Information-theoretic analysis of complex systems modeled by two dimensional pairwise Ising models

Stochastic complex systems are composed by a large number of seemingly simple variables that exhibit non-linear interactions with each other, causing the emergence of complexity and non-deterministic dynamics in the edge between order and chaos. Hence, the evolution of these systems seems to be completely out of control, with unpredictable behaviors. In this paper, using information geometry as a mathematical approach to chaos and complexity, we investigate how information theory can be used to analyze the dynamics of pairwise Ising random fields along Markov Chain Monte Carlo simulations in which phase transitions are observed. Our experiments indicate that Fisher information regarding the inverse temperature parameter can bring important insights, since it signalizes changes in the global spatial dependence structure. Information-theoretic curves are built to show that, despite the random nature of the system, it is possible to identify an asymmetric pattern of evolution when the system moves towards different entropic states.

Sampling redesign of soil penetration resistance in spatial t-Student models

Aim of study: To reduce the sample size in an agricultural area of 167.35 hectares, cultivated with soybean, to analyze the spatial dependence of soil penetration resistance (SPR) with outliers. Area of study: Cascavel, Brazil Material and methods: The reduction of sample size was made by the univariate effective sample size ( ) methodology, assuming that the t-Student model represents the probability distribution of SPR. Main results: The radius and the intensity of spatial dependence have an inverse relationship with the estimated value of the . For the depths of SPR with spatial dependence, the highest estimated value of the reduced the sample size by 40%. From the new sample size, the sampling redesign was performed. The accuracy indexes showed differences between the thematic maps with the original and reduced sampling designs. However, the lowest values of the standard error in the parameters of the spatial dependence structure evidenced that the new sampling design was appropriate. Besides, models of semivariance function were efficiently estimated, which allowed identifying the existence of spatial dependence in all depth of SPR.Research highlights: The sample size was reduced by 40%, allowing for lesser financial investments with data collection and laboratory analysis of soil samples in the next mappings in the agricultural area. The spatial t-Student model was able to reduce the influence of outliers in the spatial dependence structure.

Precipitation trends analysis by Mann-Kendall test: a case study of Paraíba, Brazil

This work aimed to select semivariogram models to estimate trends in monthly precipitation in Paraiba State-Brazil using ordinary kriging. The methodology involves the application of geostatistical interpolation of precipitation records of 51 years from 69 rainfall stations across the state. Analysis of semivariograms showed that specific months had a strong spatial dependence (Index of Spatial Dependence - IDE < 25%). The trends were subjected to the following models: circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, K-Bessel and tetraspherical. The best fit models were selected by cross-validation and Error Comparison Index (ECI). Each data set (month) had a particular spatial dependence structure, which made it necessary to define specific models of semivariogram in order to enhance the adjustment of the experimental semivariogram. Besides, the monthly trend map was plotted to justify the chosen models.

Variability and spatial correlation of soil micronutrients and organic matter with macadamia nut production

ABSTRACT Soil fertility is the key to agricultural production. The spatial correlation and location of nutrients may significantly affect the yields. The objective of this work was to evaluate the variability and spatial correlation of iron (Fe), copper (Cu), manganese (Mn), zinc (Zn), and organic matter (OM) with macadamia nut yield. The study was conducted in an Oxisol cultivated for 20 years with macadamia nut in São Mateus, state of Espírito Santo, Brazil. A 100 point grid was used comprising an area of 144 × 140 m with a minimum distance between points of 5 m, in which a single composite soil sample was collected from 0-0.20 m layer for chemical analysis of Fe, Cu, Mn, Zn and OM. Nuts under the canopy’s projection were harvested from February to June, 2015. The data were evaluated by geostatistical analysis using semivariograms, and kriging was used to map spatial distributions of nutrients and nut yield. All evaluated attributes showed strong or moderate spatial dependence structure. The OM was correlated positively with micronutrients, but only Zn was positively correlated with nut yield. Crossed semivariograms adequately explained the maps of Zn and Mn; and Fe showed opposite tendency for macadamia nut yield.

Spatial variability and sampling density of chemical attributes in archaeological black earths under pasture in southern Amazonas, Brazil

Spatial mapping of soil chemical attributes is essential for sampling efficiency and agricultural planning management, ensuring a regional development and sustainability of the unique characteristics of archaeological black earths (ABEs). Thus, this study was developed aiming at assessing the spatial variability and sampling density of chemical attributes in soils of ABEs under pasture in southern Amazonas, Brazil. A sampling grid of 56 × 80 m with regular spacings of 8 m was installed in the experimental area and samples were taken from the crossing points at depths of 0.0–0.05, 0.05–0.10, and 0.10–0.20 m, totaling 264 georeferenced points. The chemical attributes pH in water, organic carbon, Ca, Mg, K, P, Al, and potential acidity were determined in these samples, while CEC, SB, V, t, T, and m were calculated. The attributes present a spatial dependence varying from strong to moderate, being Al3+ the only chemical attribute that does not present a spatial dependence structure in the assessed depths. Scaled semivariograms satisfactorily reproduce the spatial behavior of attributes in the same pattern of individual semivariograms, allowing their use to estimate the variability of soil attributes. Sampling density is higher at a depth of 0.0–0.05 m, requiring 2 and 1 point ha−1 at depths of 0.05–0.10 and 0.10–0.20 m, respectively, to represent the spatial pattern of chemical attributes.

Spatial Dependence Structure of Total Factor Productivity in Polish Local Administrative Districts

The interaction between space (location) and the processes of accumulation (growth) is one of the most interesting and at the same time the most difficult areas of modern economic theory. The up till now empirical research on determinants of regional productivity in the case of Poland is however relatively scarce. Most studies focus on explaining the variation in regional income per capita mostly at NUTS–2 and NUTS–3 levels, and only a few take into account a highly spatially disaggregated NUTS–4 level. We aim to fill this important gap. The present article has several objectives. We try to explain the spatial patterns of productivity, to identify the spatial range of productivity spillovers empirically and to identify the determinants of the Total Factor Productivity (TFP) growth in Poland with the use of spatial econometric modeling and the extended version of the Nelson‑Phelps (1966) model. The study adopts an NUTS-4 level of local administrative districts (powiats) which we find superior on both theoretical (market closing) and empirical grounds (spatial modeling). TFP in Poland assumes the highest values in the metropolitan centers and spreads out on their nearest surroundings with the maximum value for Warsaw. The secondary local hills in TFP are located in cities or towns with county rights. TFP, in general, shows a downward trend as one moves from the west to the east with the lowest values observed in the south‑eastern part of Poland. The range of TFP spillover is found to be of roughly 175–200 km and is nonlinearly decreasing from the local productivity hills. Furthermore, the rate of growth of TFP shows spatial autocorrelation and is found to depend positively on the rate of increase in human capital endowment and on the gap from the leader under certain assumptions. We find no evidence of the channel through imports. However, the FDI channel is found to be robust and strong.

Information geometry, simulation and complexity in Gaussian random fields

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this paper, we propose to quantify how changes in the spatial dependence structure affect the Riemannian metric tensor that equips the model's parametric space. Defining Fisher curves, we measure the variations in each component of the metric tensor when visiting different entropic states of the system. Simulations show that the geometric deformations induced by the metric tensor in case of a decrease in the inverse temperature are not reversible for an increase of the same amount, provided there is significant variation in the system's entropy: the process of taking a system from a lower entropy state A to a higher entropy state B and then bringing it back to A, induces a natural intrinsic one-way direction of evolution. In this context, Fisher curves resemble mathematical models of hysteresis in which the natural orientation is pointed by an arrow of time.

Semivariogram models for estimating fig fly population density throughout the year

The objective of this work was to select semivariogram models to estimate the population density of fig fly (Zaprionus indianus; Diptera: Drosophilidae) throughout the year, using ordinary kriging. Nineteen monitoring sites were demarcated in an area of 8,200 m2, cropped with six fruit tree species: persimmon, citrus, fig, guava, apple, and peach. During a 24 month period, 106 weekly evaluations were done in these sites. The average number of adult fig flies captured weekly per trap, during each month, was subjected to the circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable semivariogram models, using ordinary kriging interpolation. The models with the best fit were selected by cross-validation. Each data set (months) has a particular spatial dependence structure, which makes it necessary to define specific models of semivariograms in order to enhance the adjustment to the experimental semivariogram. Therefore, it was not possible to determine a standard semivariogram model; instead, six theoretical models were selected: circular, Gaussian, hole effect, K-Bessel, J-Bessel, and stable.