Polygonal Contour Research Articles

Harmonic Analysis on Feed Kinematic Behaviors in Turning of Regular Polygon Section

Surface characteristics of the regular polygon contour parts and turning process,including tool movement characteristics,feed speed and feed acceleration, is analyzed with the harmonic analysis principle when cutting the parts. Using MATLAB to draw the displacement, velocity and acceleration variations chart of polygon workpiece turning.

Superpropagator and superconformal invariants

We construct a superpropagator in maximally supersymmetric Yang–Mills theory which is invariant off-shell under a chiral half of supersymmetries. Motivated by the duality with scattering amplitudes in this theory, we apply this superpropagator to supersymmetric Wilson loop on polygonal contours. By performing explicit one-loop calculations we confirm the absence of anomalies and verify the duality between the object under study and NMHV amplitudes.

A note on two-loop superloop

We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang–Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the null polygonal super Wilson loop at two loops restricting the contour kinematics to a two-dimensional subspace. This allows one to perform all computations in a concise analytical form and trace the pattern of cancellations between individual Feynman graphs in a transparent fashion. As a consequence of our consideration we obtain a dual conformally invariant result for the remainder function in agreement with one-loop NMHV amplitudes.

Conformal anomaly of super Wilson loop

Classically supersymmetric Wilson loop on a null polygonal contour possesses all symmetries required to match it onto non-MHV amplitudes in maximally supersymmetric Yang–Mills theory. However, to define it quantum mechanically, one is forced to regularize it since perturbative loop diagrams are not well defined due to presence of ultraviolet divergences stemming from integration in the vicinity of the cusps. A regularization that is adopted by practitioners by allowing one to use spinor helicity formalism, on the one hand, and systematically go to higher orders of perturbation theory is based on a version of dimensional regularization, known as Four-Dimensional Helicity scheme. Recently it was demonstrated that its use for the super Wilson loop at one loop breaks both conformal symmetry and Poincaré supersymmetry. Presently, we exhibit the origin for these effects and demonstrate how one can undo this breaking. The phenomenon is alike the one emerging in renormalization group mixing of conformal operators in conformal theories when one uses dimensional regularization. The rotation matrix to the diagonal basis is found by means of computing the anomaly in the Ward identity for the conformal boost. Presently, we apply this ideology to the super Wilson loop. We compute the one-loop conformal anomaly for the super Wilson loop and find that the anomaly depends on its Grassmann coordinates. By subtracting this anomalous contribution from the super Wilson loop we restore its interpretation as a dual description for reduced non-MHV amplitudes which are expressed in terms of superconformal invariants.

Thermodynamic bubble ansatz

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS 5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are identical to those of the Thermodynamics Bethe Ansatz. Moreover, the area is given by the free energy of this TBA system. The high temperature limit of the TBA system can be exactly solved. It leads to an explicit expression for a special class of hexagonal contours.

Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry

Scattering amplitudes in planar N=4 super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry. The presence of this additional symmetry imposes strong restrictions on the amplitudes and is connected to a duality relating scattering amplitudes to Wilson loops defined on polygonal light-like contours. The combination of the superconformal and dual superconformal symmetries gives rise to a Yangian, an algebraic structure which is known to be related to the appearance of integrability in other regimes of the theory. We discuss two dual formulations of the symmetry and address the classification of its invariants.

A Complete Set of Linear-Phase Basis Functions for Scatterers With Flat Faces and for Planar Apertures

Entire-domain basis functions are introduced for the analysis of scattering from bodies with flat portions, and of radiation from planar apertures; they are defined via the application of the sampling theorem of Shannon. These basis functions are particularly convenient for polygonal contours; however, arbitrary contours can be treated in the same framework with a very minor pre-processing time. A non-redundant set of basis functions is determined a priori by explicit approximate formulas either for currents and for radiated field. Numerical results are presented to shown the accuracy of the method.

A Monitor Gamut Description Model Based on BP Neural Network

In the printing industry, monitor gamut is one of the most important indices of the preprocess system. Usually, under some condition, monitor gamut is described as triangle by three vertex, all of them come from three monitor drive extreme values, in the channels such as red, green and blue one. In spite of the simplicity of the description method in manipulation, the triangle can not describe the monitor gamut exactly, because the number of the samples are too small too indicate the feature of the monitor gamut perfectly and the monitor gamut is related to its surround and configuration. In the research, based on mapping relation of digital image pixel value and its corresponding monitoring color, data pairs of digital image pixel values and its corresponding monitoring color blocks chroma values are sampled to establish a mapping model, which is based on BP neural network with exactitude to a perfect certainty. Then, more digital image pixel values are sampled at thicker intervals, their corresponding printing color chroma values are calculated by the mapping model, so the monitor gamut is covered by thicker chroma data not only in the gamut but also on the gamut polygon contour and vertexes, that leads to the best of its ability, much more vertexes are acquired in far much more color hue angel ranges to form the gamut polygon, and the gamut is described much more fully. The experiment shows that the gamut polygon drawn by the mapping model describes the monitor gamut much more objectively and reflects the monitor gamut factually.

New medical image segmentation algorithm based on subregion similarity

Introducing the traditional region growing method into a contour approximating method, a new segmentation algorithm based on subregion similarity was presented. Firstly, an initial polygon contour was brought in by human-computer interactive process. Then the region of interest was obtained by using a sub-region similarity which served as driving force of the contour evolution. The experimental results show that the algorithm is of more anti-noise ability than the region growing method, and can divide up the region of interest efficiently.

Y-system for scattering amplitudes

We compute super Yang–Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS5 space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of thermodynamic Bethe ansatz (TBA) equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

Analytic results for MHV Wilson loops

We obtain concise analytic formulae for Wilson loops computed on special n-point polygonal contours through two-loops in weakly coupled \( \mathcal{N} = 4 \) supersymmetric gauge theory. The contours we consider can be embedded into a (1 + 1)-dimensional subspace of the 4-dimensional gauge theory, corresponding to the boundary of the AdS 3 on the string theory side. Our analytic results hold for any number of edges, thus generalising to arbitrary n the recently derived expressions for 2-dimensional octagons. These polygonal Wilson loops have been conjectured to be equivalent to MHV scattering amplitudes in planar \( \mathcal{N} = 4 \) SYM.

Efeitos da dieta suplementada com ômega-3 no músculo sóleo de ratos submetidos à natação: análise histológica e morfométrica

As lesões musculares têm sido observadas como as mais frequentes nos esportes. Considerando a produção de espécies reativas de oxigênio como um fator de risco para instalação de lesões e características antioxidantes e anti-inflamatórias do ômega-3, o objetivo deste trabalho foi verificar as alterações histológicas e morfométricas do músculo sóleo de ratos que realizaram natação, associado a uma dieta suplementada com ômega-3. Para sua realização foram utilizados 31 ratos Wistar divididos em quatro grupos, sendo os grupos A e C suplementados com azeite de oliva e B e D com 3g/dia de ômega-3 por quatro semanas. Os grupos C e D foram submetidos à natação cinco dias/semana por 28 dias, com acréscimo de 5% do peso corporal a partir da segunda semana, enquanto que os grupos A e B não realizaram treinamento. Após este período os animais foram sacrificados, o músculo sóleo retirado e corado com Hematoxilina-eosina para avaliação morfológica. Análise de variância bifatorial, com nível de significância de 5%, foi utilizada para análise dos valores do menor diâmetro das fibras musculares. Os grupos A e B (sedentários) apresentaram padrões histológicos de normalidade. O grupo C apresentou aumento do tecido endomisial e do número de núcleos, presença de fibras fagocitadas e de contornos poligonais não mantidos, enquanto que o grupo D apresentou poucas fibras fagocitadas e de contornos poligonais preservados. Com relação à medida do menor diâmetro das fibras musculares, as análises mostraram diferenças para o fator treinamento, mas não para o fator suplementação e a interação entre eles. As alterações histológicas induzidas pelo exercício foram atenuadas no grupo suplementado com ômega-3, sugerindo um efeito protetor da suplementação, contudo, o aumento do diâmetro das fibras para os grupos expostos ao exercício está relacionado ao efeito do treinamento e não à suplementação.

Uniform offsetting of polygonal model based on Layered Depth-Normal Images

Uniform offsetting is an important geometric operation for computer-aided design and manufacturing (CAD/CAM) applications such as rapid prototyping, NC machining, coordinate measuring machines, robot collision avoidance, and Hausdorff error calculation. We present a novel method for offsetting (grown and shrunk) a solid model by an arbitrary distance r . First, offset polygons are directly computed for each face, edge, and vertex of an input solid model. The computed polygonal meshes form a continuous boundary; however, such a boundary is invalid since there exist meshes that are closer to the original model than the given distance r as well as self-intersections. Based on the problematic polygonal meshes, we construct a well-structured point-based model, Layered Depth-Normal Image (LDNI), in three orthogonal directions. The accuracy of the generated point-based model can be controlled by setting the tessellation and sampling rates during the construction process. We then process all the sampling points in the model by using a set of point filters to delete all the invalid points. Based on the remaining points, we construct a two-manifold polygonal contour as the resulting offset boundary. Our method is general, simple and efficient. We report experimental results on a variety of CAD models and discuss various applications of the developed uniform offsetting method.

GENUS STATISTICS USING THE DELAUNAY TESSELLATION FIELD ESTIMATION METHOD. I. TESTS WITH THE MILLENNIUM SIMULATION AND THE SDSS DR7

We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogues analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.

Design of multi-beam antennas based on Epsilon-Near-Zero metamaterials

A novel Epsilon-Near-Zero (ENZ) metamaterial-assisted multi-beam antenna is presented. Simulation results show that the cylindrical wave emitted from a line source can be transformed to narrow beams through an ENZ metamaterial layer with a circular inner contour and a polygonal outer contour. The number of beams of the antenna can be controlled by adjusting the number of sidelines and the shape of the polygonal ENZ metamaterial layer. The 3dB bandwidth of the designed multi-beam antenna is 218MHz. Due to ENZ metamaterials may be found naturally at infrared and optical frequency band, comparing with optical transformation approach, by which space variant media is applied to the design of high-performance antenna, the ENZ metamaterial-assisted approach is more preferable.

Simplicity of polygon Wilson loops in $$ \mathcal{N} $$ = 4 SYM

Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory. Specifically, we concentrate on the remainder function R, obtained by subtracting the known ABDK/BDS ansatz from the Wilson loop. First, we consider a particular two-dimensional eight-point kinematics studied at strong coupling by Alday and Maldacena. We find numerical evidence that R is the same at weak and at strong coupling, up to an overall, coupling-dependent constant. This suggests a universality of the remainder function at strong and weak coupling for generic null polygonal Wilson loops, and therefore for arbitrary MHV amplitudes in N=4 super Yang-Mills. We analyse the consequences of this statement. We further consider regular n-gons, and find that the remainder function is linear in n at large n through numerical computations performed up to n=30. This reproduces a general feature of the corresponding strong-coupling result.

Automatic greenhouse delineation from QuickBird and Ikonos satellite images

The area of production under greenhouses has been in rapid growth in recent years, and at present there are over 500,000 ha scattered all over the world. Due to the vast amount of inputs (water, fertilizers, fuel, etc.) required, and outputs of various agricultural residues (vegetable waste, plastic sheeting, phytosanitary product containers, etc.), the impact of this type of production system to the environment is considerable in particular if pursued without a sound and sustainable territorial planning. Thus, very high-resolution images provided by satellites such as QuickBird and Ikonos can be useful to plan the expansion of the greenhouse crop-production system in a sustainable way, as well as to reduce the environmental impact of the actual greenhouses improving the inputs use efficiency (water, fertilizers, phytosanitary products, etc.). This work is focused on automated detection of the boundaries of greenhouses using for this purpose the classification results from very high-resolution multi-spectral images of Red, Green, Blue and Near Infrared (RGBNIR) from QuickBird and Ikonos satellites. First, a supervised Maximum Likelihood Classification (MLC) and an Extraction and Classification of Homogeneous Objects (ECHO) both using all the four bands were carried out with focus on plastic greenhouses detection. In the second step, the detected greenhouses according to the classification results were vectorized automatically to generate polygons with irregular borders. In the third step, the irregular contours of polygons were converted into straight lines using an algorithm based on the Hough transformation. The input parameters of this algorithm were obtained by two different procedures: calibration and pseudo-calibration. In the calibration process, the parameter set is obtained from a sample of greenhouses minimizing the area and perimeter errors. In the pseudo-calibration process, a parameter set is obtained for each greenhouse but it is a high time-consumer task. The calibration yielded 66.7% for QuickBird and 49% for Ikonos image of correct delineation of greenhouses. Pseudo-calibration improved success rate and reduced performance difference between the two types of images. The proposed algorithm is able to delineate any greenhouse contour if the proper parameters set is correctly derived.

Geothermal refraction problem for a 2-D body of polygonal cross-section buried in the two-layered earth

We present the exact boundary integral formulae  for calculation of the geothermal  anomaly due  to  a two  dimensional body  whose  thermal conductivity  is λT   and  its cross-section is bounded by the closed general  polygonal  contour.  This  body  is buried  in the  superficial layer  of conductivity λ1 . The  half-space  z > h with  the  thermal conductivity  λ2  is considered as  a substratum of models.   The  boundary integral technique for the solution  of this  problem requires  the application of logarithmic potential  terms  in infinite  series.   Numerical calculations  based  on derived  formulae  revealed  that the  surface anomaly heat flow reflects  the “topography”  mainly  of the upper  boundary of the perturbing body.   The derived  algorithm and the developed  numerical program enable calculations for a number of interesting models:  intrusions, protrusions of the substratum etc.

SU‐GG‐T‐475: Volumetric Analysis of Moving Structures in Radiation Treatment Planning

Purpose: The purpose of this study is to design and validate a set of metrics for volumetric analysis of moving structures in radiation treatment planning. Method and Materials: 4D CT based treatment planning in thoracic radiation oncology requires a specific set of metrics for quantitative comparison of moving treatment planning volumes. For each pair of reference and test volumes axial overestimation and underestimation areas as functions of z coordinate are defined as the areas bounded by the set of contours in each axial slice. The axial underestimation and overestimation volumes are defined as integrals of corresponding areas along the z‐coordinate. The sagittal and coronal under/overestimation areas and volumes are defined analogously. An efficient and robust implementation for polygonal contours was obtained by using the Delaunay triangulation. The above metrics were used to compare different methods for determination of demonstrable respiratory motion of the GTV (iGTV) in 4‐D CT datasets. 27 patients with non‐small‐cell lung cancer (stage I: 17, stage III: 10) who underwent 4‐D CT simulation were studied. The iGTV was determined manually by (a) combining the GTV contours from 10 phases (GTVAllPhases) (b) combining the GTV contours from two extreme respiratory phases (0 and 50%) (GTV2Phases) (c) contouring using the MIP (GTVMIP) and (d) contouring using the MIP followed by modification with visual verification in individual respiratory phases (GTVMIP_Modified). For comparison of different approaches, GTVAllPhases was used as the reference. Results: The proposed metrics were successfully applied to 27 patients to show that iGTV as determined from GTVMIP and GTV2Phases underestimated iGTV as determined from the reference GTVAllPhases. Modification of iGTV determined from GTVMIP based on visual verification of contours through each individual phase reduced the degree of underestimation. Conclusion: The constructed metrics provide very good tools for volumetric analysis of moving structures.

Constructing Triangular Meshes of Minimal Area

AbstractThis paper is concerned with the problem of constructing an aesthetically pleasing triangular mesh with a given closed polygonal contour in three dimensional space as boundary. Triangular meshes of minimal area from all triangular meshes with the prescribed boundary are suggested as the candidates for this problem. An iterative algorithm of constructing such a triangular mesh from a given polygonal boundary is presented. Experimental examples show that the proposed algorithm is reliable and effective. Some related theoretical issues, possible extensions and applications are also discussed.