Internal transportation is one of the key elements in manufacturing operations, and there is a constant need to optimize this process (Antoniuk, 2021). The case company has a very large industrial are covering 3 km2, which poses significant challenges for the internal transportation. The company has too many parcel stations, lacks clear requirements for new parcel stations and documentation for the parcel stations, and faces route planning issues as a result. The purpose of this case study was to identify obstacles and problems to optimize the company’s parcel transport in terms of route planning, placement of parcel stations and the number of parcel stations. The project aimed to develop a general working model for how a parcel transport can be optimized without relying on the Industrial Internet of Things (Sinsinni et al., 2018) and digital technology. The study focused on the company’s internal and external parcel transport routes within and outside the industrial area. Observations and interviews were conducted at the case company, revealing that customers needs include receiving deliveries twice a day and ensuring correct parcel deliveries. The drivers require unchanged or reduced workload, easier training, fewer parcel stations, properly equipped parcel stations, and improved route planning. The transport manager needs a standardised work approach, fewer parcel stations, documentation of parcel stations, and an expanded requirements list. To optimize the case company’s transport, the number and placement of parcel stations, and simultaneously meet these needs, several improvement suggestions were developed. It was found that implementing a scanning system could enhance the accuracy of the parcel deliveries, but this option was not recommended due to it being expensive and gives no guarantee of correct deliveries, among other things. Instead, it is recommended that the company implements a milk run system to achieve JIT (Just-in-time) deliveries for customers and a standardized work approach standardized work approach for drivers. Additionally, a proposal for a digital map was presented to improve documentation and facilitate training, along with a suggestion to merge parcel stations to reduce workload and enhance route planning. Lastly, expanding the requirements list was suggested to ensure properly equipped parcel stations and provide clearer specifications for parcel stations. A general conceptual work model for this optimization process is outlined as follows: 1.       Observe current delivery routes and stations. 2.       Interview stakeholders (such as customers and drivers). 3.       Identify and compile requirements. 4.       Map out stations on a digital map. 5.       Apply a heuristic selection process.  a.       Examine clusters of stations of the digital map.  b.       Evaluate stations based on collected data.  c.       Assess the activity level; if multiple stations have high activity, make an individual assessment.  d.       Merge the stations.  e.       Apply the 250-meter rule to the remaining selection without available data. 6.       Create an optimal route using the selected stations. / Interna transporter är ett av de viktigaste elementen i en tillverkningsverksamhet och det finns ett konstant behov att optimera denna process (Antoniuk, 2021). Fallföretaget har ett mycket stort industriområde som omfattar 3 km2 vilket ställer stora krav på de interna transporterna. Företaget har för många paketstationer, saknar en tydlig kravbild av nya paketstationer och dokumentation över paketstationerna, och har på grund av detta ett ruttplaneringsproblem. Syftet med denna fallstudie var att identifiera hinder och problem för att kunna optimera företagets pakettransport med avseende på ruttplanering, paketstationers placering och antal paketstationer. Målet med projektet var att ta fram en generell arbetsmodell för hur en pakettransport kan optimeras utan Industrial Internet of Things och digital teknologi (Sinsinni et al., 2018). Studien avgränsades till företagets interna och externa pakettransportrutt, innanför och utanför industriområdet. Det utfördes observationer och intervjuer på fallföretaget som visade att kundernas behov är att få leverans två gånger per dag och att paketen levereras rätt. Chaufförerna har behov av oförändrad eller minskad arbetsbelastning, lättare upplärning, färre paketstationer, korrekt utrustade paketstationer och bättre ruttplanering. Transportchefen har behov av ett standardiserat arbetssätt, färre paketstationer, dokumentation över paketstationer och en utökad kravlista. För att optimera fallföretagets transporter, antalet paketstationer och placeringen och samtidigt uppfylla dessa behov tog vi fram flera förbättringsförslag. Vi kom fram till att ett skanningssystem kan öka möjligheten att kundernas paket inte kommer fel men rekommenderar inte detta då det bland annat är kostsamt och inte garanterar att paketen levereras rätt. Vi rekommenderar i stället att företaget implementerar en milk run som skapar JIT (Just-in-time) leverans för kunderna och ett standardiserat arbetssätt för chaufförerna. Det har också tagits fram ett förslag på en digital karta för ökad dokumentation och lättare upplärning, samt ett förslag på sammanslagning av paketstationer och därigenom en minskning. Detta för att minska arbetsbelastningen och skapa en förbättrad ruttplanering. Till sist ger vi även förslaget att de utökar sin kravlista för att uppfylla behovet av korrekt utrustade paketstationer och ge dem en tydligare kravbild. En generell och konceptuell arbetsmodell för denna optimering ser ut som följande: 1.       Observera nuvarande leveransrutter och stationer. 2.       Intervjua intressenter (såsom kunder och chaufförer). 3.       Identifiera och sammanställ krav. 4.       Kartlägg stationer på en digital karta. 5.       Heuristisk urvalsprocess.  a.       Undersöka kluster av stationer på digital karta.  b.       Granska stationerna utefter insamlade data.  c.       Bedöm aktiviteten, om fler stationer har hög aktivitet gör en individuell bedömning.  d.       Slå ihop stationerna.  e.       Resterande urval som inte har någon data utförs med 250 meters-regeln. 6.       Skapa optimal rutt med de valda stationerna.

This diploma thesis follows my bachelor thesis. The main purpose of the bachelor thesis was to clarify fundamental terms and to explain the sorting of particular parts of a direct flow that involves both the surface saturated flow and the hypodermic flow. This diploma thesis is focusing on the origin of direct flow in a river basin. Specifically, it deals with river sub-basin P6, P52, and P53, which are located in Kopaninský potok river basin. Furthermore, it deals with Jenín I. and II. river basins and the last analysed is Ostřice river basin (SO2). Factors influencing direct flow are researched on all river basins. It is impossible to say that the origin of direct flow is caused solely by a single factor; it is always the result of multiple factors. Among these factors belongs the atmospheric precipitation, type of soil, vegetation, climatic and anthrophogenic conditions, land use, and inclination of the area. The bachelor thesis explains the issues of multiple methods of flow separation, but this diploma thesis is primarily focused on two methods for calculation of ratio between the direct and the total flow. 1) Empirical method GROUND, which is used to separate hydrographs of medium daily river basin flow. 2) Method of digital filter by Lyne Hollick separate fast and slowcomponents from the overall concentrated flow and are based on the theory od signal analysis. Afterwards, the results of flow separation were compared to the factors influencing the origin of the direct flow. The daily total flow rates for every analysed river basin were used as the input data for calculating the flow separation.

O objetivo deste trabalho é caracterizar e analisar um novo sistema de abastecimento de suprimentos que está sendo adotado por diversas indústrias automobilísticas nacionais, denominado Milk Run. Este sistema consiste na coleta programada de peças junto aos fornecedores das montadoras, e diferentemente do sistema de abastecimento denominado Convencional, no qual o fornecedor entrega suas peças na planta da montadora. A análise visa estudar se existirá redução de estoque na cadeia de suprimentos com o novo sistema implantado, quais os custos pertinentes a esta nova técnica, qual o papel do fornecedor, da montadora e do operador logístico (transportadora) no novo processo e suas vantagens em relação ao sistema Convencional. Para levantamento do problema em estudo, a adoção do sistema Milk Run, foram realizadas visitas nas indústrias automobilísticas nacionais. Alguns fornecedores, que participam deste sistema, também foram visitados para compreender como, na prática, é realizada a coleta programada, suas vantagens e desvantagens. Operadores logísticos, que executam a operação de transporte para as montadoras também foram visitado. Esta dissertação visa relatar que o sistema Milk Run adota uma concepção de trabalho com enorme ênfase na filosofia Just-in-Time, e procura seguir alguns de seus princípios como: redução do estoque de materiais, maior freqüência de abastecimento de suprimentos e maior integração entre as partes que compõem o sistema, montadora e fornecedor. A contribuição deste trabalho está em caracterizar e analisar o novo sistema, Milk Run, e propor uma comparação dos custos da nova abordagem, com os custos pertinentes ao sistema Convencional (no qual os fornecedores entregam suas peças diretamente na planta da montadora). Esta comparação baseia-se nos custos definidos pelas literaturas em função do tamanho do lote de aquisição de peças e uma análise de Trade-offs entre as variáveis destes sistemas em função da flutuação da demanda anual. No sistema Milk Run em estudo será utilizado o Kanban como ferramenta de gerenciamento de requisição de peças. / The objective of this dissertation is to feature and analyse the new systems of procurement in Brazilian vehicle industry called Milk Run. This study compares Milk Run, which is a scheduled pick up automobile parts program, picking up automobile parts from several suppliers and returning the reusable containers to suppliers, to Conventional system of procurement (each supplier delivery its automobile parts in the vehicle assembly plant). The analysis is to study the inventory cost in both cases Milk Run and Conventional systems. Another analysis is to understand the role of the supplier, automaker and the logistic provider in Milk Run system and its advantages. Many visits have been necessary to the automakers, suppliers and logistics providers to understand this new situation in Brazil. This dissertation shows that Milk Run system is very close to Just-in-Time system and adopt the same philosophy as: reduction of inventory, increase frequency supply and increase integration between both parts, automaker and supplier. This dissertation tries to contribute to understand the costs included in both system and propose a modeling to compare the costs inherent in Milk Run and Conventional system. This modeling uses the costs defined in the literature about inventory and transportation system depending on the shipment size and one analysis of the Trade-offs in both systems.

O objetivo deste trabalho é caracterizar e analisar um novo sistema de abastecimento de suprimentos que está sendo adotado por diversas indústrias automobilísticas nacionais, denominado Milk Run. Este sistema consiste na coleta programada de peças junto aos fornecedores das montadoras, e diferentemente do sistema de abastecimento denominado Convencional, no qual o fornecedor entrega suas peças na planta da montadora. A análise visa estudar se existirá redução de estoque na cadeia de suprimentos com o novo sistema implantado, quais os custos pertinentes a esta nova técnica, qual o papel do fornecedor, da montadora e do operador logístico (transportadora) no novo processo e suas vantagens em relação ao sistema Convencional. Para levantamento do problema em estudo, a adoção do sistema Milk Run, foram realizadas visitas nas indústrias automobilísticas nacionais. Alguns fornecedores, que participam deste sistema, também foram visitados para compreender como, na prática, é realizada a coleta programada, suas vantagens e desvantagens. Operadores logísticos, que executam a operação de transporte para as montadoras também foram visitado. Esta dissertação visa relatar que o sistema Milk Run adota uma concepção de trabalho com enorme ênfase na filosofia Just-in-Time, e procura seguir alguns de seus princípios como: redução do estoque de materiais, maior freqüência de abastecimento de suprimentos e maior integração entre as partes que compõem o sistema, montadora e fornecedor. A contribuição deste trabalho está em caracterizar e analisar o novo sistema, Milk Run, e propor uma comparação dos custos da nova abordagem, com os custos pertinentes ao sistema Convencional (no qual os fornecedores entregam suas peças diretamente na planta da montadora). Esta comparação baseia-se nos custos definidos pelas literaturas em função do tamanho do lote de aquisição de peças e uma análise de Trade-offs entre as variáveis destes sistemas em função da flutuação da demanda anual. No sistema Milk Run em estudo será utilizado o Kanban como ferramenta de gerenciamento de requisição de peças. / The objective of this dissertation is to feature and analyse the new systems of procurement in Brazilian vehicle industry called Milk Run. This study compares Milk Run, which is a scheduled pick up automobile parts program, picking up automobile parts from several suppliers and returning the reusable containers to suppliers, to Conventional system of procurement (each supplier delivery its automobile parts in the vehicle assembly plant). The analysis is to study the inventory cost in both cases Milk Run and Conventional systems. Another analysis is to understand the role of the supplier, automaker and the logistic provider in Milk Run system and its advantages. Many visits have been necessary to the automakers, suppliers and logistics providers to understand this new situation in Brazil. This dissertation shows that Milk Run system is very close to Just-in-Time system and adopt the same philosophy as: reduction of inventory, increase frequency supply and increase integration between both parts, automaker and supplier. This dissertation tries to contribute to understand the costs included in both system and propose a modeling to compare the costs inherent in Milk Run and Conventional system. This modeling uses the costs defined in the literature about inventory and transportation system depending on the shipment size and one analysis of the Trade-offs in both systems.

Process models are always associated with uncertainty, due to either inaccurate model structure or inaccurate identification. If left unaccounted for, these uncertainties can significantly affect the model-based decision-making. This thesis addresses the problem of model-based optimization in the presence of uncertainties, especially due to model structure error. The optimal solution from standard optimization techniques is often associated with a certain degree of uncertainty and if the model-plant mismatch is very significant, this solution may have a significant bias with respect to the actual process optimum. Accordingly, in this thesis, we developed new strategies to reduce (1) the variability in the optimal solution and (2) the bias between the predicted and the true process optima. Robust optimization is a well-established methodology where the variability in optimization objective is considered explicitly in the cost function, leading to a solution that is robust to model uncertainties. However, the reported robust formulations have few limitations especially in the context of nonlinear models. The standard technique to quantify the effect of model uncertainties is based on the linearization of underlying model that may not be valid if the noise in measurements is quite high. To address this limitation, uncertainty descriptions based on the Bayes’ Theorem are implemented in this work. Since for nonlinear models the resulting Bayesian uncertainty may have a non-standard form with no analytical solution, the propagation of this uncertainty onto the optimum may become computationally challenging using conventional Monte Carlo techniques. To this end, an approach based on Polynomial Chaos expansions is developed. It is shown in a simulated case study that this approach resulted in drastic reductions in the computational time when compared to a standard Monte Carlo sampling technique. The key advantage of PC expansions is that they provide analytical expressions for statistical moments even if the uncertainty in variables is non-standard. These expansions were also used to speed up the calculation of likelihood function within the Bayesian framework. Here, a methodology based on Multi-Resolution analysis is proposed to formulate the PC based approximated model with higher accuracy over the parameter space that is most likely based on the given measurements. For the second objective, i.e. reducing the bias between the predicted and true process optima, an iterative optimization algorithm is developed which progressively corrects the model for structural error as the algorithm proceeds towards the true process optimum. The standard technique is to calibrate the model at some initial operating conditions and, then, use this model to search for an optimal solution. Since the identification and optimization objectives are solved independently, when there is a mismatch between the process and the model, the parameter estimates cannot satisfy these two objectives simultaneously. To this end, in the proposed methodology, corrections are added to the model in such a way that the updated parameter estimates reduce the conflict between the identification and optimization objectives. Unlike the standard estimation technique that minimizes only the prediction error at a given set of operating conditions, the proposed algorithm also includes the differences between the predicted and measured gradients of the optimization objective and/or constraints in the estimation. In the initial version of the algorithm, the proposed correction is based on the linearization of model outputs. Then, in the second part, the correction is extended by using a quadratic approximation of the model, which, for the given case study, resulted in much faster convergence as compared to the earlier version. Finally, the methodologies mentioned above were combined to formulate a robust iterative optimization strategy that converges to the true process optimum with minimum variability in the search path. One of the major findings of this thesis is that the robust optimal solutions based on the Bayesian parametric uncertainty are much less conservative than their counterparts based on normally distributed parameters.

Cette thèse étudie les différents types d'artistes-curateurs qui se manifestent depuis plus de deux siècles au moment où les artistes organisateurs d'expositions sont de plus en plus présents sur la scène artistique contemporaine. Par-delà le phénomène de mode, une vue d'ensemble des artistes-curateurs est dressée, une typologie de ceux-ci proposée. L'ensemble des réflexions et des recherches porte sur les liens entre art et réception de l'art à travers l'étude de la french theory (Gilles Deleuze, Félix Guattari, Jean-François Lyotard, Jacques Rancière, Jacques Derrida), du réalisme spéculatif (Quentin Meillassoux, Graham Harman) et de l'heccéité (Jean Duns Scot). En s'appuyant sur une étude épistémologique, les différents caractères existants de la position d'artiste-curateur sont analysés. À travers des expériences artistiques et curatoriales subjectives, la visibilité des fondements véritables de cette double pratique, assumée comme telle, est pensée. L'objectif est de rendre compte de la définition possible de l'artiste-curateur comme avant tout un créateur de lieu, de dispositifs, et d'espace d'exposition au service des autres. Les rapports qu'entretiennent les artistes avec les commissaires d'expositions sont rendus visibles, tant dans leurs relations harmonieuses que conflictuelles. Des pistes pour l'avenir se conçoivent dans le prolongement de la poétique de la relation développée par Édouard Glissant. / This thesis shows that, under various guises, the artist-curator model has been operating for more two centuries when the artists who curate exhibitions are ever more visible on the artistic scene. Across the fashion phenomenon, an overview of the more prominent artist-curators is erected, a typology of these practitioners is proposed. He particularly focuses his reflections and researches on the links between art and theory, the study of the reception of French Theory (Gilles Deleuze, Félix Guattari, Jean-François Lyotard, Jacques Rancière, Jacques Derrida), speculative realism (Quentin Meillassoux, Graham Harman) and haecceity (Jean Duns Scot). Using epistemological methodology and analyzing the state of variables, he details the various characteristics which co­exist in the artist-curator position. The author uses his own artistic and curatorial experience : he founded and curates the artist-run space Immanence. He aims to bring to life the real foundations of this double practice. The thesis posits the possible definition of the artist­curator both as the author of a creative act in place visibility and display, and simultaneously as a creator at the service of the others. At the heart, are the relationships between curated artists and artist-curator : the cooperation, consensus and correspondence, as well as the dissent and conflicts. Finally, the author looks to the possible futures drawing from the poetics of relation developed by Édouard Glissant.

L'ozone joue un rôle primordial sur l'équilibre photochimique de l'atmosphère et participe au processus d'équilibrage radiatif entre les deux hémisphères (Mecke, 1931). Dans la troposphère, l'ozone détermine la capacité oxydante de la majorité des gaz et absorbe continuellement dans la stratosphère les radiations ultraviolettes nocives (McMicheal et al., 2003). D'où l'intérêt de surveiller la variation de la couche d'ozone de façon régulière. Il a été constaté au début des années 80, une diminution inquiétante et progressive de la colonne totale de l'ozone dûe aux émissions anthropiques des substances riches en chlore, brome et fluor. Ce constat a conduit au Protocole de Montréal en 1987 dont l'objectif est de mettre en place une politique internationale visant à réduire les émissions des substances appauvrissant l'ozone. Dix ans après la signature du dit Protocole, la concentration de ces substances commence à diminuer dans l'atmosphère et la prospection d'un recouvrement progressif de la couche d'ozone demeure aujourd'hui un sujet d'actualité (UNEP/PNUE, 2009 ; OMM, 2010 et 2014). Les besoins d'aujourd'hui sont de réaliser des mesures continues et fiables de l'ozone dont leurs exploitation dans des méthodes et/ ou des modèles bien adaptés à la problématique aideront la communauté à suivre l'évolution de l'ozone et d'estimer les tendances à long terme. Dans ce travail, une variété de produits d'ozone issue de différents instruments a été combinée pour construire des bases des données fiables et homogènes afin d'étudier sa variabilité et d'estimer la tendance de l'ozone dans les régions tropicale et subtropicale sud. L'application de ces bases de données sur les ondelettes a permis d'identifier les principaux forçages qui contrôlent la variabilité de l'ozone et la période de retour associée à chaque forçage. Il s'agit des variations saisonnières du climat, les oscillations quasi-biennales, les oscillations australes El-Niño et l'activité solaire dont le cycle moyen est évalué à 11ans. Le comportement et l'influence de chacun de ces paramètres sur la viabilité de l'ozone sont étudiés. Cette étude est faite en s'appuyant sur des méthodes statistiques et sur le modèle Trend-Run. Avec ce modèle, la part de contribution et la réponse de chaque paramètre sur la variabilité de l'ozone sont quantifiées. Les résultats sur les tendances montrent une augmentation de la couche d'ozone avec un taux variant entre 0 et 2.78% par décade (selon la région et le site) sur la période 1998-2012. Cette amélioration est bien observée au-dessus de 22km, surtout aux subtropiques par rapport à la région équatoriale. / Ozone plays an important role on photochemical equilibrium of atmosphere and participate on radiative balance process between hemispheres (Mecke, 1931). In the troposphere, ozone determines the oxidizing capacity of major species and absorbs continuously in the stratosphere the harmful ultraviolet radiation (McMichael et al, 2003). Based on the above facts, it is important to monitor ozone continuously with consistency and accuracy. Global total column ozone (TCO) has depleted gradually since 1980 with an increase of chlorofluorocarbon concentrations in the stratosphere due to anthropogenic activities. In 1987, the Montreal protocol was formulated in order to regulate the emissions of substances that deplete ozone. Concentrations of these substances are observed to decrease ten years after the Montreal protocol. Thus we have been expecting an increase in ozone by now (UNEP/PNUE, 2009; WMO, 2010 and 2014). The current needs are to achieve consistent and reliable measurements in which their exploitation on adapted methods/models can help scientists to follow the ozone evolution and to estimate long term ozone trend. In this work, a variety of ozone products from different instruments was combined in order to create reliable and homogenous dataset to study the ozone variability and trend over the southern tropics and subtropics. The dataset application on wavelets method allowed to identify the dynamic parameters that control ozone variability and their periodicities. These include seasonal variations of climate, the quasi-biennial oscillations, the El-Niño Southern Oscillation and the 11-years solar cycle. The behavior of each parameter and its influence on ozone variability were analysed based on statistical method and the Trend-Run model. The contribution and response of each variable on ozone variability were quantified from the model. The obtained trends results exhibit an increase of total ozone from 1998 to 2012 with a rate varying between 0 and 2.78% par decade (depending of the site and region). The ozone increase was observed mainly above 22 km and it is more important over the subtropical region with respect to equatorial zone.

This work focuses on the Czech stock market. Work is focused on the application of the theory of efficient markets, which is one of the theories explaining the evolution of prices of securities, the stock market in the Czech Republic from 2000 to 2008. Efficient market theory represents a random walk, which is used as a tool to describe the phenomenon where the future price changes are random divergence from past prices. The thesis is divided into several parts. The first part presents an actual stock market in the Czech Republic. Because most of the work deals with the analysis yields the PX stock index was that in the next section in detail described and analyzed. Furthermore, the Czech stock market has been analyzed in terms of structure and trading volume. The next section has described the theory of efficient markets. Was described briefly the history of this theory. Another part of this work can be described as a purely practical. First, the work focuses on the market in the one year time series of returns. In second part were analyzed medium-long term consisting of three year time series of returns. The last analyzed period was long term, consisting of eight-year time series of returns from 2000 to 2008.

Essay one investigates registered insider sales as stated in the final prospectus filed with the Securities and Exchange Commission (SEC) to test managerial market timing ability during the Seasoned Equity Offering (SEO) process. Using a comprehensive sample of 1,051 SEOs between 1997 and 2005, the findings suggest that the initial market reaction and the long-run post-issue performance of issuers are negatively related to C-level executive insider sales, but unrelated to sales by non-executive insiders. Overall, the findings are consistent with the notion that executive insiders are aware of the mispricing in their firm’s securities and successfully time their sales by participating in the secondary components of SEOs. The implication is that SEOs with C-level executive sales are overvalued relative to both SEOs without insider sales and SEOs with only non-executive insider sales. In the second essay, we compare shareholder wealth effects of dual-class and single-class Seasoned Equity Offerings (SEOs) between 1997 and 2005. While there is no difference in pre-issue stock performance or the initial market reaction to the SEO announcements, dual-class issuers significantly underperform single-class issuers in the post-issue years. The mean three-year underperformance of dual-class firms relative to single-class is a significant 28.93% (30.45%) in buy-and-hold raw (abnormal) stock returns, and robust to alternative model specifications. We document that this relative long-run stock underperformance is related to differences in the impacts of post-issue capital expenditures and acquisitions for dual and single-class issuers. Similarly, post-issue corporate cash holdings also contribute less to the shareholder wealth for dual-class firms.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Bacterial chemotaxis, as observed for Escherichia coli, in a field of chemoattractant molecules is characterised by a run-and-tumble motion. The motion is effected by the clockwise (CW) or counter-clockwise (CCW) rotation of flagella; filamentous appendages attached to molecular motors on the cell body. Runs appear when all flagella turn in the CCW-direction and are used to maintain a favourable direction. Tumbles emerge as soon as one flagellum starts to turn CW and are used for reorientation. Because of the variation observed between individual bacteria displaying run-and-tumble motion, we choose to model this behaviour within a probabilistic framework. An important feature of the chemotactic ability of E.coli is that the cell increases run while moving in the right direction and shortens it in the opposite case. This underlines that tumbles are used for reorientation. It has been found from experiments that there can be significant variation in the tumble fashion depending on the fraction of CW-rotating motors (Turner et al., 2000). The change in angle produced when fewer flagella are rotating CW was found to be smaller when compared to the case for many CW-rotating flagella. In addition, the change of direction contributed by a small portion of CW-rotating flagella is rarely significant for bacteria with many flagella. Based on these observations, we have distinguished between models for the one-flagellated and the multi-flagellated cases. Furthermore, since the tumbling angle change increases with the fraction of CW-rotating motors, it would not be impossible to have some cases where the amount of turn produced by the CW-rotating motors induces the bacterium to have a change of direction greater than 2π. But, this feature could not have been observed because when the bacterium tumbles it can effectuate several revolutions before resuming to a new direction. Therefore, we do not restrict our change of direction to (0,2π) to allow the bacteria to have the possibility to effectuate change of directions of magnitude greater than 2π. To this end, we differentiate between the probability of having directional change of magnitude α and α +2π . Thus we do not use angle change distributions that are defined modulo 2π such as the von Mises distribution or the wrapped normal distribution. The chemotactic ability of the bacterium is modelled by representing the CCW-bias of a single flagellum as a function of the chemoattractant concentration. The model includes the temporal memory of chemoattractant concentration that the bacterium has, which usually spans about 4s. The information about the quality of the current direction of the bacterium is transmitted to the flagellar motor by assuming that this one varies with the chemoattractant concentration level. In addition, the saturation of the bias is incorporated by assuming that the bacterium performs a temporal comparison of the receptor occupancy. The present CCW-bias-Model accounts for the chemotactic ability of the bacterium as well as its adaptation to uniform chemoattractant environment. The models of one-flagellated and multi-flagellated bacterial motion, are used to investigate two main problems. The first one consists of determining the optimal tumbling angle strategy of the bacteria. The second one consists of looking at the effects of the tumble variation on the chemotactic efficiency of the bacteria. In order to address these questions, the chemotactic efficiency measure is defined in such a way that it reflects the ability of the bacteria to converge and to stay in a near neighbourhood of the source so that they gain more nutrients. Since its movement is entirely governed by its single flagellum, the one flagellated bacterium is more able to effectuate a run motion. Tumbling events are modelled to be all equivalent because there is not any fraction of flagella to consider. On the other hand, the tumble variation of the multi-flagellated bacteria is modelled by assuming that the directional change during a tumble is a function of the fraction of CW-rotating motors. By assuming that the number of CW-rotating flagella follows a binomial distribution, we suppose that the multi-flagellated bacteria are less able to effectuate a run motion. This also implies that the change of direction produced by fewer CW-rotating flagella are more likely to happen, and this compensates the lack of run. The models show that the optimal tumbling angle change for the bacteria is less than 2π and that higher flagellated bacteria have higher chemotacitc efficiency. As the number of flagella of the bacteria increases, there can be more tumble variation, in this case the bacteria are more capable of adjusting their direction. There could be some situation were the bacteria are not moving to the right direction, but do not require a large change of direction. This ability to adjust their direction accordingly allows them to converge nearer to the source and to gain more nutrients. In addition, the dependence of the tumbling angle on the fraction of CW-rotating flagella of the mutli-flagellated bacteria, implies that there is a correlation between the tumbling angle deviation and the external environment, because the rotational states CCW-CW of the flagella depends on the external cue. Consequently, it would not be impossible that the average magnitude of tumbling angle change depends on the external environment. To investigate this possibility we analyse the distribution of the tumbling tendency of a single bacterium over time, which is the distribution over time of the average positive tumbling change of the bacterium, within zerogradient environment and within non-zero-gradient environment. We defined the average of these tumbling tendency over time as the directional persistence. We observe that the directional persistence within these different nonzero- gradient environment remains the same. However, the difference between the directional persistence within zero-gradient and non-zeros gradient environment gets larger as the number of flagella of the cell increases. There is more correlation between the external environment and the tumbling tendency of the bacterium. Which is the reason why the higher flagellated bacteria responds the best to the external environment by having the higher chemotactic performance. Finally, the total directional persistence generated by the optimal tumbling angle change of the bacteria is the average directional persistence of the bacteria regardless of their number of flagella. Its value, predicted by the model is 1.54 rad within a non-zero-gradient environment and 1.63 rad within a zero-gradient environment. / AFRIKAANSE OPSOMMING: Bakteriese chemotakse, soos waargeneem word vir Escherichia coli, in ’n veld van chemiese lokmiddel molekules word gekenmerk deur ’n hardloopen- tuimel beweging. Die beweging word bewerkstellig deur die regsom of linksom rotasie van flagella; filamentagtige aanhangsels geheg aan molekulêre motors op die selliggaam. ’n Hardloop aksie kom voor as al die flagella linksom roteer en word gebruik om ’m voordelige koers te handhaaf. Tuimels kom voor sodra een van die flagella regsom draai en word gebruik vir heroriënteering. Van wee die variasie wat waargeneem word tussen individuele bakterieë wat hardloop-en-tuimel bewegiging vertoon, verkies ons ’n probabilistiese raamwerk om in te werk. ’n Belangrike eienskap van die chemotakse vermoë van E. coli is dat die sel meer gereeld hardloop terwyl dit in die regte rigting beweeg en minder gereeld in die teenoorgestelde geval. Dit beklemtoon dat tuimels gebruik word vir heroriënteering. Dit is al eksperimenteel vasgestel dat daar betekenisvolle variasie kan wees in die tuimel wyse, wat afhang van die breukdeel regsom roterende motors (Turner et al., 2000). Die hoekverskil afkomstig van minder regsom roterende flagella was vasgestel om kleiner te wees in vergelyking met die menig regsom roterende geval. Verder word die bydrae tot die hoekverskil van ’n klein breukdeel regsom roterende flagella selde beduidend vir bakterieë met baie flagella. As gevolg van hierdie waarnemings, tref ons onderskeid tussen modelle vir een-flagella en multiflagella gevalle. Aangesien die tuimel hoeksverskil vergroot saam met die breukdeel regsom roterende motore, is dit nie onmoontlik om gevalle te hê waar die hoeveelheid draaiaksie gegenereer deur die regsom roterende motore ’n rigtingsverskil groter as 2π kan bewerkstellig nie. Dit was nie moontlik om hierdie eienskap waar te neem nie aangesien die bakterieë ’n paar keer kan tuimel voordat ’n nuwe rigting vasgestel word. Vir hierdie rede beperk ons nie die hoeksverskil tot (0,2π) nie om die bakterieë toe te laat om rigtings veranderinge groter as 2π te ondergaan. Vir hierdie doel, onderskei ons tussen die waarskynlikheid van ’n rigtinsverskil met grootte α en α + 2π. Dus, gebruik ons nie hoekverskil verspreidings wat modulo 2 gedefinieer is nie, soos die von Mises verspreiding of omwinde normaalverdeling. Die chemotakse vermoë van die bakterium word gemodelleer deur die linksom sydigheid van ’n enkele flagellum as ’n funksie van die chemotakse lokmiddel konsentrasie voor te stel. Die model sluit in die tydelike geheue wat die bakterium besit oor chemotakse lokmiddel konsentrasie, wat gewoonlik oor 4s strek. Die informasie oor die kwaliteit van die huidige rigting van die bakterium word deur gegee na die flagella motor toe deur die aanname te maak dat dit wissel met die chemotakse lokmiddel konsentrasie vlak. Die versadiging van die sydigheid word geinkorporeer deur aan te neem dat die bakterium ’n temporale vergelyking maak tussen reseptor okkupasie. Die huidige linksom sydige model neem die bakterium chemotakse vermoë in ag, as ook aanpassing tot ’n uniforme chemotakse lokmiddel omgewing. Die modelle van een-flagella en multi-flagella bakteriële beweging word gebruik om twee hoof probleme te bestudeer. Die eerste, bestaan daaruit om vas te stel wat die optimale tuimel hoek strategie van die bakterieë is. Die tweede kyk na die uitwerking van tuimel variasie op chemotakse effektiwiteit. In orde om hierdie vra te adreseer word die chemotakse effektiwiteit op so mannier gedefinieer dat dit die bakteriese vermoë om die buurt om die oorsprong te nader en daar te bly. Aangesien die beweging heeltemal vasgestel word deur een flagella, in die een-flagella geval, is ’n bakterium meer in staat daartoe om ’n hardloop aksie te bewerkstellig. Tuimel voorvalle word as ekwivalent gemodeleer omdat daar geen breukdeel roterende flagella is om in ag te neem nie. In teenstelling, word die tuimel variasie van multi-flagella bakterieë gemodeleer deur die aanname te maak dat rigtingsverandering gedurende ’n tuimel ’n funksie is van die breukdeel regsom roterende motore. Deur die aanname te maak dat die getal regsom roterende flagella ’n binomiese verspreiding volg, veronderstel ons dat multi-flagella bakterieë minder in staat daartoe is om ’n hardloop aksie te onderneem. Hierdie impliseer ook dat rigtingverandering wat geproduseer word deur minder regsom roterende flagella meer geneig is om voor te kom en dan kompenseer vir ’n tekortkoming aan hardloop gebeure. Die modelle wys dat die optimale tuimelhoek verandering minder as 2 is en dat bakterieë met meer flagella meer chemotaksies effektief is. Soos die getal flagella vermeder, kan daar meer tuimel variasie wees, en in die geval is die bakterieë meer in staat om hul rigting te verander. Daar kan omstandighede wees waar die bakterieë nie in die regtige rigting beweeg nie, maar nie ’n groot rigtingsverskil nodig het nie. Hierdie vermoë om hul rigting byvolglik te verander stel hul in staat om nader aan die oorsprong te konvergeer en dus meer voedingstowwe op te neem. Die afhanklikheid van die tuimel hoek op die breukdeel regsom roterende flagella van multi-flagella bakterieë dui daarop dat daar ’n korrelasie is tussen die tuimel hoek afwyking en die eksterne omgewing, omdat die roterings toestand, regs- of linksom, van die flagella afhanklik is van die eksterne sein. As ’n gevolg, is dit nie onmoontlik dat die gemiddelde grootte van die tuimel hoek verandering van die eksterne omgewing afhang nie. Om hierdie moontlikheid te bestudeer, analiseer ons die verspreiding van die tuimel neiging van ’n enkele bakterium oor tyd, wat die verspreiding oor tyd van die gemiddelde positiewe tuimel verandering is, in ’n nulgradient en nie-nul-gradient omgewing. Ons het hierdie gemiddelde tuimel neigings oor tyd gedefinieer as die rigtings volharding. Ons het waargeneem dat die rigtings volharding binne verskillende nienul- gradient omgewings dieselfde bly. Nogtans is die verskil tussen die rigtings volharding binne nul-gradient en nie-nul-gradient omgewings groter soos die getal flagella vermeder. Daar is meer korrelasie tussen die eksterne omgewing en tuimel neiging van die bakterium. Dit is die rede hoekom bakterieë met meer flagella die beste reageer op die eksterne omgewing deur beter chemotakse effektiwiteit. Ten slotte, die totale rigtings volharding gegenereer deur die optimale tuimel hoek verandering is die gemiddelde rigtings volharding ongeag van die getal flagella. Die waarde wat deur die model voorspel word is 1.54 rad binne ’n nie-nul-gradient omgewing en 1.63 rad binne ’n nul-gradient omgewing.