Two-dimensional Spatial Analysis Research Articles

Optimizing convex hull discovery: Introducing a quintuple-region algorithm with enhanced computational efficiency

This paper introduces a novel algorithm for computing the convex hull of a finite set of points in two-dimensional space. Unlike traditional methods, this algorithm strategically partitions the input set into five distinct regions, isolating interior points to reduce computational efforts while determining the convex hulls of the four boundary regions. This innovative approach significantly diminishes the required number of operations, achieving a computational complexity of O(nk), where k denotes the number of vertices on the convex hull and n is the number of vertices. The study methodically elaborates on the development of this algorithm, starting with a comprehensive overview of convex hull-related terminology and existing methodologies. Subsequent sections detail the process of identifying endpoints within the set, the division of the set into specific regions, and the application of proposed algorithms for each region to efficiently compute their convex hulls. Through theoretical analysis and case studies presented in the latter sections, this paper not only enhances understanding of convex hull computation but also demonstrates the practical efficiency and effectiveness of the proposed algorithm in various scenarios. This advancement represents a significant contribution to the field of computational geometry, offering improved solutions for problems involving two-dimensional spatial analysis.

Organizing your space: The potential for integrating spatial transcriptomics and 3D imaging data in plants.

Plant cells communicate information for the regulation of development and responses to external stresses. A key form of this communication is transcriptional regulation, accomplished via complex gene networks operating both locally and systemically. To fully understand how genes are regulated across plant tissues and organs, high resolution, multi-dimensional spatial transcriptional data must be acquired and placed within a cellular and organismal context. Spatial transcriptomics (ST) typically provides a two-dimensional spatial analysis of gene expression of tissue sections that can be stacked to render three-dimensional data. For example, X-ray and light-sheet microscopy provide sub-micron scale volumetric imaging of cellular morphology of tissues, organs, or potentially entire organisms. Linking these technologies could substantially advance transcriptomics in plant biology and other fields. Here, we review advances in ST and 3D microscopy approaches and describe how these technologies could be combined to provide high resolution, spatially organized plant tissue transcript mapping.

Increment-averaged kriging: a comparison with depth-harmonized mapping of soil exchangeable sodium percentage in a cropping region of eastern Australia

Soil sodicity, generally measured through the exchangeable sodium percentage (ESP), is the most prevalent edaphic stress in Australia, particularly in the northern grains-growing region (NGR) of Australia. Farmers, scientists and policy-makers need accurate maps of sodicity for environmental modelling, and to make rational decisions for management. A common approach to mapping soil properties for multiple target depths is to first harmonize soil profile data to the target depth intervals, usually through equal-area spline functions, then undertake a two-dimensional spatial analysis (often regression kriging) for each interval; we refer to this as a ‘spline-then-krige’ (STK) approach. An alternative is to calibrate a single three-dimensional model that describes soil variation both horizontally and vertically, as is done in the increment-averaged kriging (IAK) approach. This study compares IAK and STK for mapping ESP in the NGR. A machine-learning algorithm was used to model trends based on environmental covariates in both approaches. Both IAK and STK captured the ESP variation reasonably well (concordance correlation coefficient values for IAK around 0.5 for all depths), with IAK giving slightly better predictive accuracies for all depths, most evidently in the topsoil. IAK allows the natural use of all available data, explicitly accounts for the sample support of the soil data and the horizontal and vertical auto-correlation between and within soil profiles, and enables the propagation of uncertainty from the original data through to the final predictions and prediction uncertainties. We conclude that IAK can provide a competitive alternative to STK approaches for mapping soil properties in three dimensions.

Spatial pattern and disease severity of charcoal canker in Hyrcanian forests, north of Iran

3 Abstract: In recent years, charcoal cankeraffecting the oak species (Quercus castaneifolia) in northern forests' and (Quercus persica) in Zagros forests' of Iran.This research investigated the population density of diseased trees and interaction across the severity of disease symptomatology onQ. Castaneifolia in the Quroq Park Hyrcanian Mixed Forests of Iran. We used two-dimensional spatial analysis tools with data gathered in point-centered-quarter format in 2013 to quantify the population density of diseased trees to examine the spatial pattern of tree mortality and investigated co-occurrence severity of disease symptoms using paired quadrat covariance analysis. Eventually, the percent of dead crown (total number of dead branches), depth, area and canker number in 400 trees were recorded in seven transects. Results showed that nearly 60 % of the oak trees in the park are diseased, as for the severity of disease oak trees with high probability 36% of oak trees recorded in this study offing death. Dead trees and high disease severity were strongly clustered at broader scales (800 m), trees with only a limited bleeding and signs of fungal activity Biscogniauxia mediterranea occurred in clusters away from dead trees. Crown mortality and Beetle-infested trees co-occurred with mortality were strongly correlated. These findings suggest that clustered spatial patterns of charcoal cancer can be important for the control and management of this disease in oak forests.

Two-dimensional spatial analysis of the seismic b-value and the Bouguer gravity anomaly in the southeastern part of the Zagros Fold-and-Thrust Belt, Iran: Tectonic implications

Environmental managers and protection agencies try to assess the magnitudes of earthquakes in regions of seismic activity. For several decades they have used the seismic b-values and Bouguer anomalies for evaluating the crustal character and stress regimes. We have analyzed geostatistically data on both variables to map their spatial distributions in the southeast of the Zagros of Iran. We found a strong correlation between the distribution of the b-value and the Bouguer gravity anomaly in the region. The large Bouguer gravity anomaly values and small b-values all accord with there being a thinner crustal root and a larger concentration of stress in the center. The small to moderate Bouguer gravity anomaly values and intermediate to large b-values accord with the thicker crustal root and the smaller concentration of stress in the northeast. We conclude the southeast of the Zagros, consists of heterogeneous crust, such that accounts for its varied tectonics.

Spatial pattern dynamics of oak mortality and associated disease symptoms in a California hardwood forest affected by sudden oak death

Sudden oak death is a disease affecting coastal forests in California and southern Oregon. The spatial pattern of disease dynamics is important for forest and landscape pathology; in this work we investigated the interaction across landscape scales of disease symptomology in coast live oaks, Quercus agrifolia, (trunk bleeding, presence of beetles, and presence of the fungus Hypoxylon thouarsianum) and tree mortality through time. We used two-dimensional spatial analysis tools with data gathered in point-centered-quarter format in 2001 and 2004 to quantify the population density of the disease through time; to examine the spatial pattern of tree mortality across scales through time; and to examine the spatial co-occurrence of disease symptoms with crown mortality through time. Early in the study period dead trees were strongly clustered at smaller scales (~300 m) and after three years this clustering was less pronounced. Bleeding on trees occurred in clusters away from dead trees, particularly in 2004, likely indicating a new cohort of infected trees. The presence of H. thouarsianum was strongly related to overstory mortality through time. Beetle-infested trees co-occurred with mortality in 2001. By 2004, they occurred throughout the forest, and were less strongly correlated with overstory tree mortality, suggesting a future peak of tree mortality.

Responses of V1 Neurons to Two-Dimensional Hermite Functions

Neurons in primary visual cortex are widely considered to be oriented filters or energy detectors that perform one-dimensional feature analysis. The main deviations from this picture are generally thought to include gain controls and modulatory influences. Here we investigate receptive field (RF) properties of single neurons with localized two-dimensional stimuli, the two-dimensional Hermite functions (TDHs). TDHs can be grouped into distinct complete orthonormal bases that are matched in contrast energy, spatial extent, and spatial frequency content but differ in two-dimensional form, and thus can be used to probe spatially specific nonlinearities. Here we use two such bases: Cartesian TDHs, which resemble vignetted gratings and checkerboards, and polar TDHs, which resemble vignetted annuli and dartboards. Of 63 isolated units, 51 responded to TDH stimuli. In 37/51 units, we found significant differences in overall response size (21/51) or apparent RF shape (28/51) that depended on which basis set was used. Because of the properties of the TDH stimuli, these findings are inconsistent with simple feedforward nonlinearities and with many variants of energy models. Rather, they imply the presence of nonlinearities that are not local in either space or spatial frequency. Units showing these differences were present to a similar degree in cat and monkey, in simple and complex cells, and in supragranular, infragranular, and granular layers. We thus find a widely distributed neurophysiological substrate for two-dimensional spatial analysis at the earliest stages of cortical processing. Moreover, the population pattern of tuning to TDH functions suggests that V1 neurons sample not only orientations, but a larger space of two-dimensional form, in an even-handed manner.

Synthetic array measurements of acoustical waves propagating into a water-saturated sandy bottom for a smoothed and a roughened interface

Measurements of acoustical waves propagating in an unconsolidated water-saturated porous medium that involved the use of a two-dimensional synthetic array technique are presented. From these measurements, wave-front propagation is evaluated using time domain, wave-number frequency and two-dimensional spatial analysis techniques. First, a synthetic array measurement is employed to study sound penetration for a "smoothed" interface condition. This smoothed interface measurement is then compared to an identical synthetic array measurement with a "roughened" interface. A comparison of the smoothed and roughened interface measurements shows enhanced bottom penetration at shallow grazing angles as a result of the roughened interface. At shallow grazing angles, this scattered pressure from the roughened interface has the appearance of a wave front in the water-saturated porous medium that has a virtual wave speed of approximately 1200 m/s. Slower compressional waves in the sandy bottom are not observed.

Analysis of Variety Yield Trials Using Two-Dimensional Separable ARIMA Processes

The two-dimensional spatial analysis procedure based on separable ARIMA processes, proposed by Cullis and Gleeson (1991 Biometrics 47, 1449-1460), is used to analyze 35 cereal yield trials with incomplete block designs. Models with different large-scale variation components and diverse small-scale variation processes, modeled as one-dimensional and two-dimensional (separable) ARIMA processes, were compared. Nineteen spatial models were considered and two criteria were used to assess spatial model adequacy: (a) the average standard error of the pairwise variety differences (SED) and (b) the mean squared error of prediction (MSE) based on a cross-validation approach. Spatial analysis is more efficient in reducing residual variation than incomplete block analysis. Although there was no one model that best fit all the trials, the two-dimensional firstorder autoregressive model was the most efficient in terms of the SED and MSE criteria (in 21 and 14 trials, respectively).

Spatial Analysis of Field Experiments-An Extension to Two Dimensions

The one-dimensional spatial analysis procedure proposed by Gleeson and Cullis (1987, Biometrics 43, 277-288) is extended to two dimensions using the subclass of separable lattice processes to model the errors. Residual maximum likelihood estimation of the models is described and diagnostics for testing model adequacy are derived. Results from the analysis of 24 sets of uniformity data indicate the frequent need for a two-dimensional analysis even when the plot shape is highly rectangular. These results also indicate the potential gain from using a two-dimensional spatial analysis rather than a row + column analysis. An example is presented of the analysis of a field experiment on tobacco.