京都大学 / 0048 / 新制・論文博士 / 博士(教育学) / 乙第13137号 / 論教博第157号 / 新制||教||173(附属図書館) / 京都大学大学院教育学研究科臨床教育学専攻 / (主査)教授 皆藤 章, 教授 岡野 憲一郎, 准教授 髙橋 靖恵 / 学位規則第4条第2項該当 / Doctor of Philosophy (Education) / Kyoto University / DGAM

[ES] De acuerdo con las regulaciones europeas y muchos estudios científicos, es necesario monitorear y analizar las condiciones microclimáticas en museos o edificios, para preservar las obras de arte en ellos. Con el objetivo de ofrecer herramientas para el monitoreo de las condiciones climáticas en este tipo de edificios, en esta tesis doctoral se propone una nueva metodología estadística para clasificar series temporales de parámetros climáticos como la temperatura y humedad relativa. La metodología consiste en aplicar un método de clasificación usando variables que se computan a partir de las series de tiempos. Los dos primeros métodos de clasificación son versiones conocidas de métodos sparse PLS que no se habían aplicado a datos correlacionados en el tiempo. El tercer método es una nueva propuesta que usa dos algoritmos conocidos. Los métodos de clasificación se basan en diferentes versiones de un método sparse de análisis discriminante de mínimos cuadra- dos parciales PLS (sPLS-DA, SPLSDA y sPLS) y análisis discriminante lineal (LDA). Las variables que los métodos de clasificación usan como input, corresponden a parámetros estimados a partir de distintos modelos, métodos y funciones del área de las series de tiempo, por ejemplo, modelo ARIMA estacional, modelo ARIMA- TGARCH estacional, método estacional Holt-Winters, función de densidad espectral, función de autocorrelación (ACF), función de autocorrelación parcial (PACF), rango móvil (MR), entre otras funciones. También fueron utilizadas algunas variables que se utilizan en el campo de la astronomía para clasificar estrellas. En los casos que a priori no hubo información de los clusters de las series de tiempos, las dos primeras componentes de un análisis de componentes principales (PCA) fueron utilizadas por el algoritmo k- means para identificar posibles clusters de las series de tiempo. Adicionalmente, los resultados del método sPLS-DA fueron comparados con los del algoritmo random forest. Tres bases de datos de series de tiempos de humedad relativa o de temperatura fueron analizadas. Los clusters de las series de tiempos se analizaron de acuerdo a diferentes zonas o diferentes niveles de alturas donde fueron instalados sensores para el monitoreo de las condiciones climáticas en los 3 edificios.El algoritmo random forest y las diferentes versiones del método sparse PLS fueron útiles para identificar las variables más importantes en la clasificación de las series de tiempos. Los resultados de sPLS-DA y random forest fueron muy similares cuando se usaron como variables de entrada las calculadas a partir del método Holt-Winters o a partir de funciones aplicadas a las series de tiempo. Aunque los resultados del método random forest fueron levemente mejores que los encontrados por sPLS-DA en cuanto a las tasas de error de clasificación, los resultados de sPLS- DA fueron más fáciles de interpretar. Cuando las diferentes versiones del método sparse PLS utilizaron variables resultantes del método Holt-Winters, los clusters de las series de tiempo fueron mejor discriminados. Entre las diferentes versiones del método sparse PLS, la versión sPLS con LDA obtuvo la mejor discriminación de las series de tiempo, con un menor valor de la tasa de error de clasificación, y utilizando el menor o segundo menor número de variables.En esta tesis doctoral se propone usar una versión sparse de PLS (sPLS-DA, o sPLS con LDA) con variables calculadas a partir de series de tiempo para la clasificación de éstas. Al aplicar la metodología a las distintas bases de datos estudiadas, se encontraron modelos parsimoniosos, con pocas variables, y se obtuvo una discriminación satisfactoria de los diferentes clusters de las series de tiempo con fácil interpretación. La metodología propuesta puede ser útil para caracterizar las distintas zonas o alturas en museos o edificios históricos de acuerdo con sus condiciones climáticas, con el objetivo de prevenir problemas de conservación con las obras de arte. / [CA] D'acord amb les regulacions europees i molts estudis científics, és necessari monitorar i analitzar les condiciones microclimàtiques en museus i en edificis similars, per a preservar les obres d'art que s'exposen en ells. Amb l'objectiu d'oferir eines per al monitoratge de les condicions climàtiques en aquesta mena d'edificis, en aquesta tesi es proposa una nova metodologia estadística per a classificar series temporals de paràmetres climàtics com la temperatura i humitat relativa.La metodologia consisteix a aplicar un mètode de classificació usant variables que es computen a partir de les sèries de temps. Els dos primers mètodes de classificació són versions conegudes de mètodes sparse PLS que no s'havien aplicat adades correlacionades en el temps. El tercer mètode és una nova proposta que usados algorismes coneguts. Els mètodes de classificació es basen en diferents versions d'un mètode sparse d'anàlisi discriminant de mínims quadrats parcials PLS (sPLS-DA, SPLSDA i sPLS) i anàlisi discriminant lineal (LDA). Les variables queels mètodes de classificació usen com a input, corresponen a paràmetres estimats a partir de diferents models, mètodes i funcions de l'àrea de les sèries de temps, per exemple, model ARIMA estacional, model ARIMA-TGARCH estacional, mètode estacional Holt-Winters, funció de densitat espectral, funció d'autocorrelació (ACF), funció d'autocorrelació parcial (PACF), rang mòbil (MR), entre altres funcions. També van ser utilitzades algunes variables que s'utilitzen en el camp de l'astronomia per a classificar estreles. En els casos que a priori no va haver-hi información dels clústers de les sèries de temps, les dues primeres components d'una anàlisi de components principals (PCA) van ser utilitzades per l'algorisme k-means per a identificar possibles clústers de les sèries de temps. Addicionalment, els resultats del mètode sPLS-DA van ser comparats amb els de l'algorisme random forest.Tres bases de dades de sèries de temps d'humitat relativa o de temperatura varen ser analitzades. Els clústers de les sèries de temps es van analitzar d'acord a diferents zones o diferents nivells d'altures on van ser instal·lats sensors per al monitoratge de les condicions climàtiques en els edificis.L'algorisme random forest i les diferents versions del mètode sparse PLS van ser útils per a identificar les variables més importants en la classificació de les series de temps. Els resultats de sPLS-DA i random forest van ser molt similars quan es van usar com a variables d'entrada les calculades a partir del mètode Holt-winters o a partir de funcions aplicades a les sèries de temps. Encara que els resultats del mètode random forest van ser lleument millors que els trobats per sPLS-DA quant a les taxes d'error de classificació, els resultats de sPLS-DA van ser més fàcils d'interpretar.Quan les diferents versions del mètode sparse PLS van utilitzar variables resultants del mètode Holt-Winters, els clústers de les sèries de temps van ser més ben discriminats. Entre les diferents versions del mètode sparse PLS, la versió sPLS amb LDA va obtindre la millor discriminació de les sèries de temps, amb un menor valor de la taxa d'error de classificació, i utilitzant el menor o segon menor nombre de variables.En aquesta tesi proposem usar una versió sparse de PLS (sPLS-DA, o sPLS amb LDA) amb variables calculades a partir de sèries de temps per a classificar series de temps. En aplicar la metodologia a les diferents bases de dades estudiades, es van trobar models parsimoniosos, amb poques variables, i varem obtindre una discriminació satisfactòria dels diferents clústers de les sèries de temps amb fácil interpretació. La metodologia proposada pot ser útil per a caracteritzar les diferents zones o altures en museus o edificis similars d'acord amb les seues condicions climàtiques, amb l'objectiu de previndre problemes amb les obres d'art. / [EN] According to different European Standards and several studies, it is necessary to monitor and analyze the microclimatic conditions in museums and similar buildings, with the goal of preserving artworks. With the aim of offering tools to monitor the climatic conditions, a new statistical methodology for classifying time series of different climatic parameters, such as relative humidity and temperature, is pro- posed in this dissertation.The methodology consists of applying a classification method using variables that are computed from time series. The two first classification methods are ver- sions of known sparse methods which have not been applied to time dependent data. The third method is a new proposal that uses two known algorithms. These classification methods are based on different versions of sparse partial least squares discriminant analysis PLS (sPLS-DA, SPLSDA, and sPLS) and Linear Discriminant Analysis (LDA). The variables that are computed from time series, correspond to parameter estimates from functions, methods, or models commonly found in the area of time series, e.g., seasonal ARIMA model, seasonal ARIMA-TGARCH model, seasonal Holt-Winters method, spectral density function, autocorrelation function (ACF), partial autocorrelation function (PACF), moving range (MR), among others functions. Also, some variables employed in the field of astronomy (for classifying stars) were proposed.The methodology proposed consists of two parts. Firstly, different variables are computed applying the methods, models or functions mentioned above, to time series. Next, once the variables are calculated, they are used as input for a classification method like sPLS-DA, SPLSDA, or SPLS with LDA (new proposal). When there was no information about the clusters of the different time series, the first two components from principal component analysis (PCA) were used as input for k-means method for identifying possible clusters of time series. In addition, results from random forest algorithm were compared with results from sPLS-DA.This study analyzed three sets of time series of relative humidity or temperate, recorded in different buildings (Valencia's Cathedral, the archaeological site of L'Almoina, and the baroque church of Saint Thomas and Saint Philip Neri) in Valencia, Spain. The clusters of the time series were analyzed according to different zones or different levels of the sensor heights, for monitoring the climatic conditions in these buildings.Random forest algorithm and different versions of sparse PLS helped identifying the main variables for classifying the time series. When comparing the results from sPLS-DA and random forest, they were very similar for variables from seasonal Holt-Winters method and functions which were applied to the time series. The results from sPLS-DA were easier to interpret than results from random forest. When the different versions of sparse PLS used variables from seasonal Holt- Winters method as input, the clusters of the time series were identified effectively.The variables from seasonal Holt-Winters helped to obtain the best, or the second best results, according to the classification error rate. Among the different versions of sparse PLS proposed, sPLS with LDA helped to classify time series using a fewer number of variables with the lowest classification error rate.We propose using a version of sparse PLS (sPLS-DA, or sPLS with LDA) with variables computed from time series for classifying time series. For the different data sets studied, the methodology helped to produce parsimonious models with few variables, it achieved satisfactory discrimination of the different clusters of the time series which are easily interpreted. This methodology can be useful for characterizing and monitoring micro-climatic conditions in museums, or similar buildings, for preventing problems with artwork. / I gratefully acknowledge the financial support of Pontificia Universidad Javeriana Cali – PUJ and Instituto Colombiano de Crédito Educativo y Estudios Técnicos en el Exterior – ICETEX who awarded me the scholarships ’Convenio de Capacitación para Docentes O. J. 086/17’ and ’Programa Crédito Pasaporte a la Ciencia ID 3595089 foco-reto salud’ respectively. The scholarships were essential for obtaining the Ph.D. Also, I gratefully acknowledge the financial support of the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 814624. / Ramírez Buelvas, SM. (2022). A Statistical Methodology for Classifying Time Series in the Context of Climatic Data [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/181123

[pt] O objetivo do presente trabalho é o desenvolvimento de um algoritmo estatístico de previsão da potência transmitida pela usina geradora termelétrica de Linhares, localizada no Espírito Santo, medida no ponto de entrada da rede da concessionária regional, a ser integrado em plataforma composta por sistema supervisório em tempo real em ambiente MS Windows. Para tal foram comparadas as metodologias de Modelos Arima(p,d,q), regressão usando polinômios ortogonais e técnicas de amortecimento exponencial para identificar a mais adequada para a realização de previsões 5 passos-à-frente. Os dados utilizados são provenientes de observações registradas a cada 5 minutos, contudo, o alvo é produzir estas previsões para observações registradas a cada 5 segundos. Os resíduos estimados do modelo ajustado foram analisados via gráficos de controle para checar a estabilidade do processo. As previsões produzidas serão usadas para subsidiar decisões dos operadores da usina, em tempo real, de forma a evitar a ultrapassagem do limite de 200.000 kW por mais de quinze minutos. / [en] The objective of this study is to develop a statistical algorithm to predict the power transmitted by a thermoelectric power plant in Linhares, located at Espírito Santo state, measured at the entrance of the utility regional grid, which will be integrated to a platform formed by a real time supervisor system developed in MS Windows. To this end we compared Arima (p,d,q), Regression using Orthogonal Polynomials and Exponential Smoothing techniques to identify the best suited approach to make predictions five steps ahead. The data used are observations recorded every 5 minutes, however, the target is to produce these forecasts for observations recorded in every five seconds. The estimated residuals of the fitted model were analysed via control charts to check on the stability of the process. The forecasts produced by this model will be used to help not to exceed the 200.000 kW energy generation upper bound for more than fifteen minutes.

[pt] As partículas finas (PM2.5) são um dos principais poluentes atmosféricos associados a problemas de saúde. Estas partículas penetram no sistema respiratório, carreando desde metais traços a substâncias orgânicas. Apesar disso, a legislação ambiental brasileira ainda não tem estabelecido padrões para este poluente. Entretanto, Agencia Ambiental dos Estados Unidos (US.EPA) já tem adotado limites para exposições de curto (25 (micro)g m-3/diário) e longo (15 (micro)g m-3/anual) prazo. Esta tese teve quatro principais objetivos: (1) investigar a relação das condições meteorológicas, sazonalidade e bacias aéreas sobre as concentrações de PM2.5 na atmosfera; (2) avaliar modelos de previsão de qualidade do ar inovadores para estimar concentração de PM2.5 em locais com diferentes fontes de emissão; (3) validar método de extração e determinação pseudototal de metais traços presentes no material particulado, com espectrômetro de emissão ótica por plasma indutivamente acoplado (ICP-OES) de acordo com critérios estabelecidos pelo INMETRO; (4) quantificar carbono orgânico e metais traços presentes no material particulado fino para entender melhor como a atmosfera do estado do Rio de Janeiro tem sido afetada, devido aos vários tipos de emissão e condições meteorológicas. Amostradores de grandes volumes coletaram todas as amostras de PM2.5. Estes amostradores foram operados por 24 h, a cada seis dias, em locais com diferentes fontes de emissão (industrial, veicular, poeira do solo, etc.), no estado do Rio de Janeiro. As amostras foram coletadas pelo Instituto Estadual do Ambiente (INEA), no período de janeiro/11 até dezembro/13. Variáveis meteorológicas próximas (d(menor que)2 km) aos pontos de monitoramento de PM2.5 também foram obtidas na mesma frequência e período de amostragem. Em relação a este estudo, quatro resultados podem ser destacados. O primeiro, as concentrações médias diárias de PM2.5 variaram de 1-65 (micro)g m-3, ultrapassando em alguns pontos os limites adotados pela US.EPA. Estes resultados mostraram que concentrações de PM2.5 no RJ não é influenciada, em expressão, pela sazonalidade. Além disso, foi observado que as bacias aéreas definidas no Rio de Janeiro não têm sido confirmadas, e os locais mostraram uma semelhança de comportamento em função da sua fonte de emissão. O segundo, a aplicação do modelo Holt-Winters para previsão de PM2.5 simulou melhor a zona industrial, com RMSE (raiz do erro quadrático médio) entre 5,8-14,9 (micro)g m-3. Em contrapartida, a rede neural artificial associada a variáveis meteorológicas estimou melhor os resultados das zonas urbanas e rurais, com RMSE entre 4,2-9,3 (micro)g m-3. O terceiro, o método de extração e determinação pseudototal de metais por ICP-OES atendeu aos critérios de validação estabelecidos pelo INMETRO. Além disso, mostrou-se ser equivalente ao método US.EPA IO-3.1. Finalmente, as concentrações de carbono orgânico solúvel em água variaram de 0,8-4,9 (micro)g m-3. Os principais metais determinados foram: Na (5,8-13,6 (micro)g m-3), Al (1,6-6,7 (micro)g m-3) e Zn (1,9-6,6 (micro)g m-3). Foi verificado também que os fenômenos meteorológicos de superfície aumentam em 30 por cento a explicação da variância do modelo receptor (PCA), quando adicionados aos dados das substâncias químicas analisadas do PM2.5. Contudo, é crucial a aplicação de ferramentas quimiométricas para ajudar na caracterização e estimava das concentrações de poluentes atmosféricos. / [en] Fine particulate matters (PM2.5) are one of the primary air pollutants associated with health problems. These particles penetrate in the respiratory system, loading from trace metals to organic compounds. Neverthelere4ss, the Brazilian environmental legislation has not yet established standards for this pollutant. However, the US Environmental Agency (US.EPA) has already adopted limits for short-term (25 (micro)g m-3/daily) and long-term (15 (micro)g m-3/annual) exposures. This thesis had four main objectives: (1) to investigate the relation of weather conditions, seasonality and air basins on PM2.5 concentrations in the atmosphere; (2) to evaluate innovative air quality forecast models to estimate PM2.5 concentration in sites with different emission sources; (3) to validate method to extract and pseudo total determinate trace metals present in the particulate matter by inductively coupled plasma optical emission spectrometer (ICP-OES) according to criteria established by INMETRO; (4) to quantify organic carbon and trace metals present in fine particulate matter to better understand how the Rio de Janeiro State (RJ) atmosphere has been affected due to the various types of emission and weather conditions. High volumes samplers PM2.5 collected all PM2.5 samples. These samplers were operated for 24 h, every six days, in places with different emission sources (industrial, vehicular, soil dust, et caetera), in the Rio de Janeiro State. The samples were collected by the State Environmental Institute (INEA) during the period from January/2011 still December/2013. Meteorological variables nearby (d(less than)2 km) to PM2.5 monitoring points were also obtained at the same frequency and sampling period. Regarding this study, four results can be highlighted. The first one, the PM2.5 dailly concentrations average ranged from 1-65 (micro)g m-3, exceeding in some sites the limits adopted by US.EPA. These results showed that PM2.5 concentrations in RJ is not influenced, in expression, by the seasonality. In addition, it was observed that the defined RJ air basins have not been confirmed, and the local showed a similar performance according to their emission sources. The second one, the application of the Holt-Winters model for PM2.5 forecast simulated best industrial zone, with RMSE (root mean square error) between 5.8 to 14.9 (micro)g m-3. On the others hand, the artificial neural network associated with meteorological variables estimated best results from urban and rural areas, with RMSE between 4.2 to 9.3 (micro)g m-3. The third one, the method to extract and determine pseudo total metals by ICP-OES followed the validation criteria established by INMETRO. Furthermore, it was shown to be equivalent to US.EPA IO-3.1 method. Finally, the water-soluble organic carbon concentrations ranged from 0.8 to 4.9 (micro)g m-3. The principal metals determined were: Na (5.8-13.6 (micro)g m-3), Al (1.6-6.7 (micro)g m-3) and Zn (1.9-6.6 (micro)g m-3). It was also found that the surface meteorological phenomena increase at 30 percent the explicated variance of the receiver model (PCA) when added to PM2.5 chemical analysis data. Therefore, it is crucial the application of chemometric tools to help in the characterization and estimated air pollutant concentrations.

This thesis examines how to design a mathematical inventory model for a ”Fast Moving Consumer Goods”-company (FMCG-company), which determines the optimal reorder point and order quantity such that the average inventory cost is minimized. The thesis was made in collaboration with a ”Software as a Service”- company which provided the data containing information about the products and inventory management of one of their customers, a FMCG-company. The thesis first considers a basic EOQ-model, with constant demand rate, that suggests a reorder time and order quantity for the products. Since constant demand rate might be an unrealistic assumption for a FMCG-company, the thesis also considers a (R,Q)-model, where the demand was based on a forecast made by using the Holt-Winters model on previous sales history. The solutions were found by investigating the singular points and comparing them to the critical point. The thesis shows that the EOQ-model gives useful results for the most indemand products, while the reorder times for the less popular products are instead impractically high. The (R,Q)-model showed more stable solutions for all products and therefore proves to be a better inventory model for FMCG-companies, as expected. Simulations of the (R,Q)-model showed various inventory cases, where some showed a mismatch between the inventory level and the demand. The cases shows how demand planning can be applied for different products for when to consider changing inventory strategy or discontinuing products and how the orders can be made optimally. / Detta examensarbete undersöker hur en matematisk lagermodell kan utformas för ett ”Fast Moving Consumer Goods”-företag (FMCG-företag), som bestämmer den optimala beställningspunkten och orderkvantiteten så att den genomsnittliga lagerkostnaden minimeras. Examensarbetet gjordes i samarbete med ett ”Software as a Service”-företag som tillhandahöll data innehållandes information om produkter och lagerhantering hos en av deras kunder, ett FMCG-företag. Avhandlingen behandlar först en grundläggande EOQ-modell, med konstant efterfrågan, som föreslår en återbeställningstid och orderkvantitet för produkterna. Eftersom att en konstant efterfågan kan anses vara ett orealistiskt antagande för ett FMCG-företag, tar avhandlingen även upp en (R,Q)-modell, där efterfrågan baserades på en prognos gjord med hjälp av Holt-Winters-modellen på tidigare försäljningshistorik. Lösningarna hittades genom att undersöka de singulära punkterna och jämföra dem med den kritiska punkten. Avhandlingen visar att EOQ-modellen ger användbara resultat för de mest efterfrågade produkterna medan beställningstiderna för de mindre populära produkter är ofta opraktiskt höga. (R,Q)-modellen visade mer stabila lösningar för alla produkter och visar sig därmed vara en bättre lagermodell för FMCGföretag, som förväntat. Simuleringar av (R,Q)-modellen visade olika fall, där vissa visade en obalans mellan lagernivån och efterfrågan. De olika fallen visar hur efterfrågeplanering kan tillämpas för olika produkter för när man ska överväga att ändra lagerstrategi eller avveckla produkter och hur beställningarna kan göras optimalt

This study uses aspects of time series methodology to model and forecast major taxes such as Personal Income Tax (PIT), Corporate Income Tax (CIT), Value Added Tax (VAT) and Total Tax Revenue(TTAXR) in the South African Revenue Service (SARS). The monthly data used for modeling tax revenues of the major taxes was drawn from January 1995 to March 2010 (in sample data) for PIT, VAT and TTAXR. Due to higher volatility and emerging negative values, the CIT monthly data was converted to quarterly data from the rst quarter of 1995 to the rst quarter of 2010. The competing ARIMA/SARIMA and Holt-Winters models were derived, and the resulting model of this study was used to forecast PIT, CIT, VAT and TTAXR for SARS fiscal years 2010/11, 2011/12 and 2012/13. The results show that both the SARIMA and Holt-Winters models perform well in modeling and forecasting PIT and VAT, however the Holt-Winters model outperformed the SARIMA model in modeling and forecasting the more volatile CIT and TTAXR. It is recommended that these methods are used in forecasting future payments, as they are precise about forecasting tax revenues, with minimal errors and fewer model revisions being necessary. / Statistics / M.Sc. (Statistics)

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This dissertation explores humanism, the rediscovery of the culture of ancient Greece and Rome, in late fifteenth- and early sixteenth-century England. It does so with reference to texts, institutional settings, and networks both within and beyond England, and examines the activities of several seemingly minor figures who have been absent from recent scholarship on the topic: John Holt, William Lily, Richard Croke, Leonard Cox, and Thomas Lupset. These figures made distinctive and original contributions to the genres in which they operated, whether the grammatical manual, educational treatise, dialogue, or philosophical meditation. They are also noteworthy for their considerable influence, whether in England or further abroad. With regard to Croke and Cox, the integration of previously unknown sources from France and Germany and overlooked ones from eastern Europe reveals that England could be an exporter and not merely an importer of humanism. Taken together, these individuals demonstrate that English humanism was more sophisticated and complex than its frequent characterisation as 'Erasmian' would suggest. In addition, this dissertation analyses the influence of humanism on two school foundations: St Paul's School and Ipswich College. It re-evaluates the portrayal of John Colet as an anti-intellectual, and understands St Paul's as a deeply personal endeavour, reflecting his desire to do better for the next generation. It establishes the depth and significance of humanism in Cardinal Wolsey's foundation of Ipswich College, hitherto accorded less importance by historians than his Oxford college. The examination of the little-known materials he published on the eve of his fall in 1529, together with reports from staff on its progress, show that he regarded it as central to his ambitious vision for England and to the creation of his own reputation as a civic humanist. This research therefore revises our understanding of a neglected period, and engages with the vexed questions at the heart of the study of humanism: how contemporaries dealt with the tension between their faith and their enthusiasm for pagan culture, and regarded the rival attractions of scholarly leisure and active public service.

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This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are: I. Å. Brännström, Single species population models from first principles. II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models. III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology. IV. Å. Brännström, An area integral estimate for higher order parabolic equations. In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter & Broomhead (2001) and Johansson & Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals. The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds. In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal. Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.