to three well-defined problems: (1) Video stabilization and rolling shutter removal in casually-shot, uncalibrated videos; (2) Content-aware video retargeting; and (3) spatio-temporal video segmentation to enable efficient video annotation. We showcase several real-world applications building on these techniques. We start by proposing a novel algorithm for video stabilization that generates stabilized videos by employing L1-optimal camera paths to remove undesirable motions. We compute camera paths that are optimally partitioned into constant, linear and parabolic segments mimicking the camera motions employed by professional cinematographers. To achieve this, we propose a linear programming framework to minimize the first, second, and third derivatives of the resulting camera path. Our method allows for video stabilization beyond conventional filtering, that only suppresses high frequency jitter. An additional challenge in videos shot from mobile phones are rolling shutter distortions. Modern CMOS cameras capture the frame one scanline at a time, which results in non-rigid image distortions such as shear and wobble. We propose a solution based on a novel mixture model of homographies parametrized by scanline blocks to correct these rolling shutter distortions. Our method does not rely on a-priori knowledge of the readout time nor requires prior camera calibration. Our novel video stabilization and calibration free rolling shutter removal have been deployed on YouTube where they have successfully stabilized millions of videos. We also discuss several extensions to the stabilization algorithm and present technical details behind the widely used YouTube Video Stabilizer. We address the challenge of changing the aspect ratio of videos, by proposing algorithms that retarget videos to fit the form factor of a given device without stretching or letter-boxing. Our approaches use all of the screen's pixels, while striving to deliver as much video-content of the original as possible. First, we introduce a new algorithm that uses discontinuous seam-carving in both space and time for resizing videos. Our algorithm relies on a novel appearance-based temporal coherence formulation that allows for frame-by-frame processing and results in temporally discontinuous seams, as opposed to geometrically smooth and continuous seams. Second, we present a technique, that builds on the above mentioned video stabilization approach. We effectively automate classical pan and scan techniques by smoothly guiding a virtual crop window via saliency constraints. Finally, we introduce an efficient and scalable technique for spatio-temporal segmentation of long video sequences using a hierarchical graph-based algorithm. We begin by over-segmenting a volumetric video graph into space-time regions grouped by appearance. We then construct a "region graph" over the obtained segmentation and iteratively repeat this process over multiple levels to create a tree of spatio-temporal segmentations. This hierarchical approach generates high quality segmentations, and allows subsequent applications to choose from varying levels of granularity. We demonstrate the use of spatio-temporal segmentation as users interact with the video, enabling efficient annotation of objects within the video.

In this thesis we investigate the problem of designing a control system for a modern bicycle so that the bicycle is stable and follows a path. We propose a multi-loop control architecture, where each loop is systematically designed using linear control techniques. The proposed strategy guarantees that the bicycle asymptotically converges to paths of constant curvature. A key advantage of our approach is that by using linear techniques analysis and controller design are relatively simple. We base our control design on the nonlinear (corrected) Whipple model, which has been previously verified for correctness and experimentally validated. The equations of motion for the nonlinear model are very complicated, and would take many pages to explicitly state. They also have no known closed form solution. To enable analysis of the model we linearize it about a trajectory such that the bicycle is upright and travelling straight ahead. This linearization allows us to arrive at a parameterized linear time-invariant state-space representation of the bicycle dynamics, suitable for analysis and control design. The inner-loop control consists of a forward-speed controller as well as a lean and steer controller. To keep the bicycle at a constant forward speed, we develop a high-bandwidth proportional controller that uses a torque along the axis of the rear wheel of the bicycle to keep the angular velocity of the rear wheel at a constant setpoint. To stabilize the bicycle at this forward speed, lean torque and steer torque are treated as the control signals. We design a state-feedback controller and augment integrators to the output feedback of the lean angle and steer angle to provide perfect steady-state tracking. To arrive at the gains for state feedback, linear-quadratic regulator methods are used. When following a constant-curvature path, a vehicle has a constant yaw rate. Using this knowledge, we begin designing the outer-loop path-following control by finding a map that converts a yaw rate into appropriate lean angle and steer angle references for the inner loop. After the map is completed, system identification is performed by applying a yaw-rate reference to the map and analyzing the response of the bicycle. Using the linear approximation obtained, a classical feedback controller for yaw-rate tracking is designed. In addition to yaw-rate control, to track a path the yaw angle of the bicycle must match that of the path and the bicycle must physically be on the path. To analyze these conditions a linear approximation for the distance between the bicycle to the path is found, enabling construction of a linear approximation of the entire system. We then find that by passing the signal for the difference in yaw rate and the distance through separate controllers, summing their output, and subtracting from the reference yaw rate of the path, the bicycle converges to the path. After developing the general design procedure, the final part of the thesis shows a step by step design example and demonstrates the results of applying the proposed control architecture to the nonlinear bicycle model. We highlight some problems that can arise when the bicycle is started far from the path. To overcome these problems we develop the concept of a virtual path, which is a path that when followed returns the bicycle to the actual path. We also recognize that, in practice, typical paths do not have constant curvature, so we construct more practical paths by joining straight line segments and circular arc segments, representing a practical path similar to a path that would be encountered when biking through a series of rural roads. Finally, we finish the design example by demonstrating the performance of the control architecture on such a path. From these simulations we show that using the suggested controller design that the bicycle will converge to a constant curvature path. Additionally with using the controllers we develop that in the absence of disturbance the bicycle will stay within the intended traffic lane when travelling on a typical rural road.