In the fall of 2018, programming was implemented in the swedish curriculum and then became a new element in mathematics education for grades 1-3. Teachers who took their degree before the implementation, lacks education in programming and there is interest in finding out how teaching about programming is conducted since it became part of the curriculum. The purpose of this study was to contribute with knowledge about how teachers have implemented programming in their teaching even though they lack education in it. Four semi-structured interviews have been conducted where the data from the interviews has been analyzed from Mathematical Knowledge for Teaching. The result shows that teachers without education in programming find it difficult to plan instruction in programming by themselves. In the teaching of programming the teachers focus on the central concepts in programming and that the programming should interest the students. It was difficult for teachers to assess the students in programming and the only assessment that teachers make is the formative assessment. / Sammanfattning Hösten 2018 implementerades programmering i den svenska läroplanen och blev då ett nytt moment inom matematikundervisningen för årskurs 1-3. Lärare som innan detta tog sin lärarexamen saknar utbildning inom programmering och det finns intresse att ta reda på hur undervisningen kring programmering bedrivs sedan det blev en del av läroplanen. Syftet med denna studie var att bidra med kunskap om hur lärare har implementerat programmering i sin undervisning trots att de saknar utbildning inom det. Fyra stycken semistrukturerade intervjuer har gjorts där datan från intervjuerna har analyserats utifrån Mathematical Knowledge for Teaching. Resultatet visar på att lärare utan utbildning inom programmering har svårigheter att på egen hand planera undervisning i programmering. Under genomförandet av undervisningen fokuserar lärarna på att befästa centrala begrepp inom programmering och att väcka ett intresse hos eleverna. Det upplevdes svårt för lärarna att bedöma eleverna inom programmering och den enda bedömning som lärarna gör är den formativa bedömningen.

Grunden för begreppet inkludering är Salamancadeklarationen. Den antogs 1994 men det finns fortfarande otydlighet i vad som menas med inkludering i praktiken. I den här litteraturstudien undersöks innebörden av inkludering i matematikundervisningen för elever som har matematiksvårigheter utifrån ett specialpedagogiskt perspektiv. Studien utgår ifrån tre specialpedagogiska perspektiv: individperspektivet, det kritiska perspektivet och dilemmaperspektivet. Resultaten visar att forskning med utgångspunkt i ett individperspektiv föreslår olika strategier för lärare för att möta behov hos elever som har svårigheter. Det kritiska perspektivet fokuserar på mer på en organisatorisk nivå, men resultaten understryker att lärarnas metoder är viktiga. De lyfter också fram brister på olika former av resurser, såsom lärartid och lärarutbildning. Forskning ur dilemmaperspektivet betonar att alla lösningar innebär en avvägning av för- och nackdelar och att en inkluderande undervisning samtidigt kan vara både positiv och negativ för eleven. / THe Salamanca Statement (1994) is the base for inclusive education. This international declaration came to establish the concept of inclusion. However, after all these years the meaning of inclusion in implementation is not clear. To address this unclarity, this literature review attempts to examine the impact of inclusion in mathematics education for students having difficulties with mathematics. The study focuses on special education research from three different viewpoints: the individual perspective, the critical perspective and the dilemma perspective. Results show that the research from the individual perspective suggest several strategies for a teacher to address the needs of the pupils that have difficulties. The critical perspective research focuses more on an organizational level, but the findings also suggest that teaching methods are important. These studies also imply the importance of resources such as teacher time or teacher education. The dilemma perspective focuses on the trade-offs between different solutions, inclusion can have both positive and negative impacts on the student.

Fingrar som verktyg är ett fenomen som individer både lärare, elever och vårdnadshavare runt om i världen har skilda åsikter om. Vissa ser fingrarna som ett positivt verktyg för elevers matematiska tänkande medan andra tvekar på fingrarnas tillgång. Syftet med studien är därför att ge bild av hur lärare uppfattar elevers användande av fingrar som verktyg i matematik. För att besvara syftet har studien tagit utgångspunkt i följande frågeställningar: på vilka skilda sätt uppfattar lärare i årskurs 1–6 elevers användande av fingrar som verktyg och vad karaktäriserar respektive uppfattning? Vilka kritiska aspekter kan identifieras relaterat till de skilda uppfattningarna? Studien tar sin utgångspunkt i den fenomenografiska ansatsen. I studien har fem lärare intervjuats för att få bild av hur de uppfattar användandet av fingrar som verktyg i matematik. Allt material har transkriberats och även analyserats för att kunna redogöra för ett tillförlitligt resultat. Resultatet presenteras genom ett utfallsrum som visar att samtliga lärare uppfattar fenomenet mestadels som något positivt, då en uppfattning är mer negativ. Dessa uppfattningar kan i sin tur delas in i fyra skilda uppfattningar: fingrar som ett hinder för elevers lärande, fingrar som ett konkret material, fingrar som ett stöd i matematik samt fingrar som en grund för aritmetisk förståelse. Av de fyra uppfattningarna gick det att urskilja tre kritiska aspekter, nämligen urskilja möjligheter, att fingrar är ett medierenade verktyg samt urskilja relationer/förståelse. / Fingers as a tool is a phenomenon that individuals such as teachers, pupils and caregivers around the world has different opinions about. Some consider that the fingers are a positive tool to pupils mathematical thinking, while others hesitate the fingers access. The purpose of this study is therefore to give a picture of how teacher perceive the use of fingers as a tool in mathematic. To answer the purpose, following questions have been used: In what ways perceive teacher in grade 1-6 pupils use of fingers as a tool and what characterizes each perception? Which critical aspects can be identified related to the different perceptions? The study is based on phenomenography. Five teachers have been interviewed to give a picture of how teacher perceive the use of fingers as a tool in mathematic. The material has been transcribed and analyzed to be able to account a reliable result. The result presented through an outcome space that shows each teacher perceives the phenomenon mostly as something positive, since one perception is more negative. These perceptions can be divided into four different perceptions: fingers as an obstacle for pupils learning, fingers as a concrete material, fingers as a support in mathematics and fingers as a foundation for arithmetic comprehension. Based on these four perceptions, it was possible to distinguish three critical aspects namely, distinguish possibility, that fingers are a mediating tool and distinguish relations/understanding.

Thesis (MSc)--Stellenbosch University, 2015 / ENGLISH ABSTRACT : In this study we look at the syndemic of substance abuse and drug-related crime in the Western Cape province of South Africa. The intent of this study is to provoke critical thinking about the possibilities systems thinking and system dynamics posses for social and health challenges in a diverse and complex environment like that of South Africa, especially the Western Cape. This study ventures into cross-discipline work between Epidemiology, Biomathematics and System Dynamics, with the hope of encouraging researchers from different fields to collaborate in order to curb the scourge of substance abuse and drug-related crime in South Africa. Substance abuse and the associated health and social hazards such as drug-related crime is a major problem in the Western Cape. Drug-related crime cases reported by the South African Police Services (SAPS) for the Western Cape exhibited a 311.5% growth in the past decade. This highlights how the reduction of substance abuse and drug-related crime within theWestern Cape province, will be an elixir for the safety and development of the communities. The fight against substance abuse has been driven by a multi-sectorial approach involving several government departments, non-governmental organisations and communities. With systems thinking the assumption is that the world is systemic, which means that phenomena is understood to be an emergent property of the interrelated whole. Firstly, using non-linear ordinary differential equations, we formulate a deterministic mathematical model for the substance abuse and drug-related crime syndemic, evaluate the threshold number and use sensitivity analysis to analyze the model. Secondly, a dynamic system, called the Substance Abuse and Drug-related Crime in theWestern Cape (SADC-WC) system is constructed using the STELLA in order to explore and classify the underlying relationships and structures within the substance abuse and drug-related crime system. Both the sensitivity analysis, and the simulations of the SADC-WC system indicate that an increase of successful convictions will have a significant influence on the syndemic, and promise to reduce drug-related crime cases. / AFRIKAANSE OPSOMMING : In hierdie studie ondersoek on die syndemie (‘syndemic’) van dwelmmisbruik en dwelmverwante misdaad in die Wes-Kaap provinsie, in Suid-Afrika. Die moontlikhede wat sistemiese denke en dinamiese sisteme inhou vir sosiale en gesondheid kwale in ’n diverse en komplekse omgewing soos Suid-Afrika, word ondersoek. Hierdie studie waag interdisiplinêre werk tussen Epidemiologie, Biowiskunde en Dinamiese sisteme, met die hoop om navorsers van verskillende velde aan te moedig om saam te werk om die plaag van dwelmmisbruik en dwelm-verwante misdaad in Suid-Afrika te bekamp. Dwelmmisbruik en die gepaardgaande gesondheid en maatskaplike gevare soos dwelmverwante misdaad is ’n groot probleem in dieWes-Kaap. Die SAPD se vermelde dwelmverwante midaad het ’n groei van 311,5% ondergaan in die afgelope dekade, en is aanduidend vir hoe die beheer en beperking van dwelmmisbruik en dwelm-verwante misdaad in die Wes-Kaap provinsie bevordering van beide die veiligheid en ontwikkeling van die gemeenskap sal verseker. Dit beklemtoon hoe die vermindering van dwelmmisbruik en dwelm-verwante misdaad in dieWes-Kaapland, sal ’n elikser vir die veiligheid en ontwikkeling van die gemeenskappe. Die stryd teen dwelmmisbruik is gedryf deur ’n multi-sektorale benadering waarby verskeie regeringsdepartemente, nie-regerings organisasies en gemeenskappe. Stelsels denke en dinamiese sisteme is gebasseur op die aanname, dat die wÃłreld is sistemiese en dat verskynsels verstaan word ten opsigte van die ontluikende eienskap van die omvattende geheel. Eerstens stel ons ’n kompartementele model op wat deur nie-liniêre gewone differensiële vergelykings beskryf kan word vir die dwelmmisbruik en dwelm-verwante misdaad epidemies. Ons evalueer die drumpel getal en gebruik sensitiwiteitsanalise om die parameters van die model te analiseer. Tweedens, is ’n dinamiese sisteem genaamd die Middelmisbruik en dwelmverwante misdaad in dieWes-Kaap (SADC-WC) stelsel gebou met behulp van die STELLA platform om te verken en klassifiseer die onderliggende verhoudings en strukture binne die dwelmmisbruik en dwelm-verwante misdaad stelsel. Beide die sensitiwiteitsanalise, en die simulasies van die SADC-WC stelsel dui aan dat ’n toename in suksesvolle vonisse ’n beduidende invloed op die epidemies sal hê; en beloof om sake van dwelmverwante misdaad te verminder.

當企業面對資源與競爭全球化之市場發展趨勢，如何有效地運用多樣化且散佈的全球資源，做最有效的佈局，來因應日益激烈的市場競爭與挑戰，全球運籌管理愈行重要。但隨著企業經營的全球化，面對的風險與不確定性也逐漸增加，所以企業在做全球運籌管理時不確定因素應納入考量。 許多文獻對全球運籌管理模式作了不同角度的問題探討，其中Vidal and Goetschalckx從過去的文獻中將全球運籌模式加以比較，得到三點過去模式不足的部分：(1)不確定因素都未考慮，(2)BOM的限制，(3)國際化的因素如匯率及稅都未考慮。遂即於其研究中對不確定因素如需求變化及供應商可靠度等因素的改變與最小總成本對全球運籌管理系統的影響進行分析。 吳釜蒼(2002)以Vidal的架構，增加對於貨物自原物料採購至成品完成間的正向物流過程中，所可能經過的成員如供應商、工廠、倉庫、運輸管道進均加入可靠度考量來進行分析探討。本研究延伸其做法，除正向物流外，並擴展到商品或物料退貨、維修及資源回收的逆向物流過程中，可能經過的成員均加入可靠度的考量；並且針對兩種操作情境加以分析(1)特定成本之下求最大可靠度，(2)特定可靠度之上求最小總成本。其次，利用Fault Tree Analysis方法，配合績效評核項目，對可靠度加以量化分析，使其更符合實際狀況。 最後以範例資料來分析驗證此數量模式，並提出一方法論提供決策者在進行全球佈局規劃時，能以本研究提供的決策程序，找出影響全球運籌可靠度的關鍵因子，並可對合作夥伴可靠度進行分析，改善彼此關係或對其之取捨上能有一較客觀的參考依據，使其對總成本之影響能降至最低。 / Since the late 80s, due to the tensive pressures from globalization, customer demands, uncertainties, IT innovation, as well as the shorter product life cycle, businesses were struggling in how to quick response customer desires, in an effort to retain their niches. As a consequence, Global Logistic (GL), in turn, becomes the sharp weapon in this regard. Literature studied GL from various perspectives. Among these studies, Vidal & Goetschalckx compared models in previous studies, and came up with three major challenges in this area：(1) uncertainty was not taken into account; .(2) restrictions of the BOM structure are not clearly dealt with; and (3) key financial factors of internationalization, such as the exchange rate and taxes, were not modeled. Hence, in order to deal with such problems, Vidal & Goetschalckx carried on the analysis on the effects toward key factors of GL and total cost minimization by modeling the factor of suppliers’ reliability in their study. However, in Vidal & Goetschalckx‘s study, there was no further concerns of uncertainties on other players in the logistic system. Fu-Cang Wu takes uncertainties into account on the players of forward logistic system. As a consequence, this research aims to extend Vidal & Goetschalckx’s modus. In the mathematic model, this study adds the settings of reliabilities on players either in the forward logistics or in the reverse logistics. Besides, two operation modes are provided in the model：(1) seeking minimum cost on a target of system reliability; and (2) seeking maximum system reliability on a target of cost. Then, this research makes use of the Fault Tree Analysis (FTA) for in depth analysis on reliability patterns. Finally, a methodology is established, which provides decision makers a reference basis, whenever he or she needs to place a global logistics system. Via the use of this prototype, it is believed to have a good mechanism for finding out the key influence factors of the reliability, enhancing buyer-seller relationships, and ensuring the goal of total cost minimization

Syftet med denna studie är att beskriva några särskoleintegrerade elevers uppfattningar om delaktighet vid planeringen av matematikundervisningen. Studiens frågeställningar är: Vad framkommer i elevernas utsagor om läroplanen och kunskapskraven? Vad framkommer i elevernas utsagor om kopplingen till läroplanen eller kunskapskraven vid planeringen och upplägget av matematikundervisningen? Hur beskriver eleverna sin vilja till delaktighet i matematikundervisningen och dess utformning? Hur beskriver eleverna sin delaktighet i planerandet av matematikundervisningen är i jämförelse med sina klasskamrater? De fyra intervjuade eleverna har alla diagnosen intellektuell funktionsnedsättning, de följer grundsärskolans läroplan och är placerade i grundskolan. Studiens teoretiska utgångspunkt är Harts Delaktighetsstege, vilken även har använts vid analysen av intervjuerna. Det empiriska materialet bygger på kvalitativa intervjuer som har kompletterats med metoden foto-eliciting vilket är när fotografier används som stimuli för olika frågor under intervjuerna. Fotografierna är från elevernas egna matematiklektioner. Denna studie bygger på kontakten med elever som har intellektuell funktionsnedsättning vilket ställer höga krav på etiska och moraliska riktlinjer. Studiens resultat pekar på att delaktighetsstegens steg 3 – Tokenism och steg 4 – Assigned but informed är de steg som förekommer oftast utifrån elevernas utsagor. Steg 1, 2, 7 och 8 syns inte i materialet. Vilket innebär att de två steg med lägst nivå respektive högst nivå av delaktighet inte framkom. Vanligaste anledningen till att det eleverna berättat vid intervjuerna bedöms motsvara steg 3 är för att eleverna inte har förstått syftet med uppgiften vilket är ett av kriterierna för att nå upp till det fjärde steget. Hur och när matematiken kan användas utöver matematiklektionerna tycks vara svårt att beskriva för eleverna. Det var lättare för flera av eleverna att förklara syftet med att räkna än syftet med matematiken. Alla fyra eleverna uttryckte en vilja att få delta i upplägget och planerandet av matematiklektionerna. Det skiljer i vad de vill bestämma, ibland handlade det mer om innehållet och ibland handlade det mer om arbetsmetoderna. / The purpose of this study is to describe some integrated special school group students’ perception of their participation in the planning and layout of mathematics education and their knowledge of the curriculum. The study's questions are: What appears in the students' statements about the curriculum or the proficiencies at the planning and layout of the mathematics education?　What appears in the students' statements about the connection to the curriculum or the proficiencies at the planning and layout of the mathematics education? How do the students describe their will to participate in the mathematics education and the layout of it? How do the students describe their participation in the planning of the mathematics education compared to their classmates? The four interviewed students are all diagnosed with intellectual disability, they follow the curriculum of the special school and are placed within the regular school system. The theoretical basis of the study is Hart’s Ladder of participation which has also been used when analyzing the interviews. Research studies about young people’s perception and their stories are not that common. The empirical material is based on qualitative interviews which have been supplemented with the photo-elicitation method, a method based on photographs that are used as stimuli for different questions during the interviews. The photographs were taken during mathematic lessons where the interviewed students took part. This study is based on contact with students diagnosed with intellectual disability and that places high demands on ethical and moral principles. The findings show that two steps on the Ladder of participation, step 3 – Tokenism and step 4 – Assigned but not informed are the most common steps regarding to the stories of the students. Step 1, 2, 7 and 8 are not shown in the material. This means that the two steps with the lowest grade of participation and the two steps with the highest grade of participation didn’t show in the study. The most common reason to that what the students have said at the interviews are graded as step 3 is that the students haven’t understood the purpose of the assignment, which is a criteria to reach step 4. How and when mathematics can be used beyond the lessons in mathematics seem difficult to explain to the students. Several of them found it easier to describe the purpose of counting than the purpose of mathematics. All four students expressed a will to participate in the layout and the planning of the lessons in mathematics. There are differences in what they want to be a part of in the process, sometimes it is more about the content of the lessons and sometimes more about the methods.

Le but de ce travail est de fournir une méthode de reconstruction stéréoscopique capable d'estimer la topographie des catalyseurs à partir d'images MEB. Les méthodes stéréo standard ne permettent pas d'évaluer des reconstructions 3D de bonne qualité en raison de la surface homogène de ces échantillons. Bien que particulièrement prononcé sur nos catalyseurs, le manque de texture est un problème courant dans la reconstruction stéréo, et aucune solution idéale n'a encore été trouvée.Notre approche principale à ce problème est de combiner les méthodes stéréo existantes avec la segmentation hiérarchique des images de l’échantillon. En effet, la morphologie mathématique fournit des outils efficaces permettant de diviser une image en régions et sous-régions. Nous avons utilisé ces outils pour affiner et compléter les reconstructions 3D.La méthode que nous avons développé estime des reconstructions 3D moins bruitées et plus précises que les méthodes existantes. L'approche fournit également des informations supplémentaires: la segmentation finalement retenue ainsi que la carte indiquant l’orientation de chaque région sont des données intéressantes qui peuvent être utilisées pour affiner la compréhension des catalyseurs.Bien que le but de cette thèse soit très spécifique, l'approche proposée est généraliste. Elle a été notamment testée sur la base Middlebury et les résultats obtenus sont comparables et parfois meilleurs que les méthodes de pointe.L’approche pourrait aussi être étendue à d’autres cas d’utilisation. Tant que des données spatiales sont combinées avec une image, notre méthode TDSR peut être utilisée pour améliorer et compléter ces données spatiales. Les images RGBD et la segmentation sémantique sont quelques exemples d'applications potentielles. / The aim of this work is to provide a stereo reconstruction method able to estimate the topography of catalysts from SEM images. Standard stereo methods fail to evaluate adequate 3D reconstructions because of the homogeneous surface of these samples. Though particularly pronounced on our catalysts, the lack of texture is a common issue in stereo reconstruction, and no ideal solution has yet been found.Our main approach to this issue is to combine existing stereo methods with the hierarchical segmentation of the sample's images. Indeed, Mathematical Morphology provides efficient tools that divide an image into regions and subregions. We have used these tools to refine and complete the 3D reconstructions.The method we have developed estimates 3D reconstructions that are less noisy and more precise than state of the art methods. The approach also provides additional information: the final segmentation as well as the normal map are interesting data that can be used to refine the understanding of the catalysts.Though this thesis' purpose is very specific, the proposed approach is general.It has been notably used in the Middlebury database which contains images of in-door scenes, and obtained results were comparable and sometimes better than state of the art methods.It could also be extended to other uses. As long as spatial data is combined with an image, our TDSR method can be used to refine it. RGBD images and semantic segmentation are a few potential applications.

Syftet med studien var att belysa och problematisera framställningarna i och problematisera framställningarna i åtgärdsprogram inom matematik samt att få insikt i pedagogernas bild av hur de arbetar med åtgärdsprogrammen i verkligheten och vilken syn de har på åtgärdsprogram. Vidare syftade studien till att ta fram riktlinjer för skrivandet av åtgärdsprogram för att det ska bli ett levande dokument som blir ett stöd för eleverna och pedagogerna. Studien genomfördes med två metoder, dokumentanalys och halvstrukturerade kvalitativa intervjuer. Först genomförds en textanalys av fyra åtgärdsprogram och sedan följdes analysen upp av intervjuer med två speciallärare i matematik samt två klasslärare. Respondenterna kom från två olika skolor. Resultatet av studien visar att det är en signifikant skillnad mellan pedagogerna och speciallärarna i matematik kring hur de ser på åtgärdsprogram. Pedagogerna anser inte att det arbetas med åtgärdsprogram på ett effektivt sätt men speciallärarna i matematik tycker att det är ett levande dokument. Alla fyra respondenterna anser att det nuförtiden är enklare och bättre att arbeta med åtgärdsprogram sedan de började använda det digitala verktyget UNIKUM. Alla de fyra eleverna i denna studie har ett åtgärdsprogram där insatserna är att gå till specialläraren i matematik för intensivträning. Under denna intensivundervisning är fokus på den grundläggande taluppfattningen och att hjälpa eleven att få en bättre självkänsla och motivation inom matematik. Ett annat resultat av studien var att flera skolor som kontaktades inte hade några upprättade åtgärdsprogram inom matematik. istället skedde de insatserna genom att göra generella anpassningar för alla elever i klassrummet. / The aim of the present study was to illuminate and problematize supportive educational measures in mathematics and to examine how they are applied in reality and how they interpret educational measures. Further, it aims at finding guidelines for how Supportive educational measures should be written to become a living document to be a support for the students and teachers. The study was conducted with two methods, document analysis and semi-structured qualitative interviews. First an analysis of four supportive educational measures was performed and then the analysis was followed up by interviews of two special educators in mathematics and two teachers. The respondents came from two different schools. The results of the study indicate that there is a significant difference between teachers and special educators in mathematics about how they think about supportive educational measures. The teachers don’t think that they work with the supportive educational measures in an efficient way but the special educators in mathematics find it to be a living document. But all four respondents found that it nowadays is easier and better to work with supportive educational measures since they started it use the digital tool UNIKUM. All four students in this study were offered supportive education measures, where they had several appointments per week with the special educator in mathematics. At these appointments the students receive individual, intensive training regarding basic numeracy and worked together with the educator to achieve the goal of a higher level of mathematics self esteem and motivation. Another result of the study was that several schools that was contacted didn’t have any supportive educational measures written in mathematics. Instead their efforts where maid by doing general adjustments for all students in the classroom.

Este trabalho objetivou determinar a disponibilidade do aqüífero Serra Grande e estabelecer as diretrizes para o seu gerenciamento sustentável no município de Picos, localizado no sudeste do Estado do Piauí. Principal sistema de água subterrânea da região, este aqüífero é o único com capacidade para atender as demandas futuras da população. Porém, a falta de regras básicas na exploração dos seus recursos poderá comprometer sua sustentabilidade. O desenvolvimento deste estudo teve início com a elaboração do modelo conceitual da área e a análise das condições de uso dos recursos hídricos. Nesta etapa, verificando-se que os conceitos hidrogeológicos vigentes consideravam apenas o limite físico do sistema para definir sua disponibilidade, foi estabelecido um novo princípio para determinação do volume de recursos que pode ser explorado de um aqüífero, denominado de princípio sustentável, tendo como base os fatores econômicos envolvidos na sua exploração. Para determinação da disponibilidade física e econômica do aqüífero Serra Grande, primeiramente, foi estimado o déficit hídrico acumulado desde o início da exploração do sistema, estabelecida sua relação com a posição do nível potenciométrico e calculado o custo atual de produção da água. Em seguida, foram traçados dois cenários futuros para a exploração dos recursos hídricos no município, representando os modelos de gestão da oferta e gestão da demanda, para o período de 15 e 50 anos. Posteriormente, foi construído um modelo matemático para representar o sistema de subsuperfície, no qual foi simulada a evolução futura do nível d’água. Com base nos valores obtidos, foi estimado o volume de água a ser produzido do armazenamento, a quantidade de recursos que deverão ser incorporados ao sistema e o custo futuro de produção. Os resultados mostraram que o aqüífero precisará incorporar um volume significativo de recursos, que talvez não esteja disponível na região estudada, e que a elevação real do custo da água poderá comprometer a capacidade de pagamento da população para dispor destes recursos. Verificada esta situação, foram definidas as medidas que precisam ser implementadas para o gerenciamento sustentável do aqüífero estudado, de modo a garantir o abastecimento futuro do município e da região. Com a elaboração deste trabalho, concluiu-se que o aqüífero Serra Grande não é “intensamente explorado" em Picos, porém é mal explorado atualmente, o que deverá provocar prejuízos na exploração futura dos seus recursos. / This work’s goals were to determinate the availability of the Serra Grande aquifer and to establish the governess for its sustainable management in the municipality of Picos, located on the southeast of Piauí State. This aquifer, the region’s most important groundwater system, has an unique capacity of fulfilling the population’s future demand. However, the absence of basic rules for the exploitation of its resources would compromise its sustainability. The study began with the development of the conceptual model of the area and the analyses of the water resources use. During this step, after verify that the hydrological actual concepts only observe the physical limit of the system to define its availability, it was established a new principle to determinate the volume of resources that can be exploited from an aquifer, named sustainable principle, based on the economical factors involved in its exploitation. In order to determine the physical and economical availability of the Serra Grande aquifer, first, it was estimated the water deficit accumulated since the begging exploitation of the system, established its relationship with the potenciometric level and was calculated the present cost of water production. Later on, two hypothetical scenarios concerning future exploration of water resources were drawn, representing the models of supply and demand management, for a period of 15 and 50 years. Furthermore, a mathematic model was built to represent the subsurface system, which was simulated the evolution of the water level. Based on the values found, it was estimated the amount of water that should be produced from storage, the quantity of resources that have to be incorporated to the system and the future production cost. Moreover, the results showed that the aquifer will need to incorporate a meaningful quantity of resources, that may be not available in the studied region, and that the real increase of the cost of the water would compromise the payment capacity of the population to dispose those resources. After verify this situation, it was defined the actions that must be taken for the sustainable management of the studied aquifer, to guarantee the future water supply of the municipality and the region. In conclusion, this work confirmed that the Serra Grande aquifer is not “overexploited" in Picos, instead, it is not being correctly exploited, which will negatively affect the future exploitation of its resources.

Le volet applicatif de cette thèse porte sur l'agencement d'un logement destiné à une personne en situation de handicap. L'agencement désigne le choix de la position, de la forme et des dimensions des pièces, des portes et des couloirs. L'agencement est généralement élaboré par un architecte, dans le respect d'un nombre si élevé de contraintes qu'il lui est difficile de parvenir qu'il parvienne à toutes les satisfaire : il y a d'abord des contraintes architecturales évidentes : non recouvrement des pièces, largeur suffisante des couloirs, accessibilité à tout point du lieu à partir de tout autre point, nécessité de placer certaines pièces sur des arrivées ou évacuations … Il y a ensuite les contraintes imposées par le handicap : largeur accrue des couloirs (déplacement en fauteuil), nécessité d'assurer un effort quotidien minimum (lutte contre le vieillissement), limitation des escaliers (asthme sévère), éloignement d'une pièce des murs mitoyens (surdité) .... Et il y a finalement les souhaits exprimés par le futur occupant, par exemple minimiser certains trajets, maximiser l’éloignement entre deux pièces ou imposer l’orientation d’une pièce. D’un point de vue formel, notre travail a consisté à développer d'une part des modèles mathématiques et des méthodes algorithmiques capables de gérer ces contraintes et d'autre part des prototypes logiciels opérationnels. Les méthodes élaborées relèvent de deux approches : l'optimisation d'un agencement conçu par l'architecte et la synthèse d'un agencement sans suggestion initiale de l'architecte. La synthèse d'un plan a été abordée comme un problème de type « bin-packing » (réputé NP-difficile) avec des contraintes additionnelles : les objets à placer - les pièces - ont des tailles variables et ils sont soumis à des contraintes fonctionnelles. La méthode de résolution s'appuie sur un premier modèle mathématique, qui prend la forme d’un programme quadratique (linéarisé par la suite) en variables mixtes. Elle a été appliquée avec succès pour placer les pièces d'un logement, pour les dimensionner, pour déterminer les couloirs assurant une complète accessibilité au logement et pour prendre en compte certaines contraintes imposées par le handicap du futur occupant. Un deuxième modèle mathématique a été élaboré pour le placement des portes et une heuristique a enfin été développée pour affecter l'espace occupé par les couloirs non indispensables aux pièces avoisinantes. La totalité de cette démarche a été programmée dans un prototype logiciel pleinement opérationnel. Le deuxième ensemble de contributions concerne l'optimisation d'un agencement existant. Cette optimisation a été conçue comme un processus itératif enchaînant évaluation et modification (amélioration) d'un agencement. Il est décliné de quatre manières : une métaheuristique de type « recuit simulé » et trois méthodes de type « recherche locale », qui explorent l’espace des solutions en utilisant des voisinages spécialement définis. Cette approche a d'une part permis d’appréhender le caractère multicritère de cette problématique et a d'autre part exigé la mise en œuvre de nombreux algorithmes géométriques. Ces travaux sont implantés dans un deuxième prototype logiciel. Ce projet a nécessité la participation à de nombreuses manifestations au-delà du domaine de l’informatique, nationales et régionales, scientifiques et non-scientifiques, organisées par différents organismes politiques et associatifs travaillant sur la problématique du handicap et de l’accessibilité, afin de bien appréhender les attentes du monde scientifique et socioprofessionnel. Cette phase prospective a été concrétisée par la rédaction de nombreux rapports qui ont alimentés la bibliographie du mémoire de thèse / At an application level, this thesis deals with the layout of an accommodation intended for a disabled person. Determining the layout means choosing the position, shape and dimensions of rooms, doors and corridors. It is usually an architect's job but the complexity is such that it is very unlikely that he succeeds in optimally fulfilling all the constraints: first, there are architectural constraints: no room overlapping, sufficient width for the corridors, accessibility to and from any point, mandatory positioning of some rooms on some areas (e.g. water supply and outlet) … Then, there are constraints imposed by disabilities: enlarged corridors (wheelchairs), mandatory daily amount of efforts (fight against aging), reducing the number of steps (severe asthma), moving a room away from shared walls (deafness)... Finally, there are the wishes expressed by the future occupant, such as minimizing some journeys, maximizing the distance between two rooms or fixing a room's orientation. From a formal point of view, our work has consisted, firstly, in developing mathematical models and algorithmic methods to deal with all these constraints and, secondly, in realizing software prototypes applying these concepts. The tools we propose aim either at optimizing a layout previously designed by an architect or at synthesising a layout without any initial suggestions from the architect. Synthesis has been tackled as bin-packing-type problem (known to be NP-hard) but with additional constraints: the objects to be placed (the rooms) have variable sizes and they are submitted to functional constraints. The resolution is based on a first, initially quadratic and then linearized, mixed integer mathematical model. It has been successfully applied to position and dimension the rooms of an accommodation, to determine corridors allowing a full accessibility to all the rooms and to take into account a number of constraints coming from the disabilities of the future occupant. A second mathematical model has been formulated for the positioning of the doors and, finally, a heuristic method has been designed to assign the space used by useless corridors to adjacent rooms. The whole process has been embedded in a fully operational software. The second set of contributions is about the optimization of an existing layout. This task has been tackled through an iterative process, looping on evaluation and modification (improvement) of an accommodation. It has been implemented in four different ways: a metaheuristic (simulated annealing) and three local-search-type methods, which traverse the solution space by using specific definitions of the neighbourhood. This approach has firstly underlined the multicriteria feature of our problem and, secondly, has required the development of many computational geometry algorithms. All this work is integrated in another functional prototype software. To understand the expectations of the scientific, social and professional worlds, this project has implied to take part to various manifestations which were national or regional, in the computer science domain or in others, scientific or non-scientific, organised by various political or non-political organisations working in the field of disabilities and accessibility. This phase has resulted in many reports which have directly fed into the bibliography of this thesis.