Análise multiespectral de medidas de complexidade utilizando o software CompPlexus aplicado a dados do sensor ASTER.

Neste trabalho, será avaliado a eficiência do software CompPlexus na análise multiespectral de complexidade de alvos distintos utilizando bandas do sensor ASTER ? Advanced Spaceborne Thermal Emission and Reflection Radiometer

Criticalidade auto-organizada no cerrado? Invariância escalar dos padrões texturais e espectrais de fitosionomias do cerrado paulista.

Padrões presentes em uma paisagem podem estar associados importantes processos relativos à organização e dinâmica do sistema. Objetivo: O objetivo do presente trabalho foi avaliar, a partir de algumas métricas derivadas do paradigma da complexidade, a complexidade dos padrões texturais e espectrais de fisionomias do Cerrado paulista a fim de verificar quais propriedades relativas à sua organização e dinâmica tais padrões podem revelar. Metodologia: Para tanto, imagens do sensor Aster de três unidades de conservação do estado de São Paulo foram analisadas, utilizando-se dois tipos de medidas (dimensão fractal e medidas baseadas na entropia informacional) para avaliar a complexidade dos padrões texturais e espectrais das fisionomias. Resultados e discussão: Todas as fisionomias, nas três localidades estudadas e para todas as medidas usadas, apresentarem em diversas ocasiões a ocorrência de padrões texturais e espectrais que se repetem em diferentes escalas. A principal implicação desses resultados diz respeito às inferências sobre a dinâmica do Cerrado: a invariância escalar é uma característica marcante de sistemas que se desenvolvem longe do equilíbrio. Mais do que isso, é um grande indicativo de que o sistema pode apresentar criticalidade auto-organizada.Edição especia

Optimal control measures for a susceptible-carrier-infectious-recovered-susceptible malware propagation model

Purposing to lessen malware propagation, this paper proposes optimal control measures for a susceptible-carrier-infectious-recovered-susceptible (SCIRS) epidemiological model formed by a system of ordinary differential equations. By taking advantage of real-world data related to the number of reported cybercrimes in Japan from 2012 to 2017, an optimal control problem is formulated to minimize the number of infected devices in a cost-effective way. The existence and uniqueness of the results related to the optimality system are proved. Overall, numerical simulations show the usefulness of the proposed control strategies in reducing the spread of malware infections.- Fundação para a Ciência e Tecnologia, Grant/Award Number: UID/MAT/04106/2019 and UID/CEC/00319/201

Assessment of complexity metrics applied to analysis of spectral patterns generated by aster sensor.

Landscape metrics are traditionally used in the analysis and search for spatial patterns in complex environmental systems through of establishing numeric relationships between different types of targets on Earth's surface. Under this perspective, remote sensing has had great importance as a tool for data generation, providing several levels of land use and occupancy information isonomically for large areas. For that purpose, remote sensing uses regular pixel matrices (Picture Element) with associated quantitative values (e.g. digital numbers, radiance, reflectance) which constitute a direct measurement of the variation of electromagnetic radiation (EMR) after interaction with the target. The variations in pixel values may be considered in terms of their textural patterns, regarding pixel neighborhood relationships, or spectral patterns, when EMR variations are considered along different wavelengths for a same pixel. Thus, the objective of this work was to assess the results of spectral measurements to different area extensions in images taken by the ASTER sensor, which operates with 9 bands within the visible to shortwave infrared region (0.556 to 2.400 µm) and has a spatial resolution of 15 m. For this purpose, cerrado phytophysiognomies in two hillsides at Jataí Ecological Station, in the city of Luiz Antônio, northeast portion of the state of São Paulo, Brazil, were considered reference targets, and encompassed to its greatest extent the cerradão domain and also "campo sujo" and "cerrado strictu sensu" physiognomies. The metrics used for spectral analyses are based on information entropy: measure (SDL), in which most complexity values are associated to more disorderly patterns; and measure, LMC, which is represent by a convex entropy of function that attributes greater complexity values to patterns located in an intermediate zone between order and disorder. These measures was applied to values extracted from spectral response curve generated by a wavelength X reflectance graphic which represented the target's behavior in different bands of the electromagnetic spectrum. In this work, was used two bands (8 and 9) that emphasize important components of cerrado phytophysiognomies, as lignin and water cell. For each hillside, was analysed three positions: base, medium and top, and each of these position, two spatial scales (150x150m and 75x75m). The results shows that, when taken alone, any measure presented a consistent behavior when compared of different spatial scales and bands used. However, both measures show identical behavior to attribute greater and lesser values of complexity to different positions and spatial scale at the same hillside. This results appoint that its can be used in combined as complementary measures, demonstrating in case LMC measure ? heterogeneity degrees of spectral patterns analysed and, from SDL measure, your respective location along of continuum that have in your extremes, one side, more ordered condition (therefore, more homogeneous) and, in the other extremity, more disordered conditions

Landscape complexity analysis based on texture patterns and satellite image for a São Paulo's Cerrado site.

We analysed the spatial heterogeneity complexity of Cerrado vegetation of São Paulo. Spatial heterogeneity was obtained by quantity texture patterns on ASTER images for Jataí Ecological Station (JES; Luiz Antônio ‐ SP) conservation unit. Two hillsides of JES where cerradão physiognomy was present were analyzed, and for each of them we sampled three positions: base, medium and top. Vertical structure and canopy cover density varied along hillsides. For each site, we extracted the texture pattern for two spatial scales (150x150m and 75x75m). Spatial complexity were estimated by two landscape metrics, both based on informational entropy: a) maximum entropy (H/Hmax), in which high values of complexity are assigned to patterns more disordered; and b) convex function of entropy (LMC), which attribute high values of complexity to patterns situated in intermediate range between order and disorder. Comparing different sites of the same hillside, both metrics had identical results in relation to greatest and smallest values of complexity. In hillside 1, the top side showed greater values. In these area, the cerradão shows high trees with less density of canopy in comparison to others sites of this hillside, which provides more spatial heterogeneity. For the smaller values of complexity, there was difference in comparison of analyzed extensions in hillside 1: for 150 x 150m spatial scale, was attributed medium hillside site to smaller values of complexity; for 75 x 75m, the base had the smallest values. However, the value of complexity of medium and low hillsides for the same spatial extension were very close. In hillside 2, on the base of site, which shows a cerradão with shorter trees and lesser canopy cover density in relation to others sites of hillside, texture patterns had highest values of complexity for both entropy measures. The most homogeneity site, located in medium position of hillside and with presence of high trees and canopy density, smallest values were recorded. Based on our findings we can concluded that there is a tendency of sites situated in the top and in the base of hillside showed great values of complexity, while sites located in medium hillside tend to be less complex in terms of spatial heterogeneity. Also, for local scale, the canopy density is more relevant than tree vertical structure on determining the complexity of texture patterns of vegetation

O sonho de Bernouilli

Este artigo apresenta, dentro de uma perspectiva histórica, algumas ideias sobre a aplicação de ferramentas matemáticas no estudo de problemas relacionados à biologia. Usando a Teoria dos Sistemas Dinâmicos, alguns modelos para sistemas biológicos apresentando emergência de comportamentos globais complexos são discutidos.This paper presents some ideas about the application of mathematical tools to the study of Biological problems, in a historic context. By using the Dynamical System Theory, some models for biological systems presenting emergence of global complex behavior are discussed

Mapas de complexidade de fragmentos de Cerrado a partir da variabilidade espacial de dados do sensor Thematic Mapper5.

No estudo em questão, o programa CompPlexus tem seu potencial e eficiência explorada no que tange ao efeito de borda e, de forma geral, à dinâmica ecológica de uma área previamente estudada. Assim, o objetivo aqui buscado é o de mapear os fragmentos de Cerrado a partir do cálculo de valores de complexidade dos padrões obtidos de imagem orbital e subsequentemente a aplicação de Geoestatística para interpolação dos dados

Metrics based on information entropy applied to evaluate complexity of landscape patterns.

Abstract: Landscape is an ecological category represented by a complex system formed by interactions between society and nature. Spatial patterns of different land uses present in a landscape reveal past and present processes responsible for its dynamics and organisation. Measuring the complexity of these patterns (in the sense of their spatial heterogeneity) allows us to evaluate the integrity and resilience of these complex environmental systems. Here, we show how landscape metrics based on information entropy can be applied to evaluate the complexity (in the sense of spatial heterogeneity) of patches patterns, as well as their transition zones, present in a Cerrado conservation area and its surroundings, located in south-eastern Brazil. The analysis in this study aimed to elucidate how changes in land use and the consequent fragmentation affect the complexity of the landscape. The scripts CompPlex HeROI and CompPlex Janus were created to allow calculation of information entropy (He), variability (He/Hmax), and López-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison, and Landsberg (SDL) measures. CompPlex HeROI enabled the calculation of these measures for different regions of interest (ROIs) selected in a satellite image of the study area, followed by comparison of the complexity of their patterns, in addition to enabling the generation of complexity signatures for each ROI. CompPlex Janus made it possible to spatialise the results for these four measures in landscape complexity maps. As expected, both for the complexity patterns evaluated by CompPlex HeROI and the complexity maps generated by CompPlex Janus, the areas with vegetation located in a region of intermediate spatial heterogeneity had lower values for the He and He/Hmax measures and higher values for the LMC and SDL measurements. So, these landscape metrics were able to capture the behaviour of the patterns of different types of land use present in the study area, bringing together uses linked to vegetation with increased canopy coverage and differentiating them from urban areas and transition areas that mix different uses. Thus, the algorithms implemented in these scripts were demonstrated to be robust and capable of measuring the variability in information levels from the landscape, not only in terms of spatial datasets but also spectrally. The automation of measurement calculations, owing to informational entropy provided by these scripts, allows a quick assessment of the complexity of patterns present in a landscape, and thus, generates indicators of landscape integrity and resilience

CompPlexus: programa para avaliação de complexidade de padrões em imagens de sensores remotos.

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