Self-organizing cultured neural networks: Image analysis techniques for longitudinal tracking and modeling of the underlying network structure

Esta tesis estudia la evolución estructural de conjuntos de neuronas como la capacidad de auto-organización desde conjuntos de neuronas separadas hasta que forman una red (clusterizada) compleja. Esta tesis contribuye con el diseño e implementación de un algoritmo no supervisado de segmentación basado en grafos con un coste computacional muy bajo. Este algoritmo proporciona de forma automática la estructura completa de la red a partir de imágenes de cultivos neuronales tomadas con microscopios de fase con una resolución muy alta. La estructura de la red es representada mediante un objeto matemático (matriz) cuyos nodos representan a las neuronas o grupos de neuronas y los enlaces son las conexiones reconstruidas entre ellos. Este algoritmo extrae también otras medidas morfológicas importantes que caracterizan a las neuronas y a las neuritas. A diferencia de otros algoritmos hasta el momento, que necesitan de fluorescencia y técnicas inmunocitoquímicas, el algoritmo propuesto permite el estudio longitudinal de forma no invasiva posibilitando el estudio durante la formación de un cultivo. Además, esta tesis, estudia de forma sistemática un grupo de variables topológicas que garantizan la posibilidad de cuantificar e investigar la progresión de las características principales durante el proceso de auto-organización del cultivo. Nuestros resultados muestran la existencia de un estado concreto correspondiente a redes con configuracin small-world y la emergencia de propiedades a micro- y meso-escala de la estructura de la red. Finalmente, identificamos los procesos físicos principales que guían las transformaciones morfológicas de los cultivos y proponemos un modelo de crecimiento de red que reproduce el comportamiento cuantitativamente de las observaciones experimentales. ABSTRACT The thesis analyzes the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. In particular, it contributes with the design and implementation of a graph-based unsupervised segmentation algorithm, having an associated very low computational cost. The processing automatically retrieves the whole network structure from large scale phase-contrast images taken at high resolution throughout the entire life of a cultured neuronal network. The network structure is represented by a mathematical object (a matrix) in which nodes are identified neurons or neurons clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocyto- chemistry techniques, our measures are non invasive and entitle us to carry out a fully longitudinal analysis during the maturation of a single culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main networks characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graphs micro- and meso-scale properties emerge. Finally, we identify the main physical processes taking place during the cultures morphological transformations, and embed them into a simplified growth model that quantitatively reproduces the overall set of experimental observations.

Self-organizing cultured neural networks: Image analysis techniques for longitudinal tracking and modeling of the underlying network structure (versión actualizada)

Esta tesis estudia la evolución estructural de conjuntos de neuronas como la capacidad de auto-organización desde conjuntos de neuronas separadas hasta que forman una red (clusterizada) compleja. Esta tesis contribuye con el diseño e implementación de un algoritmo no supervisado de segmentación basado en grafos con un coste computacional muy bajo. Este algoritmo proporciona de forma automática la estructura completa de la red a partir de imágenes de cultivos neuronales tomadas con microscopios de fase con una resolución muy alta. La estructura de la red es representada mediante un objeto matemático (matriz) cuyos nodos representan a las neuronas o grupos de neuronas y los enlaces son las conexiones reconstruidas entre ellos. Este algoritmo extrae también otras medidas morfológicas importantes que caracterizan a las neuronas y a las neuritas. A diferencia de otros algoritmos hasta el momento, que necesitan de fluorescencia y técnicas inmunocitoquímicas, el algoritmo propuesto permite el estudio longitudinal de forma no invasiva posibilitando el estudio durante la formación de un cultivo. Además, esta tesis, estudia de forma sistemática un grupo de variables topológicas que garantizan la posibilidad de cuantificar e investigar la progresión de las características principales durante el proceso de auto-organización del cultivo. Nuestros resultados muestran la existencia de un estado concreto correspondiente a redes con configuracin small-world y la emergencia de propiedades a micro- y meso-escala de la estructura de la red. Finalmente, identificamos los procesos físicos principales que guían las transformaciones morfológicas de los cultivos y proponemos un modelo de crecimiento de red que reproduce el comportamiento cuantitativamente de las observaciones experimentales. ABSTRACT The thesis analyzes the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. In particular, it contributes with the design and implementation of a graph-based unsupervised segmentation algorithm, having an associated very low computational cost. The processing automatically retrieves the whole network structure from large scale phase-contrast images taken at high resolution throughout the entire life of a cultured neuronal network. The network structure is represented by a mathematical object (a matrix) in which nodes are identified neurons or neurons clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocyto- chemistry techniques, our measures are non invasive and entitle us to carry out a fully longitudinal analysis during the maturation of a single culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main networks characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graphs micro- and meso-scale properties emerge. Finally, we identify the main physical processes taking place during the cultures morphological transformations, and embed them into a simplified growth model that quantitatively reproduces the overall set of experimental observations.

Formación y determinación del valor del suelo: confrontación y discrepancias entre mecanismos de mercado y regulaciones administrativas

La determinación del valor del suelo implicado en los procesos de urbanización se mueve en una compleja dialéctica en la que algunos fenómenos de naturaleza morfológica como el modelado del espacio social, o el que se deduce de las determinaciones del planeamiento (aprovechamiento especialmente) se enfrentan a instrumentos de regulación que se rigen por normas de carácter administrativo (urbanísticas y expropiatorias, fiscales, financieras-hipotecarias etc.). En ese marco en el que las discrepancias son frecuentes se pretende analizar las posibles actuaciones encaminadas a influir sobre la formación de ese valor en el sentido de limitar las expectativas de aprovechamiento tradicionalmente vinculadas al sistema urbanístico establecido, destacando al respecto la implantación de criterios de sostenibilidad y participación ciudadana, así como que la utilización de normas administrativas de valoración con la finalidad de reducir tales expectativas y tratar de influir sobre el sistema urbanístico en su conjunto, no se considera suficiente para conseguir el logro de tales objetivos. Añadiendo, respecto del conjunto de normas administrativas de determinación del valor del suelo, que si bien las reglas urbanísticas y expropiatorias establecen actualmente reglas objetivas de valoración, a través de la normativa de valoración destinada a entidades financieras, o de carácter fiscal, se introducen criterios subjetivos que tratan de aproximarse al mercado, incluso en el caso del valor catastral, estructuralmente reglado. Esta separación de criterios ha llevado a un enfrentamiento al que ha venido a dar respuesta la reciente sentencia del Tribunal Supremo de 30 de mayo de 2014, que impone los criterios urbanísticos de consideración de situaciones básicas de suelo, frente a los fiscalmente regulados en relación con la normativa catastral en cuanto a la consideración de suelo urbanizable sin desarrollar, que pasa a ser considerado como en situación rural, siendo por tanto aplicables sobre el mismo las reglas de valoración que la normativa catastral establece para esta categoría de suelo (rústico) que no considera, incluso con la posterior modificación, de junio de 2015, incorporada para adaptarse a la mencionada sentencia, expectativas de aprovechamiento. Pero como se ha señalado, la exclusiva utilización de la normativa urbanística de valoración no se considera suficiente para evitar los efectos que sobre el valor de suelo produce la asignación de tales aprovechamientos, por lo que acuerdo con la actual legislación de suelo, deben asimismo potenciarse actuaciones encaminadas a un desarrollo sostenible así como a la participación ciudadana, la transparencia y el control, con la finalidad de lograr un mayor rigor en la utilización del suelo que ha de traducirse en su valoración. ABSTRACT Determining the land value involved in the urbanisation process implies a complex dialectic in which certain morphological natural phenomena like the modelling of social space or that deduced from planning determinations (especially land use) face regulatory instruments governed by administrative norms (urban planning and expropriator, tax, financial-mortgage etc.). In this context where discrepancies are common, the purpose is to analyse the possible actions geared to influence the formation of that value in the sense of limiting land use expectations traditionally linked to the established urban planning system, highlighting the implementation of sustainability criteria and citizen participation, as well as to consider that the administrative standards of evaluation for reducing said expectations, and trying to influence the urban system as a whole, are not considered sufficient for achieving these objectives. We might add, with respect to the set of administrative norms for determining the land value, that while urban and expropriations norms currently provide objective rules of valuation, subjective criteria are introduced trying to approach the market, including the structurally regulated cadastral value through valuation rules aimed at financial or fiscal institutions. This separation of criteria has led to a confrontation to which the recent ruling of the Supreme Court of May 30, 2014 responds. The aforementioned judgement imposes the urban core criteria for basic land use situations against those fiscally regulated in relation to cadastral regulations regarding the consideration of undeveloped building land, which is considered to be in a rural situation, making it subject to the same rules that cadastral valuation norms established for this category of land use (rustic) which do not consider, even with the subsequent amendment of June 2015, introduced to fit that judgment, use expectations. But as noted, the exclusive use of valuation planning regulations is not considered sufficient to avoid the effects on the land value produced by the allocation of said uses, so that according to the current land use legislation, actions aimed at sustainable development as well as citizen participation, transparency and control, shall be enhanced in order to achieve greater rigor in the use of land which should be translated in their valuation.

Expansión y transformación del territorio : la ineficiencia de los fraccionamientos urbanizados : zona conurbada de Veracruz, México

La expansión de la ciudad y zona conurbada de Veracruz, se encuentra en una dinámica en donde convergen el medio artificial construido por el hombre y que ha generado una ciudad fragmentada; el medio natural, en el que se encuentran importantes componentes ecosistémicos de la zona costera; las políticas y estrategias que establecen los cinco Programas de ordenamiento urbano vigentes, sujetos al patrón de acumulación de capital, favoreciendo los intereses de la iniciativa privada. Bajo este panorama encontramos un territorio complejo que se encuentra cada vez más vulnerado y en riesgo de que los sistemas humano y natural colapsen. Lo anterior se evidencia en los nuevos desarrollos urbanizados, a partir del estudio de la problemática que presentan los fraccionamientos habitacionales, donde cada vez son más vulnerables, lo que constata su ineficiencia dentro del sistema urbano. ABSTRACT The expansion of the city and metropolitan area of Veracruz, is in a dynamic where converge the artificial environment built by the man and that has generated a fragmented city; natural environment, in which there are important ecosystem components of the coastal zone; policies and strategies that establish the five existing urban planning programs, subject to the pattern of accumulation of capital, favoring the private enterprises interests. Under this scenario is found a complex area that is more vulnerable every time and at risk of human and natural systems collapse. The above mentioned is evident in the new urbanized development, from studies of the problem posed by housing developments, finding that more and more vulnerable, which finds its inefficiency within the urban system.

Visualization of biochemical networks in living cells

Functional annotation of novel genes can be achieved by detection of interactions of their encoded proteins with known proteins followed by assays to validate that the gene participates in a specific cellular function. We report an experimental strategy that allows for detection of protein interactions and functional assays with a single reporter system. Interactions among biochemical network component proteins are detected and probed with stimulators and inhibitors of the network. In addition, the cellular location of the interacting proteins is determined. We used this strategy to map a signal transduction network that controls initiation of translation in eukaryotes. We analyzed 35 different pairs of full-length proteins and identified 14 interactions, of which five have not been observed previously, suggesting that the organization of the pathway is more ramified and integrated than previously shown. Our results demonstrate the feasibility of using this strategy in efforts of genomewide functional annotation.

Modelagem e análise das cadeias de suprimentos globais e resilientes baseadas em rede de Petri.

Em um cenário de aumento de competitividade, crescente expectativa por inovações do produto e necessidade de atender diferentes perfis de consumidores, o conceito de gerenciamento de cadeias de suprimentos globais (GSCM) surge como uma estratégia para coordenar mais eficazmente as atividades dispersas geograficamente dos sistemas produtivos. Na adoção do GSCM, as organizações devem lidar com rupturas que impactam no gerenciamento das suas atividades, tais como a interrupção de vias de transporte, pane no fornecimento de energia, desastres naturais e até ataques terroristas. Nesse contexto, o trabalho introduz um procedimento sistematizado para modelagem das cadeias de suprimentos visto como um sistema a eventos discretos e sua análise por simulação das atividades do GSCM baseada em técnicas formais como a rede de Petri (PN) e o Production Flow Schema (PFS). Um exemplo é também apresentado para ilustrar e comprovar as vantagens do método proposto na análise do GSCM.

Obtenção e caracterização de PLA reforçado com nanocelulose.

A celulose é o polímero natural renovável disponível em maior abundância atualmente. Por possuir estrutura semicristalina, é possível extrair seus domínios cristalinos através de procedimentos que ataquem sua fase amorfa, como a hidrólise ácida, obtendo-se assim partículas cristalinas chamadas nanopartículas de celulose (NCs). Estas nanopartículas têm atraído enorme interesse científico, uma vez que possuem propriedades mecânicas, como módulo de elasticidade e resistência à tração, semelhantes a várias cargas inorgânicas utilizadas na fabricação de compósitos. Além disso, possuem dimensões nanométricas, o que contribui para menor adição de carga à matriz polimérica, já que possuem maior área de superfície, quando comparadas às cargas micrométricas. Nanocompósitos formados pela adição destas cargas em matrizes poliméricas podem apresentar propriedades comerciais atraentes, como barreira a gases, melhores propriedades térmicas e baixa densidade, quando comparados aos compósitos tradicionais. Como se trata de uma carga com dimensões nanométricas, obtida de fontes renováveis, uma das principais áreas de interesse para aplicação deste reforço é em biopolímeros biodegradáveis. O poli(ácido lático) (PLA), é um exemplo de biopolímero com propriedades mecânicas, térmicas e de processamento superiores a de outros biopolímeros comerciais. No presente trabalho foram obtidas nanopartículas de celulose (NCs), por meio de hidrólise ácida, utilizando-se três métodos distintos, com o objetivo de estudar o método mais eficiente para a obtenção de NCs adequadas à aplicação em compósitos de PLA. Os Métodos I e II empregam extração das NCs por meio do H2SO4, diferenciando-se apenas pela neutralização, a qual envolve diálise ou neutralização com NaHCO3, respectivamente. No Método III a extração das NCs foi realizada com H3PO4. As NCs foram caracterizadas por diferentes técnicas, como difração de raios X (DRX), análise termogravimétrica (TG), espectroscopia vibracional de absorção no infravermelho (FTIR), microscopia eletrônica de transmissão (MET) e microscopia de força atômica (MFA). Os resultados de caracterização das NCs indicaram que, a partir de todos os métodos utilizados, há formação de nanocristais de celulose (NCCs), entretanto, apenas os NCCs obtidos pelos Métodos II e III apresentaram estabilidade térmica suficiente para serem empregados em compósitos preparados por adição da carga no polímero em estado fundido. A incorporação das NCs em matriz de PLA foi realizada em câmara de mistura, com posterior moldagem por prensagem a quente. Compósitos obtidos por adição de NCs obtidas pelo Método II foram caracterizados por calorimetria exploratória diferencial (DSC), análise termogravimétrica, microscopia óptica, análises reológicas e microscopia eletrônica de varredura (MEV). A adição de NCs, extraídas pelo Método II, em matriz de PLA afetou o processo de cristalização do polímero, o qual apresentou maior grau de cristalinidade. Além disso, a adição de 3% em massa de NCs no PLA foi suficiente para alterar seu comportamento reológico. Os resultados reológicos indicaram que a morfologia do compósito é, predominantemente, composta por uma dispersão homogênea e fina da carga na fase matriz. Micrografias obtidas por MEV corroboram os resultados reológicos, mostrando, predominantemente a presença de partículas de NC em escala nanométrica. Compósitos de PLA com NCs obtidas pelo Método III apresentaram aglomerados de partículas de NC em escala micro e milimétrica, ao longo da fase matriz, e não foram extensivamente caracterizados.

Removal of endocrine disrupting compounds from wastewater: a comparison between a conventional activated sludge with tertiary treatment and membrane bioreactors

Póster presentado en 19th International Congress of Chemical and Process Engineering, Prague, Czech Republic August 28th-September 1st, 2010.

The evolution of mass tourism destinations: new approaches beyond deterministic models in Benidorm (Spain)

Although deterministic models of the evolution of mass tourism coastal resorts predict an almost inevitable decline over time, theoretical frameworks of the evolution and restructuring policies of mature destinations should be revised to reflect the complex and dynamic way in which these destinations evolve and interact with the tourism market and global socio-economic environment. The present study examines Benidorm because its urban and tourism model and large-scale tourism supply and demand make it one of the most unique destinations on the Mediterranean coast. The investigation reveals the need to adopt theories and models that are not purely deterministic. The dialectic interplay between external factors and the internal factors inherent in this destination simultaneously reveals a complex and diverse stage of maturity and the ability of destinations to create their own future.

La localización de la clase creativa en ciudades turísticas. Un análisis a escala local del sistema urbano Mediterráneo español

La tendencia a la concentración de flujos económicos y humanos en las principales aglomeraciones ha generado unos polos de atracción global en detrimento de las opciones de desarrollo del resto de territorios. Sin embargo la recomposición territorial está siendo más compleja y afecta también al territorio no metropolitano. La introducción de elementos de creatividad en las economías urbanas es un ejemplo de la relativa dispersión territorial de nuevas actividades productivas. La localización de actividades económicas creativas ha sido analizada para el caso de ciudades medias, periferias urbanas y espacios rurales, pero no para el de ciudades turísticas. El objetivo del trabajo es analizar, a escala local y partiendo del cálculo de un índice sintético de creatividad, el comportamiento de dicho índice y en qué medida la clase creativa se localiza en los destinos turísticos del mediterráneo español y las Islas Canarias en comparación con otros tipos de municipios y entre municipios turísticos según su grado de especialización. Los resultados obtenidos permiten formular la hipótesis sobre cómo contribuyen los espacios turísticos a la reorganización productiva del territorio y valorar sus posibilidades de competitividad basadas en la mejora de la tolerancia, la innovación y el emprendimiento, proporcionando oportunidades de desarrollo más integrales y diversificadas en el momento de crisis actual.

Explaining variations in the knowledge economy in three small wealthy countries

At a broad level, it has been shown that different institutional contexts, policy regimes and business systems affect the kinds of activities in which a nation specialises. This paper is concerned with the way in which different national business systems affect the nature of participation of a nation in the knowledge economy. The paper seeks to explain cross-national variations in the knowledge economy in the Australia, Denmark and Sweden with reference to dominant characteristics of the business system. Although Australia, Denmark and Sweden are all small wealthy countries, they each have quite distinctive business systems. Australia has been regarded as a variant of the competitive business system and has generally been described as an entrepreneurial economy with a large small firm population. In contrast Sweden has a coordinated business system that has favoured large industrial firms. The Danish variant of the coordinated model, with its well-developed vocational training system, is distinguishable by its large population of networked small and medium size enterprises. The three countries also differ significantly on two dimensions of participation in the knowledge economy. First, there is cross-national variation in patterns of specialisation in knowledge intensive industries and services. Second, the institutional infrastructure of the knowledge economy (or the existing stock of knowledge and competence in the economy, the potential for generation and diffusion a new knowledge and the capacity for commercialisation of new ideas) differs across the three countries. This paper seeks to explain variations in these two dimensions of the knowledge economy with reference to characteristics of the business system in the three countries.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Neo-Nazism in West Germany

The oharaoter of right-wing extremism in the Federal Republic has undergone extensive transformations in the seventies. As electoral support for the extreme Right declined, a whole range of new groupings emerged pursuing a militant extra-parliamentary strategy. Essential charaoteristics are an increasing tendency to use violence and a close ideological affinity to the NSDAP. They attract a growing number of young people. The increasing susceptibility of young people to rightist ideologies coincides with an economic recession of which young people especially are the victims. Widespread ignorance about Nazism and the prevalence of anti-democratic political attitudes constitute important contributary factors and point to a considerable potential for right-extremism in the Federal Republic., This potential can be attributed. to the negative effects of much of the material dealing with the NS past, to serious deficiencies in the area of historical-political education in schools and, above all, to the absence of any :real process of "coming to terms with the past" in the postwar period. Neo-Nazism is not completely isolated from other trends in West German society. Rightist elements within the established party system and broad sections of the population hold similar views and attitudes. This similarity, linked with an over-exaggerated concern with a perceived threat from the extreme Left may explain the absence of any concerted effort to deal with nee-Nazi tendencies. The response of the courts exemplifies a widespread tendency to under-estimate the significance of the extreme Right. Opposition to the Right is restricted primarily to those circles which suffered most under the Nazi regime. The analysis suggests that one must reject the simplistic view that at the present time the Right does not constitute a serious threat to West German democracy. The study evaluates the wide range of views to be found in secondary sources on the subject of neo-Nazism and is :intended, to contribute to the ongoing discussion conceming the potential for right-extremism in West Germany.

Evaluating the impact of design decisions on the financial performance of manufacturing companies

Product design decisions can have a significant impact on the financial and operation performance of manufacturing companies. Therefore good analysis of the financial impact of design decisions is required if the profitability of the business is to be maximised. The product design process can be viewed as a chain of decisions which links decisions about the concept to decisions about the detail. The idea of decision chains can be extended to include the design and operation of the 'downstream' business processes which manufacture and support the product. These chains of decisions are not independent but are interrelated in a complex manner. To deal with the interdependencies requires a modelling approach which represents all the chains of decisions, to a level of detail not normally considered in the analysis of product design. The operational, control and financial elements of a manufacturing business constitute a dynamic system. These elements interact with each other and with external elements (i.e. customers and suppliers). Analysing the chain of decisions for such an environment requires the application of simulation techniques, not just to any one area of interest, but to the whole business i.e. an enterprise simulation. To investigate the capability and viability of enterprise simulation an experimental 'Whole Business Simulation' system has been developed. This system combines specialist simulation elements and standard operational applications software packages, to create a model that incorporates all the key elements of a manufacturing business, including its customers and suppliers. By means of a series of experiments, the performance of this system was compared with a range of existing analysis tools (i.e. DFX, capacity calculation, shop floor simulator, and business planner driven by a shop floor simulator).

Essays on city size distribution and real estate bubbles

This is a dissertation about urban systems; within this broad subject I tackle three issues, one that focuses on an observed inter-city relationship and two that focus on an intra-city phenomenon. In Chapter II I adapt a model of random emergence of economic opportunities from the firm growth literature to the urban dynamics situation and present several predictions for urban system dynamics. One of these predictions is that the older the city the larger and more diversified it is going to be on average, which I proceed to verify empirically using two distinct datasets. In Chapter III I analyze the Residential Real Estate Bubble that took place in Miami-Dade County from 1999 to 2006. I adopt a Spatial-Economic model developed for the Paris Bubble episode of 1984–1993 and formulate an innovative test of the results in terms of speculative intensity on the basis of proxies of investor activity available in my dataset. My results support the idea that the best or more expensive areas are also where the greatest speculative activity takes place and where the rapid increase in prices begins. The most significant departure from previous studies that emerges in my results is the absence of a wider gap between high priced areas and low priced areas in the peak year. I develop a measure of dispersion in value among areas and contrast the Miami-Dade and Paris episodes. In Chapter IV I analyze the impact on tax equity of a Florida tax-limiting legislation known as Save Our Homes. I first compare homesteaded and non-homesteaded properties, and second, look within the subset of homesteaded properties. I find that non-homesteaded properties increase their share of taxes paid relative to homesteaded properties during an up market, but that this is reversed during a down market. For the subset of homesteaded properties I find that the impact on tax equity of SOH will depend on differential growth rates among higher and lower valued homes, but during times of rapid home price appreciation, in a scenario of no differential growth rates in property values, SOH increases progressivity relative to the prior system.