Capillary electrophoresis is one of the prominent analytical separation methods. Currently, many computer programs exist which are able to predict the result of an electrophoretic experiment. Firstly, there are programs based on numerical solving of corresponding continuity equations and equations of chemical equilibria. Secondly, there are programs based on approximative models of capillary electrophoresis. Programs belonging to the first group are applicable to a wide range of modes of capillary electrophoresis and provide a precise solution. Their disadvantage is though a considerable time demand. On the other hand, the approximative models give the results almost immediately and, in addition, provide some theoretical relationships which are useful for optimization of the separation process. This dissertation thesis is focused on improvement and extension of validity of existing approximative models of capillary electrophoresis. As a part of this thesis, a model capable of a full-blown description of capillary electrokinetic chromatography is introduced. This model is implemented into program PeakMaster 6. The attention is also paid to a nonlinear model of electromigration without diffusion. This model enables a very good description of electromigration dispersion including effects related to...

Pathogens and parasites are increasingly recognized as important components within host populations, communities, and ecosystems. Parasite contributions to ecosystem function most likely manifest as density-mediated impacts of parasites on their hosts, the direct contributions of parasite biomass to a system, and via parasite-induced changes in host behavior and physiology (trait-mediated impacts). Here, a framework was constructed that can be used to conceptualize parasite contributions to ecosystem function (Chapter 1). Then the influence of parasite attack on host movement was explored to further evince the mechanistic underpinnings of trait-mediated parasite impacts (Chapter 2). Additionally, mesocosms were created across a gradient of parasitism to examine how these mechanisms are likely to unfold at larger biological scales (Chapter 3). Lastly, a series of differential equations was created to model host-parasite-ecosystem interactions and generate theoretical predictions about how and when parasites are likely to influence ecosystem processes (Chapter 4). Parasites have many characteristics of ecosystem engineers, but their role has historically been ignored. These studies begin to explore the role that parasitism may have as one of the drivers of ecosystem processes.

<div>Smart warehouses have become more popular in these days, with Automated Guided Vehicles (AGVs) being used for order pickups. They also allow efficient cost management with optimized storage and retrieval. Moreover, optimization of resources in these warehouses is essential to ensure maximum efficiency. In this thesis, we consider a three dimensional smart warehouse system equipped with heterogeneous AGVs (i.e., having different speeds). We propose scheduling and placement policies that jointly consider all the different design parameters including the scheduling decision probabilities and storage assignment locations. In order to provide differentiated service levels, we propose a prioritized probabilistic scheduling and placement policy to minimize a weighted sum of mean latency and latency tail probability (LTP). Towards this goal, we first derive closed-form expressions for the mean latency and LTP. Then, we formulate an optimization problem to jointly optimize a weighted sum of both the mean latency and LTP. The optimization problem is solved efficiently over the scheduling and decision variables. For a given placement of the products, scheduling decisions of customers’ orders are solved optimally and derived in closed forms. Evaluation results demonstrate a significant improvement of our policy (up to 32%) as compared to the state of other algorithms, such as the Least Work Left policy and Join the Shortest Queue policy, and other competitive baselines.</div>

Inom matematikdidaktik beskrivs matematisk modellering som en process bestående av olika delprocesser. Forskare inom området menar att ett holistiskt förhållningssätt behövs i undervisningen för att alla delprocesser i modelleringsprocessen ska kunna utvecklas. Syftet med denna studie är att undersöka kursplaners synliggörande (intended curriculum) av olika delprocesser vid matematisk modellering med differentialekvationer i svenska lärosätens ämneslärarprogram för gymnasiet med matematik som huvudämne. För att analysera kursplanerna används ett teoretiskt ramverk formulerat av Blomhøj &amp; Jensen (2003). Resultatet visar stora skillnader i vilka delprocesser som synliggörs. Från nästan alla kursplaner som analyserades kunde man tydligt utläsa att i kursplanen synliggjordes delprocesser om matematisering av modelleringsproblem samt undersökning och lösning av uppkomna matematiska problem, medan andra delprocesser som speglar identifiering av ett verklighetsnära modelleringsproblem och tolkning av beräkningsresultatsynliggörs i mycket liten utsträckning. Delprocessen om analys av modellens giltighet synliggjordes i några enstaka kursplaner. En slutsats är att alla delprocesser inte synliggörs i kursplaner för matematikkurser i ämneslärarprogram för gymnasiet som behandlar modellering med differentialekvationer. Studien belyser behov av fortsatt forskning inom området, till exempel av det tillämpade genomförandet eller det uppnådda kursresultatet. / In mathematics education, mathematical modelling is described as a process consisting of different sub-processes. Researchers in the area believe that a holistic approach needs to be included in teaching where all sub-processes in the modelling process can be developed. The aim of this study is to investigate the visibility of different sub-processes in mathematical modelling in curricula (intended curriculum) with differential equations for Swedish teachers’programme with mathematics as core subject. To analyse the curricula, a theoretical framework formulated by Blomhøj &amp; Jensen (2003) is used. The results show that there is a difference in the visibility of the sub-processes. From almost all curricula that were analysed, sub-processes on mathematization of modelling problems and investigation and solution of emerging mathematical problems could be clearly seen, while other sub-processes such as identification of a realistic modelling problem, interpretation and analysis of results could be seen to a lesser extent. The sub-process of analysing the validity of modelswas visible in a few curricula. Hence possible conclusions can be drawn, one is that curricula in modelling with differential equations for Swedish secondary education teacher programme in mathematics do not showcase all modellingsub-processes. The thesis highlights further need in studies of the implemented and attained curricula.

The exploratory study sought to elicit and document mathematics teachers‟ views on how they enacted the process of transition between contexts and mathematics. The study pursued to understand teachers‟ beliefs and knowledge of mathematics. A mixed methods sequential explanatory research design was employed where a quantitative phase was followed by the connecting phase and concluded through a qualitative phase involving three case studies. A purposive sample of 165 practicing teachers who had registered for a professional advancement developmental course at a university participated in the study by voluntarily completing a survey questionnaire. From this sample, three cases of individual teachers were pursued. The first two cases involved conducting in-depth interviews with the teacher who had rated sentences in the questionnaire differently while the last case involved the recording of an interview of one individual using field notes. The questionnaire sought teachers‟ biographical details (section A), their views on contexts and mathematics (section B) and their rating of sentences in a passage with regard to the mathematics embedded in the sentences (section C). Semi-structured interviews were conducted in the qualitative phase to elicit in-depth views of the teachers‟ regarding the research problem. All the instruments were tested for validity and reliability. Quantitative data gathered was analysed using frequencies, percentages, cross tabulations, bar charts and pie charts as well as the calculation of Pearson chi-square tests (Cohen, Manion & Morrison, 2011). Descriptive and inferential statistics were used to collate teachers‟ views from which themes were drawn and related to make inferences. It was found that teachers‟ positive views about contexts and mathematics did not translate into them recognising mathematics in some mathematics potent contexts as captured in their ratings in section C of the questionnaire. Statistically significant associations were recorded to support this. The study also conceptualised a mathematical participation model (MP-model) as a tool to describe and analyse participation that involves the use of real world data in the teaching and learning of mathematics. The MP-model involves four components, viz. the community of practice (CoP), real world data, mathematics and a model in which members of the CoP tap into the real world data and mathematics to model their participation. The study recommends the MP-model as tool for description and enactment of full mathematical participation. / Mathematical Sciences / D.Litt.et. Phil. (Mathematics Education)

This thesis deals with the methods of Terahertz (THz) spectroscopy to observe the kinetics of haemostatic materials used for supporting the native mechanism of haemostasis. The theoretical part follows the physical principles of THz time-domain spectroscopy (THz TDS), mentions the advantages and limitations of this method and its application possibilities for the characterization of biomedical materials. Further, there are specified properties of actual haemostats, described principles of their function and usage in practice, including their interaction with the living tissue. There were performed experiments monitoring the kinetics of physiologic reaction of the tissue adhesive based on the cyanoacrylates and absorbable haemostats. The mechanisms of monitored reactions were explained based on the physical-chemical principles that are used also for the kinetic models’ derivation. Modelling of the measured data results in the estimation of the parameters characterizing the observed samples. The most interesting parameter is the time constant of the reaction because of the possibility to compare reaction rates of different types of haemostats. The detailed analysis of this parameter is performed using the means of statistical methods. Tissue adhesive samples were measured by other spectroscopic and microscopic methods to compare the findings with the experimental results of the THz TDS. Data were processed using algorithms designed especially for this experiment and analysed using mathematical methods.

Subject of the dissertation is a probability analysis on creation of embankment subsoil filtration deformations. Out of the broad topic of filtration deformations, the dissertation is focused at initiation of the process. At this phase, the overlying layers downstream of levee get uplifted, and eventually get breached. The process of downstream subsoil failure probability estimation is formulated using mathematical and statistical modelling. Within the scope of parametrical study the suggested method is applied onto a test environment. Results of the probability estimation are compared with results obtained using Limit state design method. The results of stochastic modelling can be used for improvement of Limit state design method precision.

<p>Regardless of their origin or pathology, many, if not all, diseases have long been regarded as complex. Yet, despite the progression in the understanding of complexity and the development of systems biology, the majority of biomedical research has been derived from qualitative principles. In comparison to the ethical, temporal and logistical limitations of human experimentation, <em>in vivo</em> animal models have served to provide a more advantageous means to elucidate the underlying disease mechanisms. However, given the additional limitations presented by such models, <em>in silico </em>models have emerged as an effective complement, and, in some cases, a replacement for <em>in vivo</em> experimentation. The <em>in silico </em>models presented in this thesis were developed using mathematical and computational methods to investigate the evolution of two complex, diverse diseases from a systems biology perspective: allergic asthma and cancer.</p> <p>We generated two novel <em>in silico</em> models of allergic asthma aimed at clarifying some dynamic aspects of allergic responses. Experimentally, we utilized an <em>in vivo</em> murine model of chronic exposure to the most pervasive aeroallergen worldwide, house dust mite (HDM), for up to 20 weeks, equivalent to at least 20 human years. Using a range of HDM concentrations, experimental data were collected to study local and systemic effects. The first model applied empirical mathematical techniques to establish equations for airway inflammation and HDM-specific immunoglobulins using an iterative approach of experimentation and validation. Using the equations generated, we showed that the model was able to accurately predict and simulate data. The model also demonstrated the non-linear relationship between HDM exposure and both airway inflammation and allergic sensitization and identified system thresholds.</p> <p>The second model used mechanistic mathematical techniques to investigate the trafficking of eosinophils as they migrated from bone marrow to the blood and, ultimately, to the lungs. Making use of a limited data set, the model determined the effect of individual processes on the system. We identified eosinophil production, survival and death as having the greatest impacts, while migration played a relatively minor role. Furthermore, the model was used to simulate knockout models and the use of antibodies <em>in silico</em>.</p> <p>In the context of cancer growth and metastasis, we developed a theoretical model demonstrating the spatio-temporal development of a tumour in two-dimensions. The model was encoded to create a computer graphic simulation program, which simulated the effects of various parameters on the size and shape of a tumour. Through simulations, we demonstrated the importance of the diffusion process in cancer growth and metastasis.</p> <p>Ultimately, we believe the greatest benefit of each <em>in silico</em> model is the ability to provide an understanding of each respective disease recognized as dynamic and formally complex, but predominantly studied in reductionist, static or un-integrated approaches.</p> / Doctor of Philosophy (Medical Science)

Introduction: Discontinuation of tyrosine kinase inhibitor (TKI) treatment is emerging as the main therapy goal for Chronic Myeloid Leukemia (CML) patients. The DESTINY trial showed that TKI dose reduction prior to cessation can lead to an increased number of patients achieving sustained treatment free remission (TFR). However, there has been no systematic investigation to evaluate how dose reduction regimens can further improve the success of TKI stop trials. Methods: Here, we apply an established mathematical model of CML therapy to investigate different TKI dose reduction schemes prior to therapy cessation and evaluate them with respect to the total amount of drug used and the expected TFR success. Results: Our systematic analysis confirms clinical findings that the overall time of TKI treatment is a major determinant of TFR success, while highlighting that lower dose TKI treatment for the same duration is equally sufficient for many patients. Our results further suggest that a stepwise dose reduction prior to TKI cessation can increase the success rate of TFR, while substantially reducing the amount of administered TKI. Discussion: Our findings illustrate the potential of dose reduction schemes prior to treatment cessation and suggest corresponding and clinically testable strategies that are applicable to many CML patients.

Tesis por compendio / The Lack of Homogeneity in the Product (LHP) appears in productive processes with raw materials, which directly stem from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. LHP appears in different sectors such as ceramic tile, horticulture, marble, snacks, among others. LHP becomes a managerial problem when customers require to be served with homogeneous product. Supply chains responsible to provide homogeneous product face the need to include classification activities in their productive processes to obtain sub-lots of homogeneous product. Due to the inherent LHP uncertainty, these homogeneous sub-lots will not be known until the product have been produced and classified. An improper management of the LHP can have a very negative impact on the customers' satisfaction due to inconsistencies in the answer to their requirements and also on the Supply Chain's efficiency. The Order Promising Process (OPP) appears as a key element for properly managing the LHP in order to ensure the matching of uncertain homogeneous supply with customer order proposals. The OPP refers to the set of business activities that are triggered to provide a response to the orders from customers. These activities are related to the acceptance/rejection decision, and to set delivery dates. For supply chains affected by the LHP, the OPP must consider the homogeneity as another requirement in the answer to the orders. Besides, due to the LHP inherent uncertainty, discrepancies between the real and planned homogeneous quantities might provoke that previously committed orders cannot be served. The Shortage Planning (SP) process intends to find alternatives in order to minimise the negative impact on customers and the supply chain. Considering LHP in the OPP brings a set of new challenging features to be addressed. The conventional approach of assuming homogeneity in the product for the master production schedule (MPS) and the quantities Available-To-Promise (ATP) derived from it is no longer adequate. Instead, both the MPS and ATP should be handled in terms of homogeneous sub-lots. Since the exact quantity of homogeneous product from the planned lots in the MPS is not exactly known until the classification activities have been performed, the ATP also inherits this uncertainty, bringing a new level of complexity. Non-homogeneous product cannot be accumulated in order to fulfil future incoming orders. Even more, if the product handled is perishable, the homogeneity management becomes considerably more complex. This is because the state of the product is dynamic with time and related variables to it, like quality, price, etc., could change with time. This situation could bring unexpected wasting costs apart from the shortages already mentioned. The perishability factor is itself another source of uncertainty associated to the LHP. This dissertation proposes a conceptual framework and different mathematical programming models and tools, in both deterministic and uncertainty environments, in order to support the OPP and SP under LHP's effect. The aim is to provide a reliable commitment with customer orders looking for a high service level not just in the due date and quantity but also in the homogeneity requirements. The modelling of the characteristics inherent to LHP under deterministic context constitutes itself one of the main contribution of this dissertation. Another novelty consists in the inclusion of uncertainty in the definition of homogeneous sub-lots, their quantities and their dynamic state and value. The uncertainty modelling approach proposed is mainly based on the application of fuzzy set theory and possibility theory. The proposed mathematical models and tools have been validated in real cases of SC, specifically in the ceramic tile sector for non perishables, and in the fruit sector for perishables. The results show a ... / La Falta de Homogeneidad en el Producto (LHP, por sus siglas del inglés ``Lack of Homogeneity in the Product'') aparece en procesos productivos con materias primas que derivan directamente de la naturaleza y/o procesos de producción con operaciones que confieren heterogeneidad a las características de los productos obtenidos, incluso cuando los insumos utilizados son homogéneos. La LHP aparece en diferentes sectores como la cerámica, horticultura, mármol, snacks, entre otros. Se convierte en un problema gerencial cuando los clientes requieren homogeneidad en el producto y las cadenas de suministro enfrentan la necesidad de incluir actividades de clasificación en sus procesos productivos para obtener sub-lotes de producto homogéneo. Debido a la incertidumbre inherente a la LHP, los sub-lotes homogéneos y su cantidad no serán conocidos hasta que el producto haya sido producido y clasificado. Una gestión inadecuada de la LHP puede tener un impacto muy negativo en la satisfacción de los clientes debido a inconsistencias en la respuesta a sus requerimientos y también en la eficacia de la Cadena de Suministro. El Proceso de Comprometer de Pedido (OPP, por sus siglas del inglés ``Order Promising Process'') aparece como un elemento clave para gestionar adecuadamente la LHP, con el fin de asegurar la coincidencia entre el suministro incierto de producto homogéneo y las propuestas de pedido del cliente. El OPP se refiere al conjunto de actividades empresariales realizadas para proporcionar una respuesta a las órdenes de los clientes. Estas actividades están relacionadas con las decisiones de aceptación/rechazo, y establecimiento de fechas de entrega para las órdenes del cliente. En las cadenas de suministro afectadas por la LHP, el OPP debe considerar la homogeneidad como otro requisito adicional en la respuesta a los pedidos. Además, debido a la incertidumbre intrínseca de la LHP, las discrepancias entre las cantidades homogéneas reales y planificadas podrían provocar que las órdenes comprometidas anteriormente no puedan ser completadas debido a la escasez de producto. El proceso de planificación de la escasez (SP, por sus siglas del inglés "Shortage Planning") se encarga de encontrar alternativas para minimizar este impacto negativo en los clientes y la cadena de suministro. Considerar la LHP dentro del OPP implica un conjunto nuevo de características desafiantes que deben ser abordadas. El enfoque convencional de asumir la homogeneidad en el producto para el programa maestro de producción (MPS, por sus siglas del inglés "Master Production Schedule") y las cantidades disponibles a comprometer (ATP, por sus siglas del inglés "Available-To-Promise") derivadas de él, no es adecuado. En cambio, tanto el MPS como el ATP deben manejarse en términos de sub-lotes homogéneos. Dado que la cantidad exacta de producto homogéneo de los lotes previstos en el MPS no se sabe exactamente hasta que se han realizado las actividades de clasificación, el ATP también hereda esta incertidumbre, trayendo un nuevo nivel de complejidad. El producto no homogéneo no se puede acumular para satisfacer futuras órdenes entrantes. Más aún, si el producto manipulado es perecedero, el manejo de la homogeneidad se vuelve mucho más complejo. Esto se debe a que el estado del producto es dinámico en el tiempo, y variables relacionadas como calidad, precio, etc., podrían también cambiar con el tiempo. Esta situación puede provocar costos inesperados de desperdicio aparte de la escasez ya mencionada. El factor de perecedero es en sí mismo otra fuente de incertidumbre asociada a la LHP. Esta disertación propone un marco conceptual y diferentes modelos y herramientas de programación matemática, tanto en entornos deterministas como de incertidumbre, para apoyar al OPP y SP considerando el efecto de LHP. El objetivo es proporcionar un compromiso fiable con los pedidos de los clientes en busca de un alto nivel de servicio no s / La Falta d'Homogeneïtat en el Producte (LHP, per les seues sigles de l'anglés ''Lack of Homogeneity in the Product'') apareix en processos productius amb matèries primes que deriven directament de la natura i/o processos de producció amb operacions que conferixen heterogeneïtat a les característiques dels productes obtinguts, fins i tot quan les entrades utilitzades són homogènies . La LHP apareix en diferents sectors com la ceràmica, horticultura, marbre, snacks, entre altres. Es convertix en un problema gerencial quan els clients requereixen homogeneïtat en el producte i les cadenes de subministrament enfronten la necessitat d'incloure activitats de classificació en els seus processos productius per a obtindre sublots de producte homogeni. A causa de la incertesa inherent a la LHP, els sublots homogenis i la seua quantitat no seran coneguts fins que el producte haja sigut produït i classificat. Una gestió inadequada de la LHP pot tindre un impacte molt negatiu en la satisfacció dels clients degut a inconsistències en la resposta als seus requeriments i també en l'eficàcia de la Cadena de Subministrament. El Procés de Comprometre Comandes (OPP, per les seues sigles de l'anglés ''Order Promising Process'') apareix com un element clau per a gestionar adequadament la LHP, a fi d'assegurar la coincidència entre el subministrament incert de producte homogeni i les propostes de comanda del client. L'OPP es refereix al conjunt d'activitats empresarials realitzades per a proporcionar una resposta a les ordres dels clients. Aquestes activitats estan relacionades amb les decisions d'acceptació/rebuig, i establiment de dates de lliurament per a les ordres del client. En les cadenes de subministrament afectades per la LHP, l'OPP ha de considerar l'homogeneïtat com un altre requisit addicional en la resposta a les comandes. A més, a causa de la incertesa intrínseca de la LHP, les discrepàncies entre les quantitats homogènies reals i planificades podrien provocar que les ordres compromeses anteriorment no puguen ser completades a causa de l'escassetat de producte. El procés de planificació de l'escassetat (SP, per les seues sigles de l'anglés "Shortage Planning") s'encarrega de trobar alternatives per a minimitzar aquest impacte negatiu en els clients i en la cadena de subministrament. Considerar la LHP dins de l'OPP implica un conjunt nou de característiques desafiants que han de ser abordades. L'enfocament convencional d'assumir l'homogeneïtat en el producte per al programa mestre de producció (MPS, per les seues sigles de l'anglés "Master Production Schedule") i les quantitats disponibles a comprometre (ATP, per les seues sigles de l'anglés "Available-To-Promise") derivades d'ell, no és adequat. En canvi, tant el MPS com l'ATP han de manejar-se en termes de sublots homogenis. Atés que la quantitat exacta de producte homogeni dels lots previstos en el MPS no se sap exactament fins que s'han realitzat les activitats de classificació, l'ATP també hereta aquesta incertesa, portant un nou nivell de complexitat. El producte no homogeni no es pot acumular per a satisfer futures ordees entrants. Més encara, si el producte manipulat és perible, el maneig de l'homogeneïtat es torna molt més complex. Açò es deu al fet que l'estat del producte és dinàmic en el temps, i variables relacionades com qualitat, preu, etc., podrien també canviar amb el temps. Aquesta situació pot provocar costos inesperats de rebuig a banda de l'escassetat ja esmentada. El factor de perible és en si mateix un altra font d'incertesa associada a la LHP. Aquesta dissertació proposa un marc conceptual i diferents models i eines de programació matemàtica, tant en entorns deterministes com d'incertesa, per a recolzar a l'OPP i SP considerant l'efecte de LHP. L'objectiu és proporcionar un compromís fiable amb les comandes dels clients a la recerca d'un alt nivell de servei no sols en la data i la quantitat esperades, s / Grillo Espinoza, H. (2017). Advanced methods and models in uncertainty for the order promising process in supply chain characterized by the lack of homogeneity in product [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/91110 / Compendio