This thesis focuses on fractal analysis of economic time series. Chapter One introduces fractal analysis as a method of exploring time series and gathers information about progress and current state of understanding in this field. Chapter Two focuses on design and development of computer software, which will calculate selected fractal indices. Chapter Three is experimental and shows the results and discussion of economic time series (popular stock market indexes and currency exchange rate) analysis that have been obtained from the software developed in Chapter Two.

Due to the increasing amount and complexity of data processed in real world applications, similarity search became a vital task to store and retrieve such data. However, missing attribute values are very frequent and metric access methods (MAMs), designed to support similarity search, do not operate on datasets when attribute values are missing. Currently, the approach to use the existing indexing techniques on datasets with missing attribute values just use an indicator to identify the missing values and employ a traditional indexing technique. Although, this approach can be applied over multidimensional indexing techniques, it is impractical for metric access methods. This dissertation presents the results of a research conducted to identify and deal with the issues related to indexing and querying datasets with missing values in metric spaces. An empirical analysis of the metric access methods when applied on incomplete datasets leads us to identify two main issues: distortion of the internal structure of the index when data are missing at random and skew of the index structure when data are not missing at random. Based on those findings, a new variant of the Slim-tree access method, called Hollow-tree, is presented. It employs new techniques that are capable to handle missing data issues when missingness is ignorable. The first technique includes a set of indexing policies that allow to index objects with missing attribute values and prevent distortions to occur in the internal structure of the indexes. The second technique targets the similarity queries to improve the query performance over incomplete datasets. This technique employs the fractal dimension of the dataset and the local density around the query object to estimate an ideal radius able to achieve an accurate query answer, considering data with missing values as a potential response. Results from experiments with a variety of real and synthetic datasets show that Hollow-tree achieves nearly 100% of precision and recall for Range queries and more than 90% for k Nearest Neighbor queries, while Slim-tree access method deteriorates with the increasing amount of missing values. The results confirm that the indexing technique helps to establish consistency in the index structure and the searching technique achieves a remarkable performance. When combined, the new techniques allow to explore properly all the available data even with high amounts of missing attribute values. As they are independent of the underlying access method, they can be adopted by a broad range of metric access methods, allowing to extend the class of MAMs. / O crescimento em quantidade e complexidade dos dados processados e armazenados torna a busca por similaridade uma tarefa fundamental para tratar esses dados. No entanto, atributos faltantes ocorrem freqüentemente, inviabilizando os métodos de acesso métricos (MAMs) projetados para apoiar a busca por similaridade. Assim, técnicas de tratamento de dados faltantes precisam ser desenvolvidas. A abordagem mais comum para executar as técnicas de indexação existentes sobre conjuntos de dados com valores faltantes é usar um indicador de valores faltantes e usar as técnicas de indexação tradicionais. Embora, esta técnica seja útil para os métodos de indexação multidimensionais, é impraticável para os métodos de acesso métricos. Esta dissertação apresenta os resultados da pesquisa realizada para identificar e lidar com os problemas de indexação e recuperação de dados em espaços métricos com valores faltantes. Uma análise experimental dos MAMs aplicados a conjuntos de dados incompletos identificou dois problemas principais: distorção na estrutura interna do índice quando a falta é aleatória e busca tendenciosa na estrutura do índice quando o processo de falta não é aleatório. Uma variante do MAM Slim-tree, chamada Hollow-tree foi proposta com base nestes resultados. A Hollow-tree usa novas técnicas de indexação e de recuperação de dados com valores faltantes quando o processo de falta é aleatório. A técnica de indexação inclui um conjunto de políticas de indexação que visam a evitar distorções na estrutura interna dos índices. A técnica de recuperação de dados melhora o desempenho das consultas por similaridade sobre bases de dados incompletas. Essas técnicas utilizam o conceito de dimensão fractal do conjunto de dados e a densidade local da região de busca para estimar um raio de busca ideal para obter uma resposta mais correta, considerando os dados com valores faltantes como uma resposta potencial. As técnicas propostas foram avaliadas sobre diversos conjuntos de dados reais e sintéticos. Os resultados mostram que a Hollow-tree atinge quase 100% de precisão e revocação para consultas por abrangência e mais de 90% para k vizinhos mais próximos, enquanto a Slim-tree rapidamente deteriora com o aumento da quantidade de valores faltantes. Tais resultados indicam que a técnica de indexação proposta ajuda a estabelecer a consistência na estrutura do índice e a técnica de busca pode ser realizada com um desempenho notável. As técnicas propostas são independentes do MAM básico usado e podem ser aplicadas em uma grande variedade deles, permitindo estender a classe dos MAMs em geral para tratar dados faltantes.

A complexidade é uma característica de grande importância em processos de reconhecimento de padrões, especialmente naqueles que envolvem imagens biológicas. Este trabalho tem como objetivo estudar métodos que realizam a análise de imagens por meio da análise de sua complexidade. Os métodos a serem estudados foram selecionados com base na similaridade de seus algoritmos e metodologia: dimensão fractal, Caminhada Determinística do Turista e Redes Complexas. Estes métodos permitem realizar a análise e segmentação de formas ou texturas contidas em uma imagem com base na sua variação de complexidade. Dos três métodos considerados, dois deles fazem parte do estado da arte em análise de complexidade, enquanto que a dimensão fractal já é aplicada a mais tempo na análise de formas e texturas. Os trabalhos aqui desenvolvidos visam comparar e analisar os métodos selecionados por meio de experimentos com imagens de forma e texturas, sendo utilizadas texturas naturais e de Brodatz, freqüentemente utilizadas na literatura como benchmark para texturas. Com base no conhecimento adquirido, novas técnicas voltadas para a análise e segmentação de formas e texturas foram desenvolvidas, assim como foram analisadas as deficiências e propostas melhorias às técnicas estudadas. Além disso, diversos experimentos com estas metodologias foram realizados em aplicações de Bioinformática / Complexity is a feature of great importance in pattern recognition processes, especially those involving biological images. This work aims to study methods that perform image analysis by the analysis of its complexity. The methods to be studied were selected based on similarity of their algorithms and methodology: fractal dimension, Deterministic Tourist Walk and Complex Networks. These methods enable us to perform the analysis and segmentation of shapes and textures contained in an image based on the variation of its complexity. Of the three methods considered, two of them are part of the state of the art in complexity analysis, while the fractal dimension is already applied in shapes and textures analysis. The work developed here aims to compare and analyze the selected methods through experiments with shape and texture images, utilizing for this natural and Brodatz textures samples, often used in literature as benchmark for textures analysis. Based on the knowledge acquired, new techniques for analysis and segmentation of shapes and textures were developed, as also were analyzed the deficiencies and proposed improvements to the techniques studied. Moreover, several experiments with these methods were performed in bioinformatics applications

Submitted by Adriana Martinez (amartinez@unoeste.br) on 2018-02-20T17:29:34Z No. of bitstreams: 1 Gabriela Haro de Melo.pdf: 1119579 bytes, checksum: f99d268fab2103015abb1dca2740c64b (MD5) / Made available in DSpace on 2018-02-20T17:29:34Z (GMT). No. of bitstreams: 1 Gabriela Haro de Melo.pdf: 1119579 bytes, checksum: f99d268fab2103015abb1dca2740c64b (MD5) Previous issue date: 2017-09-18 / Due to its high concentration of growth factors, platelet-rich plasma (PRP) has become the subject of much research, either as an isolated or adjuvant treatment for wound repair. The fractal dimension has been used as an innovative method for the characterization and quantification of tissue structural alterations without any interference from the evaluator. The objective of this study was characterizing collagen types I and III in experimentally induced wounds and treated with different PRP sources by means of fractal dimension and other histological analyzes using blades stained with picrocirius-red and hematoxylin-eosin (HE). In statistical analysis, the variables presented a non-parametric distribution; thus, Mann-Whitney and Kruskall-Wallis tests (p<0,05) were performed using the Student-Newman-Keuls method. It was observed an increase of the collagen fibers by measuring the area with Threshold Color in the different treatments, especially with autologous PRP (p = 0.009) and heterologous PRP (p = 0.016). The fractal dimension of type I collagen had a significant increase for the autologous group (p = 0.028) in relation to the control, but, on average (p <0.05), type III collagen was higher than type I. Fractal dimension was efficient to separately characterize type I and type III collagen fibers. In this study, collagenization was higher in autologous, heterologous and homologous PRP treatments. / Devido a alta concentração em fatores de crescimento, o plasma rico em plaquetas (PRP) tornou-se objeto de estudos para pesquisadores de todo o mundo, seja como tratamento isolado ou adjuvante e demonstra efeitos benéficos em processos de cicatrização com maior produção de colágeno. Contudo, são escassos estudos que avalim a qualidade do tecido cicatricial em feridas tratadas com diferentes tipos de PRP e que qualificam o colágeno, proteína importante na elasticidade e resistência da pele. A dimensão fractal (DF), método utilizado em lâminas histológicas, permite a caracterização de estruturas. Geralmente, quanto maior a DF, mais complexa a forma do objeto e dentre os vários cálculos de DF existente, a técnica de box-couting é a mais indicada. Levantamos a hipótese de que a DF, como método auxiliar na avaliação da fisiopatologia da reparação tecidual, pode contribuir na tomada de decisão do protocolo terapêutico mais indicado para cicatrização de feridas. Objetivou-se Avaliar as características do colágeno na reparação tecidual de feridas experimentalmente induzidas e tratadas com diferentes fontes de plasma rico em plaquetas (PRP) gel por meio de achados histológicos e análise fractal. Para avaliar os efeitos de diferentes tipos de PRP sob a forma de gel em cicatrização cutânea in vivo, foram utilizados 18 coelhos Nova Zelândia, divididos em três grupos de seis animais nos quais foram induzidas duas feridas com punch de 8 mm, o lado esquerdo (controle) foi tratado com NaCl 0,9%, e o direito (tratado) foi aplicado gel de PRP. As feridas foram avaliadas por um período de 17 dias. Ao 17º dia, foram realizadas biópsias para avaliação histológica pelo software Image J®. Seis animais foram doadores para PRP homólogo e um cão adulto foi usado para obtenção do PRP heterólogo. Observou-se incremento das fibras colágenas, por meio de medição de área com Threshold Colour nos diferentes tratamentos, sobretudo com PRP de fontes autóloga (p=0,009) e homóloga (p=0,016). A DF do colágeno tipo I mostrou aumento significativo para o grupo autólogo (p=0,028) em relação ao controle, porém, em média (p<0,05) o colágeno tipo III foi maior em relação ao tipo I. A coloração de picrosirius sob luz polarizada permitiu a visualização do colágeno tipo I mostrando marcada birrefringência laranja e vermelha e do colágeno tipo III com birrefringência verde. Nos grupos tratados, as fibras colágenas do tipo I, foram mais evidentes e organizadas do que as do tipo III, que estavam distribuídas irregularmente, quando comparadas com as do tipo I. Em microscopia optica, em lâminas coradas com HE, não foram observados indicativos de necrose ou inflamação nos tecidos analisados, assim como em outros estudos. A dimensão fractal foi eficaz para caracterizar separadamente as fibras de colágeno tipo I e tipo III. Os métodos utilizados neste estudo demonstraram que o emprego de PRP gel de diferentes fontes para o tratamento de feridas dérmicas é eficiente, porém o gel autólogo demonstrou melhor colagenização quando comparado ao heterólogo e homólogo, respectivamente, homólogo e heterólogo, respectivamente.

Submitted by Michele Mologni (mologni@unoeste.br) on 2018-08-17T13:30:36Z No. of bitstreams: 1 Danielle Alves Silva.pdf: 1187936 bytes, checksum: 4436228a6d8425a8ba13dd03636f218a (MD5) / Made available in DSpace on 2018-08-17T13:30:36Z (GMT). No. of bitstreams: 1 Danielle Alves Silva.pdf: 1187936 bytes, checksum: 4436228a6d8425a8ba13dd03636f218a (MD5) Previous issue date: 2018-03-21 / The objective of this study was to compare the efficacy of two omega 3 oral formulations with different ratios of EPA, DHA and antioxidants, as an adjuvant in the treatment of dogs affected by KCS and to evaluate by fractal analysis the palpebral conjunctiva of the treated dogs. Forty-five dogs with KCS were evaluated monthly for 6 months by the Schirmer Tear Test (TLS), Fluorescein Test (TF), Tear Film Break-up Time (TBUT), Lissamine Green Test (LGT), cytology of the conjunctiva at the beginning, middle and end of the study, biopsy and fractal analysis of the conjunctiva at the beginning and end of the study. The dogs were randomly assigned into 3 groups (n = 15): T group (tacrolimus 0.03% topical), TO group (tacrolimus + omegas EPA/DHA) and TOA group (tacrolimus + omegas EPA/DHA + Antioxidants). The result demonstrated that there was a significant improvement in clinical signs in both groups. In TBUT, all groups presented increase during the treatment, and the TO group presented the best result at all times when compared to the other groups. At the end of the experiment, the groups T, TO and TOA presented cytological analysis, reduction of lymphocytes, neutrophils, metaplastic and squamous cells, and histopathological analysis, reduction of lymphocytes and neutrophils and increase of goblet cells highlighting the best performance at TO. In the fractal analysis, at the end of the experiment, the TO group presented the best result and the values close to the values found in the fractals of healthy eyes. The difference between the TO group and the other groups is in the higher EPA concentration, being a natural anti-inflammatory, which may be one of the causes of its better performance. We concluded that oral omega 3, which contains a higher proportion of EPA than DHA, has shown greater benefit in terms of the improvement of clinical signs and the inflammatory process in the treatment of KCS in dogs. / O objetivo deste estudo foi comparar a eficácia de duas formulações de ômega 3 por via oral, com diferentes proporções de EPA, DHA e antioxidantes, como adjuvante no tratamento de cães acometidos por CCS e avaliar por meio da análise fractal a conjuntiva palpebral dos cães tratados. Quarenta e cinco cães atendidos no HV da UNOESTE portadores de CCS foram avaliados mensalmente por 6 meses pelo Teste Lacrimal de Schirmer (TLS), Teste de Fluoresceína (TF), Tempo de Ruptura do Filme Lacrimal (TRFL), Teste de Rosa Bengala, citologia da conjuntiva no início, meio e fim do projeto, biopsia e análise fractal da conjuntiva no início e final do projeto. Os cães foram distribuídos aleatoriamente em 3 grupos (n=15): grupo T (tacrolimus 0.03% tópico), grupo TO (tacrolimus + ômegas EPA/DHA oral) e grupo TOA (tacrolimus + ômegas EPA/DHA + antioxidantes oral). Os resultados demonstraram que houve uma melhora significativa nos sinais clínicos em ambos os grupos. No TRFL todos os grupos apresentaram aumento no decorrer do tratamento, sendo que o grupo TO foi o que apresentou melhor resultado em todos momentos quando comparado aos demais grupos. Ao final do experimento, os grupos T, TO e TOA apresentaram na análise citológica, diminuição de linfócitos, neutrófilos, células metaplásicas e escamosas, e na análise histopatológica, diminuição de linfócitos e neutrófilos e aumento das células caliciformes, ressaltando o melhor desempenho ao TO. Na análise fractal, ao final do experimento, o grupo TO que apresentou melhor resultado e os valores próximos aos valores encontrados nos parâmetros fractais de olhos sadios. A diferença entre o grupo TO e os demais grupos está na concentração de EPA maior, sendo um anti-inflamatório natural, o que pode ser uma das causas de seu melhor desempenho. Concluímos que o ômega 3 oral que contém maior proporção de EPA do que DHA trouxe maior benefício quanto a melhora dos sinais clínicos e do processo inflamatório no tratamento de CCS em cães.

Functional coatings produced using scalable and cost-effective processes such as electrodeposition and etching lead to the creation of random roughness at multiple length scales on the surface. The first part of thesis work aims at developing a fundamental mathematical understanding of multiscale coatings by presenting a fractal model to describe wettability on such surfaces. These surfaces are described with a fractal asperity model based on the Weierstrass-Mandelbrot function. Using this description, a model is presented to evaluate the apparent contact angle in different wetting regimes. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. Superhydrophobic surfaces have myriad industrial applications, yet their practical utilization has been severely limited by their poor mechanical durability and longevity. Toward addressing this gap, the second and third parts of this thesis work present low cost, facile processes to fabricate superhydrophobic copper and zinc-based coatings via electrodeposition. Additionally, systematic studies are presented on coatings fabricated under different processing conditions to demonstrate excellent durability, mechanical and underwater stability, and corrosion resistance. The presented processes can be scaled to larger, durable coatings with controllable wettability for diverse applications. Apart from their use as superhydrophobic surfaces, the application of multiscale coatings in photo-thermal conversion systems as solar selective coatings is explored in the final part of this thesis. The effects of scale-independent fractal parameters of the coating surfaces and heat treatment are systematically explored with respect to their optical properties of absorptance, emittance, and figure of merit (FOM). / Master of Science / Coatings are extensively used through various industries and serve a range of purposes such as providing protection, changing the physical and chemical properties, decoration, and adding other new properties to the base surface. Coatings produced using scalable and cost-effective processes such as electrodeposition and etching are inherently rough and have features ranging from micro- to nano-scale, leading to their multiscale nature. The first part of thesis work aims at developing a fundamental mathematical understanding of these rough coatings by presenting a model to describe and predict the wettability on such surfaces. Wettability of a surface is its ability to maintain contact with a liquid, resulting from intermolecular interactions when the two are brought together. Wettability for a solid surface is generally quantified by the contact angle, measured through the liquid, where a liquid-vapor interface meets the solid surface. A mathematical model is presented to evaluate the apparent contact angle on such multiscale rough surfaces. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. Superhydrophobic surfaces do not get wet by water and water droplet contact angle on these surfaces exceed 150°. Such surfaces have extensive industrial applications, yet their practical utilization has been severely limited by their poor mechanical durability and longevity. Toward addressing this gap, the second and third parts of this thesis work present low cost, facile processes to fabricate superhydrophobic copper and zinc-based coatings via electrodeposition. Additionally, systematic studies are presented on coatings fabricated under different processing conditions to demonstrate excellent durability, mechanical and underwater stability, and corrosion resistance. The presented processes can be scaled to larger, durable coatings with controllable wettability for diverse applications. Apart from their use as superhydrophobic surfaces, the application of multiscale coatings in photo-thermal conversion systems as solar selective coatings is explored in the final part of this iv thesis. Solar selective coatings aim to improve photo-thermal conversion efficiency by providing a high solar absorptance and low thermal emittance. Solar selective coatings ensure that maximum incoming solar radiation is absorbed into the surface and radiative losses due to emissions at high temperatures are minimized. The effects of scale-independent mathematical parameters of the coating surfaces and heat treatment are systematically explored with respect to their optical properties of absorptance, emittance, and figure of merit (FOM).

Scale is an essential notion in geography and geographic information science (GIScience). However, the complex concepts of scale and traditional Euclidean geometric thinking have created tremendous confusion and uncertainty. Traditional Euclidean geometry uses absolute size, regular shape and direction to describe our surrounding geographic features. In this context, different measuring scales will affect the results of geospatial analysis. For example, if we want to measure the length of a coastline, its length will be different using different measuring scales. Fractal geometry indicates that most geographic features are not measurable because of their fractal nature. In order to deal with such scale issues, the topological and scaling analyses are introduced. They focus on the relationships between geographic features instead of geometric measurements such as length, area and slope. The scale change will affect the geometric measurements such as length and area but will not affect the topological measurements such as connectivity.   This study uses three case studies to demonstrate the scale issues of geographic features though fractal analyses. The first case illustrates that the length of the British coastline is fractal and scale-dependent. The length of the British coastline increases with the decreased measuring scale. The yardstick fractal dimension of the British coastline was also calculated. The second case demonstrates that the areal geographic features such as British island are also scale-dependent in terms of area. The box-counting fractal dimension, as an important parameter in fractal analysis, was also calculated. The third case focuses on the scale effects on elevation and the slope of the terrain surface. The relationship between slope value and resolution in this case is not as simple as in the other two cases. The flat and fluctuated areas generate different results. These three cases all show the fractal nature of the geographic features and indicate the fallacies of scale existing in geography. Accordingly, the fourth case tries to exemplify how topological and scaling analyses can be used to deal with such unsolvable scale issues. The fourth case analyzes the London OpenStreetMap (OSM) streets in a topological approach to reveal the scaling or fractal property of street networks. The fourth case further investigates the ability of the topological metric to predict Twitter user’s presence. The correlation between number of tweets and connectivity of London named natural streets is relatively high and the coefficient of determination r2 is 0.5083.   Regarding scale issues in geography, the specific technology or method to handle the scale issues arising from the fractal essence of the geographic features does not matter. Instead, the mindset of shifting from traditional Euclidean thinking to novel fractal thinking in the field of GIScience is more important. The first three cases revealed the scale issues of geographic features under the Euclidean thinking. The fourth case proved that topological analysis can deal with such scale issues under fractal way of thinking. With development of data acquisition technologies, the data itself becomes more complex than ever before. Fractal thinking effectively describes the characteristics of geographic big data across all scales. It also overcomes the drawbacks of traditional Euclidean thinking and provides deeper insights for GIScience research in the big data era.

It is perhaps paradoxical that many material properties arise from the absence of material rather than the presence of it. For example, the strength, stiffness, and toughness of a concrete are related to its pore structure. Furthermore, the volume, size distribution, and interconnectivity of porosity is important for understanding permeability, diffusivity, and capillary action occurring in concrete, which are necessary for predicting service lives in aggressive environments. This research advances the state-of-the-art of multiscale characterization of cement-based materials, and uses this characterization information to model the material behavior under competing durability concerns. In the first part of this research, a novel method is proposed to characterize the entrained air void system. In the second and third parts of this research, microstructural characterization is used in tandem with mechanical models to investigate the behavior of cementitious materials when exposed to rapid rates of loading and to cyclic freezing and thawing. First, a novel analytical technique is presented which reconstructs the 3D entrained air void distribution in hardened concrete using 2D image analysis. This method proposes a new spacing factor, which is believed to be more sensitive to microstructural changes than the current spacing factor commonly utilized in practiced, and specified in ASTM C457, as a measure of concrete's ability to resist to damage under cyclic freeze/thaw loading. This has the potential to improve economy by improving the quality of petrographic assessment and reducing the need for more expensive and time-consuming freeze/thaw tests, while also promoting the durability of concrete. Second, quantitative measurements of the sizes, shapes, and spatial arrangements of flaws which are through to drive failure at strain rates above 100/s were obtained in order to model mortar subjected to high strain-rate loading (i.e., extremes in load rate). A micromechanics model was used to study the ways in which flaw geometry and flaw interaction govern damage. A key finding suggests that dynamic strength may be multimodal, with larger flaws shifting the dynamic strength upwards into the highest strength failure mode. Third, a robust theoretical approach, based upon poroelasticity, is presented to further validate the utility of the novel spacing factor proposed this research. The model is truly multiscale, using in its formulation pore size data ranging from the nanoscale to the micro-scale, entrained air data from the micro-scale to the millimeter scale, and infers a representative volume element on the centimeter scale. The results provide an underlying physical basis for the performance of the novel spacing factor. Furthermore, the framework could be used as a forensic tool, or as a tool to optimize the entrained air void system against freeze/thaw damage.

Tropical wildfires account for up to 93% of global burnt area and approximately 85% of the resulting carbon emissions, yet are significantly under-represented in existing fire models. These models are predominantly process-based, require a multitude of input datasets, parameters and calculations, and are difficult to reproduce or use independently from a dynamic global vegetation model (DGVM). The aim of this thesis is to develop empirical parameterisations of tropical fire occurrence and spread that represent an improvement in accuracy over existing models and that can be easily implemented both as standalone models or within a DGVM. These models are based on well-documented relationships from the literature. An index of potential fire is produced based on the observed peak of fire activity at intermediate levels of productivity and aridity. This can be converted into expected fire counts using a simple, observation-derived parameter map. Fire sizes have been shown to follow an approximately fractal distribution in a range of ecosystems, which is used to develop a new burnt area model. Replacing the fire count and burnt area calculations of existing fire models with these new parameterisations improves the spatial distribution of the resulting estimates, while giving temporally comparable predictions to the original models. The magnitude of the resulting burnt area estimates is also improved. The use of empirical fire modelling is therefore a viable alternative to current process-based methods, and makes practical use of theories that are well-documented in the literature. These models require few input variables and can be easily incorporated into a DGVM. However, further work to improve the temporal accuracy and dynamicity of these models would be beneficial, as would a method to link these models to parameterisations of combustion and trace gas emissions.

Background. Lacunar strokes account for 25% of all ischaemic stroke but the exact nature of the causative cerebral small vessel abnormality remains unknown. Pathological studies are technically difficult and brain imaging cannot adequately characterise the cerebral small vessels. The retinal blood vessels are of similar size and physiology to the cerebral small vessels and may act as a surrogate marker for these cerebral small vessels. We therefore investigated retinal microvascular abnormalities in lacunar stroke. Methods. We performed a systematic review of retinal microvascular abnormalities in lacunar stroke to clarify associations and identify where further research was required. We then established a cohort of patients presenting with lacunar stroke with cortical stroke controls to investigate differences in retinal microvascular abnormalities between stroke subtypes. All patients had MRI brain at presentation and digital retinal photography of both eyes. We investigated the prevalence of retinopathy (hard and soft exudates or haemorrhages/microaneurysms), focal arteriolar narrowing and arteriovenous nicking . We developed, validated and used novel semi-automated techniques for measuring retinal arteriolar and venular widths, retinal arteriolar geometry (branching co-efficients (change in arteriolar cross sectional area across a bifurcation) and branching angles) and fractal dimensions (reflecting branching complexity) of the vasculature. We also assessed MRI parameters in lacunar stroke. We used multivariable analysis to correct for baseline imbalances in vascular risk factors. Results. From the systematic review we demonstrated that retinal microvascular abnormalities are associated with incident and prevalent stroke but that in general, strokes were inadequately characterised and there were no data regarding retinal microvascular abnormalities in ischaemic stroke subtypes. We recruited 253 patients, 129 lacunar strokes and 124 cortical strokes, mean age 68 years. We found no difference in the prevalence of retinopathy, arteriovenous nicking, focal arteriolar narrowing or arteriolar widths between lacunar and cortical stroke subtypes. We found that venules were wider in lacunar stroke. We found no differences in arteriolar branching co-efficients or arteriolar branching angles between lacunar and cortical strokes but found that deep white matter white matter hyperintensities on MRI were associated with increased branching co-efficients and periventricular white matter hyperintensities associated with decreased branching co-efficients. We found that the fractal dimension of the vascular tree was decreased in lacunar stroke. Furthermore we found that enlarged perivascular spaces on MRI are associated with lacunar stroke and white matter disease. Conclusions. We have clearly demonstrated that retinal microvascular abnormalities differ between lacunar and cortical stroke suggesting that a distinct small vessel vasculopathy may cause lacunar stroke. We have also identified MR markers of lacunar stroke. These results suggest that venular disease (a hitherto underresearched area) may play a role in the pathophysiology of lacunar stroke. Retinal microvascular abnormalities can act as markers for cerebral small vessel disease. We plan collaborative analyses with colleagues who have performed similar studies to further assess retinal abnormalities in lacunar stroke.