In this paper we endeavor to test the controversial ideas that exist about the role of fragmentation in a conservation context. In line with earlier understanding, we find that habitat fragmentation alone results in a strong detrimental effect (especially for the predator population). Connecting the fragmented habitats facilitates predator survival and hence prey survival as compared to the unconnected fragmented case. Our main result is counterintuitive: in the presence of a high quality predator, connected fragmented habitats ensure a better chance for coexistence than does even the unfragmented case. We explain why a connected fragmented habitat might thus be beneficial for the stabilization of the system, and how connections between sub-habitats are able to protect prey population from over-exploitation. In the model, habitat fragmentation is separated from the effects of habitat destruction, in order to better understand how populations react to habitat transformation.

La flore adventice est à la base des chaînes trophiques dans les agroécosystèmes. Leur diminution dans les parcelles cultivées est une des causes de la baisse de la biodiversité. Par conséquent, des alternatives sont étudiées pour diminuer l’utilisation des herbicides dans le cadre du plan ECOPHYTO. Par exemple, la gestion de la flore adventice via les consommateurs de graines. En effet, les agroécosystèmes sont des milieux où des espèces granivores ont les capacités de consommer les graines d’adventices. Parmi les vertébrés, nous pouvons y trouver des oiseaux (alouette des champs) ainsi que des micromammifères (mulot). Parmi les invertébrés, les carabes sont identifiés comme principaux granivores dans les agroécosystèmes tempérés. L’objectif général de cette thèse est d’étudier les interactions entre carabes et graines d’adventices afin d’apporter des connaissances sur les interactions interspécifiques et d’identifier les traits physiologiques des espèces influençant la force des interactions entre les espèces. Un protocole a été établi afin de standardiser toutes les expériences et de garder comme variables uniquement l’espèce de graines et celle du carabe. Ensuite, nous avons étudié les interactions entre les graines d’adventices et les carabes selon deux axes de recherche. Le premier a permis de comparer les niveaux de consommation de la communauté de carabes sur une même espèce de graines. Nous avons pu ainsi observer que la masse corporelle des carabes n’était pas en relation avec la variation des niveaux de consommation. Mais le ratio entre la longueur des mandibules et la largeur du labrum (force mandibulaire) a un effet significatif lorsque seules les espèces consommant plus de cinq graines sont prises en compte. Pour le deuxième axe, nous avons mesuré la consommation des carabes sur 42 espèces de graines pour identifier les capacités de consommation et explorer la stratégie d’alimentation selon deux caractéristiques : la masse des graines (taille) et leur concentration lipidique. Les graines de faibles masses avec un taux lipidique élevé sont mangées en plus grand nombre. Enfin, nous avons déterminé les types de réponse fonctionnelle pour évaluer le potentiel de régulation de 4 espèces de carabes sur deux espèces de graines d’adventices. Pour chaque espèce (mâle et femelle) nous avons trouvé une réponse fonctionnelle de type II, sauf pour les femelles de P.rufipes. Cependant nos résultats doivent être interprétés avec précaution car en milieu naturel d’autres facteurs interviennent dans les interactions, telle que la présence de proies alternatives ou d’autres prédateurs. En conclusion, nous montrons que les interactions entre les graines d’adventices et les carabes sont nombreuses et complexes. Les caractéristiques physiologiques intervenant dans les interactions sont très nombreuses et très variables selon les espèces. Des études supplémentaires sont nécessaires pour évaluer l’intérêt agronomique des carabes dans la gestion des adventices. / Weed flora limits crop yields therefore herbicides inputs are important in order to manage weeds. Weeds are at the bottom of the trophic pyramid in agroecosystems, and this explains partly the decrease of biodiversity. Alternatives to manage weeds are studied to reduce negative effect of herbicides on the environment in order to preserve biodiversity. For example, weeds could be managed with granivorous species. Indeed, weed seeds are the origin of the weed community, thus seed consumption could limit weed abundance in cultivated fields. In agroecosystems, several taxa are known to be granivorous such as vertebrates (birds and rodents) and invertebrates (ground beetles). Ground beetles are considered as the main granivorous taxa in agroecosystems and are abundant in temperate agroecosystems. The main goal of this PhD was to study trophic interactions between communities, weed seed and ground beetles, with a prey-predator system in order to estimate the role of ground beetles through their seed consumption in weed seeds management. First, we established a protocol with standardize steps in order to restrain variables to weed seed species at ground beetles’ species. A similar protocol has been adapted to replicate experimentation with the same individuals to measure consumption at different weed seed densities. We then studied interactions between weed seeds and ground beetles with two research axes. We first explored interspecific variation of consumption on the same weed seeds species, Viola arvensis, by ground beetles. Body mass and ratios between mandible length and labrum width had no relation with seed consumption by ground beetles. Thus, other factors were suggested to explain consumption variation such as gut symbionts of ground beetles or preferences for specific weed seed species. Secondly, we measured consumption of 42 weed seed species by four ground beetles to identify abilities in weed seed consumption for these beetles and to explore feeding strategy according to two seed characteristics, seed mass (size) and seed lipid content. Generalism degrees are different according to ground beetles’ species and seem affected by physiological characteristics in both communities. Finally, to assess the potential in weed seed management of ground beetles we determined functional response to four ground beetles on two weed seeds species. We determined type II response for all species (male and female) tested, except for females of P.rufipes. Our results should be interpreted cautiously as, under natural conditions, generalist predators meet many alternatives prey and it could influence functional response type. We showed that there are many complex interactions between weed seed and ground beetles communities, especially due to a wide range of diversity in physiological characteristics in both communities. The potential of ground beetles to regulate seeds must be more precisely explored to evaluate their agronomic interest in weed management.

The European Commission manages fish stocks by applying a fishing mortality based on the maximum sustainable yield concept. So far most Baltic Sea fishing maximum sustainable yieldmodels have focused on one species at a time. The few existing multi-species models have assumed that a species’ maturity and growth is dependent on the availability of food. Our two-species models make it possible to investigate if there is a conflict between fishing maximum sustainable yield for cod and herring in the Baltic Sea. This two-species model of cod, as a predator and herring as prey, takes into account environmental drivers on cod and herring recruitment. Reproductive volume together with year-growth, (a year specific effect on growth of external variables like food availability) and predation by grey seals was included in the cod model. The herring model was dependent on cod spawning stock biomass and year-growth. The result shows that the reproductive volume is the main factor that affects the maximum sustainable yield for cod. The spawning stock biomass at maximum sustainable yield is more sensitive to reproductive volume than year-growth. When predation from seals is added in mortality and high environmental factors occurs the spawning stock biomass would be 50% compared to the spawning stock biomass at high environmental effects without seal predation. Four simulations of high cod spawning stock biomass were devastating for the herring population that was eradicated with high predation pressure. The herring maximum sustainable yield depends on the amount of cod spawning stack biomass i.e. the effect of high or low reproductive volume. Two analyses were made on a current environmental state for both species. The first analysis had a natural mortality of 0.2 for cod, which gave an fishing mortality of 0.20 and maximum sustainable yield of 410 000 tons. The herring had a fishing mortality of 0.03 and maximum sustainable yield of 11 000 tons. The second simulation included seal predation in cod mortality which decreased the cod maximum sustainable yield by 98% at a fishing mortality of 0.02, which gave a fishing mortality of 0.19 and maximum sustainable yield of 275 000 tons for herring. This gives a 25 times increase of herring maximum sustainable yield compared to the result without predation on cod. The cod population dynamics is vulnerable to environmental changes and to secure a healthy and productive cod population the target fishing mortality should be kept in phase with current reproductive volume. / Europeiska kommissionen förvaltar fiskbestånden genom att tillämpa fiskekvoter baserat på konceptet maximalt hållbart uttag. Hittills har de flesta maximalt hållbara fiske-fångst modeller för Östersjön fokuserat på en art i taget. De få befintliga fler-arts-modeller har antagit att en arts mognad och tillväxt är beroende av tillgången på föda. Vår två-arts-modell gör det möjligt att undersöka om det finns en konflikt mellan maximal hållbar fiske-fångst på torsk och sill i Östersjön. Denna två-arts-modell med torsk som ett rovdjur och sill som byte, tar hänsyn till miljön som drivkraft på deras rekrytering. I torskmodellen ingick reproduktiv volym tillsammans med årlig tillväxt (ett års specifika effekt på tillväxten beroende av externa variabler som tillgången till föda) och predation av gråsäl. Sill-modellen var beroende av årlig tillväxt och lekbeståndets biomassa hos torsk. Resultaten visar att den viktigaste faktorn som påverkar maximalt hållbart uttag för torsk är reproduktiv volym. Lekbeståndets biomassa vid maximalt hållbart uttag är mer känsligt för förändringar i reproduktiv volym än årlig tillväxt. När predation från säl tillsätts och höga gynnsamma miljöfaktorer råder är lekbeståndets biomassa 50 % jämfört med lekbeståndets biomassa vid höga gynnsamma miljöeffekter utan säl predation. Fyra simuleringar gav hög lekbestånds biomassa för torsk vilket var förödande för sillpopulationen som utrotades pga. högt predationstryck. Sillens maximala hållbara uttag beror på mängden lekbestånds biomassa hos torsk, d.v.s. effekten av hög eller låg reproduktiv volym. Två analyser gjordes på nuvarande miljömässiga nivåer för båda arterna. Den första analysen hade en naturlig dödlighet på 0,2 för torsk, vilket gav en fiske-mortalitet på 0,20 och maximalt hållbart uttag på 410 000 ton. Sillen hade en fiske-mortalitet på 0,03 och maximalt hållbart uttag på 11 000 ton. I den andra simuleringen ingår sälpredation på torsk vilket minskade torskens maximala hållbara uttag med 98 % vid en fiske-mortalitet på 0,02, vilket gav en fiske-mortalitet på 0,19 och maximalt hållbart uttag på 275 000 ton för sill. Detta ger en ökning av maximalt hållbart uttag för sill 25 gånger jämfört med resultatet utan predation på torsk. Torskens populationsdynamik är sårbar för miljöförändringar och för att säkra ett sunt och produktivt torskbestånd bör fiskemortaliteten hållas i fas med nuvarande reproduktiva volym.

Fundação de Amparo a Pesquisa no Estado do Rio Grande do Sul / In this work we propose a discrete predator-prey model with the purpose of analyzing the spatio-temporal dynamics of herbivorous and their predators. For that, we explicitly consider the dispersion of both species through Coupled Map Lattice models, that is, systems of difference equations coupled by dispersal. We suppose that the prey population presents density-dependent growth and predators, Holling type II functional response. In order to analyze the effects of prey-taxis showed by predators, which means, that predators direct their movement to regions of high prey densities, we computationally implemented our model for different movement schemes: difusion for both species, immobile prey and taxis for predators and, difusion for prey and taxis for predators. We conclude that the dispersal behavior of predators and preys plays a crucial role on their spatio-temporal dynamics and hence cannot be omitted when modeling predator-prey interactions. / Neste trabalho construímos um modelo presa-predador discreto com objetivo de analisar a dinâmica espaço-temporal de insetos herbívoros e seus predadores. Para tal, consideramos explicitamente a dispersão de ambas as espécies através de modelos de Rede de Mapas Acoplados, isto é, sistemas de equações a diferenças acopladas pela dispersão. Consideramos que as presas apresentam crescimento dependente da densidade e os predadores, resposta funcional Holling do tipo II. Para analisar os efeitos da movimentação de taxia dos predadores, isto é, o movimento direcionado às regiões de maiores densidades de presas, implementamos computacionalmente o modelo para diferentes esquemas de movimentação: difusão para ambas as espécies, presas imóveis e taxia para predadores e difusão para presas e taxia para predadores. Concluímos que o comportamento de movimentação de presas e predadores tem um papel relevante na sua dinâmica espaço-temporal e não pode ser ignorado na modelagem destes sistemas.

Collective intelligence (CI) emerges from local coordination, collaboration and competition among the individuals within a social group. CI mainly results in a global intelligent behavior. One of the fundamental interactional channels within a CI system is energy flow. Each agent within an artificial or physical ecosystem must absorb energy in order to survive, evolve, breed, and reshape its local environment. In addition because the energy resources are limited in the environment, each agent has to compete with other agents to reach the required level of energy. Understanding the internal energy flow can potentially provide a deep insight into internal activities and external emergent behaviors of a given complex system. This study proposes a stochastic scheme for modeling a multi-species prey-predator artificial ecosystem with two levels of food chain. This will enable us to investigate the influence of energy flow on the ecosystem’s lifetime. The proposed model consists of a stationary hosting environment with dynamic weather condition and fruit trees. The inhabitants of this ecosystem are herbivore and carnivore birds each consisting of species. In our model, the collective behavior emerges in terms of flocking with more added rules consist of breeding, competing, resting, hunting, escaping, seeking and foraging behaviors. Using multi-species scheme, we define the ecosystem as a combination of prey and predator species with inter-competition among species within same level of food chain and intra-competition among those belonging to different levels of food chain. Furthermore, in order to model the energy within the ecosystem, some energy variables as functions of behaviors are incorporated in to the model. Finally, a simulation and visualization structure for implementing the proposed model is developed in this study. The experimental results of 11,000 simulations analyzed by Cox univariate analysis and hazard function suggest that only five out of eight behaviors can statistically significant influence the ecosystem’s lifetime. Furthermore, the results of survival analysis show that out of all possible interactions among energy factors, only two of them, interaction between flocking and seeking energies, and interaction between flocking and hunting energies, have statistically significant impact on the system’s lifetime. In addition, software implementation of the proposed framework validates the stability of simulation and visualization architecture. At last regression results using Nelson-Aalen cumulative hazard function and Cox-Snell variable and scaled Schoenfeld residuals test strongly validate our experimental results. To the best of our knowledge, there are three contributions in this research: First, the high level of complexity in the structure of the proposed model in comparison with the other systems which mostly contains only one species of prey, one species of predator and a kind of resource. While this study introduces two species of prey, capability of competition among species, dynamic weather condition with two element of wind and rain and dynamic resources, various behavioral rules such as escaping, breeding, hunting, resting, etc. Energy flow analysis within an artificial ecosystem is the second contribution. To the best of author’s knowledge there is no similar comprehensive model in the previous literature that investigates the life span of a stochastic multi-species predator-prey artificial ecosystem based on energy flow using Survival Analysis method. Lastly, the simulation results show that the flocking and seeking energy and flocking and hunting energy interactions are the most significant interactions which match with the Thompson iii et al. [ 65] observations in the real life. Their findings indicate that in the real life, birds use flocking behavior for better movement, more efficient food searching and social learning. Flocking motion also decrease predation risk as much as the flock size increases.

Les stratégies alimentaires peuvent être définies comme la mise en place d'ensembles cohérents de réponses morphologiques, physiologiques, écologiques ou comportementales permettant d’optimiser le succès alimentaire d’une espèce. Le présent travail s'est proposé d'aller au-delà de la simple analyse taxonomique des régimes alimentaires en utilisant les caractéristiques des proies pour explorer certains aspects des stratégies alimentaires et de l’énergétique de la prédation chez les mammifères marins de l’atlantique nord-est. L'objectif majeur était de contribuer à une meilleure compréhension du "pourquoi une proie est une proie ?" La valeur énergétique des proies est apparue comme un élément central des stratégies de prédation. Il en résulte que des coûts d'existence importants chez les mammifères marins doivent être soutenus par une alimentation de qualité élevée et ne peuvent pas être satisfaits simplement par une plus grande quantité de proies de qualité moyenne ou faible. Les résultats obtenus lors de cette thèse ont ainsi permis de progresser de la description des régimes alimentaires vers la compréhension de certaines relations fonctionnelles entre proies et prédateurs. Ainsi, les traits descriptifs de la qualité des proies, comme la teneur en lipides et la valeur énergétique, et les traits descriptifs des coûts d’existence des mammifères marins, comme l’indice mitochondrial et la teneur en lipides des muscles, sont significativement corrélés. Enfin, ce travail souligne que pour comprendre l'écologie alimentaire d'un prédateur, il faut surtout bien connaitre les caractéristiques de ses proies. / Foraging strategies can be defined as the establishment of a consistent set of morphological, physiological, ecological and behavioural responses allowing the optimization of foraging success. Beyond the simple description of the diet, the present work attempted to explore some aspects of foraging strategies and of the energetic of predation among northeast Atlantic marine mammals. The main goal of the study was to contribute to a better understanding of "why a prey is a prey?" Prey energy density appeared to be a key point of predation strategies. Hence, marine mammal species with high existence costs would need high quality prey items, and cannot fulfil their energy requirement just by ingesting more prey items of low to medium quality. The results of this thesis permitted to progress from a taxonomic description of marine mammal diets to the identification of functional relationships between prey and predators. Hence, traits of prey quality such as lipid content or energy density, and traits of predator cost of existence such as muscle mitochondrial density or muscle lipid content, were significantly correlated. Finally, this work underlines that in order to understand the foraging ecology of a predator, its prey characteristics have to be known.

GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the features of a spreadsheet and the objects of dynamic geometry.

Made available in DSpace on 2015-03-26T13:35:24Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1414332 bytes, checksum: 6e2f42018f3e3dcdf9e8cbccab567e7a (MD5) Previous issue date: 2006-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Pattern, structure and emergent collective properties are ubiquitous in systems with many units (alive or inanimated) coupled through nonlinear interactions. Within this context, the study of cooperative phenomena in population dynamics of ecological interest has attracted the attention of the mathematicians and physicists since Lotka and Volterra in the 1920s. Thenceforth, in addition to differential equations, theoretical ecology has continuously incorporated powerful and well-established techniques of contacts processes, cellular automata models and others, developed in the fields of condensed matter physics, statistical physics and computational physics. In the present work, a predator-prey model with pursuit and escape triggered by alarm pheromones is proposed and studied through analytical methods and computer simulations. Such models can show oscillatory behavior of the population density, phase transitions that belong to distinct universality classes and rich stationary phase diagrams. Two distinct levels of description were used. In a first approach, we consider a model of cellular automata in which predators and preys walk on a square lattice, according specific rules for each species, in a homogeneous environment and with periodic boundary conditions. The second part of our study is based on the analysis of partial differential equations that also describes the dynamics of a prey-predator system with the same characteristics above. Both, spatially uniform or mean field like and explicit spatio-temporal partial differential equations were considered. These models can represent relevant tools to design better strategies of biological control of pests by predators. In successful cases, the pests and its predators must persist in stable interactions at a low level of pest density. / Padrões, estruturas, propriedades coletivas emergentes são ubíquas em sistemas com muitas unidades (vivas ou inanimadas) acopladas por meio de interações não-lineares. Dentro desse contexto, o estudo de fenômenos cooperativos em dinâmica de populações de interesse ecológico tem atraído a atenção de físicos e matemáticos desde os anos de 1920 com Lotka e Volterra. Portanto, além de equações diferenciais, a teoria ecológica tem continuamente incorporado poderosas e bem-estabelecidas técnicas dos processos de contatos, modelos de autômatos celulares e outros, desenvolvidos no campo de física da matéria condensada, física estatística e física computacional. No presente trabalho, um modelo presa-predador com perseguição e fuga mediada por um feromônio de alarme é proposto e estudado através de métodos analíticos e simulações computacionais. Tais modelos podem exibir comportamentos oscilatórios da densidade de população, transições de fases que pertencem a classes de universalidade distintas e um diagrama de fases rico. Duas abordagens distintas de descrição foram usadas. Numa primeira abordagem, propomos um modelo de Autômato Celular (AC) onde predadores e presas se movimentam, segundo regras específicas para cada espécie, num ambiente homogêneo e com condições de contorno periódicas. A outra parte do nosso estudo é baseado na análise de EDP s que também descrevem a dinâmica de um sistema presa-predador com as mesmas características citadas acima. É feito um estudo considerando as equações sem termos espaciais, isto é, tipo campo médio e depois considerando esses termos. Esses modelos podem representar ferramentas relevantes para o estudo das melhores estratégias para o controle biológico de pragas por predadores. Em casos bem sucedidos, as pestes e seus predadores devem persistir em interações estáveis e com uma baixa densidade da população de pragas.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-05-04T14:55:37Z No. of bitstreams: 0 / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-05-07T15:11:50Z (GMT) No. of bitstreams: 0 / Made available in DSpace on 2018-05-07T15:11:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-03-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O e-Learning é a representação tecnológica da Educação a Distância, sendo uma al-ternativa que as pessoas têm encontrado para adquirir conhecimento acadêmico ou extra-curricular. Os usuários desses sistemas podem acessar os conteúdos a qualquer momento e lugar, bastando possuir um dispositivo computacional com acesso à Internet. Todavia, para que essa tecnologia seja ainda mais utilizada, não somente como um complemento, mas também como uma alternativa primária, é necessário tratar diversos desafios da área. O foco das principais tecnologias baseadas na melhoria da educação, por muitos anos, tem sido a transferência de informação baseada na figura central de um professor. Esse aspecto, em conjunto a omissões relevantes, tais como a contextualização da experiência de aprendizagem de acordo com o perfil do aluno, são considerados os principais obstá-culos na adoção do e-Learning. Nesse contexto, um dos desafios mais interessantes nessa área é a seleção de uma sequência de materiais didáticos que considere as características do aluno no momento da entrega de conteúdo didático — Sequência Curricular Adaptativa (SCA). A geração da SCA é considerada um problema da classe NP-Difícil estimulando a utilização de metaheurísticas, particularmente de abordagens de Computação Evoluci-onista, na solução do problema. O presente trabalho propõe uma solução para geração de uma SCA que considere as informações intrínsecas e extrínsecas do aluno. O Algoritmo Presa-Predador foi escolhido para o problema mostrando-se adequado. Os resultados da solução proposta, se deram a partir de experimentos com uma turma real de alunos e mostram que a adaptação proposta, além de conseguir selecionar materiais didáticos que atendam aos objetivos de aprendizagem do aluno, interfere positivamente na qualidade do entendimento dos conceitos. Ademais, o grupo de alunos que recebeu a SCA a par-tir da proposta apresentou menor desistência, sugerindo um fator motivacional. Ainda como contribuição do trabalho, foi gerada uma base de materiais didático que poderá ser utilizada em experimentos futuros, contribuindo para o desenvolvimento da área. / e-Learning is the technological representation of Distance Education, being an alterna-tive that people have found to acquire academic or extracurricular knowledge. The users of these systems can access the contents anytime, anywhere simply by having a computer device with Internet access. However, for this technology to be even more used, not only as a complement, but also as a primary alternative, it is necessary to address several challenges. The focus of the main technologies based on the improvement of education, for many years, has been the transfer of information based on the central figure of a tea-cher. This aspect, together with relevant omissions, such as the contextualization of the learning experience according to the student profile, are considered the main obstacles in e-Learning adoption. One of the most interesting challenges in this field is the selection of the sequence of learning resources that considers learners characteristics at the content delivery time - Adaptive Curriculum Sequence (ACS). The ACS generation is considered a NP-Hard problem, stimulating the use of metaheuristics, particularly of Evolutionary Computing approaches. The present work proposes a solution to generate an ACS that considers the intrinsic and extrinsic information of the learner. The Prey-Predator Al-gorithm was chosen for the problem and it have been proved suitable. The proposed solution results were based on a real learning enviroment (with real learners) and show that the proposed adaptation, besides being able to select learning resources that meet the learners learning goals, positively affects the quality of understanding. Besides, the group of students who received the ACS from the proposal presents less dropout, sugges-ting a motivational factor. In addtion, the database of learning resouces was generated which may be used in future experiments, contributing to the development of this field of research.

GeoGebra is a free, open-source, and multi-platform software that combines dynamic geometry, algebra and calculus in one easy-to-use package. Students from middle-school to university can use it in classrooms and at home. In this workshop, we will introduce the features of GeoGebra with a special focus on not very common applications of a dynamic geometry program. We will inform about plans for developing training and research networks connected to GeoGebra. We can expect that at the time of the conference a spreadsheet will be integrated into GeoGebra which offers new ways teaching mathematics using the interplay between the features of a spreadsheet and the objects of dynamic geometry.