Quantum walks are the quantum mechanical analogue of classical random walks. Discrete-time quantum walks have been introduced and studied mostly on the line Z or higher dimensional space Z d but rarely defined on graphs with fractal dimensions because the coin operator depends on the position and the Fourier transform on the fractals is not defined. Inspired by its nature of classical walks, different quantum walks will be defined by choosing different shift and coin operators. When the coin operator is uniform, the results of classical walks will be obtained upon measurement at each step. Moreover, with measurement at each step, our results reveal more information about the classical random walks. In this dissertation, two graphs with fractal dimensions will be considered. The first one is Sierpinski gasket, a degree-4 regular graph with Hausdorff di- mension of df = ln 3/ ln 2. The second is the Cantor graph derived like Cantor set, with Hausdorff dimension of df = ln 2/ ln 3. The definitions and amplitude functions of the quantum walks will be introduced. The main part of this dissertation is to derive a recursive formula to compute the amplitude Green function. The exiting probability will be computed and compared with the classical results. When the generation of graphs goes to infinity, the recursion of the walks will be investigated and the convergence rates will be obtained and compared with the classical counterparts. / Mathematics

Over the centuries, cities have gained limelight and have significantly grown powerful with an increased level of importance. The rapid growth and urbanization posing a fatally critical threat to the future as the population is growing with each day. The development from the rural to urban life and the journey to an urban civilization has left the city in tatters. It has had adverse impacts on both social and environmental frontiers. Such rapid growth has led to the uncontrolled growth of population in countries that are in the process of development, and this growth is interpreted by means of concrete structuring with no apparent thought given to fundamentals such as feasibility, aesthetics, health, safety, road network or transportation. This leaves a very small window for even accommodating places for recreation in unplanned cities. Such spaces use shared spaces for recreation. Spaces like markets or public squares or streets. The cultural heritage of India lies solely in its old cities, towns and ancient settlements. Due to globalization and groundbreaking pace of urbanization in the recent times, the historic fabric has been radically altered. As cities have evolved through aspirations and ideas only, with no functional thought whatsoever, it is vital for a developing country like India to recognize that without regard for its heritage it cannot build a future, or that a development without its heritage would be only unsustainable. / Master of Science

This study explores optimal strategies for maximizing scores and winning in the popular dice game Qwixx, analyzing both single and multiplayer gameplay scenarios. Through extensive simulations, various strategies were tested and compared, including a scorebased approach that uses a formula tuned by MCMC random walks, and race-to-lock approaches which use absorbing Markov chain qualities of individual score sheet rows to find ways to lock rows as quickly as possible. Results indicate that employing a scorebased strategy, considering gap, count, position, skip, and likelihood scores, significantly improves performance in single player games, while move restrictions based on specific dice roll sums in the race-to-lock strategy were found to enhance winning and scoring points in multiplayer games. While the results do not achieve the optimal scores attained by prior informal work, the study provides valuable insights into decision-making processes and gameplay optimization for Qwixx enthusiasts, offering practical guidance for players seeking to enhance their performance and strategic prowess in the game. It also serves as a lesson for how to approach optimization problems in the future.

Lumbal spinal stenos är ett av de vanligaste patologiska tillstånden i ryggen. Primärt mål för de flesta av interventionerna vid lumbal spinal stenos är en förbättring av gångförmågan. I det Svenska ryggregistret för uppföljning av kirurgi saknas utvärdering av objektivt uppmätt gångförmåga. Syfte: Att undersöka hur objektivt uppmätt gångförmåga påverkas efter en operation av lumbal spinal stenos samt hur den korrelerar mot subjektivt skattad gångförmåga och mot skattad rygghälsa samt livskvalitet. Metod: Etthundrasjuttiotre patienter i ålder 50-81 år utförde pre och 24 månader postoperativt ett standardiserat six minutes walk test (6 MWT) samt besvarade enkäter om självskattad gångförmåga, livskvalitet (EQ5D) och rygghälsa (ODI). Signifikans på förändring av medelvärdet av gångförmågan beräknades med ett parat t-test och 95 % konfidensintervall. Korrelation mellan uppmätt gångförmåga och självskattad gångförmåga samt mot EQ5D och ODI beräknades med Spearmans rangkorrelation. Resultat: Gångförmågan mätt med 6MWT förbättrades från 314 meter preoperativt till 396 meter 24 månader postoperativt. Korrelationen mellan uppmätt gångförmåga och självskattad gångförmåga var 0,68 postoperativt. Korrelationen mellan 6 MWT och EQ5D var 0,60 och mot ODI 0,65, 2 år postoperativt. Konklusion: Resultatet i denna studie visade på en signifikant förbättring av objektivt uppmätt gångförmåga två år efter en operation av lumbal spinal stenos. Korrelationen mellan självskattad gångförmåga och 6 MWT var moderat. Korrelationen mellan 6 MWT och EQ5D var moderat och moderat till stark mot ODI. / Lumbar spinal stenosis is one of the most common pathological conditions in the lower back. A primary goal for most of the interventions for lumbar spinal stenosis is an improvement of walking ability. In the Swedish back registry for follow-up surgery objectively measured gait is missing. Objective: To examine how objectively measured walking capacity is affected by an operation of lumbar spinal stenosis and how it correlates with subjective estimated walking capacity, back health (ODI) and quality of life (EQ5D). Method: Onehundredseventythree patients in age 50-81 years performed pre and 24 months postoperatively a standardized six minutes walk test (6 MWT) and responded to questionnaires about self-rated gait, EQ5D and ODI. Significance of the change in mean walking ability was calculated by using a paired t-test and 95% confidence intervals. Correlation between the measured gait and self-rated gait as well as against EQ5D and ODI were calculated with Spearman rank correlation. Result: Walking capacity measured by the 6MWT improved from 314 to 396 meters, 24 months postoperatively. The correlation between the measured and self-rated gait were 0,68 postoperatively. Correlation between 6MWT and EQ5D were 0,60 and against ODI 0.65, 2 years postoperatively. Conclusion: The results of this study showed a significant improvement in objectively measured walking capacity, two years after an operation of lumbar spinal stenosis. Correlation between self-rated gait and 6 MWT were moderate. Correlation between 6MWT and EQ5D were moderate and against ODI moderately strong.

A pesquisa apresenta um estudo sobre a superioridade dos analistas de mercado com relação aos modelos random walk na previsão de resultados futuros das empresas brasileiras de capital aberto a curto e longo prazo. A literatura tradicional indica superioridade irrestrita dos analistas de mercado sobre os modelos de séries temporais por conta das vantagens de tempo e informação desses agentes. No entanto, estudos recentes da literatura internacional apontam para a necessidade de reavaliação dessa superioridade indicando que, para determinadas características da empresa e principalmente para estimativas de longo prazo, não se verifica superioridade dos analistas com relação aos modelos de séries temporais. Partindo desses achados, essa pesquisa defende a TESE de que para o caso brasileiro a superioridade dos analistas não é irrestrita. Este trabalho avalia as previsões de lucro dos analistas e dos modelos random walk, simples e com crescimento, a curto e longo prazo, para as empresas brasileiras de capital aberto no período de 2010 a 2015. Os dados foram obtidos via plataforma da Thomson Reuters®, nas bases de dados do I/B/E/S® e Thomson Financial. Seguindo a literatura, foram utilizados testes de diferença de média. Como diferencial da pesquisa, foi realizada uma análise de dados em painel no sentido de permitir uma avaliação mais precisa sobre os determinantes da superioridade dos analistas para o caso brasileiro. Ainda, foi proposto um modelo de regressão linear simples para avaliar o conteúdo informacional das previsões dos analistas de mercado e dos modelos random walk. Os resultados indicam: i) maior acurácia de previsão paras os modelos random walk simples quando comparados com os modelos de random walk com crescimento; ii) para a amostra total, nota-se maior acurácia da previsão dos modelos random walk a curto e longo prazo, com superioridade dos analistas apenas para previsões com três meses de defasagem; iii) além da defasagem de previsão, a variabilidade dos lucros, a quantidade de analistas, a dispersão das estimativas dos analistas, o tamanho da empresa, o resultado positivo ou negativo, a listagem em índice de mercado e a idade da empresa no mercado de capitais são fatores que alteram a superioridade dos analistas para o caso brasileiro; iv) maior conteúdo informacional das previsões random walk para previsão de lucros futuros das empresas. Esses resultados são importantes nas decisões de investimento. Ainda, os achados são relevantes para pesquisas da área de finanças e contabilidade que utilizam essa variável para responder a diferentes questões de pesquisa, uma vez que, ao contrário do apontado pela literatura internacional, as evidências sugerem superioridade de previsão dos modelos random walk quando comparados às previsões dos analistas de mercado / The research presents a study regarding the superiority of market analysts in relation to the random walk models in the forecast of future results of Brazilian companies in the short and long term. The traditional literature indicates unrestricted superiority of market analysts on time series models because of the time and information advantages of these agents. However, recent studies in the international literature point to the need for a reassessment of this superiority, indicating that, for certain company characteristics and especially for long-term estimates, there is no superiority of analysts with respect to time series models. Based on these findings, this research advocates that in the case of Brazil, the superiority of analysts is not unrestricted. This paper evaluates the analysts\' forecasts and the random walk models, both simple and with growth, in the short and long term, for Brazilian publicly traded companies during the period from 2010 to 2015. Data was obtained via the Thomson Reuters® platform, in the I/B/E/S® and Thomson Financial®databases. Following the literature, mean-comparison tests (t-test) were used. As a research differential, a panel data analysis was carried out in order to allow a more precise evaluation of the determinants of analysts\' superiority for the case of Brazil. Furthermore, a simple linear regression model was proposed to evaluate the informational content of market analysts\' forecasts and random walk models. The results indicate: i) greater accuracy of prediction for the simple random walk models, when compared to the random walk models with growth ii) that for the total sample, we can see a greater accuracy of the forecast of random walk models in the short and long term, with analyst superiority only for forecasts with a 3-month lag; (iii) in addition to forecast lag, profit variability, analyst size, dispersion of analysts\' estimates, company size, positive or negative result, market index listing and age of the company in the capital market are factors that alter the superiority of the analysts in the case of Brazil; iv) greater informational content of the random walk forecasts for the prediction of future companies\' profits. These results are important for investment decisions. Moreover, the findings are relevant for research in the field of finance and accounting that use this variable to answer different research questions, since, contrary to the international literature, the evidence suggests forecasting superiority of the random walk models when compared to the market analysts\' forecasts.

A caminhada do turista pode ser enunciada num meio desordenado formado por N pontos espalhados aleatoriamente num hipercubo de d dimensoes. Um caminhante, partindo de um ponto qualquer desse meio, se desloca seguindo a regra determinista de dirigir-se sempre ao ponto mais proximo que nao tenha sido visitado nos ultimos µ pas- sos. Esta dinamica de movimentacao leva a trajetorias formadas por uma parte inicial transiente de t pontos, e uma parte final c?clica de p pontos. As trajetorias obtidas sao altamente dependentes da configuracao do meio. Este cenario sugere que este modelo possa ser usado como uma ferramenta de reconhecimento de padroes em conjuntos de dados. O objetivo desta tese e mostrar que as propriedades da caminhada do turista permitem a sua utilizacao na caracterizacao e exploracao de diversos tipos de sistemas. Aplicamos o modelo descrito em dois tipos distintos de sistemas, sistemas cont´?nuos e redes regulares, estudando suas ropriedades em funcao de parametros como tamanho do sistema, valor de memoria (µ), condicoes de contorno e regras de movimentacao. Finalmente, propomos e exploramos duas novas metodologias de reconhecimento de padroes baseadas nesta caminhada. A primeira consiste de um algoritmo de an´alise de imagens para caracterizar texturas que utiliza os resultados da matriz conjunta S(t, p) que carrega as informacoes sobre todas as trajetorias obtidas, reduzindo sua dimensionalidade e permitindo a classificacao eficiente de diferentes classes de imagens por um algoritmo de analise discriminante. O diferencial desta metodologia esta em sua capacidade de extrair da imagem as informacoes presentes em diversas escalas simultaneamente. A segunda metodologia e um algoritmo de agrupamento de dados n~ao supervisionado que considera cada atrator formado num dado valor de µ como um agrupamento natural e tem como resultado final uma arvore hierarquica geral, onde os grupos se conectam conforme se aumenta o valor de µ. Os resultados desta metodologia comparam-se em eficiencia aos resultados obtidos pela metodologia adicional para os dados testados e, entre as vanta- gens obtidas, podemos citar (i) independencia de uma metrica relacionando os elementos do conjunto, ja que trabalha apenas com uma matriz de vizinhancas, (ii) respeito a estrutura natural embutida no conjunto de dados, gerando uma arvore geral ao inves de uma arvore binaria e (iii) a representacao de maneira identica de conjuntos que sofreram transformacao de escala devido a independencia de uma metrica. / The tourist walk is defined in a disordered environment characterized by N points randomly distributed in a d-dimensional hypercube. Leaving from a given point, a wal- ker moves according to the deterministic rule of going to next point not visited in the last µ time steps. This dynamics leads to trajectories consisting in a transient part of t points e a final cyclic part of p points. The obtained trajectories are strongly dependent on the configuration of points. This described scenario suggests that the model can be treated as a tool for pattern recognition. The aim of this thesis is to demonstrate that the tourist walk\'s properties allow for its use in the characterization and exploration of various kinds of systems. We have applied the model in two distinct kinds of systems - continuous systems and regular networks and studied its properties as a function of the following parameters: system size, memory (µ), boundary conditions and movimentation rule. Eventually we have proposed and explored two new pattern recognition methodolo- gies based on this deterministic walk. The first one consists of an image analysis algorithm to characterize textures that makes use of the joint matrix S(t, p) which carries the data about all trajectories obtained, reducing its dimensionality and allowing an efficient clas- sification of different classes of images by a discriminant analysis algorithm. Its distinctive feature is its ability to extract informations in all scales from an image simultaneously. The second methodology proposed is a non-supervised clustering algorithm that considers each attractor in a given µ as a natural cluster. Its final result is a general hierarchical tree where groups coalesce as µ is increased. The results obtained with this methodology are comparable in efficiency with the results obtained with the tradicional method for the datasets tested. Among the advantages presented we can cite (i) independence from a metrics relating the elements since it works only with a neighborhood ranking table, (ii) respect for the natural structure hidden in the dataset, generating a general tree instead of a binary one and (iii) the representation of two sets transformed by scale in an identic manner due to the independence from a metrics.

Passeio aleatório é uma classe de modelos matemáticos que têm por objetivo descrever processos estocásticos cujo resultado observável é dado por uma soma de variáveis aleatórias. O termo foi cunhado em 1905 pelo estatístico inglês Karl Pearson, estando na época interessado na modelagem da migração de insetos, e hoje possui uma ampla gama de aplicações, indo desde a biologia, passando pela física e química, e chegando na economia. Tendo sido estudado por inúmeros cientistas, muitas variações surgiram, chegando aos passeios aleatórios correlacionados, processos estocásticos não-Markovianos nos quais as variáveis aleatórias que se somam, chamadas de passos, possuem dependências umas com as outras, com correlações de caudas longas. Em 2004, surge na literatura o passeio aleatório do elefante, um passeio aleatório correlacionado com um mecanismo microscópico de memória de longo alcance muito bem definido e com soluções analíticas. Além desses dois fatos, também despertou o interesse da comunidade científica por exibir superdifusão. Muitas variações desse modelo foram propostas e vários resultados foram obtidos nos anos que se seguiram. A presente dissertação contem uma compilação dos principais modelos e resultados da área, tentando ser um texto introdutório ao assunto, focando sempre no que diz respeito à difusão. No caso unidimensional, propomos uma generalização desse tipo de passeio aleatório, o qual envolve decisões probabilísticas com respeito a passos lembrados do passado. Já no caso multi-muldimensional, apresentamos o conceito de acoplamento de memória e o modelo de Vaca e Boi, introduzidos pelo autor deste trabalho em 2018, como uma maneira de incluir interações entre elefantes. Também obtivemos um limite do contínuo para esse último processo, permitindo calcular os regimes de difusão para o Boi e construir um diagrama de fases para o mesmo. Esses últimos pontos constituem as principais contribuições do presente trabalho. / Random walk is a class of mathematical models which has the objective of describing a stochastic process whose observable result is given by a sum of aleatory variables. The term was coined in 1905 by the english statistician Karl Pearson while he was interested in the insects migration modeling, but today it has a myriad of applications, from biology to stock markets, passing through physics and chemestry. It has been studied by an uncountable number of scientists and a lot of variations have appeared, including those called correlated random walks, which are stochastic non-Markovian process in which those random variables that are summed, called steps, depends one of each other with fat tails correlations. In 2004, the elephant random walk appeared in the literature. It is a correlated random walk with a microscopic well defined memory mechanism and that has analitical solutions. Besides these facts, it also arouse the interest of scientific community because it exhibits superdifusion behaviour. In the one-dimensional case, we propose a generalization of this kind of random walk, which involves probabilistic decisions with respect to remembered steps given in the past. In the multi-dimensional case, we present the concept of memory coupling and the Cow and Ox model, which were introduced by the author of this work in 2018 as a manner of including interactions among elephants. We have also obtained a continuum limit of this process, allowing us to calculate the Ox diffusion regimes and to build its phase diagram. These last points constitute the main contributions of the present work.

In the presence of a solid-liquid or liquid-air interface, bacteria can choose between a planktonic and a sessile lifestyle. Depending on environmental conditions, cells swimming in close proximity to the interface can irreversibly attach to the surface and grow into three-dimensional aggregates where the majority of cells is sessile and embedded in an extracellular polymer matrix (biofilm). We used microfluidic tools and time lapse microscopy to perform experiments with the polarly flagellated soil bacterium Pseudomonas putida (P. putida), a bacterial species that is able to form biofilms. We analyzed individual trajectories of swimming cells, both in the bulk fluid and in close proximity to a glass-liquid interface. Additionally, surface related growth during the early phase of biofilm formation was investigated. In the bulk fluid, P.putida shows a typical bacterial swimming pattern of alternating periods of persistent displacement along a line (runs) and fast reorientation events (turns) and cells swim with an average speed around 24 micrometer per second. We found that the distribution of turning angles is bimodal with a dominating peak around 180 degrees. In approximately six out of ten turning events, the cell reverses its swimming direction. In addition, our analysis revealed that upon a reversal, the cell systematically changes its swimming speed by a factor of two on average. Based on the experimentally observed values of mean runtime and rotational diffusion, we presented a model to describe the spreading of a population of cells by a run-reverse random walker with alternating speeds. We successfully recover the mean square displacement and, by an extended version of the model, also the negative dip in the directional autocorrelation function as observed in the experiments. The analytical solution of the model demonstrates that alternating speeds enhance a cells ability to explore its environment as compared to a bacterium moving at a constant intermediate speed. As compared to the bulk fluid, for cells swimming near a solid boundary we observed an increase in swimming speed at distances below d= 5 micrometer and an increase in average angular velocity at distances below d= 4 micrometer. While the average speed was maximal with an increase around 15% at a distance of d= 3 micrometer, the angular velocity was highest in closest proximity to the boundary at d=1 micrometer with an increase around 90% as compared to the bulk fluid. To investigate the swimming behavior in a confinement between two solid boundaries, we developed an experimental setup to acquire three-dimensional trajectories using a piezo driven objective mount coupled to a high speed camera. Results on speed and angular velocity were consistent with motility statistics in the presence of a single boundary. Additionally, an analysis of the probability density revealed that a majority of cells accumulated near the upper and lower boundaries of the microchannel. The increase in angular velocity is consistent with previous studies, where bacteria near a solid boundary were shown to swim on circular trajectories, an effect which can be attributed to a wall induced torque. The increase in speed at a distance of several times the size of the cell body, however, cannot be explained by existing theories which either consider the drag increase on cell body and flagellum near a boundary (resistive force theory) or model the swimming microorganism by a multipole expansion to account for the flow field interaction between cell and boundary. An accumulation of swimming bacteria near solid boundaries has been observed in similar experiments. Our results confirm that collisions with the surface play an important role and hydrodynamic interactions alone cannot explain the steady-state accumulation of cells near the channel walls. Furthermore, we monitored the number growth of cells in the microchannel under medium rich conditions. We observed that, after a lag time, initially isolated cells at the surface started to grow by division into colonies of increasing size, while coexisting with a comparable smaller number of swimming cells. After 5:50 hours, we observed a sudden jump in the number of swimming cells, which was accompanied by a breakup of bigger clusters on the surface. After approximately 30 minutes where planktonic cells dominated in the microchannel, individual swimming cells reattached to the surface. We interpret this process as an emigration and recolonization event. A number of complementary experiments were performed to investigate the influence of collective effects or a depletion of the growth medium on the transition. Similar to earlier observations on another bacterium from the same family we found that the release of cells to the swimming phase is most likely the result of an individual adaption process, where syntheses of proteins for flagellar motility are upregulated after a number of division cycles at the surface. / Bakterien sind einzellige Mikroorganismen, die sich in flüssigem Medium mit Hilfe von rotierenden Flagellen, länglichen Fasern aus Proteinen, schwimmend fortbewegen. In Gegenwart einer Grenzfläche und unter günstigen Umweltbedingungen siedeln sich Bakterien an der Oberfläche an und gehen in eine sesshafte Wachstumsphase über. Die Wachstumsphase an der Oberfläche ist gekennzeichnet durch das Absondern von klebrigen, nährstoffreichen extrazellulären Substanzen, welche die Verbindung der Bakterien untereinander und mit der Oberfläche verstärken. Die entstehenden Aggregate aus extrazellulärer Matrix und Bakterien werden als Biofilm bezeichnet. In der vorliegenden Arbeit untersuchten wir ein Bodenbakterium, Pseudomonas putida (P. putida), welches in wässriger Umgebung an festen Oberflächen Biofilme ausbildet. Wir benutzten photolithographisch hergestellte Mikrokanäle und Hochgeschwindigkeits-Videomikroskopie um die Bewegung schwimmender Zellen in verschiedenen Abständen zu einer Glasoberfläche aufzunehmen. Zusätzlich wurden Daten über das parallel stattfindende Wachstum der sesshaften Zellen an der Oberfläche aufgezeichnet. Die Analyse von Trajektorien frei schwimmender Zellen zeigte, dass sich Liniensegmente, entlang derer sich die Zellen in eine konstante Richtung bewegen, mit scharfen Kehrtwendungen mit einem Winkel von 180 Grad abwechseln. Dabei änderte sich die Schwimmgeschwindigket von einem zum nächsten Segment im Mittel um einen Faktor von 2. Unsere experimentellen Daten waren die Grundlage für ein mathematisches Modell zur Beschreibung der Zellbewegung mit alternierender Geschwindigkeit. Die analytische Lösung des Modells zeigt elegant, dass eine Population von Bakterien, welche zwischen zwei Geschwindigkeiten wechseln, signifikant schneller expandiert als eine Referenzpopulation mit Bakterien konstanter Schwimmgeschwindkeit. Im Vergleich zu frei schwimmenden Bakterien beobachteten wir in der Nähe der Oberfläche eine um 15% erhöhte Schwimmgeschwindigkeit der Zellen und eine um 90 % erhöhte Winkel-geschwindigkeit. Außerdem wurde eine signifikant höhere Zelldichte in der Nähe der Grenzfläche gemessen. Während sich der Anstieg in der Winkelgeschwindigkeit durch ein Drehmoment erklären lässt, welches in Oberflächennähe auf den rotierenden Zellkörper und die rotierenden Flagellen wirkt, kann die Beschleunigung und Akkumulation der Zellen bei dem beobachteten Abstand nicht durch existierende Theorien erklärt werden. Unsere Ergebnisse lassen vermuten, dass neben hydrodynamischen Effekten auch Kollisionen mit der Oberfläche eine wichtige Rolle spielen und sich die Rotationsgeschwindigkeit der Flagellenmotoren in der Nähe einer festen Oberfläche grundsätzlich verändert. Unsere Experimente zum Zellwachstum an Oberflächen zeigten, dass sich etwa sechs Stunden nach Beginn des Experiments größere Kolonien an der Kanaloberfläche auflösen und Zellen für ca. 30 Minuten zurück in die schwimmende Phase wechseln. Ergebnisse von mehreren Vergleichsexperimenten deuten darauf hin, dass dieser Übergang nach einer festen Anzahl von Zellteilungen an der Oberfläche erfolgt und nicht durch den Verbrauch des Wachstumsmediums bedingt wird.

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A pesquisa apresenta um estudo sobre a superioridade dos analistas de mercado com relação aos modelos random walk na previsão de resultados futuros das empresas brasileiras de capital aberto a curto e longo prazo. A literatura tradicional indica superioridade irrestrita dos analistas de mercado sobre os modelos de séries temporais por conta das vantagens de tempo e informação desses agentes. No entanto, estudos recentes da literatura internacional apontam para a necessidade de reavaliação dessa superioridade indicando que, para determinadas características da empresa e principalmente para estimativas de longo prazo, não se verifica superioridade dos analistas com relação aos modelos de séries temporais. Partindo desses achados, essa pesquisa defende a TESE de que para o caso brasileiro a superioridade dos analistas não é irrestrita. Este trabalho avalia as previsões de lucro dos analistas e dos modelos random walk, simples e com crescimento, a curto e longo prazo, para as empresas brasileiras de capital aberto no período de 2010 a 2015. Os dados foram obtidos via plataforma da Thomson Reuters®, nas bases de dados do I/B/E/S® e Thomson Financial. Seguindo a literatura, foram utilizados testes de diferença de média. Como diferencial da pesquisa, foi realizada uma análise de dados em painel no sentido de permitir uma avaliação mais precisa sobre os determinantes da superioridade dos analistas para o caso brasileiro. Ainda, foi proposto um modelo de regressão linear simples para avaliar o conteúdo informacional das previsões dos analistas de mercado e dos modelos random walk. Os resultados indicam: i) maior acurácia de previsão paras os modelos random walk simples quando comparados com os modelos de random walk com crescimento; ii) para a amostra total, nota-se maior acurácia da previsão dos modelos random walk a curto e longo prazo, com superioridade dos analistas apenas para previsões com três meses de defasagem; iii) além da defasagem de previsão, a variabilidade dos lucros, a quantidade de analistas, a dispersão das estimativas dos analistas, o tamanho da empresa, o resultado positivo ou negativo, a listagem em índice de mercado e a idade da empresa no mercado de capitais são fatores que alteram a superioridade dos analistas para o caso brasileiro; iv) maior conteúdo informacional das previsões random walk para previsão de lucros futuros das empresas. Esses resultados são importantes nas decisões de investimento. Ainda, os achados são relevantes para pesquisas da área de finanças e contabilidade que utilizam essa variável para responder a diferentes questões de pesquisa, uma vez que, ao contrário do apontado pela literatura internacional, as evidências sugerem superioridade de previsão dos modelos random walk quando comparados às previsões dos analistas de mercado / The research presents a study regarding the superiority of market analysts in relation to the random walk models in the forecast of future results of Brazilian companies in the short and long term. The traditional literature indicates unrestricted superiority of market analysts on time series models because of the time and information advantages of these agents. However, recent studies in the international literature point to the need for a reassessment of this superiority, indicating that, for certain company characteristics and especially for long-term estimates, there is no superiority of analysts with respect to time series models. Based on these findings, this research advocates that in the case of Brazil, the superiority of analysts is not unrestricted. This paper evaluates the analysts\' forecasts and the random walk models, both simple and with growth, in the short and long term, for Brazilian publicly traded companies during the period from 2010 to 2015. Data was obtained via the Thomson Reuters® platform, in the I/B/E/S® and Thomson Financial®databases. Following the literature, mean-comparison tests (t-test) were used. As a research differential, a panel data analysis was carried out in order to allow a more precise evaluation of the determinants of analysts\' superiority for the case of Brazil. Furthermore, a simple linear regression model was proposed to evaluate the informational content of market analysts\' forecasts and random walk models. The results indicate: i) greater accuracy of prediction for the simple random walk models, when compared to the random walk models with growth ii) that for the total sample, we can see a greater accuracy of the forecast of random walk models in the short and long term, with analyst superiority only for forecasts with a 3-month lag; (iii) in addition to forecast lag, profit variability, analyst size, dispersion of analysts\' estimates, company size, positive or negative result, market index listing and age of the company in the capital market are factors that alter the superiority of the analysts in the case of Brazil; iv) greater informational content of the random walk forecasts for the prediction of future companies\' profits. These results are important for investment decisions. Moreover, the findings are relevant for research in the field of finance and accounting that use this variable to answer different research questions, since, contrary to the international literature, the evidence suggests forecasting superiority of the random walk models when compared to the market analysts\' forecasts.