Distribution Of Polygons Research Articles

COMPARING MODIS AND ETM+ IMAGE DATA FOR INLAND WATER STUDIES: SPATIAL RESOLUTION CONSTRAINTS

The objective of this paper is to compare the performance of medium spatial resolution (250 m and 500 m) Terra MODIS images to finer resolution Landsat ETM+ images. MODIS Terra images have high frequency of acquisition (1 day revisit at high latitudes) and that makes them more useful for inland water studies. Assessing the performance of ETM and MODIS to map relevant features for the functioning of aquatic systems is very important for fostering water resource remote sensing. To carry out the comparison, concurrent ETM+ and MODIS images were acquired over the Lago Grande de Curaui Lake. The images were georeferenced and resample to the 100 x 100 m ground resolution using a next neighbor algorithm to make the data comparable. The resampling rationale was making the digital processing easier, without changing the effective resolution properties of the original data. It was assumed that the improved MODIS radiometric resolution as compared to the ETM+.would make both data set comparable at a 100m x 100m resolution. In the next step, a series of tests were carry out in order to define the best approach to map aquatic system features such as lakes, islands, and levees in the study area. The tests indicated that the best approach was the segmentation of the shadow fraction derived from the application of the linear unmixing model to both ETM+ and MODIS images. The segmentation was then followed by the application of a non-supervised region classifier. The final classes were mapped into two categories: lakes (water) and island (land). The polygon distribution generated by the classification procedure was then statistically analyzed to assess the polygon size frequency of features mapped by each data set. The results showed that ETM+ and MODIS were able to recover the water surface area in the studied region with a difference of 11 %. The analyses of polygon distribution, however, showed that there were many polygons which were detected in MODIS image data, but not in ETM+ image data. This result suggests that the spectral and radiometric resolution improvements presented by MODIS image tend to compensate for the losses in spatial resolution. That is to say that under the boundary conditions adopted in this study, MODIS images performed better than degraded ETM+ images of 100m x 100m. This explains the small difference in performance presented by comparing two sensors with such large differences in nominal spatial resolution.

Pectoral fins of Micropogonias furnieri: a histochemical and ultrastructural study

The myotomal fibres of the pectoral fins of white croaker (Micropogonias furnieri) have been studied using histochemical techniques and transmission electron microscopy (TEM). Succinic dehydrogenase (SDH) for mitochondria, periodic acid Schiff (PAS) for glycogen, Sudan Black for lipids and myosin-adenosintriphosphatase (mATPase) pre-incubated at alkaline and acid pHs were used to visualize the contraction velocity. Three zones were determined: superficial (SZ), medium (MZ) and deep (DZ). Staining for SDH, PAS and Sudan Black was positive only in the SZ. The level of alkaline mATPase was the highest in fibres from the DZ, intermediate in the MZ and low in the SZ; at an acid pH, the reverse was obtained. Fibres from the SZ were small with large quantities of subsarcolemmal mitochondria, scarce intermyofibrilar mitochondria and a well-developed sarcoplasmic reticulum; the myofibrils displayed a polygonal distribution along the entire length of the fibre. Fibres in the MZ were larger than those in the SZ, the myofibrils were densely packed, mitochondria prevailed under the sarcolemma and the sarcoplasmic reticulum was not abundant. Fibres from the DZ were the largest, with ribbon-shaped myofibrils and scarce mitochondria. The intercellular space was abundant and nervous endings were frequently observed.

Dynamic Instability of a Sol−Gel-Derived Thin Film

We present a study on the dynamic instability of a sol-gel-derived (SG) thin film on a nonwettable substrate. Because of the structural instability accompanied by syneresis stress in a film deposited on the substrate, there exists a regular distribution of dewetting patterns required to relieve the in-plane stress, such as holes in the earlier stages, and droplets accompanying a regular polygonal distribution in the later stages of the dynamic instability. The characteristic length scales in each stage scaled linearly with the film thickness during the duration of dewetting. For the formation of holes during the earlier stages of rupture of the film, the dewetting velocity was analyzed with a viscous sintering theory of a SG thin film. In the earlier stages of the dynamic instability, the dewetting velocity decreases with increasing dewetting time and increases with increasing the initial film thickness, which indicates that the SG thin film behaves partially like a slipping polymer thin film. In the final times of the film rupture, the radius of the hole has a linear relationship with the film thickness, and the growth rate of the hole (dewetting velocity) is nearly constant, regardless of the film thickness. These dewetting behaviors indicate that the SG thin film in the final times of the rupture is somewhat similar to nonslipping film. From these observations, we found that the dewetting behavior of a SG thin film has ambivalent dewetting characteristics of slipping and nonslipping films and that a SG thin film is not a purely viscous film.

The emergence of geometric order in proliferating metazoan epithelia

The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.

Computerized Database of Salt Affected Soils for Agro‐climatic Regions in the Indo–Gangetic Plain of India Using GIS

Indo_Gangetic Plain (IGP) of India that stretched from the foothills of Himalayas near the Punjab State to the Gangetic delta in West Bengal State was known for highly fertile soil and favorable climatic condition for highest production of rice‐wheat. Appearance of soil salinity in large areas of IGP caused a major concern due to loss of productivity. The salt affected soils maps of India (NRSA 1997) showed vast areas of salt affected soils distributed along the Gangetic Plain covering the States of Haryana, Punjab, Uttar Pradesh, Bihar and West Bengal. In the analogue form, these maps contain voluminous data were difficult to handle without messing the whole dataset. An attempt was made to prepare a digitized database of salt affected soils to facilitate easy access, retrieval and map calculations required for reclamation and management of salt affected soil. The salt affected soils maps on 1:250, 000 scale were digitized for the States of Punjab, Haryana, Uttar Pradesh, Bihar and West Bengal using ILWIS. GIS. The Survey of India topomap was used for geo‐referencing and basemap preparation overlaying thematic layers for administrative and political boundaries, infrastructure, irrigation and drainage and settlements. The attribute data on physiography and the soil characteristics were stored in an attribute table and linked with the digitized polygons to prepare a relational database. Combining geo‐referenced (State) maps of Haryana, Punjab, Uttar Pradesh, Bihar and West Bengal using GIS, a composite map for Indo‐Gangetic plain was prepared. Four Agroclimatic regions (ACRs) and seventeen Agroclimatic zones (ACZs) were identified in the Indo‐Gangetic Plain (The Planning Commission of India) for planning and development of natural resources at regional level. The boundaries of ACZs and ACRs were delineated from the primary (master) database of IGP using ILWIS.GIS. The distribution of SAS polygons at regional and zonal level was delineated superimposing digitized boundaries of ACRs and ACZs over the master database of IGP. The state‐wise, region‐wise and zone‐wise extent of SAS was calculated. Soils were essentially saline at Lower‐ and Middle Gangetic Plain regions but highly variable and complex saline‐sodic in the Upper‐ and Trans‐Gangetic Plain regions. The area statistics showed that maximum SAS area occurred in ACR V (Upper Gangetic Plain) in Uttar Pradesh (UP) followed by ACR IV (Middle Gangetic Plain) in UP and Bihar, ACR III (Lower Gangetic Plain) in West Bengal and ACR VI (Trans‐Gangetic Plain) of Haryana and Punjab. Such database in digital format provides geo‐referenced, easy to access and retrievable, relational database comprising of thematic and attribute information of salt affected soils at state, regional and zonal level to facilitate overlay and map calculation of related data such as water quality, climatic, landform etc, useful for planning and decision making in reclamation and management of salt affected soils in IGP and other similar regions.

Maturation of crack patterns.

Superficial (two-dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in order to reduce its energy. The process models the evolution in depth of cracks in geological formations and in starch samples ("columnar jointing"), and also the time evolution (over thousands of years) of crack patterns in frozen soils. We observe an evolution towards a polygonal pattern that consists of a fixed distribution of polygons with mainly five, six, and seven sides. They compare very well with known experimental examples. The evolution of one of these "mature" patterns upon reduction of the degree of contraction is also considered. We find that the pattern adapts by closing some of the cracks and rearranging those in the immediate neighborhood. This produces a change of the mean size of the polygons, but remarkably no changes of the statistical properties of the pattern. Comparison with the same behavior recently observed in starch samples is presented.

A computational approach for the analysis of changes in polygon distributions

This paper develops a computational method for analyzing changes in polygon distributions. Unmovable polygons that change discontinuously without explicit functional linkage information are discussed. Six types of primitive events are used to describe the change: 1) generation, 2) disappearance, 3) expansion, 4) shrinkage, 5) union, and 6) division. The change of polygon distributions is decomposed into a combination of these events. A computational procedure for deducing a set of events from polygon distributions of two times is proposed. The method is applied to the analysis of the spatial competition between the major and small chains of convenience stores in Tokyo, Japan. Some empirical findings are shown.

Exploratory Method for Analyzing Changes in Polygon Distributions

In this paper I develop an exploratory method for analyzing changes in polygon distributions. Changes are deduced from a set of polygon distributions of different times, and represented by a directed graph. Three viewpoints for representing individual changes are proposed: topology, size, and direction. They are described qualitatively, and used for exploratory analysis of spatiotemporal distribution of changes. In addition to individual changes, their sequences are analyzed through classification, visualization, and calculation of summary statistics. The method proposed is applied to the analysis of changes in market areas of a convenience-store chain in Tokyo, Japan. The empirical study reveals the spatial structure of changes in a global scale.

A large class of random tessellations with the classic Poisson polygon distributions

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Body Size and Energy Use in Termites (Isoptera): The Responses of Soil Feeders and Wood Feeders Differ in a Tropical Forest Assemblage

Studies of log body size/log energy use in local animal assemblages reveal a range of distributional patterns from those with a negative upper bound slope (NUBS), showing energy use to be dominated by smaller bodied species, to those with a positive upper bound slope (PUBS), indicating that larger bodied species dominate energy use. We investigated the log body size/log energy use relationships for a local termite assemblage at the Mbalmayo Forest Reserve in Cameroon, and compared the patterns for wood and soil feeding groups. We measured the biomass densities of 75 species of termites across three forest sites. Termite species metabolic rates were derived either directly (25 species), or by regression estimates (50 species), from Warburg manometry measurements of termite xO 2 at 28°C. The combined data from the three sites revealed a marked difference in log body size/log energy use distributions between wood and soil feeding groups. While wood feeders showed a polygonal distribution, with a negative upper bound slope (NUBS), soil feeders showed a (statistically very significant) positive distribution. The data for soil feeders are also exceptional, in comparison with the vast majority of other animal assemblage data, in showing significantly greater 'total' energy use for larger, compared with smaller, body size categories. Furthermore, the modal body size category for number of individual termites does not coincide with that for number of termite species. We interpret these results in the context of the likely constraints imposed by the food substrates of termites and the economies of scale. Specifically, soil feeders utilise a low energy, universally abundant substrate compared with wood feeders which feed on a patchily distributed, higher energy resource. Digestive efficiency is likely to be at a premium in soil feeders, driving selection towards larger body size (and hence larger gut volume and transit time), compared with wood feeders.

Further random tessellations with the classic Poisson polygon distributions

It is well-known that Poisson lines in the plane, with orientation distribution Θ on [0, π), generate a (random) tessellation M 0 of (random) convex polygons whose characteristics (area, perimeter, etc.) conform, in an ergodic sense, to a certain class {D Θ} of distributions.

Further random tessellations with the classic Poisson polygon distributions

It is well-known that Poisson lines in the plane, with orientation distribution Θ on [0, π), generate a (random) tessellation M0 of (random) convex polygons whose characteristics (area, perimeter, etc.) conform, in an ergodic sense, to a certain class {DΘ} of distributions.

Is water structure around hydrophobic groups clathrate-like?

The term "clathrate structure" is quantified for solvation of nonpolar groups by enumerating hydrogen-bonded ring sizes both in the solvation shell and through the shell-bulk interface and comparing it to a bulk control using the ST4 water model. For clathrate-like structure to be evident, the distributions along the hydrophobic surface are expected to be dominated by pentagons, with significant depletion of hexagons and larger polygons. While the distribution in this region is indeed distinguished by a large number of pentagons, there are significant contributions from hexagons and larger rings as well. Calculated polygon distributions through the shell-bulk interface indicate that when water structure is highly cooperative along the hydrophobic surface, hydrogen-bonded pathways leading back into bulk are then reduced. These results are qualitatively consistent with the observation that hydrophobicity is proportional to the nonpolar solute surface area.

Symmetry and other geometric constraints of surface networks in nature and science

Three basic equations for topological constraints upon inhomogeneous surface networks of solids are derived from the Euler equation and other identities which lead to some insight into the essential issues of this area. In particular, a symmetry between vertices and polygons of a general surface network is shown to exist, and variations in a surface network can simply be described as a kind of reciprocal exchange between vertices and polygons. The number of three-ordered or threefold vertices, as well as many-edged polygons and many-ordered vertices, is controlled by the ratio of the number of three-edged and/or four-edged polygons to the total number of polygons. When the minimum-edged polygon has five edges, the number of three-ordered vertices is automatically greater than two-thirds of the total number of vertices. The dominant occupation of three-ordered vertices can still retain under certain conditions after appearance of three-edged and/or four-edged polygons. The critical distribution of polygons for the maintenance of this kind of domination is determined. The gap between the critical distribution and natural or artificial surface networks allows the geometric structure of a network to be changed greatly without loss of the domination. This finding establishes a quantitative basis for the description of granular and biological materials in terms of microstructures. It will also be seen that classical models correspond to a very special case of constraints. Theoretical results are in agreement with experimental data for networks that arise in surfaces, such as fracture, biological cells, metallurgical grains, bubbles, leaf-vein networks and the coat pattern of a giraffe.

Flat-Top Polygonal Temperature Profiles by Laser Beams

AbstractA method was proposed to generate flat-top polygonal temperature distributions in substrates from a Gaussian-shaped laser source. The original Gaussian beam is equally and diametrically separated into several portions and is then rearranged so that the each portion has its peak intensity allocated toward outside. This can be realized by a symmetrical multi-facet prism. A mathematical model was derived to calculate the temperature rise induced the rearranged portions of the laser beam. Flat-top polygonal temperature profiles with two, three, four and six corners have been investigated by numerical calculations. It is shown that flat-top polygonal temperature distributions can be obtained by this method if the distance between the peaks of the beam portions is arranged to be certain proportions to the original Gaussian beam. It is also found the shape of the temperature profile is almost with the same size as the original Gaussian beam size and does not depend on the incident laser power and the substrate material.

A Statistical Comparison of Two Hidden Surface Techniques: the Scan‐line and Z‐buffer Algorithms

AbstractThis paper compares two image space hidden surface removal algorithms for polygonal scenes. These are the z‐buffer and scan‐line algorithms. There is first an overview of each algorithm, followed by a simulation experiment, designed to compare the number of polygons per second which can be rendered by each algorithm. The simulation varies the number of polygons in the scene, and the size and distribution of polygons over the display. The results suggest that the z‐buffer is preferred for a large enough number of polygons, however, smaller polygons and uniform distribution of polygons favour the scan‐line approach. The analysis does not take into account the complexity of the shading rule, which is likely also to favour the scan‐line method.

Probabilistic analysis of the stability of massive bridge abutments using simulation methods

This study provides a probabilistic procedure for analysing the stability of massive bridge abutments. The procedure is based on simulation techniques. To analyse the stability a model is applied which considers five cases of losing the equilibrium. To describe the random variability of soil properties, polygonal probability distributions are proposed, which are especially useful in sumulation calculations. Examples of description of some soil parameters by polygonal distributions together with verification by statistical testing are presented. The proposed method is examined in numerical examples and applied to the analysis of the influence of individual parameters on the probability of loss stability. The problem of the accuracy of calculations is also discussed. Numerical examples show the usefulness of the presented methodology. The randomness of the friction angle of the geotechnical layer directly under the base of an abutment is shown to have the greatest effect on the probabilistic characteristics of the stability. The probability distribution of the stability measures in the case of exceeding the bearing capacity may differ significantly from the normal distribution.

Size of rings in two dimensions

The authors report enumeration results for the radius of gyration and caliper size distribution of self-avoiding unrooted polygons of up to 28 steps, on the square lattice. The (second moment) radius of gyration series is sufficiently smooth to allow verification of the theoretical prediction v(rings)=v(walks) to 0.2% accuracy.

Stochastic Geometry of Two-Dimensional Fiber Assemblies

It is clarified that the orientational anisotropy affects the formation and distribution of polygons in a planar random system of line segments. The probability, P (n), of finding an n-sided polygon in an anisotropic line system is related to the same, P (n |0), corresponding to the isotropic case by the equations : P (n) = (2GI-8/π2-8) P (n|0), for n=3 or n≥5, andP (4) = (2GI-8/π2-8) P(4|0)+(π2-2GI/π2-8) where, I and G are defined, in terms of the density function, q (θ), of orientation distribution, as I=∫π/2-π/2∫π/2-π/2q (θ) q (θ') |sin(θ-θ') |dθdθ' and G=∫π/2-π/2 (∫π/2-π/2q (θ) |sin (θ-θ') |dθ) -2dθ' The validities of these theoretical estimations are practically verified through Monte-Carlo simulations for two special cases.

The fine structure of the Kolmogoroff–Avrami theorem

The fundamental processes underlying phase changes at electrode surfaces are often described in terms of the Kolmogoroff–Avrami theorem.Some aspects of the 'fine structure' of this theorem are considered. Particular attention is paid to the case of two-dimensional nucleation and growth under the influence of an applied electrode potential (equivalent to supersaturation). A probabilistic analysis is presented for circularly-symmetric nuclei which obviates the need for concepts such as 'overlap' between emergent nuclei. The concept of a 'collision front' is introduced which is defined as the line of contact along which neighbouring nuclei collide. It is shown that for instantaneous nucleation (potentiostatic double step method) the extended set of collision fronts constitutes a net composed of irregular convex polygons. The properties of this net are investigated in some detail. In particular, the extent of applicability of the Kolmogoroff–Avrami equation is delineated, the distribution of collisional polygons is calculated, and an approximate treatment for the variance of the surface coverage function is presented. The general approach exposes clearly the relationship between the single nucleus and the multinuclear situations.