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The study of behavioral pattern under various nourishing conditions for ciliates using spatial analysis.Yan, Jang-Ching 01 August 2007 (has links)
It is a research of the move trajectory of the ciliates while feeding the food, in order to estimate, differentiate from the movement behavior under different environments. First, discuss the differently distinguish with the single indicator. Second, discuss with integrate four kinds of indicator whether can distinguish differently. Finally, combine the indicator data and through different analysis technology look out the features of movement behavior, expect to be able to look out suitable information and knowledge from the indicator data.
After deal with analytical technology, the result of decision tree is most suitable for predicted and have credibilities. If according to energy of biological, the analysis result is similar to optimal foraging theory. And learn from result under different condition, the movement behavior of the ciliates similar to the optimal foraging theory.
In the matter of the result of analysis technology, data of the density of low food similar to data of the density of extremely high food. Besides, data of medium food and high food are analogous. The rule of decision tree can distinguish the density of different food, and can offer follow-up study to distinguish the environmental conditions. Those models are evaluated by predicting accuracies, and rules extracted from decision tree models are also of great help to prediction as well.
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\"Identificação de correlações usando a Teoria dos Fractais\" / Correlation identification using the fractal theorySousa, Elaine Parros Machado de 29 March 2006 (has links)
O volume de informação manipulada em sistemas apoiados por computador tem crescido tanto no número de objetos que compõem os conjuntos de dados quanto na quantidade e na complexidade dos atributos. Em conjuntos de dados do mundo real, a uniformidade na distribuição de valores e a independência entre atributos são propriedades bastante incomuns. De fato, dados reais são em geral caracterizados pela ampla presença de correlações entre seus atributos. Além disso, num mesmo conjunto podem existir correlações de naturezas diversas, como correlações lineares, não-lineares e não-polinomiais. Todo esse cenário pode degradar a performance dos algoritmos que manipulam e, principalmente, dos que realizam análises dos dados. Além da grande quantidade de objetos a serem tratados e do número elevado de atributos, as correlações nem sempre são conhecidas, o que pode comprometer a eficácia de tais algoritmos. Nesse contexto, as técnicas de redução de dimensionalidade permitem diminuir o número de atributos de um conjunto de dados, minimizando assim os problemas decorrentes da alta dimensionalidade. Algumas delas são baseadas na análise de correlações e, com o objetivo de reduzir a perda de informação relevante causada pela remoção de atributos, procuram eliminar apenas aqueles que sejam correlacionados aos restantes. No entanto, essas técnicas geralmente analisam como cada atributo está correlacionado a todos os demais, tratando o conjunto de atributos como um todo e usando ferramentas de análise estatística. Esta tese propõe uma abordagem diferente, baseada na Teoria dos Fractais, para detectar a existência de correlações e identificar subconjuntos de atributos correlacionados. Para cada correlação encontrada é possível ainda identificar quais são os atributos que melhor a descrevem. Conseqüentemente, um subconjunto de atributos relevantes para representar as características fundamentais dos dados é determinado, não apenas com base em correlações globais entre todos os atributos, mas também levando em consideração especificidades de correlações que envolvem subconjuntos reduzidos. A técnica apresentada é uma ferramenta a ser utilizada em etapas de pré-processamento de atividades de descoberta de conhecimento, principalmente em operações de seleção de atributos para redução de dimensionalidade. A proposta para a identificação de correlações e os conceitos que a fundamentam são validados por meio de estudos experimentais usando tanto dados sintéticos quanto reais. Finalmente, os conceitos básicos da Teoria dos Fractais são aplicados na análise de comportamento de data streams, também constituindo uma contribuição relevante desta tese de doutorado. / The volume of information processed by computer-based systems has grown not only in the amount of data but also in number and complexity of attributes. In real world datasets, uniform value distribution and independence between attributes are rather uncommon properties. In fact, real data is usually characterized by vast existence of correlated attributes. Moreover, a dataset can present different types of correlations, such as linear, non-linear and non-polynomial. This entire scenario may degrade performance of data management and, particularly, data analysis algorithms, as they need to deal with large amount of data and high number of attributes. Furthermore, correlations are usually unknown, which may jeopardize the efficacy of these algorithms. In this context, dimensionality reduction techniques can reduce the number of attributes in datasets, thus minimizing the problems caused by high dimensionality. Some of these techniques are based on correlation analysis and try to eliminate only attributes that are correlated to those remaining, aiming at diminishing the loss of relevant information imposed by attribute removal. However, techniques proposed so far usually analyze how each attribute is correlated to all the others, considering the attribute set as a whole and applying statistical analysis tools. This thesis presents a different approach, based on the Theory of Fractals, to detect the existence of correlations and to identify subsets of correlated attributes. In addition, the proposed technique makes it possible to identify which attributes can better describe each correlation. Consequently, a subset of attributes relevant to represent the fundamental characteristics of the dataset is determined, not only based on global correlations but also considering particularities of correlations concerning smaller attribute subsets. The proposed technique works as a tool to be used in preprocessing steps of knowledge discovery activities, mainly in feature selection operations for dimensionality reduction. The technique of correlation detection and its main concepts are validated through experimental studies with synthetic and real data. Finally, as an additional relevant contribution of this thesis, the basic concepts of the Theory of Fractals are also applied to analyze data streams behavior.
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A metáfora e a metonímia sob a perspectiva dos sistemas dinâmicos complexos e da teoria fractal no processo de conceitualização da violência urbana na cidade de Fortaleza-CE / The metaphor and metonymy from the perspective of the complex dynamical systems and fractal theory in the conceptualization process of urban violence in the city of FortalezaMarques, Pedro Jorge da Silva January 2014 (has links)
MARQUES, Pedro Jorge da Silva. A metáfora e a metonímia sob a perspectiva dos sistemas dinâmicos complexos e da teoria fractal no processo de conceitualização da violência urbana na cidade de Fortaleza-CE. 2014. 300f. – Dissertação (Mestrado) – Universidade Federal do Ceará, Departamento de Letras Vernáculas, Programa de Pós-graduação em Linguística, Fortaleza (CE), 2014. / Submitted by Márcia Araújo (marcia_m_bezerra@yahoo.com.br) on 2014-06-05T13:26:02Z
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Previous issue date: 2014 / The metaphor has always occupied an important place in meaning studies and with the advances on Cognitive Linguistics researches this figure presents itself more evident when put in relation with metonym, which has less importance on academic researches. In this context, this very work aims: (i) establish the primacy of metonym over metaphor by the dynamic discourse analysis of focal group participants when discussing urban violence in the city of Fortaleza; (ii) verify if the metonymic relations appear both in context and wording; and (iii) demonstrate that metonyms are responsible for the emerging of great part of metaphorical vehicles, so important to the construction of meaning. Thus, it was necessary to discuss the main approaches of these phenomena in light of Complex Dynamic Systems theory, anchored on Larsen-Freeman (1997); Larsen-Freeman e Cameron (2008), on fractal theory, based in Paiva (2010) e Mandelbrot (1982), as Capra (2006). This theoretical reference served as base to verify the hypothesis that great part of metaphors emerge from metonyms and that the relations contribute to the emerging of that both contextual and wording levels arise fragmented in the real discourse of focal group participants. Furthermore, the research proposes itself to also describe the process of conceptualization of urban violence based in the criteria of complexity paradigm, showing its importance to the current researches. To give consistency to that discussion we based ourselves in authors such as Goosens (1990, 1995), Barcelona (1997) and Radden (2003), who also discuss the complex relation between metaphor and metonym. Our study is ruled by a qualitative and theoretical research that allows us to reflect about the primacy of metonym over metaphor, analyzing the transcription of three focal groups that discussed the urban violence in the city of Fortaleza. The analysis allowed until this moment the ascertainment that in some cases, in the process of conceptualization, the metaphor arises from metonym, as relations that structure metonym, such as take a tree for a forest, institution for its responsible ones, effect by cause, permeate both wording and context of the discussion of the focal group participants. This made us come to the conclusion that a series of metaphors come from metonyms, what shows that although metaphor and metonym interact themselves, there is a primacy of the second over the first in some cases. / A metáfora sempre ocupou um lugar de destaque nos estudos do significado e, com o avanço das pesquisas em Linguística Cognitiva, essa figura apresenta-se mais evidente quando posta em relação com a metonímia, que ganha pouco destaque nas pesquisas acadêmicas. Nesse contexto, a presente pesquisa tem como objetivos: (i) estabelecer a primazia da metonímia sobre a metáfora por meio da análise dinâmica do discurso dos participantes de grupos focais, ao discutirem a violência urbana na cidade de Fortaleza; (ii) verificar se as relações metonímicas dão-se tanto em nível contextual como de enunciado; e (iii) demonstrar que as metonímias são responsáveis pela emergência de grande parte dos veículos metafóricos, tão importantes para a construção do sentido. Para tanto, fez-se necessário discutir as principais abordagens dos fenômenos à luz da teoria dos Sistemas Dinâmicos Complexos, ancorados em Larsen-Freeman (1997); Larsen-Freeman e Cameron (2008), na teoria fractal, com fundamentos em Paiva (2010) e Mandelbrot (1982), assim como Capra (2006). Esse referencial teórico serviu de base para verificarmos a hipótese de que grande parte das metáforas será oriunda de metonímia e de que as relações que contribuem para a emergência dessa figura deram-se tanto em nível contextual como de enunciado, surgindo de forma fragmentada no discurso real dos participantes dos grupos focais. Além disso, a pesquisa propõe-se também a descrever o processo de conceitualização da violência urbana com base nos critérios do paradigma da complexidade, mostrando sua importância para as atuais pesquisas. Para dar consistência à nossa discussão, embasamo-nos em autores como Goosens (1990, 1995), Barcelona (1997) e Radden (2003) que também discutem a complexa relação entre metáfora e metonímia. Nosso estudo está pautado em uma pesquisa qualitativa e teórica, que nos permite refletir acerca da primazia da metonímia em relação à metáfora, analisando a transcrição de três grupos focais que discutiram a questão da violência urbana na cidade de Fortaleza-CE. A análise permitiu constatar, até o momento que, em alguns casos, no processo de conceitualização da violência urbana, a metáfora tem procedência na metonímia, visto que as relações que estruturam a metonímia, como parte pelo todo, instituição pelos responsáveis, efeito pela causa, entre outros, permeiam tanto o enunciado como o contexto da discussão dos participantes dos grupos focais. Isso nos fez chegar à conclusão de que uma série de metáforas provém de metonímias o que mostra que, apesar de a metáfora e a metonímia interagirem entre si, em alguns casos, há primazia desta sobre aquela.
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\"Identificação de correlações usando a Teoria dos Fractais\" / Correlation identification using the fractal theoryElaine Parros Machado de Sousa 29 March 2006 (has links)
O volume de informação manipulada em sistemas apoiados por computador tem crescido tanto no número de objetos que compõem os conjuntos de dados quanto na quantidade e na complexidade dos atributos. Em conjuntos de dados do mundo real, a uniformidade na distribuição de valores e a independência entre atributos são propriedades bastante incomuns. De fato, dados reais são em geral caracterizados pela ampla presença de correlações entre seus atributos. Além disso, num mesmo conjunto podem existir correlações de naturezas diversas, como correlações lineares, não-lineares e não-polinomiais. Todo esse cenário pode degradar a performance dos algoritmos que manipulam e, principalmente, dos que realizam análises dos dados. Além da grande quantidade de objetos a serem tratados e do número elevado de atributos, as correlações nem sempre são conhecidas, o que pode comprometer a eficácia de tais algoritmos. Nesse contexto, as técnicas de redução de dimensionalidade permitem diminuir o número de atributos de um conjunto de dados, minimizando assim os problemas decorrentes da alta dimensionalidade. Algumas delas são baseadas na análise de correlações e, com o objetivo de reduzir a perda de informação relevante causada pela remoção de atributos, procuram eliminar apenas aqueles que sejam correlacionados aos restantes. No entanto, essas técnicas geralmente analisam como cada atributo está correlacionado a todos os demais, tratando o conjunto de atributos como um todo e usando ferramentas de análise estatística. Esta tese propõe uma abordagem diferente, baseada na Teoria dos Fractais, para detectar a existência de correlações e identificar subconjuntos de atributos correlacionados. Para cada correlação encontrada é possível ainda identificar quais são os atributos que melhor a descrevem. Conseqüentemente, um subconjunto de atributos relevantes para representar as características fundamentais dos dados é determinado, não apenas com base em correlações globais entre todos os atributos, mas também levando em consideração especificidades de correlações que envolvem subconjuntos reduzidos. A técnica apresentada é uma ferramenta a ser utilizada em etapas de pré-processamento de atividades de descoberta de conhecimento, principalmente em operações de seleção de atributos para redução de dimensionalidade. A proposta para a identificação de correlações e os conceitos que a fundamentam são validados por meio de estudos experimentais usando tanto dados sintéticos quanto reais. Finalmente, os conceitos básicos da Teoria dos Fractais são aplicados na análise de comportamento de data streams, também constituindo uma contribuição relevante desta tese de doutorado. / The volume of information processed by computer-based systems has grown not only in the amount of data but also in number and complexity of attributes. In real world datasets, uniform value distribution and independence between attributes are rather uncommon properties. In fact, real data is usually characterized by vast existence of correlated attributes. Moreover, a dataset can present different types of correlations, such as linear, non-linear and non-polynomial. This entire scenario may degrade performance of data management and, particularly, data analysis algorithms, as they need to deal with large amount of data and high number of attributes. Furthermore, correlations are usually unknown, which may jeopardize the efficacy of these algorithms. In this context, dimensionality reduction techniques can reduce the number of attributes in datasets, thus minimizing the problems caused by high dimensionality. Some of these techniques are based on correlation analysis and try to eliminate only attributes that are correlated to those remaining, aiming at diminishing the loss of relevant information imposed by attribute removal. However, techniques proposed so far usually analyze how each attribute is correlated to all the others, considering the attribute set as a whole and applying statistical analysis tools. This thesis presents a different approach, based on the Theory of Fractals, to detect the existence of correlations and to identify subsets of correlated attributes. In addition, the proposed technique makes it possible to identify which attributes can better describe each correlation. Consequently, a subset of attributes relevant to represent the fundamental characteristics of the dataset is determined, not only based on global correlations but also considering particularities of correlations concerning smaller attribute subsets. The proposed technique works as a tool to be used in preprocessing steps of knowledge discovery activities, mainly in feature selection operations for dimensionality reduction. The technique of correlation detection and its main concepts are validated through experimental studies with synthetic and real data. Finally, as an additional relevant contribution of this thesis, the basic concepts of the Theory of Fractals are also applied to analyze data streams behavior.
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Micro-nano scale pore structure and fractal dimension of ultra-high performance cementitious composites modified with nanofillersWang, J., Wang, X., Ding, S., Ashour, Ashraf F., Yu, F., Lv, X., Han, B. 11 May 2023 (has links)
Yes / The development of ultra-high performance cementitious composite (UHPCC) represents a significant advancement in the field of concrete science and technology, but insufficient hydration and high autogenous shrinkage relatively increase the pores inside UHPCC, in turn, affecting the macro-performance of UHPCC. This paper, initially, optimized the pore structure of UHPCC using different types and dimensions of nanofillers. Subsequently, the pore structure characteristics of nano-modified UHPCC were investigated by the mercury intrusion porosimeter method and fractal theory. Finally, the fluid permeability of nano-modified UHPCC was estimated by applying the Katz-Thompson equation. Experimental results showed that all incorporated nanofillers can refine the pore structure of UHPCC, but nanofillers with different types and dimensions have various effects on the pore structure of UHPCC. Specifically, CNTs, especially the thin-short one, can significantly reduce the porosity of UHPCC, whereas nanoparticles, especially nano-SiO2, are more conducive to refine the pore size. Among all nanofillers, nano-SiO2 has the most obvious effect on pore structure, reducing the porosity, specific pore volume and most probable pore radius of UHPCC by 31.9%, 35.1% and 40.9%, respectively. Additionally, the pore size distribution of nano-modified UHPCC ranges from 10-1nm to 105nm, and the gel pores and fine capillary pores in the range of 3-50nm account for more than 70% of the total pore content, confirming nanofillers incorporation can effectively weaken pore connectivity and induce pore distribution to concentrate at nanoscale. Fractal results indicated the provision of nanofillers reduces the structural heterogeneity of gel pores and fine capillary pores, and induces homogenization and densification of UHPCC matrix, in turn, decreasing the UHPCC fluid permeability by 15.7%-79.2%. / The authors thank the funding supported from the National Science Foundation of China (51978127, 52178188 and 51908103), the China Postdoctoral Science Foundation (2022M720648 and 2022M710973) and the Fundamental Research Funds for the Central Universities (DUT21RC(3)039). / The full-text of this article will be released for public view at the end of the publisher embargo on 11 May 2024.
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A Computational Study of Elastomer Friction and Surface Topography Characterization using Fractal TheorySeranthian, Kalay Arasan 12 September 2016 (has links)
No description available.
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Micro-nano scale pore structure and fractal dimension of ultra-high performance cementitious composites modified with nanofillersWang, J., Wang, X., Ding, S., Ashour, Ashraf, Yu, F., Xinjun, L., Han, B. 16 March 2023 (has links)
Yes / The development of ultra-high performance cementitious composite (UHPCC) represents a significant advancement in the field of concrete science and technology, but insufficient hydration and high autogenous shrinkage relatively increase the pores inside UHPCC, in turn, affecting the macro-performance of UHPCC. This paper, initially, optimized the pore structure of UHPCC using different types and dimensions of nanofillers. Subsequently, the pore structure characteristics of nano-modified UHPCC were investigated by the mercury intrusion porosimeter method and fractal theory. Finally, the fluid permeability of nano-modified UHPCC was estimated by applying the Katz-Thompson equation. Experimental results showed that all incorporated nanofillers can refine the pore structure of UHPCC, but nanofillers with different types and dimensions have various effects on the pore structure of UHPCC. Specifically, CNTs, especially the thin-short one, can significantly reduce the porosity of UHPCC, whereas nanoparticles, especially nano-SiO2, are more conducive to refine the pore size. Among all nanofillers, nano-SiO2 has the most obvious effect on pore structure, reducing the porosity, specific pore volume and most probable pore radius of UHPCC by 31.9%, 35.1% and 40.9%, respectively. Additionally, the pore size distribution of nano-modified UHPCC ranges from 10-1nm to 105nm, and the gel pores and fine capillary pores in the range of 3-50nm account for more than 70% of the total pore content, confirming nanofillers incorporation can effectively weaken pore connectivity and induce pore distribution to concentrate at nanoscale. Fractal results indicated the provision of nanofillers reduces the structural heterogeneity of gel pores and fine capillary pores, and induces homogenization and densification of UHPCC matrix, in turn, decreasing the UHPCC fluid permeability by 15.7%-79.2%. / National Science Foundation of China (51978127, 52178188 and 51908103), the China Postdoctoral Science Foundation (2022M720648 and 2022M710973) and the Fundamental Research Funds for the Central Universities (DUT21RC(3)039).
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NANOPARTICLE ADDITIVES FOR MULTIPHASE SYSTEMS: SYNTHESIS, FORMULATION AND CHARACTERIZATIONKanniah, Vinod 01 January 2012 (has links)
Study on nanoparticle additives in multiphase systems (liquid, polymer) are of immense interest in developing new product applications. Critical challenges for nanoparticle additives include their synthesis, formulation and characterization. These challenges are addressed in three application areas: nanofluids for engine lubrication, ultrathin nanocomposites for optical devices, and nanoparticle size distribution characterization.
Nanoparticle additives in oligomer mixtures can be used to develop extended temperature range motor oils. A model system includes poly(α-olefin) based oligomers with a modest fraction of poly(dimethylsiloxane) oligomers along with graphite as nanoparticle additive. Partition coefficients of each oligomer are determined since the oligomer mixture phase separated at temperatures less than -15 °C. Also, the surface of graphite additive is quantitatively analyzed and modified via silanization for each oligomer. Thus, upon separation of the oligomer mixture, each functionalized graphite additive migrates to its preferred oligomers and forms a uniform dispersion.
Similarly, nanoparticle additives in polymer matrices can be used to develop new low haze ultrathin film optical coatings. A model system included an acrylate monomer as the continuous phase with monodisperse or bidisperse mixtures of silica nanoparticles deposited on glass and polycarbonate substrates. Surface (root mean squared roughness, Wenzel’s contact angle) and optical properties (haze) of these self assembled experimental surfaces were compared to simulated surface structures. Manipulating the size ratios of silica nanoparticle mixtures varied the average surface roughness and the height distributions, producing multimodal structures with different packing fractions.
In both nanofluid and nanocomposite applications, nanoparticle additives tend to aggregate/agglomerate depending on various factors including the state of nanoparticles (powder, dispersion). A set of well-characterized ceria and titania nanoparticle products from commercial sources along with in-lab synthesized nanoparticles were studied via fractal theory. Fractal coefficients were obtained through two-dimensional images (from electron microscopy) and particle size distributions (from electron microscopy and dynamic light scattering). For some arbitrary collections of aggregated nanoparticle materials, the fractal coefficients via two-dimensional images correlated well to the average primary particle size. This complementary tool could be used along with conventional nanoparticle characterization techniques when not much is known about the nanoparticle surfaces to characterize agglomeration or aggregation phenomena.
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Effective and unsupervised fractal-based feature selection for very large datasets: removing linear and non-linear attribute correlations / Seleção de atributos efetiva e não-supervisionada em grandes bases de dados: aplicando a Teoria de Fractais para remover correlações lineares e não-linearesFraideinberze, Antonio Canabrava 04 September 2017 (has links)
Given a very large dataset of moderate-to-high dimensionality, how to mine useful patterns from it? In such cases, dimensionality reduction is essential to overcome the well-known curse of dimensionality. Although there exist algorithms to reduce the dimensionality of Big Data, unfortunately, they all fail to identify/eliminate non-linear correlations that may occur between the attributes. This MSc work tackles the problem by exploring concepts of the Fractal Theory and massive parallel processing to present Curl-Remover, a novel dimensionality reduction technique for very large datasets. Our contributions are: (a) Curl-Remover eliminates linear and non-linear attribute correlations as well as irrelevant attributes; (b) it is unsupervised and suits for analytical tasks in general not only classification; (c) it presents linear scale-up on both the data size and the number of machines used; (d) it does not require the user to guess the number of attributes to be removed, and; (e) it preserves the attributes semantics by performing feature selection, not feature extraction. We executed experiments on synthetic and real data spanning up to 1.1 billion points, and report that our proposed Curl-Remover outperformed two PCA-based algorithms from the state-of-the-art, being in average up to 8% more accurate. / Dada uma grande base de dados de dimensionalidade moderada a alta, como identificar padrões úteis nos objetos de dados? Nesses casos, a redução de dimensionalidade é essencial para superar um fenômeno conhecido na literatura como a maldição da alta dimensionalidade. Embora existam algoritmos capazes de reduzir a dimensionalidade de conjuntos de dados na escala de Terabytes, infelizmente, todos falham em relação à identificação/eliminação de correlações não lineares entre os atributos. Este trabalho de Mestrado trata o problema explorando conceitos da Teoria de Fractais e processamento paralelo em massa para apresentar Curl-Remover, uma nova técnica de redução de dimensionalidade bem adequada ao pré-processamento de Big Data. Suas principais contribuições são: (a) Curl-Remover elimina correlações lineares e não lineares entre atributos, bem como atributos irrelevantes; (b) não depende de supervisão do usuário e é útil para tarefas analíticas em geral não apenas para a classificação; (c) apresenta escalabilidade linear tanto em relação ao número de objetos de dados quanto ao número de máquinas utilizadas; (d) não requer que o usuário sugira um número de atributos para serem removidos, e; (e) mantêm a semântica dos atributos por ser uma técnica de seleção de atributos, não de extração de atributos. Experimentos foram executados em conjuntos de dados sintéticos e reais contendo até 1,1 bilhões de pontos, e a nova técnica Curl-Remover apresentou desempenho superior comparada a dois algoritmos do estado da arte baseados em PCA, obtendo em média até 8% a mais em acurácia de resultados.
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How Irrational Behavour Creates Order and How This Order Can Be Determined : The Theory and Practice of Fractal Market AnalysisBargman, Daniil January 2011 (has links)
This paper analyzes two main frameworks that challenge the “mainstream” finance theory and the random walk hypothesis. The first framework is based on investor irrationality and is called Behavioural Finance. The second framework views the financial market as a chaotic system and is called Fractal Theory of a financial market. Behavioural Finance attacks the assumption of investor rationality, thus challenging the conventional finance theories on the micro level. Fractal Theory challenges the EMH and the “macroeconomics” of finance. This paper presents a step towards unifying the frameworks of Behavioural Finance and Fractal Theory. After a review of the relevant literature, a model of the financial market is suggested that rests on the predictions of both Behavioural Finance and Fractal Theory. As a next step, a mathematical algorithm is described that allows to test the financial market for consistency with the presented model. The mathematical algorithm is applied to 10 years of daily S&P500 price quotes, and consistent statistical evidence shows that the predicted fractal pattern reveals itself in the S&P500 prices. The new model outperforms the random walk in out-of-sample forecasting.
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