La tomographie optique diffuse (TOD) est une technique d’imagerie médicale relativement récente qui utilise la lumière dans le proche infrarouge pour acquérir des images in vivo de façon non invasive. Cette technique est en utilisation croissante par de nombreux chercheurs et biologistes et plusieurs équipes dans le monde travaillent sur le développement de scanners par TOD y compris notre groupe de recherche (groupe TomOptUS). Le Centre d’imagerie moléculaire de Sherbrooke dispose d’un appareil pour imagerie optique sur petit animal développé par la compagnie Quidd, soit le QOS (Quidd Optical imaging System). Cet appareil est utilisé par des biologistes et chercheurs pour diverses études précliniques sur modèles animaux (souris) de maladies humaines comme le cancer. Le QOS est entièrement contrôlé par ordinateur à l’aide d’un logiciel sophistiqué (le QOSoft) qui permet d’obtenir des images en fluorescence et en bioluminescence. Il est toutefois limité en ne permettant d’acquérir que des images planaires de la lumière sortant d’un animal ; il ne permet pas la tomographie, à savoir obtenir des images tridimensionnelles (3D) des sources fluorescentes ou bioluminescentes situées en profondeur à l’intérieur de l’animal. Bien que le QOS offre une grande flexibilité en terme d’angle d’acquisition d’images autour de l’animal avec sa caméra montée sur un bras rotatif, il a une sensibilité limitée pour de l’imagerie en profondeur, notamment parce qu’il fonctionne en mode épiillumination (détection de la lumière du même côté que l’injection de la lumière excitatrice dans l’animal) et aussi à cause de la sensibilité limitée de sa caméra. Afin d’augmenter les capacités tomographiques et la sensibilité du QOS, ainsi que le contraste des images qu’il fournit, le présent projet propose des développements logiciels intégrés au QOSoft. Ces ajouts logiciels au niveau du contrôle d’instrumentation et de l’interface graphique permettent d’intégrer une caméra EMCCD à ultra-haute sensibilité et ultra-faible bruit pour remplacer la caméra CCD refroidie existante ainsi qu’un module d’illumination laser rotatif. Ce module d’illumination, développé par le groupe TomOptUS, permet l’imagerie en mode transillumination ainsi que toutes les configurations intermédiaires jusqu’à l’épi-illumination. Ce module permet en outre d’injecter une densité de puissance lumineuse supérieure à celle possible avec la configuration actuelle du QOS. Le QOS et son logiciel mis à jour avec les ajouts faisant l’objet du présent projet sont validés par des expériences de fluorescence et de bioluminescence sur fantômes et animaux vivants.

This paper attempts to evaluate Training for Trainers (T4T) as an aid for developing healthy and sustained church planting movements (CPMs). The thesis is that Training for Trainers (T4T) can enable and sustain (by the Spirit’s power) healthy church planting movements because a discipleship process is built into the methodology that develops believers in their personal and communal growth and equips them to repeat the process with other individuals they reach. The very format of the T4T process provides a context for developing disciples inwardly and training disciples to minister outwardly. The T4T process continues over the course of months and years to systematically move believers through the essential stages of sustained church planting movements: Bridges in conversations with the lost from non-spiritual topics to the gospel in order to find those God is preparing (knowing whom to talk to and how to start) • Reproducible evangelism methods that are effective in the local context and can be learned by any new believer • Reproducible discipleship that addresses both short-term and long-term spiritual growth in a manner appropriate to the local worldview and able to be passed on by a new believer • Reproducible church models appropriate to the local context and able to be led and passed on by new believers • Leadership development and multiplication patterns that develop leaders rapidly in the context of ministry and enable the number of leaders to keep pace with the number of new churches. T4T moves each new generation of disciples (trainers) and churches through this process because it casts vision for and gives loving accountability for disciples to truly become trainers of others. It does this primarily through a three-thirds training process. T4T is training for trainers who will train trainers who will train trainers. T4T attempts to initiate movements of God in which at least four generations of new disciples and churches emerge. This paper evaluates T4T is based on case studies, survey instruments and biblical principles and then offers recommendations for CPM practitioners. / Christian Spirituality, Church History & Missiology / D. Th.(Missiology)

Nous avons étudié au cours de cette thèse le transport dépendant du spin d'électrons chauds injectés depuis le vide dans des structures hybrides métal ferromagnétique/interface/semi-conducteur. Cette configuration de mesure à trois terminaux est analogue à celle d'un transistor à vanne de spin à géométrie perpendiculaire mais dans lequel l'émetteur est physiquement découplé de la base et du collecteur. Cette configuration de mesure originale permet l'étude du transport d'électrons polarisés sur une large gamme d'énergie d'injection tout en contrôlant la polarisation des électrons injectés.<br /> Sur des jonctions Fe/oxyde/GaAs réalisées au laboratoire, nous avons mis en évidence quatre régimes de fonctionnement du transistor à vanne de spin dans la gamme d'énergie 10 eV-3000 eV. Lorsque l'énergie d'injection augmente, le gain du transistor augmente sur plus de 6 ordres de grandeur, pour atteindre des valeurs aussi élevées que 300. Simultanément, la dépendance en spin du courant transmis augmente sur près de 5 ordres de grandeur pour atteindre un maximum aux alentours de 1500 eV qui représente environ 30% du courant incident (pour une polarisation incidente de 100%). Nous montrons également que l'ensemble de ces propriétés de transport est modulable en variant l'épaisseur totale de la base métallique, ainsi que la nature de l'interface entre la base et le collecteur.<br /> Les quatre régimes de fonctionnement du transistor sont ensuite interprétés dans un modèle original qui décrit de façon quantitative les différents régimes observés. Ce modèle incorpore d'une part la multiplication qui a lieu dans la base métallique ainsi que dans le semi-conducteur (ionisation par impact), et d'autre part le coefficient de transmission à l'interface entre la base et le collecteur. Nous avons mis en évidence l'existence d'énergies seuil, liées à la nature de l'interface base/collecteur, à partir desquelles l'efficacité de collection augmente brutalement. En variant l'énergie d'injection, il est possible d'augmenter la largeur de la distribution électronique à l'interface base/collecteur jusqu'à environ 10 eV, et donc de sonder le profil d'interface. L'augmentation de la largeur de la distribution peut-être reliée à la variation particulière du libre parcours moyen inélastique dans la base métallique.<br /> Ces résultats et leurs interprétations ouvrent de nouvelles perspectives en électronique de spin, et en particulier dans la réalisation d'un transistor à vanne de spin tout solide associant à la fois une grande sélectivité en spin, un gain élevé et un faible bruit de fonctionnement.

We provide a formal mathematical definition of the Shortest Paths for All Flows (SP-AF) problem and provide many efficient algorithms. The SP-AF problem combines the well known Shortest Paths (SP) and Bottleneck Paths (BP) problems, and can be solved by utilising matrix multiplication. Thus in our research of the SP-AF problem, we also make a series of contributions to the underlying topics of the SP problem, the BP problem, and matrix multiplication. For the topic of matrix multiplication we show that on an n-by-n two dimensional (2D) square mesh array, two n-by-n matrices can be multiplied in exactly 1.5n ‒ 1 communication steps. This halves the number of communication steps required by the well known Cannon’s algorithm that runs on the same sized mesh array. We provide two contributions for the SP problem. Firstly, we enhance the breakthrough algorithm by Alon, Galil and Margalit (AGM), which was the first algorithm to achieve a deeply sub-cubic time bound for solving the All Pairs Shortest Paths (APSP) problem on dense directed graphs. Our enhancement allows the algorithm by AGM to remain sub-cubic for larger upper bounds on integer edge costs. Secondly, we show that for graphs with n vertices, the APSP problem can be solved in exactly 3n ‒ 2 communication steps on an n-by-n 2D square mesh array. This improves on the previous result of 3.5n communication steps achieved by Takaoka and Umehara. For the BP problem, we show that we can compute the bottleneck of the entire graph without solving the All Pairs Bottleneck Paths (APBP) problem, resulting in a much more efficient time bound. Finally we define an algebraic structure called the distance/flow semi-ring to formally introduce the SP-AF problem, and we provide many algorithms for solving the Single Source SP-AF (SSSP-AF) problem and the All Pairs SP-AF (APSP-AF) problem. For the APSP-AF problem, algebraic algorithms are given that utilise faster matrix multiplication over a ring.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Large integers are used in several key areas such as RSA (Rivest-Shamir-Adleman) public-key cryptographic system and elliptic curve public-key cryptographic system. To achieve higher levels of security requires larger key size and this becomes a limiting factor in prime finite field GF(p) arithmetic using large integers because operations on large integers suffer from the long carry propagation problem. Large integer representation has direct impact on the efficiency of the calculations and the hardware and software implementations. Attempts to use different representations such as residue number systems suffer from their own problems. In this dissertation, we propose a novel and efficient attribute-based large integer representation scheme capable of efficiently representing the large integers that are commonly used in cryptography such as the five NIST primes and the Pierpont primes used in supersingular isogeny Diffie-Hellman (SIDH) used in post-quantum cryptography. Moreover, we propose algorithms for this new representation to perform arithmetic operations such as conversions from and to binary representation, two’s complement, left-shift, numbers comparison, addition/subtraction, modular addition/subtraction, modular reduction, multiplication, and modular multiplication. Extensive numerical simulations and software implementations are done to verify the performance of the new number representation. Results show that the attribute-based large integer arithmetic operations are done faster in our proposed representation when compared with binary and residue number representations. This makes the proposed representation suitable for cryptographic applications on embedded systems and IoT devices with limited resources for better security level. / Graduate / 2020-07-04

This thesis introduces a new tower field representation, optimal tower fields (OTFs), that facilitates efficient finite field operations. The recursive direct inversion method presented for OTFs has significantly lower complexity than the known best method for inversion in optimal extension fields (OEFs), i.e., Itoh-Tsujii's inversion technique. The complexity of OTF inversion algorithm is shown to be O(m^2), significantly better than that of the Itoh-Tsujii algorithm, i.e. O(m^2(log_2 m)). This complexity is further improved to O(m^(log_2 3)) by utilizing the Karatsuba-Ofman algorithm. In addition, it is shown that OTFs are in fact a special class of OEFs and OTF elements may be converted to OEF representation via a simple permutation of the coefficients. Hence, OTF operations may be utilized to achieve the OEF arithmetic operations whenever a corresponding OTF representation exists. While the original OTF multiplication and squaring operations require slightly more additions than their OEF counterparts, due to the free conversion, both OTF operations may be achieved with the complexity of OEF operations. Furthermore, efficient finite field algorithms are introduced which significantly improve OTF multiplication and squaring operations. The OTF inversion algorithm was implemented on the ARM family of processors for a medium and a large sized field whose elements can be represented with 192 and 320 bits, respectively. In the implementation, the new OTF inversion algorithm ran at least six to eight times faster than the known best method for inversion in OEFs, i.e., Itoh-Tsujii inversion technique. According to the implementation results obtained, it is indicated that using the OTF inversion method an elliptic curve scalar point multiplication operation can be performed at least two to three times faster than the known best implementation for the selected fields.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-05-03T17:56:24Z No. of bitstreams: 1 2016 - Eduardo Castro Brittes.pdf: 1568575 bytes, checksum: f11844cc4540daf8a36fe1a5dca0c9c6 (MD5) / Made available in DSpace on 2017-05-03T17:56:24Z (GMT). No. of bitstreams: 1 2016 - Eduardo Castro Brittes.pdf: 1568575 bytes, checksum: f11844cc4540daf8a36fe1a5dca0c9c6 (MD5) Previous issue date: 2016-08-31 / CAPES / In one of the public networks of teaching in which the author acts as a teacher, many students arrive at the beginning of the second segment of the elementary school without mastering the four basic arithmetic operations and, specifically, with many difficulties in multiplication and division of natural numbers. There is also the little interest of several of them for mathematical content in General. Considering this reality, noted a need to seek innovations, finding ways to stimulate this learning curriculum component. Over the years, researched some methods and algorithms to multiply and divide natural numbers. Testing several of them over the years, the classroom experience pointed out the Lattice and the Long Division with Estimation as potentially motivating algorithms for arithmetic operations, by format and for simplicity. The aim of this work was to carry out an action research in a class of sixth grade of elementary school, involving the use of these two algorithms, evaluating motivational aspects and learning during the trial. Initially, were applied in that class a test to evaluate the motivation for studying mathematics and a pre-test, where if asked to solve simple issues of multiplication and division of natural numbers, the way each student wanted. After this step, some activities were carried out, using the above algorithms. Finally, we conducted a post-test and was reapplied the test of motivation, which granted the necessary data to the conclusions of the research. The resemblance to the traditional "Tic-Tac-Toe", the Lattice was introduced as a handmade board game, which stimulated competition and generated a lot of interest in most. The long division with estimation already used in most movements, the subtraction, what is a content well assimilated by students in this age group and educational level, since, typically, these students have a better development of thought. So I received a lot of attention from students, who have improved their concepts of orders (units, tens, hundreds), to better carry out the algorithm. Based on the questionnaire assessed the motivation to study mathematics, it was possible to observe not only the improvement of the interest in the various activities involving Mathematical content, but also an increase of confidence and credibility in the relationship between teacher x student. The approach has yielded satisfactory results. This kind of experience can leave as a legacy to students for the abandonment of the initial bad impression you might have regarding the arithmetic and, often, removing the fear and disgust in having to do the math, replacing this feeling of security generated by the domain in a differentiated way to solve problems that require multiplication and division. Moreover this experience can increase the ability of the students to absorb the multiplicative principle, paving the way for it to deepen the learning in this field of knowledge. / Em uma das redes p?blicas de ensino em que o autor atua como professor, v?rios alunos chegam ao in?cio do segundo segmento do Ensino Fundamental sem dominar as quatro opera??es aritm?ticas b?sicas e, especificamente, com muitas dificuldades na multiplica??o e na divis?o de n?meros naturais. Verifica-se tamb?m o pouco interesse de v?rios deles por conte?dos de matem?tica de uma forma geral. Considerando essa realidade, notou-se uma necessidade de buscar inova??es, encontrando formas de estimular a aprendizagem deste componente curricular. Ao longo dos anos, pesquisaram-se alguns m?todos e algoritmos para multiplicar e para dividir n?meros naturais. Testando v?rios deles ao longo dos anos, a experi?ncia em sala de aula apontou a Gelosia e a Divis?o Americana como algoritmos potencialmente motivadores para o ensino de opera??es aritm?ticas, pelo formato e pela simplicidade. O objetivo deste trabalho foi realizar uma pesquisa-a??o numa turma do sexto ano do Ensino Fundamental, envolvendo o uso desses dois algoritmos, avaliando aspectos motivacionais e de aprendizagem durante a experi?ncia. Inicialmente, foram aplicados nessa turma um teste para avaliar a motiva??o para estudar matem?tica e um pr?-teste, onde se pedia para resolver quest?es simples de multiplica??o e divis?o de n?meros naturais, da forma como cada aluno desejasse. Depois dessa etapa, foram realizadas algumas atividades, usando os algoritmos supracitados. Finalmente, foi realizado um p?s-teste e foi reaplicado o teste de motiva??o, que concedeu os dados necess?rios para as conclus?es da pesquisa. Pela semelhan?a com o tradicional "Jogo da Velha", a Gelosia foi introduzida como um jogo de tabuleiro artesanal, o que estimulou a competi??o e gerou muito interesse na maioria. J? a divis?o americana usou, na maioria dos movimentos, a subtra??o, que ? um conte?do bem assimilado por alunos nesta faixa et?ria e de escolaridade, uma vez que, normalmente, esses alunos possuem um melhor desenvolvimento do pensamento aditivo. Por isso recebeu muita aten??o dos alunos, que aprimoraram seus conceitos de ordens (unidade, dezena, centena), para melhor desempenhar o algoritmo. Baseado no question?rio que avaliou a motiva??o para estudar Matem?tica, foi poss?vel n?o s? observar a melhora do interesse pelas diversas atividades que envolvem o conte?do de Matem?tica, como tamb?m um aumento de confian?a e credibilidade na rela??o professor x aluno. A abordagem rendeu resultados satisfat?rios. Esse tipo de experi?ncia pode deixar como legado para os alunos o abandono da impress?o inicial ruim que poderiam ter em rela??o ? Aritm?tica e, por muitas vezes, retirando o medo e repulsa em ter que fazer contas, substituindo este sentimento pela seguran?a gerada pelo dom?nio de uma forma diferenciada de resolver problemas que exigem multiplica??o e divis?o. Al?m disso, tal experi?ncia pode aumentar a capacidade dos alunos em absorver o princ?pio multiplicativo, abrindo caminho para que se aprofunde a aprendizagem neste campo de conhecimento.

Made available in DSpace on 2017-07-10T19:24:17Z (GMT). No. of bitstreams: 1 DENISE_M_GR_ZEGOZEWSKI.pdf: 8188144 bytes, checksum: 045f54782a1ea2161edf5aa7046a8c1c (MD5) Previous issue date: 2016-02-03 / Estimates of agricultural production are greatly important especially in economy field. However, they depend on area knowledge and cropping yield. Thus, this study aimed to propose a methodology to estimate the areas cropped with soybeans and corn in Paraná State according to multi-temporal EVI/MODIS vegetation index images for 2010/2011, 2011/2012 and 2012/2013 crop years. In addition, there was a research with spatial autocorrelation soybean yield in Paraná, with EVI vegetation index and meteorological variables in a decennial scale and estimate yield using CAR, SAR and GWR models. In Paraná State, there is a drawback to map soybeans crop since corn sowing period is very close to the first one. Therefore, images from the maximum and minimum vegetative vigour were drawn of each studied crop for mapping soybean and corn crops in order to obtain both cropping areas. Although, for the separation, Spectro Angle Mapper algorithm (SAM) was applied by one of the studied crops, while mapping was obtained by multiplying the other bands. Thus, for spatial statistics application of mapped data, the average EV profile of each municipality was extracted as well as for each multi-temporal image, in order to change them into a decennial scale. According to the spatial statistics of such areas, the descriptive analysis of univariate spatial autocorrelation (global and local) of each ten-day variable was used based on the soybean cycle. A bivariate autocorrelation analysis between soybean yield and the studied varieties were also performed. Finalizing the methodology, variables with the highest significant level by stepwise method were selected and SAR, CAR and GWR models were generated to estimate soybean yield. As results, regarding mappings, the following answers for soybean were found out: r = 0.95 and r = 0.99, and while for corn, the answers were: r = 0.72 and r = 0.95 for 2012/2013 and 2013/2014 crop years in relation to the official data from SEAB. So, it has been proved some great efficiency of this methodology to separate and identify crops. When the descriptive statistics of municipalities for each variable was carried out, it was found out that some regions began an early sowing in relation to other ones in Paraná by the decennial vegetation index. The ten-day scale was also possible to be identified according to the climatic factors that caused soybean yield damage. Based on the analysis of spatial autocorrelation, the greatest similarities occurred in 2011/2012 crop year, the one affected by the weather change, whose yields were similar in the municipalities of Paraná State. For spatial modelling, it was observed that selection of decennial variables was different for each studied crop year, and the best model selected by the validation. And GWR was chosen as the best model by the AIC, BIC and adjusted R² validation criteria. The residuals were randomly distributed throughout all the State, so that spatial autocorrelation could be eliminated. / As estimativas das produções agrícolas têm grande importância, principalmente, no âmbito econômico. No entanto, elas são dependentes do conhecimento da área de cultivo e da produtividade da cultura. Desta forma, este trabalho teve por objetivo propor uma metodologia para estimar as áreas cultivadas com soja e milho em escala municipal no Estado do Paraná a partir de imagens multi-temporais do índice de vegetação EVI/MODIS, para os anos-safras 2010/2011, 2011/2012 e 2012/2013. Além disto, trabalhar com a autocorrelação espacial da produtividade da soja nesse Estado, com o índice de vegetação EVI e variáveis agrometeorológicas em escala decendial bem como estimar a produtividade a partir dos modelos CAR, SAR e GWR. No Paraná, há o inconveniente para mapear a soja devido à proximidade de datas de semeadura do milho. Assim, para o mapeamento da soja e do milho, utilizaram-se imagens englobando o período de máximo e mínimo vigor vegetativo de cada cultura, para se obter a área cultivada das duas. Para a separação, utilizou-se o algoritmo Spectro Angle Mapper (SAM) para uma das culturas e obteve-se o mapeamento da outra pela multiplicação de bandas. Para aplicação da estatística espacial dos dados mapeados, extraiu-se o perfil médio do EVI de cada município e para cada imagem multi-temporal para transformá-los em escala decendial. De acordo com a estatística espacial de áreas, utilizou-se a análise descritiva, de autocorrelação espacial univariada (global e local) de cada variável decendial com foco no ciclo da soja. Também realizou-se a análise de autocorrelação bivariada entre a produtividade da soja com as variáveis em estudo. Finalizando a metodologia, selecionaram-se as variáveis com maior índice de significância pelo método de stepwise e, em seguida, foram gerados os modelos estimados (SAR, CAR e GWR) da produtividade da soja. Como resultados, foram encontradas as seguintes respostas para os mapeamentos da soja r= 0,95 e 0,99, e para o milho de r = 0,72 e r= 0,95 para os anos-safras 2012/2013 e 2013/2014 em relação aos dados oficiais da SEAB. Logo, comprovou-se a grande eficiência da metodologia para separação e identificação das culturas. Quando realizada a estatística descritiva dos municípios para cada variável, verificaram-se regiões que iniciam as semeaduras antecipadas em relação a outras regiões do Estado pelos decêndios do índice de vegetação. Foi também possível identificar os decêndios em que os fatores climáticos causaram danos à produtividade da soja. Na análise da autocorrelação espacial, as maiores similaridades ocorreram no ano-safra 2011/2012, ano afetado pela variação climática, cujas produtividades foram semelhantes nos municípios do Paraná. Para a modelagem espacial, verificou-se que a seleção das variáveis decêndiais foi diferente para cada ano-safra estudado, e o GWR foi escolhido como melhor modelo pelos critérios de validação, AIC, BIC e R² ajustado. Foram encontrados resíduos distribuídos aleatoriamente por todo o Estado, para que assim se eliminasse a autocorrelação espacial

Made available in DSpace on 2017-05-12T14:47:34Z (GMT). No. of bitstreams: 1 DENISE_M_GR_ZEGOZEWSKI.pdf: 8188144 bytes, checksum: 045f54782a1ea2161edf5aa7046a8c1c (MD5) Previous issue date: 2016-02-03 / Estimates of agricultural production are greatly important especially in economy field. However, they depend on area knowledge and cropping yield. Thus, this study aimed to propose a methodology to estimate the areas cropped with soybeans and corn in Paraná State according to multi-temporal EVI/MODIS vegetation index images for 2010/2011, 2011/2012 and 2012/2013 crop years. In addition, there was a research with spatial autocorrelation soybean yield in Paraná, with EVI vegetation index and meteorological variables in a decennial scale and estimate yield using CAR, SAR and GWR models. In Paraná State, there is a drawback to map soybeans crop since corn sowing period is very close to the first one. Therefore, images from the maximum and minimum vegetative vigour were drawn of each studied crop for mapping soybean and corn crops in order to obtain both cropping areas. Although, for the separation, Spectro Angle Mapper algorithm (SAM) was applied by one of the studied crops, while mapping was obtained by multiplying the other bands. Thus, for spatial statistics application of mapped data, the average EV profile of each municipality was extracted as well as for each multi-temporal image, in order to change them into a decennial scale. According to the spatial statistics of such areas, the descriptive analysis of univariate spatial autocorrelation (global and local) of each ten-day variable was used based on the soybean cycle. A bivariate autocorrelation analysis between soybean yield and the studied varieties were also performed. Finalizing the methodology, variables with the highest significant level by stepwise method were selected and SAR, CAR and GWR models were generated to estimate soybean yield. As results, regarding mappings, the following answers for soybean were found out: r = 0.95 and r = 0.99, and while for corn, the answers were: r = 0.72 and r = 0.95 for 2012/2013 and 2013/2014 crop years in relation to the official data from SEAB. So, it has been proved some great efficiency of this methodology to separate and identify crops. When the descriptive statistics of municipalities for each variable was carried out, it was found out that some regions began an early sowing in relation to other ones in Paraná by the decennial vegetation index. The ten-day scale was also possible to be identified according to the climatic factors that caused soybean yield damage. Based on the analysis of spatial autocorrelation, the greatest similarities occurred in 2011/2012 crop year, the one affected by the weather change, whose yields were similar in the municipalities of Paraná State. For spatial modelling, it was observed that selection of decennial variables was different for each studied crop year, and the best model selected by the validation. And GWR was chosen as the best model by the AIC, BIC and adjusted R² validation criteria. The residuals were randomly distributed throughout all the State, so that spatial autocorrelation could be eliminated. / As estimativas das produções agrícolas têm grande importância, principalmente, no âmbito econômico. No entanto, elas são dependentes do conhecimento da área de cultivo e da produtividade da cultura. Desta forma, este trabalho teve por objetivo propor uma metodologia para estimar as áreas cultivadas com soja e milho em escala municipal no Estado do Paraná a partir de imagens multi-temporais do índice de vegetação EVI/MODIS, para os anos-safras 2010/2011, 2011/2012 e 2012/2013. Além disto, trabalhar com a autocorrelação espacial da produtividade da soja nesse Estado, com o índice de vegetação EVI e variáveis agrometeorológicas em escala decendial bem como estimar a produtividade a partir dos modelos CAR, SAR e GWR. No Paraná, há o inconveniente para mapear a soja devido à proximidade de datas de semeadura do milho. Assim, para o mapeamento da soja e do milho, utilizaram-se imagens englobando o período de máximo e mínimo vigor vegetativo de cada cultura, para se obter a área cultivada das duas. Para a separação, utilizou-se o algoritmo Spectro Angle Mapper (SAM) para uma das culturas e obteve-se o mapeamento da outra pela multiplicação de bandas. Para aplicação da estatística espacial dos dados mapeados, extraiu-se o perfil médio do EVI de cada município e para cada imagem multi-temporal para transformá-los em escala decendial. De acordo com a estatística espacial de áreas, utilizou-se a análise descritiva, de autocorrelação espacial univariada (global e local) de cada variável decendial com foco no ciclo da soja. Também realizou-se a análise de autocorrelação bivariada entre a produtividade da soja com as variáveis em estudo. Finalizando a metodologia, selecionaram-se as variáveis com maior índice de significância pelo método de stepwise e, em seguida, foram gerados os modelos estimados (SAR, CAR e GWR) da produtividade da soja. Como resultados, foram encontradas as seguintes respostas para os mapeamentos da soja r= 0,95 e 0,99, e para o milho de r = 0,72 e r= 0,95 para os anos-safras 2012/2013 e 2013/2014 em relação aos dados oficiais da SEAB. Logo, comprovou-se a grande eficiência da metodologia para separação e identificação das culturas. Quando realizada a estatística descritiva dos municípios para cada variável, verificaram-se regiões que iniciam as semeaduras antecipadas em relação a outras regiões do Estado pelos decêndios do índice de vegetação. Foi também possível identificar os decêndios em que os fatores climáticos causaram danos à produtividade da soja. Na análise da autocorrelação espacial, as maiores similaridades ocorreram no ano-safra 2011/2012, ano afetado pela variação climática, cujas produtividades foram semelhantes nos municípios do Paraná. Para a modelagem espacial, verificou-se que a seleção das variáveis decêndiais foi diferente para cada ano-safra estudado, e o GWR foi escolhido como melhor modelo pelos critérios de validação, AIC, BIC e R² ajustado. Foram encontrados resíduos distribuídos aleatoriamente por todo o Estado, para que assim se eliminasse a autocorrelação espacial