This thesis proposes a novel and efficient method (Method of Evolving Junctions) for solving optimal control problems with path constraints, and whose optimal paths are separable. A path is separable if it is the concatenation of finite number of subarcs that are optimal and either entirely constraint active or entirely constraint inactive. In the case when the subarcs can be computed efficiently, the search for the optimal path boils down to determining the junctions that connect those subarcs. In this way, the original infinite dimensional problem of finding the entire path is converted into a finite dimensional problem of determine the optimal junctions. The finite dimensional optimization problem is then solved by a recently developed global optimization strategy, intermittent diffusion. The idea is to add perturbations (noise) to the gradient flow intermittently, which essentially converts the ODE's (gradient descent) into a SDE's problem. It can be shown that the probability of finding the globally optimal path can be arbitrarily close to one. Comparing to existing methods, the method of evolving junctions is fundamentally faster and able to find the globally optimal path as well as a series of locally optimal paths. The efficiency of the algorithm will be demonstrated by solving path planning problems, more specifically, finding the optimal path in cluttered environments with static or dynamic obstacles.

In today’s competitive business world, every company wants to be more profitable. In order to keep the profit margin high, the companies need to work more. It is very hard to find any company which works on a single project. Actually it is not only any specific company’s practice rather it is a practice of the entire human being to do multiple works at the same time. The practice has also become quite common in the companies. Although the practice of working on multiple projects simultaneously has become popular for the companies overtime, the important thing is to manage all the projects efficiently so that all projects can be finished according to the plan. Multiple project management deals with a lot of challenges in terms of resource and time. The facts like resource sharing and resource constraint add more complexity to the management of such multiple simultaneous projects. It is difficult to understand the correct workload during the project and the effects of running all the simultaneous projects to the project deployment time. The situation becomes even critical if the projects run in a dynamic environment which may provide changes during any phase of it. Software development is such a process that deals with multiple projects and also the dynamic environment. The master study will focus on such case where the study has conducted in a software development company named ActionWave Development AB. ActionWave Development AB is dealing with multiple projects with having resource constraint. In this study, readers will come to know about the challenges of ActionWave Development AB in terms of resource scenario and deployment time in case of managing multiple projects simultaneously. The study will analyze the effect of having multiple simultaneous projects to the limited resource of ActionWave Development AB and will also show the effects on projects deployment time. The study does the analysis for the current case and an imaginary test case. Later solution has been provided to overcome the problem. Further recommendations were made in order to conduct an effective project management within the company.

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The mobility that wireless communication offers to users, added to the ease of installation have increased the demand on such communication systems. However, the main drawback of wireless communication is the degradation of the signal as it travels through the channel due to the different propagation mechanisms the signal undergoes. To minimise the effect of the channel and get the best service, the base stations must be appropriately located within the environment. This requires proper knowledge of the channel characteristics. Ray tracing software is used throughout this work to generate the channel characteristics of an indoor environment. After getting the channel characteristics, a novel cost function is defined based on the path loss values and it is then optimised. Once the optimal base stations’ positions are found, the minimal amount of power required to cover a predefined percentage of the possible receivers’ locations is calculated. On the other hand, a receiver’s position acquiring enough field strength does not necessarily enjoy the service. This depends on the time dispersion parameters values relative to the symbol rate. The time dispersion parameters have always been ignored in the literature while finding the optimal base stations’ locations. Three cost functions that take into consideration both the path loss and rms delay spread, for the first time in the literature, are therefore defined. The cost functions are optimised and their corresponding results are compared. Furthermore, indoor environments have always been considered static which is never realistic. They are subject to continuous changes such as opening doors and windows as well as the presence of people. The first detailed analysis and quantified results of the effect of a dynamic environment on the optimal base stations’ positions and minimal emitted power are presented. It is shown that the optimal base stations’ locations and minimal emitted power are sensitive to such environment changes. The environment changes can also disturb the service for active receivers. Three techniques to overcome the effect of environment changes and bring the disturbed service back to receivers are proposed. The first two techniques rely on increasing the emitted power or changing the antenna polarisation. The third technique is a novel technique that gives the base station the ability to automatically move in various directions within a limited distance. The techniques are tested and their efficiency and limitations are discussed.

Path planning is a crucial issue for virtual environments where autonomous agents try to navigate from a specific location to a desired one. There are several algorithms developed for path planning, but several domain requirements make engineering of these algorithms difficult. In complex environments, considering single objective for searching and finding optimal or sub-optimal paths becomes insufficient. Thus, multi objective cases are distinguished and more complicated algorithms to be employed is required. It can be seen that more realistic and robust results can be obtained with these algorithms because they expand solution perspective into more than one criteria. Today, they are used in various games and simulation applications. On the other hand, most of these algorithms are off-line and delimitate interactive behaviours and dynamics of real world into a stationary virtuality. This situation reduces the solution quality and boundaries. Hence, the necessity of solutions where multi objectivity is considered in a dynamic environment is obvious. With this motivation, in this work, a novel multi objective incremental algorithm, MOD* Lite, is proposed. It is based on a known complete incremental search algorithm, D* Lite. Solution quality and execution time requirements of MOD* Lite are compared with existing complete multi objective off-line search algorithm, MOA*, and better results are obtained.

Successful and high precision localization is an important feature for autonomous vehicles in an urban environment. GPS solutions are not good on their own and laser, sonar and radar are often used as complementary sensors. Localization with these sensors requires the use of techniques grouped under the acronym SLAM (Simultaneous Localization And Mapping). These techniques work by comparing the current sensor inputs to either an incrementally built or known map, also adding the information to the map.Most of the SLAM techniques assume the environment to be static, which means that dynamics and clutter in the environment might cause SLAM to fail. To ob-tain a more robust algorithm, the dynamics need to be dealt with. This study seeks a solution where measurements from different points in time can be used in pairwise comparisons to detect non-static content in the mapped area. Parked cars could for example be detected at a parking lot by using measurements from several different days.The method successfully detects most non-static objects in the different test datasets from the sensor. The algorithm can be used in conjunction with Pose-SLAM to get a better localization estimate and a map for later use. This map is good for localization with SLAM or other techniques since only static objects are left in it.

Mobile agent planning (MAP) is increasingly viewed as an important technique of information retrieval systems to provide location aware services of minimum cost in mobile computing environment. Although Hopfield-Tank neural network has been proposed for solving the traveling salesperson problem, little attention has been paid to the time constraints on resource validity for optimizing the cost of the mobile agent. Consequently, we hypothesized that Hopfield-Tank neural network can be used to solve the MAP problem. To test this hypothesis, we modify Hopfield-Tank neural network and design a new energy function to not only cope with the dynamic temporal features of the computing environment, in particular the server performance and network latency when scheduling mobile agents, but also satisfy the location-based constraints such as the starting and end node of the routing sequence must be the home site of the traveling mobile agent. In addition, the energy function is reformulated into a Lyapunov function to guarantee the convergent stable state and existence of the valid solution. The connection weights between the neurons and the activation function of state variables in the dynamic network are devised in searching for the valid solutions. Moreover, the objective function is derived to estimate the completion time of the valid solutions and predict the optimal routing path. Simulations study was conducted to evaluate the proposed model and algorithm for different time variables and various coefficient values of the energy function. The experimental results quantitatively demonstrate the computational power and speed of the proposed model by producing solutions that are very close to the minimum costs of the location-based and time-constrained distributed MAP problem rapidly. The spatio-temporal technique proposed in this work is an innovative approach in providing knowledge applicable to improving the effectiveness of solving optimization problems.

31 Reunión Latinoamericana de Matemática Educativa (Relme), evento desarrollado en la Universidad de Medellín, Colombia, del 31 Julio al 04 de Agosto de 2017. / En esta Comunicación Breve, se expone el proyecto “Aprendizaje digital como estrategia metodológica en la enseñanza de la Matemática en estudiantes de la Facultad de Negocios en la Universidad Peruana de Ciencias Aplicadas” que se aplicó de manera pre-experimental durante ciclo 2016-2 y ciclo verano 2017-0. Los estudiantes desarrollaron habilidades de interpretación, comprobación de cálculos y análisis de resultados en resolución de problemas contextualizados sobre Oferta y Demanda lineal usando el software Geogebra. Los estudiantes desarrollaron habilidades tecnológicas, la experiencia en el aula fue alentadora pues interactuaron con sus compañeros, realizaron preguntas desarrollando pensamiento crítico y razonamiento cuantitativo de situaciones reales. / This brief communication, the project "Digital learning as a methodological strategy in the teaching of mathematics in students of the Faculty of Business at the Peruvian University of Applied Sciences", was applied pre-experimentally during the 2016-2 and summer cycle 2017-0. Students developed skills in interpretation, calculation and analysis of results in problem solving contextualized on offer and demand linear using Geogebra software. Students they also developed technological skills the experience in the classroom was encouraging because they interacted with their peers, asked questions acquiring critical thinking and quantitative reasoning of real situations.

The present study analysed the modeling of occurrence of the human Shistosomosis in Lagarto City, State of Sergipe from 1999 to 2008 in combination with physiographic, social, cultural and sanitation data from 41 municipalities. The main objective of this study is to develop a map with the main potential areas of the risk for the occurrence of Shistosomosis in Lagarto,SE. Bassing a anterior of vulnerability built with epidemiological environmental and sociocultural data. Firstly, we perfomed a spacelation of the operational data of activities of vigilance of the Schistosomiasis Control Program obtained at the secretariat of municipalities health and permited the generation of maps containg the areas of occurrence of the disease in the period from 1999 to 2008. The methodology followed first analysis of epidemiological official data from the Shistosomosis Control Program (PCE) from the State of Sergipe. Secondly, an epidemiological survey was performed using a questionnaire to evaluate several social, cultural and sanitation data in 1893 houses. These data were tabulated and distributed in 8 Health Units from the City of Lagarto. The analysis of these combined data in SPRING, developed by National Institute of Space Research (NISP) and Statistical Package for Social Science - SPSS identified some more specific measurements that can be used as risk factors for the occurrence of Shistosomosis in Lagarto. The analyses of these combinated data using Geographic information system in a Synthesis map made possible to identify the health unit of Jacaré as the area with higher levels of occurrence of Shistosomosis in Lagarto (43,47% of the studied sample). In conclusion, the applied methodoly was able to create a mathematical modeling for mapping risk areas of occurrence of Shistosomosis that will be important to guide the epidemiological control measures in Shistosomiasis. / O presente estudo analisa o quadro atual da ocorrência de esquistossomose no município de Lagarto-SE, mediante a modelagem dos dados epidemiológicos de 1999 a 2008 combinados com dados atuais fisiográficos, sociais, culturais e de cobertura do saneamento básico em 41 localidades. O principal objetivo deste é fazer um zoneamento dos principais focos de esquistossomose no município de Lagarto com base em critério de vulnerabilidade construído a partir da análise de dados epidemiológicos, ambientais e socioculturais. Inicialmente foi realizado um levantamento e espacialização dos dados operacionais das atividades de vigilância do Programa de controle da Esquistossomose (PCE), obtidos na Secretaria Municipal da Saúde do município, a qual permitiu a geração dos mapas representativos das áreas de ocorrência da doença no período de 1999 a 2008, Dados obtidos em pesquisa de campo obtidos através de questionários foram tabulados e distribuídos de acordo com 8 unidades de planejamento estabelecidas no município pela SRH. O artifício utilizado permitiu a redução do conjunto, homogeneizando os resultados de forma a facilitar o tratamento estatístico dos dados. Em seguida foram procedidas as manipulações e análises das variáveis que permitiram a determinação das vulnerabilidades das unidades de planejamento do município de Lagarto/Se. Para tanto, foi utilizado o Sistema de Informações Geográficas ―SPRING‖, desenvolvido pelo Instituto Nacional de Pesquisas Espaciais (INPE) em conjunto com o soft de análise estatística Statistical Package for the Social Sciences - SPSS. Na comparação dos resultados representados nos mapas temáticos entre as unidades de planejamento foi possível identificar os fatores (similares ou não) que concorrem para tornar-las endêmicas, que combinados resultou no mapa síntese das áreas mais vulneráveis à ocorrência da doença, fato este confirmado principalmente nas localidades pertencentes a Unidade de Planejamento Jacaré que apresenta historicamente um dos maiores registros de casos de esquistossomose em Lagarto no período estudado (43,47%). Admitindo-se satisfatório o enquadramento alcançado e a metodologia aplicada, concluiu-se que o zoneamento proposto a partir do modelo matemático gerado comportou-se de forma satisfatória na análise de fatores considerados de risco para a aquisição da doença, constituindo-se de uma ferramenta adequada para o auxilio das estratégias de controle da doença no município de Lagarto/SE.

Antibiotic resistance is a worldwide health threat, as bacteria continue to evade antibiotic treatment. In order to survive, bacteria utilize a number of resistance mechanisms, including efflux pumps, which efficiently export antibiotics outside of the cell to reduce intracellular damage. While such mechanisms are well known, there remains a significant gap in knowledge regarding how different environmental dynamics, such as the rate of antibiotic introduction or the diversity within a microbial community, play a role in resistance. In this work, we used the AcrAB-TolC efflux pump as a case study to explore how such complex dynamics promote antibiotic resistance and its evolution. First, through a combined effort using experiments and mathematical modeling, we discovered that the rate of antibiotic introduction impacts the fraction of resistant bacteria in a population. We then explored the impact of mixed populations on survival following antibiotic treatment. In mixed microcolonies, we found that resistant cells can harm their susceptible neighbors by exporting antibiotics to increase the local concentrations of these drugs. Next, we aimed to understand how these environmental effects may impact longer-term survival of an antibiotic treatment, focusing on the evolution of resistance over ~72 hours. Through a series of adaptive evolution experiments, we identified that near-MIC treatments were the most likely to promote antibiotic resistance, regardless of whether the strains contained the AcrAB-TolC pump at wild type or overexpressed levels, or whether the strains lacked the pump altogether. In studying antibiotic introduction rates on evolution, we found that slower introduction rates facilitated the evolution of high levels of resistance with a minimal fitness cost. Meanwhile, mixed populations demonstrated limited evolvability after rapid antibiotic introductions. This work provides important insights into the impacts of environmental factors, such as the rate of antibiotic introduction and the homogeneity of populations, on the promotion and evolution of antibiotic resistance. These lessons may help inform future policies on antibiotic use and mitigate the continued pattern of resistance evolution.