Polygonal Fields Research Articles

Analysis of heterogeneous Markov media for particle transport problems.

Markov media provide a prototype class of stochastic geometries that are widely used in order to model several complex and disordered systems encompassing, e.g., turbulent fluids and plasma, atmospheric layers, or biological tissues, especially in relation to particle transport problems. In several key applications, the statistical properties of random media may display spatial gradients due to material stratification, which means that the typical spatial scale and the probability of finding a given material phase at a spatial location become nonhomogeneous. In this paper we investigate the main features of spatially heterogeneous Markov media, using Poisson hyperplane tessellations and Arak polygonal fields. We show that both models can generate geometry realizations sharing Markov-like properties, and discuss their distinct advantages and drawbacks in terms of flexibility and ease of use. The impact of these models on the observables related to particle transport will be assessed using Monte Carlo simulations.

Design and field testing of a polygonal paddy infield path planner for unmanned tillage operations

Path commands, obtained through a traveling route strategy for auto-steering control in a test field, are essential for the operation of an autonomous tractor from a given starting point to an end destination. Planning an agricultural field operation can increase the work rate and quality of field tilling, particularly in complex fields, minimizing the time loss and non-working traveling costs. With the diversification of farming products and environments, it is critical to seek feasible paths that have a good balance between time efficiency and path length, with the consideration for irregularities of field boundaries. However, the existing field path planning algorithms do not guarantee global optimality because traditional planners generate paths in rectangular fields and not in all the possible geometrical route generation for infield and headland turning found in polygonal fields. To overcome this drawback, this paper presents a novel and practical infield path planner that can generate infield coverage routes and headland turnings for polygonal paddy fields. An infield route-planning program was developed to automatically generate an X-type turning, pattern-based coverage path map that provides guidance lines for autonomous tillage tractors executing efficient operations in polygonal fields. The planning parameters related to the equipment characteristics of the tractor and implement variables, waypoint-setting variables, and field boundaries entered into the developed infield route-planning program can provide useful information to users in terms of selecting the most appropriate solution based on all related field operational capacities such as field traveled distance, field time, and field efficiency. A small-scale prototype of an autonomous tillage tractor equipped with the proposed infield path planner and a slip estimation-based path-tracking algorithm was built and tested in Korean paddy fields with two different shapes of farm-field boundaries. The field tests performed using the autonomous tractor in a trapezoidal field and an L-shaped field showed tracking errors of 14.9 and 21.8 cm, respectively; field efficiencies of 62.1–70.6%; and ratios of effective operation areas of 91.4–92.7%. These measurement data were similar to those obtained from a human-operated tillage method, implying that the infield path planner developed here and the slip estimation-based path-tracking controller can lead a tractor with acceptable accuracy and performance.

Decomposition‐based mission planning for fixed‐wing UAVs surveying in wind

AbstractThis paper presents a new method for planning fixed‐wing aerial survey paths that ensures efficient image coverage of a large complex agricultural field in the presence of wind. By decomposing any complex polygonal field into multiple convex polygons, the traditional back‐and‐forth boustrophedon paths can be used to ensure coverage of these decomposed regions. To decompose a complex field in an efficient and fast manner, a top‐down recursive greedy approach is used to traverse the search space to minimize the flight time of the survey. This optimization can be computed fast enough for use in the field. As wind can severely affect flight time, it is included in the flight time calculation in a systematic way using a verified cost function that offers greatly reduced survey times in the wind. Other improved cost functions have been developed to take into account real‐world problems, for example, No‐Fly Zones, in addition to flight time. A number of real surveys are performed to show the flight time in wind model is accurate, to make further comparisons to previous techniques and to show that the proposed method works in real‐world conditions providing total image coverage. A number of missions are generated and flown for real complex agricultural fields. In addition to this, the wind field around a survey area is measured from a multirotor carrying an ultrasonic wind speed sensor. This shows that the assumption of steady uniform wind holds true for the small areas and time scales of an unmanned aerial vehicle aerial survey.

Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields.

Nanoparticles tend to aggregate once integrated into soft matter and consequently, self-assembling nanoparticles into large-scale, regular, well-defined, and ultimately chiral patterns remains an ongoing challenge toward the design and realization of organized superstructures of nanoparticles. The patterns of nanoparticles that are reported in liquid crystals so far are all static, and this lack of responsiveness extends to assemblies of nanoparticles formed in topological singularities and other localized structures of anisotropic matter. Here, it is shown that gold nanoparticles form spiral superstructures in polygonal fields of cholesteric liquid crystals. Moreover, when the cholesteric liquid crystals incorporate molecular photoswitches in their composition, the pitch of the nanoparticulate spirals follows the light-induced reorganization of the cholesteric liquid crystals. These experimental findings indicate that chiral liquid crystals can be used as chiral and dynamic templates for soft photonic nanomaterials. Controlling the geometry of these spirals of nanoparticles will ultimately allow modulating the plasmonic signature of hybrid and chiral systems.

Individuality testing of new Glock pistol barrels “Marksman Barrel”

The Glock company’s newest generation of pistols (G42/43, Gen5) is equipped with so-called “Glock Marksman Barrels” (GMB). These barrels feature an enhanced polygonal profile with right-hand twist and a small rifled profile on either side of the main polygonal field impression (Hernandez et al., 2016). Up until now, using the usual methods of comparison (automatic ballistic identification systems, ABIS and comparison microscope) it was difficult to assign bullets fired from a polygonal barrel to their origin with a high evidentiary value (Murdock et al., 1990) [5] (Northcutt, 2010).In this study, test shots from 18 Glock Gen5 pistols (9 Glock 17 pistols and 9 Glock 19 pistols) were compared to examine their differentiability. In addition, a Gen5 Glock 17 pistol was used to shoot 500 cartridges to determine to what degree the first projectile could be matched with the 500th (Zhang and Luo, 2018) [10].This study was able to demonstrate that the new “Glock Marksman Barrel” (GMB) leaves marks of sufficient quality on projectiles to make high evidentiary value assignments of those projectiles to an individual firearm, both by using the comparison microscope as well as with an ABIS (Evofinder®). Further, it was possible to assign the cartridge casings to an individual pristine firearm.

An incertae sedis organic-walled microfossil from the Mississippian (Early Carboniferous): Kirby Misperton-1 borehole, North Yorkshire, UK

The organic-walled microfossil Mispertonia desiccata gen. et sp. nov. is described from the Arnsbergian (Mississippian, Early Carboniferous) of borehole Kirby Misperton-1, North Yorkshire, UK. This species includes thin-walled, originally spherical or sub-spherical vesicles; with a single polygonal field surrounded by a rim and a thickened collar which is interrupted by grooves radiating out from the angles of the polygonal field. The form is recovered from marine strata of the Silsden Formation equivalent, but is not necessarily of marine origin. Similar specimens, here synonymised with M. desiccata , are known from the non-marine Late Permian or Early Triassic of India.

Cluster: A New Application for Spatial Analysis of Pixelated Data for Epiphytotics.

Spatial analysis of epiphytotics is essential to develop and test hypotheses about pathogen ecology, disease dynamics, and to optimize plant disease management strategies. Data collection for spatial analysis requires substantial investment in time to depict patterns in various frames and hierarchies. We developed a new approach for spatial analysis of pixelated data in digital imagery and incorporated the method in a stand-alone desktop application called Cluster. The user isolates target entities (clusters) by designating up to 24 pixel colors as nontargets and moves a threshold slider to visualize the targets. The app calculates the percent area occupied by targeted pixels, identifies the centroids of targeted clusters, and computes the relative compass angle of orientation for each cluster. Users can deselect anomalous clusters manually and/or automatically by specifying a size threshold value to exclude smaller targets from the analysis. Up to 1,000 stochastic simulations randomly place the centroids of each cluster in ranked order of size (largest to smallest) within each matrix while preserving their calculated angles of orientation for the long axes. A two-tailed probability t test compares the mean inter-cluster distances for the observed versus the values derived from randomly simulated maps. This is the basis for statistical testing of the null hypothesis that the clusters are randomly distributed within the frame of interest. These frames can assume any shape, from natural (e.g., leaf) to arbitrary (e.g., a rectangular or polygonal field). Cluster summarizes normalized attributes of clusters, including pixel number, axis length, axis width, compass orientation, and the length/width ratio, available to the user as a downloadable spreadsheet. Each simulated map may be saved as an image and inspected. Provided examples demonstrate the utility of Cluster to analyze patterns at various spatial scales in plant pathology and ecology and highlight the limitations, trade-offs, and considerations for the sensitivities of variables and the biological interpretations of results. The Cluster app is available as a free download for Apple computers at iTunes, with a link to a user guide website.

Disturbance-effects on treeline larch-stands in the lower Kolyma River area (NE Siberia)

Tree stands in the boreal treeline ecotone are, in addition to climate change, impacted by disturbances such as fire, water-related disturbances and logging. We aim to understand how these disturbances affect growth, age structure, and spatial patterns of larch stands in the north-eastern Siberian treeline ecotone (lower Kolyma River region), an insufficiently researched region. Stand structure of Larix cajanderi Mayr was studied at seven sites impacted by disturbances. Maximum tree age ranged from 44 to 300 years. Young to medium-aged stands had, independent of disturbance type, the highest stand densities with over 4000 larch trees per ha. These sites also had the highest growth rates for tree height and stem diameter. Overall lowest stand densities were found in a polygonal field at the northern end of the study area, with larches growing in distinct “tree islands”. At all sites, saplings are significantly clustered. Differences in fire severity led to contrasting stand structures with respect to tree, recruit, and overall stand densities. While a low severity fire resulted in low-density stands with high proportions of small and young larches, high severity fires resulted in high-density stands with high proportions of big trees. At waterdisturbed sites, stand structure varied between waterlogged and drained sites and latitude. These mixed effects of climate and disturbance make it difficult to predict future stand characteristics and the treeline position.

In Situ Visualization and Production of Extract Databases

Simulations running at high concurrency on HPC systems generate large volumes of data that are impractical to write to disk due to time and storage constraints. Applications often adapt by saving data infrequently, resulting in datasets with poor temporal resolution. This can make datasets difficult to interpret during post hoc visualization and analysis, or worse, it can lead to lost science. In Situ visualization and analysis can enable efficient production of small data products such as rendered images or surface extracts that consist of polygonal geometry plus fields. These data products are far smaller than their source data and can be processed much more economically in a traditional post hoc workflow using far fewer computational resources. We used the SENSEI and Libsim in situ infrastructures to implement rendering workflow and surface data extraction workflows in the AVF-LESLIE combustion code. These workflows were then demonstrated at high levels of concurrency and showed significant data reductions and limited impact on the simulation runtime.

The taxonomic position of the Cyprideis species (Ostracoda, Cytheroidea, Cytherideidae) that occurs in Lake Issyk-Kul, N.E. Kyrgystan

As a result of detailed comparative-morphological studies of Cyprideis pedashenkoi (Daday 1909), considered by many authors to be synonymous with Cyprideis torosa (Jones 1850), it is now possible to demonstrate that it is a separate species endemic to Lake Issyk-Kul. Morphologically it is no less variable than C. torosa, can be consistently distinguished from that species by its double (vs. V-shaped) frontal muscle scar, the pronounced fossa-mural nature of the surface sculpture, with punctate sculpture grouped into polygonal fields forming a second-order reticulation, as well as by the proportions of some parts of appendage armature and details of the penis structure.

A Generic Three-Sided Rearrangeable Switching Network for Polygonal FPGA Design

We propose a new Polygonal Field Programmable Gate Array (PFPGA) that consists of many logic blocks interconnected by a generic three-stage three-sided rearrangeable polygonal switching network (PSN). The main component of this PSN consists of a polygonal switch block interconnected by crossbars. In comparing our PSN with a three-stage three-sided clique-based (Xilinx 4000-like FPGAs) (Palczewski; 1992) switching network of the same size and with the same number of switches, we find that the three-stage three-sided clique-based switching network is not rearrangeable. Also, the effects of the rearrangeable structure and the number of terminals on the network switch-efficiency are explored and a proper set of parameters is determined to minimize the number of switches. Moreover, we explore the effect of the PSN structure and granularity of cluster logic blocks on the switch efficiency of PFPGA. Experiments on benchmark circuits show that switches and speed performance are significantly improved. Based on experiment results, we can determine the parameters of PFPGA for the VLSI implementation.

Discrete Multicolour Random Mosaics with an Application to Network Extraction

AbstractWe introduce a class of random fields that can be understood as discrete versions of multicolour polygonal fields built on regular linear tessellations. We focus first on a subclass of consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation is used to design new sampling techniques for Gibbsian modifications of such fields, a class which covers lattice‐based random fields. A flux‐based modification is applied to the extraction of the field tracks network from a Synthetic Aperture Radar image of a rural area.

Arak-Clifford-Surgailis Tessellations. Basic Properties and Variance of the Total Edge Length

Non-homogeneous random tessellations in the plane with T-shaped vertices are considered, which are defined as Gibbsian modifications of a Poisson line process with arbitrary locally finite intensity measure. In the homogeneous set-up they can be regarded as a specific case of the general Arak-Surgailis polygonal fields in the plane and share some properties with the iteration stable (STIT) tessellations. In the non-homogeneous and anisotropic environment an explicit expression for the partition function is provided and first- and second-order properties of the random length measure of the tessellations restricted to a convex sampling window are derived. In the more special isotropic regime a closed formula for the pair-correlation function and the variance of the total edge length is obtained.

A three-sided rearrangeable switching network for a binary fat tree

A binary fat tree needs an internal node to interconnect the left-children, right-children and parent terminals to each other. In this article, we first propose a three-stage, 3-sided rearrangeable switching network for the implementation of a binary fat tree. The main component of this 3-sided switching network (3SSN) consists of a polygonal switch block (PSB) interconnected by crossbars. With the same size and the same number of switches as our 3SSN, a three-stage, 3-sided clique-based switching network is shown to be not rearrangeable. Also, the effects of the rearrangeable structure and the number of terminals on the network switch-efficiency are explored and a proper set of parameters has been determined to minimise the number of switches. We derive that a rearrangeable 3-sided switching network with switches proportional to N 3/2 is most suitable to interconnect N terminals. Moreover, we propose a new Polygonal Field Programmable Gate Array (PFPGA) that consists of logic blocks interconnected by our 3SSN, such that the logic blocks in this PFPGA can be grouped into clusters to implement different logic functions. Since the programmable switches usually have high resistance and capacitance and occupy a large area, we have to consider the effect of the 3SSN structure and the granularity of its cluster logic blocks on the switch efficiency of PFPGA. Experiments on benchmark circuits show that the switch and speed performances are significantly improved. Based on the experimental results, we can determine the parameters of PFPGA for the VLSI implementation.

Polygonal Web Representation for Higher Order Correlation Functions of Consistent Polygonal Markov Fields in the Plane

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1982,1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of salient features with the two-dimensional Ising model. The purpose of this paper is to establish an explicit stochastic representation for the higher-order correlation functions of polygonal Markov fields in their consistency regime. The representation is given in terms of the so-called crop functionals (defined by a Moebius-type formula) of polygonal webs which arise in a graphical construction dual to that giving rise to polygonal fields. The proof of our representation formula goes by constructing a martingale interpolation between the correlation functions of polygonal fields and crop functionals of polygonal webs.

Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation

Abstract. We introduce a class of Gibbs–Markov random fields built on regular tessellations that can be understood as discrete counterparts of Arak–Surgailis polygonal fields. We focus first on consistent polygonal fields, for which we show consistency, Markovianity and solvability by means of dynamic representations. Next, we develop disagreement loop as well as path creation and annihilation dynamics for their general Gibbsian modifications, which cover most lattice-based Gibbs–Markov random fields subject to certain mild conditions. Applications to foreground–background image segmentation problems are discussed.

Non-homogeneous Polygonal Markov Fields in the Plane: Graphical Representations and Geometry of Higher Order Correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.

Perfect Simulation for Length‐interacting Polygonal Markov Fields in the Plane

Abstract. The purpose of this paper was to construct perfect samplers for length‐interacting Arak–Clifford–Surgailis polygonal Markov fields in the plane with nodes of order 2 (V‐shaped nodes). This is achieved by providing for the polygonal fields a hard core marked point process representation with individual points carrying polygonal loops as their marks, so that the coupling from the past and clan of ancestors routines can be adopted.

Dobrushin-Kotecký-Shlosman Theorem for Polygonal Markov Fields in the Plane

We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes — a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. For these polygonal fields we establish a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecký-Shlosman theory, with the corresponding Wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model. As an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process, following the ideas of Fernandez, Ferrari and Garcia.

Random dynamics and thermodynamic limits for polygonal Markov fields in the plane

We construct random dynamics for collections of nonintersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the dynamic construction of consistent polygonal fields, as presented in the original articles by Arak (1983) and Arak and Surgailis (1989), (1991), and it provides an easy-to-implement Metropolis-type simulation algorithm. The second dynamics leads to a graphical construction in the spirit of Fernándezet al.(1998), (2002) and yields a perfect simulation scheme in a finite window in the infinite-volume limit. This algorithm seems difficult to implement, yet its value lies in that it allows for theoretical analysis of the thermodynamic limit behaviour of length-interacting polygonal fields. The results thus obtained include, in the class of infinite-volume Gibbs measures without infinite contours, the uniqueness and exponential α-mixing of the thermodynamic limit of such fields in the low-temperature region. Outside this class, we conjecture the existence of an infinite number of extreme phases breaking both the translational and rotational symmetries.