Cadeias de suprimentos podem ter operações seguindo diferentes estratégias de distribuição e a utilização de cada uma dessas estratégias pode resultar em diferentes operações e custos. A estratégia de cross-docking auxilia na redução dos custos de distribuição de produtos, consolidando cargas, e a redução de tempo e custos de armazenamento, uma vez que o tempo máximo de estoque permitido pela estratégia é de cerca de 24 horas. O objetivo deste trabalho é apresentar um modelo para o problema de cross-docking, em que cargas são entregues e reorganizadas de forma a atender a outras cargas que são coletadas e garantir que as janelas de tempo para início das operações sejam atendidas. Devido à falta de instâncias para o problema disponíveis na literatura, buscou-se gerar um benchmark e disponibilizá-las à comunidade científica. Uma vez que o problema é de difícil solução exata, um método heurístico para a resolução do problema foi desenvolvido. Os resultados mostraram que o modelo proposto resulta em boas soluções quando comparado ao modelo da literatura. O estudo de calibração do software IBM CPLEX mostrou que a calibração dos parâmetros pode resultar em melhores soluções e, por fim, a matheurística se mostrou competitiva com o CPLEX, principalmente para cenários em que a proporção de entregas e coletas diverge. / Supply chains may have operations which follow different distribution strategies and each one of these strategies may result in different operations and costs. The Cross-docking strategy helps to reduce the products distribution costs by consolidating loads and reducing storage costs as the maximum inventory time is approximately 24 hours. The aim of this research is to present a model for the cross-docking problem where loads are delivered and reorganized so as to cater for other loads that are collected and ensure that time windows are respected. Due to the lack of instances available in the literature, a benchmark was generated and was made available to the scientific community. As the problem is difficult to obtain the exact solution, a heuristic method was developed. The results showed that the proposed model has good solutions when compared to the literature model. A study of the IBM CPLEX software showed that tuning can result in better solutions and the matheuristcs was competitive with the software, mainly in scenarios where deliveries and pickups are very different.

The brain – the organ that allows us to be aware of our surroundings – consists of a complex network of neurons, which seemingly allows the human brain to be able of abstract thinking, emotions, and cognitive function. To learn how the brain is capable of this, the two main branches of neuroscience study either neurons in detail, or how they communicate within neuronal networks. Both these branches often tackle the complexity using a combination of experiments and mathematical modelling. A third and less studied aspect of neuroscience concerns the neurovascular coupling (NVC), for which my research group has previously developed mathematical models. However, these NVC models have still not integrated valuable data from rodents and primates, and the NVC models are also not connected to existing neuronal network models. In this project, I address both of these two shortcomings. First, an existing model for the NVC was connected with a simple model for neuronal networks, establishing a connection between the NVC models and the software NEURON. Second, we established a way to preserved information from NVC data from rodents and mice into NVC models humans. This work thus connects the previously developed NVC model both with data from other species and with other types of models. This brings us one step closer to a more holistic and interconnected understanding of the brain and its many intriguing cognitive and physiological functions.

The main goal of this diploma thesis is to analyse financial productivity of a chosen company, to find deficiencies and suggest possibilities for improvement of the situation. First there is theoretical part consisting of an introduction of chosen financial indicators, such as profitability, indebtedness etc., and also a description of Maple, programme used for mathematical exercises. In the practical part there is a description of Brno company TRON, the business objective of which is LED lighting. The financial indocators are made in the programme Maple, the balance and also profit and loss accounts for a few consecutive years are analysed, from which we can determine the financial situation of the company. The result should help the chosen company with future decisions.

MSc (Applied Mathematics) / Department of Applied Mathematics / See the attached abstract below

<p>Michelle N. Ingle. M.S., Purdue University, December 2019. Computational Modeling of Transforming Growth Factor-β2 Receptor Complex Assembly. Major Professor: David M. Umulis.</p> <p> </p> <p> Transforming growth factor (TGF)-β1, TGF-β2, and TGF-β3 are secreted signaling proteins that play an essential role in tissue development, immune response, and physiological homeostasis. TGF-β ligands signal through a tetrameric complex made up of two type I receptors (TβRI) and two type II receptors (TβRII). Dysregulation of TGF-β signaling has been linked to uncontrolled cell proliferation and cancer metastasis. An accurate understanding of TGF-β’s receptor complex assembly pathway may allow for pharmacological intervention and/or preservation of proper TGF-β signaling.</p> <p> Amongst the ligand types, TGF-β1 and TGF-β3 are efficient signalers, presumably by strong binding to both type I and II receptors. However, TGF-β2 has a very weak affinity for TβRII and requires an additional membrane-bound protein called betaglycan (BG) to achieve similar levels of downstream signaling. While computational modeling has been performed on the signaling pathway of the TGF-β system, to date no computational modeling has aimed to decipher BG’s role in the potentiation of TGF-β2 signal. To determine the role of BG in selectively facilitating signaling by TGF-β2, we developed computational models with different assumptions based on the levels of cooperativity between receptor subtypes and types of BG behavior (No Receptor Recruitment model, Single-stage Receptor Recruitment model, and Two-stage Receptor Recruitment model). </p> <p> With each of the receptor recruitment models we hypothesized that BG uses two domains to successfully enhance TGF-β2 signaling. This model was first proposed in Villarreal et al., 2016 and is further investigated in this work using a two-step computational approach. First, a root mean square error (RMSE) calculation was performed between our computational models with no BG present and published experimental signaling data in cell lines with no BG present. Lower RMSE values indicate the simulated data is more representative of experimental signaling behavior when no BG is present. The second round of model validation was performed by adding BG into the simulations and comparing its behavior to experimentally determined and hypothesized behaviors of BG. </p> <p> In summary, the simulations indicate there may be more cooperative receptor recruitment present in the system then stated in literature. Furthermore, it appears that BG binding to TGF-β2 ligand through two domains provides an effective transfer mechanism that can be tuned to control differential signaling between TGF-β ligand subtypes. Experiments were then suggested in order to support or refute one of the models offered in this thesis. For the purpose of uncovering how BG enhances TGF-β2 signaling, the computational work performed in this thesis highlights the areas where researchers should focus their experimental efforts and provides a baseline model for further computational work in the TGF-β system.</p>

Magister Educationis - MEd / Mathematical modelling is gaining extensive interest across the schooling sector worldwide, as it is deemed to develop learners with competencies set to deal with the demands of the fourth industrial revolution and being creative problem solvers. As mathematical modelling has only recently gained momentum across the mathematics curricula for schools in South Africa, many teachers may not be aware of the competencies that are needed to be developed in their learners through solving word problems, and even learners may not be aware of these essential modelling competencies. Hence, this mixed-methods approach study adopted a case-study design located within an interpretative paradigm to explore the levels of mathematical modelling competencies a sample of Grade 10 learners attending a Western Cape School demonstrated as they solved a set of word problems associated with the use of simultaneous equations. Additionally, data collected through observations and limited sets of semi-structured interviews were considered in the data analysis processes, which were largely driven by qualitative content analysis methods and supplemented with elementary descriptive statistical methods. The findings of this study showed that most of the learners demonstrated non-competency in modelling mainly because of their inability to understand the problem as evident in their failure to comprehend the context of a problem, inability to recognise important quantities associated with a problem, and muddled relationships if any. The study conjecture that the use of the English language could have been a barrier to the sample of English second language speakers understanding the problem. However, a very limited number of students showed partial modelling competency, as they were only able to understand the problem and build a correct model to solve the problem. Regrettably, these students lacked the knowledge of the heuristics for solving a system of linear equations correctly and completely and did not check or verify their answers. The extremely small number of learners, who demonstrated sufficient modelling competency, demonstrated sufficient understanding of the problem, built and solved the system of simultaneous linear equations successfully without necessarily checking or testing whether their answers satisfied the conditions of the problem. Hence, this study recommends that adequate focus be given to the role of language in understanding a problem, heuristic competencies to solve a system of linear equations should be strengthened, and the habit of checking the reasonableness of the solution should be encouraged and developed continuously across problem-solving tasks. Studying learners’ modelling competencies requires further work to add to the repertoire of this knowledge domain.

Dams are amongst the most important components of water resource systems. In many places the water regulated by and stored in dams is essential to meet the development objectives of water supply, flood control, agriculture (i.e. irrigation and livestock), industry, energy generation and other sectors. Previous studies (Gourbesvive, 2008) indicate that in the next 30 years water use will increase by 50% in the world. By 2025 about 4 billion people will live under conditions of severe water stress. Continuous deterioration in water quality in most developing countries is additional challenge. Therefore, development of priority water infrastructures and improvements of water management have essential and complementary roles in contributing to sustainable growth and energy reduction in developing countries like Sweden. One way of improving water management is through increasing the efficiency of utilization of dam reservoirs (Bosona, 2010). Reservoir operation is a complex task involving numerous hydrological, technical, economical, environmental, institutional and political considerations. There is no general algorithm that covers all type of reservoir operation problems. The choice for techniques usually depends on the reservoir specific system characteristics, data availability, the objectives specified and the constraints imposed. Goal of the mathematical modelling and simulation of a physical system is to provide the user with the relevant information used in design and/or management decision-making. However, in the absence of adequate foresight and planning for adverse impacts, past dam construction has often resulted in devastating effects for ecosystems and the livelihoods of affected communities. In this project with Hec-ResSim simulation model four reservoirs in Ore River Basin and 3 reservoirs in Lule River Basin in different location in Sweden are considered and by new operation rules, model is simulated. With consideration of two high floods event model is calibrated and new operation rules for flood control and hydropower melioration was rendered and suggested.

The emergence of drug resistance is a serious threat to the long-term virologic success and durability of HIV-1 therapy. Adherence has been shown to be a major determinant of drug resistance; however, each pharmacologic class of antiretroviral drugs has a unique adherence–resistance relationship. We develop an immunological model of the HIV-1 infected human immune system that integrates the unique mechanisms of action of reverse transcriptase and protease inhibiting drugs. A system of impulsive differential equations is used to examine the drug kinetics within CD4⁺ T cells. Stability analysis was preformed to determine the long-term dynamics of the model. Using the endpoints of an impulsive periodic orbit in the drug levels, the maximal length of a drug holiday while avoiding drug resistance is theoretically determined; the minimum number of doses that must be subsequently taken to return to pre-interruption drug levels is also established. Heterogeneity in inter-individual differences on drug-holiday length is explored using sensitivity analysis based on Latin Hypercube Sampling and Partial Rank Correlation Coefficient analysis. Extremely short drug holidays are acceptable, as long as they are followed by a period of strict adherence. Numerical simulations demonstrate that if the drug holiday exceeds these recommendations, the cost in virologic rebound is unacceptably high. These theoretical predictions are in line with clinical results and may also help form the basis of future clinical trials.

Magister Educationis - MEd / The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in co~parison to those of other countries. Based on these observations, the present study is an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of this study was thus to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study pays more attention to mathematics education 111 real life situations. Data was collected using the ROSME questionnaire that deals with contexts preferred by students for mathematics education. A sample made up of over 1600 learners in grades 8 to 10 were randomly selected from 21 schools. Data collected from these learners was analysed using Kendall's W mean rank method in the SPSS 12.0 program since the data for this study were ordinal. The most important finding of this study was that, "Mathematics that entertains and surprises us" came up the highest ranked item. This indicates that mathematics education must be directed towards raising learners' interests. The lowest ranked item was, "Mathematics used to calculate the number of seats for parliament given to political parties after elections," and this might indicate among other things that political activity does not attract students' interest in a society where the concept of well-being is dominant. In general, Korean learners appear to favour learning mathematics in technological contexts and show less interest in political and agricultural contexts. In conclusion, this study suggests that teachers should use contexts that increase learners' interest in classroom activities. Korea has today become one of the strongest Information Technology countries. Therefore mathematics curricula and textbooks which are appropriate to this context must be provided for more efficient mathematics education. Thus, it becomes imperative that the Korean school system must develop a particular program for nurturing learners' mathematical power. Furthermore, mathematics education policy makers must reconsider whether the current education system, Pyungjunhwa Kyoyuk system, should be used or not.

This thesis attempts to provide new insight into some population-dynamical problems and also proposes a new perspective on certain models of ecological communities. Following a short introduction into the field of mathematical modelling of population dynamics, the first chapter investigates the paradoxical Hydra Effect, the increase of mean population size as a response to an increase in mortality rate, in a class of simple predator-prey models. The main result is that a Hydra Effect occurs if and only if the system dynamics are oscillatory, which has interesting implications for the theory of optimal harvesting and biocontrol of invasive species. The second chapter discusses how coordinate transformations change the structure of intraguild predation food webs, establishing a close connection of certain cases of intraguild predation to simpler community modules such as exploitative competition and food chains. These results and possible generalizations of them could have wide-ranging implications for the question of how structural properties of food webs determine population-dynamical properties such as ecological stability and persistence. The last chapter presents numerical investigations of how random environmental fluctuations affect the spatiotemporal dynamics of oscillatory reaction-diffusion models, such as classical predator-prey and simple lambda-omega systems. These results in particular question whether travelling waves arising from these models can explain similar spatiotemporal waves found in natural populations.