A simple algorithm for computing positively weighted straight skeletons of monotone polygons.
Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter
2015-02-01
We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in [Formula: see text] time and [Formula: see text] space, where n denotes the number of vertices of the polygon.
Logarithmic solution to the line-polygon intersection problem. 127
International Nuclear Information System (INIS)
Siddon, R.L.; Barth, N.H.
1987-01-01
Algorithmic solution for a special case of the line - polygon intersection problem has been developed. The special case involves repeated solution to the problem where one point on the line is held fixed and the other allowed to vary. In addition, the fixed point on the line must lie outside the rectangle defined by the extrema of the polygon and varying point. In radiotherapy applications, the fixed point corresponds to the source of radiation, whereas the varying points refer to the grid of multiple calculation points. For smooth contours of 100-200 vertices, it is found that the new algorithm results in a CPU savings of approximately a factor of 3-5. 3 refs.; 4 figs
Franklin, Elda
1981-01-01
Reviews studies on the etiology of monotonism, the monotone being that type of uncertain or inaccurate singer who cannot vocally match pitches and who has trouble accurately reproducing even a familiar song. Neurological factors (amusia, right brain abnormalities), age, and sex differences are considered. (Author/SJL)
Hathout, Leith
2007-01-01
Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…
A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons
Energy Technology Data Exchange (ETDEWEB)
Graham, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Yao, J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-08-28
We present a method for computing the intersection and union of non- convex polyhedrons without decomposition in O(n log n) time, where n is the total number of faces of both polyhedrons. We include an accompanying Python package which addresses many of the practical issues associated with implementation and serves as a proof of concept. The key to the method is that by considering the edges of the original ob- jects and the intersections between faces as walking routes, we can e ciently nd the boundary of the intersection of arbitrary objects using directional walks, thus handling the concave case in a natural manner. The method also easily extends to plane slicing and non-convex polyhedron unions, and both the polyhedron and its constituent faces may be non-convex.
Scott, Paul
2006-01-01
A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…
Heckman, James J; Pinto, Rodrigo
2018-01-01
This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogenous agents and discrete-valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.
A simple algorithm for computing positively weighted straight skeletons of monotone polygons☆
Biedl, Therese; Held, Martin; Huber, Stefan; Kaaser, Dominik; Palfrader, Peter
2015-01-01
We study the characteristics of straight skeletons of monotone polygonal chains and use them to devise an algorithm for computing positively weighted straight skeletons of monotone polygons. Our algorithm runs in O(nlogn) time and O(n) space, where n denotes the number of vertices of the polygon. PMID:25648376
Department of the Interior — Shapefile Format –The fully intersected data is the atomic level of the PLSS that is similar to the coverage or the smallest pieces used to build the PLSS. Polygons...
A Min-max Relation for Monotone Path Systems in Simple Regions
DEFF Research Database (Denmark)
Cameron, Kathleen
1996-01-01
A monotone path system (MPS) is a finite set of pairwise disjointpaths (polygonal arcs) in the plane such that every horizontal line intersectseach of the paths in at most one point. We consider a simple polygon in thexy-plane which bounds the simple polygonal (closed) region D. Let T and B betwo...
2004-01-01
16 January 2004 Looking somewhat like a roadmap, this 3 km (1.9 mi) wide view of a cratered plain in the martian south polar region shows a plethora of cracks that form polygonal patterns. This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image is located near 78.9oS, 357.3oW. Polygons such as these, where they are found on Earth, would be indicators of the presence of subsurface ice. Whether the same is true for Mars is uncertain. What is certain is that modern, seasonal frost on the surface enhances the appearance of the polygons as the frost persists longer in the cracks than on adjacent plains. This southern springtime image is illuminated by sunlight from the upper left.
2005-01-01
18 August 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows dark-outlined polygons on a frost-covered surface in the south polar region of Mars. In summer, this surface would not be bright and the polygons would not have dark outlines--these are a product of the presence of seasonal frost. Location near: 77.2oS, 204.8oW Image width: width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Spring
Maldeghem, Hendrik
1998-01-01
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near...
Van Maldeghem, Hendrik
1998-01-01
Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the ...
International Nuclear Information System (INIS)
2000-01-01
In Russian, ''The Polygon'' stands for a nuclear test site of 19.000 square kilometers in Kazakhstan, used by the former Soviet Union for hundreds of nuclear tests from 1947 to 1991. This film looks at the legacy of what was once a top secret area, now abandoned, but still sparsely populated, and at the work to be done to detect and map the areas of elevated radiation levels
Probing convex polygons with X-rays
International Nuclear Information System (INIS)
Edelsbrunner, H.; Skiena, S.S.
1988-01-01
An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necessary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known
Monotone piecewise bicubic interpolation
International Nuclear Information System (INIS)
Carlson, R.E.; Fritsch, F.N.
1985-01-01
In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C 1 piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables
International Nuclear Information System (INIS)
Korshunov, A D
2003-01-01
Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years
Lu, Yanyan; Lien, Jyh-Ming; Ghosh, Mukulika; Amato, Nancy M.
2012-01-01
Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method called α-decomposition. The α-decomposition generates a space of decompositions parameterized by α, the diameter of a circle convolved with the input polygon. As we vary the value of α, some structural features appear and disappear quickly while others persist. Therefore, by analyzing the persistence of the features, we can determine better decompositions that are more robust to both geometrical and topological noises. © 2012 Elsevier Ltd. All rights reserved.
Lu, Yanyan
2012-08-01
Decomposing a shape into visually meaningful parts comes naturally to humans, but recreating this fundamental operation in computers has been shown to be difficult. Similar challenges have puzzled researchers in shape reconstruction for decades. In this paper, we recognize the strong connection between shape reconstruction and shape decomposition at a fundamental level and propose a method called α-decomposition. The α-decomposition generates a space of decompositions parameterized by α, the diameter of a circle convolved with the input polygon. As we vary the value of α, some structural features appear and disappear quickly while others persist. Therefore, by analyzing the persistence of the features, we can determine better decompositions that are more robust to both geometrical and topological noises. © 2012 Elsevier Ltd. All rights reserved.
Fair partitions of polygons: An elementary introduction
Indian Academy of Sciences (India)
In this paper we discuss only convex polygonal regions with finite number of sides. But we think this property holds ... trivial interest and have updated [9] into the present paper. 2. Proof of the conjecture N = .... surface have a proper intersection if they cut through each other either at a point or after being coincident in a finite ...
Scott, Paul
2006-01-01
A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.
Stephenson, Paul
2009-01-01
In order to find its circumference, Archimedes famously boxed the circle between two polygons. Ending the first of a series of articles (MT179) with an aside, Francis Lopez-Real reverses the situation to ask: Which polygons can be boxed between two circles? (The official term for such polygons is "bicentric".) The sides of these polygons are…
Colleu , Thomas; Morin , Luce; Pateux , Stéphane; Labit , Claude
2011-01-01
International audience; This paper presents a new representation called floating polygon soup for applications like 3DTV and FTV (Free Viewpoint Television). This representation is based on 3D polygons and takes as input MVD data. It extends the previously proposed polygon soup representation which is appropriate for both compression, transmission and rendering stages. The floating polygon soup conserves these advantages while also taking into account misalignments at the view synthesis stage...
Aichholzer, Oswin; Aurenhammer, Franz; Hurtado Díaz, Fernando Alfredo; Ramos, Pedro A.; Urrutia, J.
2009-01-01
We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.
Ergodicity of polygonal slap maps
International Nuclear Information System (INIS)
Del Magno, Gianluigi; Pedro Gaivão, José; Lopes Dias, João; Duarte, Pedro
2014-01-01
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflection laws. We study the absolutely continuous invariant probabilities (acips) of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps with more than one ergodic acip. (paper)
Knotting in stretched polygons
International Nuclear Information System (INIS)
Rensburg, E J Janse van; Orlandini, E; Tesi, M C; Whittington, S G
2008-01-01
The knotting in a lattice polygon model of ring polymers is examined when a stretching force is applied to the polygon. By examining the incidence of cut-planes in the polygon, we prove a pattern theorem in the stretching regime for large applied forces. This theorem can be used to examine the incidence of entanglements such as knotting and writhing. In particular, we prove that for arbitrarily large positive, but finite, values of the stretching force, the probability that a stretched polygon is knotted approaches 1 as the length of the polygon increases. In the case of writhing, we prove that for stretched polygons of length n, and for every function f(n)=o(√n), the probability that the absolute value of the mean writhe is less than f(n) approaches 0 as n → ∞, for sufficiently large values of the applied stretching force
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2012-01-01
Roč. 58, č. 3 (2012), s. 177-187 ISSN 0942-5616 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional support: RVO:67985840 Keywords : proof complexity * monotone sequent calculus Subject RIV: BA - General Mathematics Impact factor: 0.376, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/malq.201020071/full
Atmospheres of polygons and knotted polygons
International Nuclear Information System (INIS)
Janse Rensburg, E J Janse; Rechnitzer, A
2008-01-01
In this paper we define two statistics a + (ω) and a - (ω), the positive and negative atmospheres of a lattice polygon ω of fixed length n. These statistics have the property that (a + (ω))/(a - (ω)) = p n+2 /p n , where p n is the number of polygons of length n, counted modulo translations. We use the pivot algorithm to sample polygons and to compute the corresponding average atmospheres. Using these data, we directly estimate the growth constants of polygons in two and three dimensions. We find that μ=2.63805±0.00012 in two dimensions and μ=4.683980±0.000042±0.000067 in three dimensions, where the error bars are 67% confidence intervals, and the second error bar in the three-dimensional estimate of μ is an estimated systematic error. We also compute atmospheres of polygons of fixed knot type K sampled by the BFACF algorithm. We discuss the implications of our results and show that different knot types have atmospheres which behave dramatically differently at small values of n
Homotopic Polygonal Line Simplification
DEFF Research Database (Denmark)
Deleuran, Lasse Kosetski
This thesis presents three contributions to the area of polygonal line simplification, or simply line simplification. A polygonal path, or simply a path is a list of points with line segments between the points. A path can be simplified by morphing it in order to minimize some objective function...
2003-01-01
MGS MOC Release No. MOC2-357, 11 May 2003This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) picture shows a pattern of polygons on the floor of a northern plains impact crater. These landforms are common on crater floors at high latitudes on Mars. Similar polygons occur in the arctic and antarctic regions of Earth, where they indicate the presence and freeze-thaw cycling of ground ice. Whether the polygons on Mars also indicate water ice in the ground is uncertain. The image is located in a crater at 64.8oN, 292.7oW. Sunlight illuminates the scene from the lower left.
2003-01-01
MGS MOC Release No. MOC2-564, 4 December 2003This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows patterned ground, arranged in the form of polygons, on the undulating plains associated with ejecta from the Lyot impact crater on the martian northern plains. This picture was acquired in October 2003 and shows that the polygon margins are ridges with large boulders--shown here as dark dots--on them. On Earth, polygon patterns like this are created in arctic and antarctic regions where there is ice in the ground. The seasonal and longer-term cycles of freezing and thawing of the ice-rich ground cause these features to form over time. Whether the same is true for Mars is unknown. The polygons are located near 54.6oN, 326.6oW. The image covers an area 3 km (1.9 mi) wide and is illuminated from the lower left.
2005-01-01
26 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows polygonal patterned ground on a south high-latitude plain. The outlines of the polygons, like the craters and hills in this region, are somewhat enhanced by the presence of bright frost left over from the previous winter. On Earth, polygons at high latitudes would usually be attributed to the seasonal freezing and thawing cycles of ground ice. The origin of similar polygons on Mars is less certain, but might also be an indicator of ground ice. Location near: 75.3oS, 113.2oW Image width: width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Spring
Matching by Monotonic Tone Mapping.
Kovacs, Gyorgy
2018-06-01
In this paper, a novel dissimilarity measure called Matching by Monotonic Tone Mapping (MMTM) is proposed. The MMTM technique allows matching under non-linear monotonic tone mappings and can be computed efficiently when the tone mappings are approximated by piecewise constant or piecewise linear functions. The proposed method is evaluated in various template matching scenarios involving simulated and real images, and compared to other measures developed to be invariant to monotonic intensity transformations. The results show that the MMTM technique is a highly competitive alternative of conventional measures in problems where possible tone mappings are close to monotonic.
BIMOND3, Monotone Bivariate Interpolation
International Nuclear Information System (INIS)
Fritsch, F.N.; Carlson, R.E.
2001-01-01
1 - Description of program or function: BIMOND is a FORTRAN-77 subroutine for piecewise bi-cubic interpolation to data on a rectangular mesh, which reproduces the monotonousness of the data. A driver program, BIMOND1, is provided which reads data, computes the interpolating surface parameters, and evaluates the function on a mesh suitable for plotting. 2 - Method of solution: Monotonic piecewise bi-cubic Hermite interpolation is used. 3 - Restrictions on the complexity of the problem: The current version of the program can treat data which are monotone in only one of the independent variables, but cannot handle piecewise monotone data
FEMA DFIRM Panel Scheme Polygons
Minnesota Department of Natural Resources — This layer contains information about the Flood Insurance Rate Map (FIRM) panel areas. The spatial entities representing FIRM panels are polygons. The polygon for...
Near polygons and Fischer spaces
Brouwer, A.E.; Cohen, A.M.; Hall, J.I.; Wilbrink, H.A.
1994-01-01
In this paper we exploit the relations between near polygons with lines of size 3 and Fischer spaces to classify near hexagons with quads and with lines of size three. We also construct some infinite families of near polygons.
2005-01-01
3 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows polygons enhanced by subliming seasonal frost in the martian south polar region. Polygons similar to these occur in frozen ground at high latitudes on Earth, suggesting that perhaps their presence on Mars is also a sign that there is or once was ice in the shallow subsurface. The circular features are degraded meteor impact craters. Location near: 72.2oS, 310.3oW Image width: width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Spring
Optimal Monotone Drawings of Trees
He, Dayu; He, Xin
2016-01-01
A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists abpath P_{uw} in G that is monotone in some direction l_{uw}. (Namely, the order of the orthogonal projections of the vertices of P_{uw} on l_{uw} is the same as the order they appear in P_{uw}.) The problem of finding monotone drawings for trees has been studied in several recent papers. The main focus is to reduce the size of the drawing. Currently, the smallest drawi...
Nanopatterning by molecular polygons.
Jester, Stefan-S; Sigmund, Eva; Höger, Sigurd
2011-07-27
Molecular polygons with three to six sides and binary mixtures thereof form long-range ordered patterns at the TCB/HOPG interface. This includes also the 2D crystallization of pentagons. The results provide an insight into how the symmetry of molecules is translated into periodic structures.
2002-01-01
[figure removed for brevity, see original site] This jumble of eroded ridges and mesas occurs within Ares Vallis, one of the largest catastrophic outflow channels on the planet. Floods raged through this channel, portions of which are up to 25 km wide, pouring out into the Chryse Basin to the north. Close inspection of the THEMIS image reveals polygonal shapes on the floor of the channel system. Polygonal terrain on Mars is fairly common although the variety of forms and scales of the polygons suggests multiple modes of origin. Those in Ares Vallis resemble giant desiccation polygons that form in soils on Earth when a moist layer at depth drys out. While polygons can form in icy soils (permafrost) and even lava flows, their presence in a channel thought to have been carved by flowing water is at least consistent with a mode of origin that involved liquid water.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
DEFF Research Database (Denmark)
Marfelt, Mikkel Mouritz
2016-01-01
associated with intersectional research. The findings assist in positioning the proposed methodological framework within recent intersectional debates. Findings – The review shows a rise in intersectional publications since the birth of the “intersectionality” term in 1989. Moreover, the paper points to four...... oriented but still emphasizes stable concepts. Moreover, it does not give primacy to oppression. Finally, it adopts a critical stance on the nature of the macro, meso, and micro levels as dominant analytical perspectives. As a result, this paper focusses on the importance of intersectionality...
2008-01-01
This image shows a small-scale polygonal pattern in the ground near NASA's Phoenix Mars Lander. This pattern is similar in appearance to polygonal structures in icy ground in the arctic regions of Earth. Phoenix touched down on the Red Planet at 4:53 p.m. Pacific Time (7:53 p.m. Eastern Time), May 25, 2008, in an arctic region called Vastitas Borealis, at 68 degrees north latitude, 234 degrees east longitude. This image was acquired by the Surface Stereo Imager shortly after landing. On the Phoenix mission calendar, landing day is known as Sol 0, the first Martian day of the mission. The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.
PolyFit: Polygonal Surface Reconstruction from Point Clouds
Nan, Liangliang; Wonka, Peter
2017-01-01
We propose a novel framework for reconstructing lightweight polygonal surfaces from point clouds. Unlike traditional methods that focus on either extracting good geometric primitives or obtaining proper arrangements of primitives, the emphasis of this work lies in intersecting the primitives (planes only) and seeking for an appropriate combination of them to obtain a manifold polygonal surface model without boundary.,We show that reconstruction from point clouds can be cast as a binary labeling problem. Our method is based on a hypothesizing and selection strategy. We first generate a reasonably large set of face candidates by intersecting the extracted planar primitives. Then an optimal subset of the candidate faces is selected through optimization. Our optimization is based on a binary linear programming formulation under hard constraints that enforce the final polygonal surface model to be manifold and watertight. Experiments on point clouds from various sources demonstrate that our method can generate lightweight polygonal surface models of arbitrary piecewise planar objects. Besides, our method is capable of recovering sharp features and is robust to noise, outliers, and missing data.
PolyFit: Polygonal Surface Reconstruction from Point Clouds
Nan, Liangliang
2017-12-25
We propose a novel framework for reconstructing lightweight polygonal surfaces from point clouds. Unlike traditional methods that focus on either extracting good geometric primitives or obtaining proper arrangements of primitives, the emphasis of this work lies in intersecting the primitives (planes only) and seeking for an appropriate combination of them to obtain a manifold polygonal surface model without boundary.,We show that reconstruction from point clouds can be cast as a binary labeling problem. Our method is based on a hypothesizing and selection strategy. We first generate a reasonably large set of face candidates by intersecting the extracted planar primitives. Then an optimal subset of the candidate faces is selected through optimization. Our optimization is based on a binary linear programming formulation under hard constraints that enforce the final polygonal surface model to be manifold and watertight. Experiments on point clouds from various sources demonstrate that our method can generate lightweight polygonal surface models of arbitrary piecewise planar objects. Besides, our method is capable of recovering sharp features and is robust to noise, outliers, and missing data.
2005-01-01
14 April 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a typical view of polygon-cracked and pitted surfaces unique to western Utopia Planitia. No other place on Mars has this appearance. Some Mars scientists have speculated that ground ice may be responsible for these landforms. Location near: 42.3oN, 275.6oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Summer
2003-01-01
MGS MOC Release No. MOC2-339, 23 April 2003This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a pattern of polygonal cracks and aligned, elliptical pits in western Utopia Planitia. The picture covers an area about 3 km (about 1.9 mi) wide near 44.9oN, 274.7oW. Sunlight illuminates the scene from the left.
Monotonicity of social welfare optima
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Østerdal, Lars Peter Raahave
2010-01-01
This paper considers the problem of maximizing social welfare subject to participation constraints. It is shown that for an income allocation method that maximizes a social welfare function there is a monotonic relationship between the incomes allocated to individual agents in a given coalition...
Origin of giant Martian polygons
Mcgill, George E.; Hills, L. S.
1992-01-01
Extensive areas of the Martian northern plains in Utopia and Acidalia planitiae are characterized by 'polygonal terrane'. Polygonal terrane consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on earth. However, the Martian polygons are orders of magnitude larger than these potential earth analogues, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Plate-bending and finite element models indicate that shrinkage of desiccating sediment or cooling volcanics accompanied by differential compaction over buried topography can account for the stresses responsible for polygon troughs as well as the large size of the polygons. Although trough widths and depths relate primarily to shrinkage, the large scale of the polygonl pattern relates to the spacing between topographic elevations on the surface buried beneath polygonal terrane material. Geological relationships favor a sedimentary origin for polygonal terrane material, but our model is not dependent on the specific genesis. Our analysis also suggests that the polygons must have formed at a geologically rapid rate.
2003-01-01
MGS MOC Release No. MOC2-428, 21 July 2003This June 2003 Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a polygonal pattern developed in seasonal carbon dioxide frost in the martian southern hemisphere. The frost accumulated during the recent southern winter; it is now spring, and the carbon dioxide frost is subliming away. This image is located near 80.4oS, 200.2oW; it is illuminated by sunlight from the upper left, and covers an area 3 km (1.9 mi) across.
Casimir effect in hyperbolic polygons
International Nuclear Information System (INIS)
Ahmedov, H
2007-01-01
Using the point splitting regularization method and the trace formula for the spectra of quantum-mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two-dimensional hyperboloid we calculate the Casimir energy for massless scalar fields in hyperbolic polygons. The dependence of the vacuum energy on the number of vertices is established
Metric inequalities for polygons
Directory of Open Access Journals (Sweden)
Adrian Dumitrescu
2013-07-01
Full Text Available Let A1,A2,…,An be the vertices of a polygon with unit perimeter, that is Σi |Ai Ai+1|=1. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of pairwise squared distances among its vertices. In most cases such estimates on these sums in the literature were known only for convex polygons.In the second part, we turn to a problem of Braß regarding the maximum perimeter of a simplen-gon (n odd contained in a disk of unit radius. The problem was recently solved by Audet et al. 2009, who gave an exact formula. Here we present an alternative simpler proof of this formula. We then examine what happens if the simplicity condition is dropped, and obtain an exact formula for the maximum perimeter in this case as well.
2004-01-01
8 February 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a summertime scene in the south polar region of the red planet. A patch of bright frost--possibly water ice--is seen in the lower third of the image. Polygon patterns that have developed in the ice as it sublimes away can be seen; these are not evident in the defrosted surfaces, so they are thought to have formed in the frost. This image is located near 82.6oS, 352.5oW. Sunlight illuminates this scene from the upper left; the image covers an area 3 km (1.9 mi) wide.
Generalized monotone operators in Banach spaces
International Nuclear Information System (INIS)
Nanda, S.
1988-07-01
The concept of F-monotonicity was first introduced by Kato and this generalizes the notion of monotonicity introduced by Minty. The purpose of this paper is to define various types of F-monotonicities and discuss the relationships among them. (author). 6 refs
The average crossing number of equilateral random polygons
International Nuclear Information System (INIS)
Diao, Y; Dobay, A; Kusner, R B; Millett, K; Stasiak, A
2003-01-01
In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form (3/16)n ln n + O(n). A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type K can be described by a function of the form = a(n-n 0 )ln(n-n 0 ) + b(n-n 0 ) + c where a, b and c are constants depending on K and n 0 is the minimal number of segments required to form K. The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the profile of all closed walks. These points of intersection define the equilibrium length of K, i.e., the chain length n e (K) at which a statistical ensemble of configurations with given knot type K-upon cutting, equilibration and reclosure to a new knot type K'-does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration g >
Measuring Historical Coastal Change using GIS and the Change Polygon Approach
Smith, M.J.; Cromley, R.G.
2012-01-01
This study compares two automated approaches, the transect-from-baseline technique and a new change polygon method, for quantifying historical coastal change over time. The study shows that the transect-from-baseline technique is complicated by choice of a proper baseline as well as generating transects that intersect with each other rather than with the nearest shoreline. The change polygon method captures the full spatial difference between the positions of the two shorelines and average coastal change is the defined as the ratio of the net area divided by the shoreline length. Although then change polygon method is sensitive to the definition and measurement of shoreline length, the results are more invariant to parameter changes than the transect-from-baseline method, suggesting that the change polygon technique may be a more robust coastal change method. ?? 2012 Blackwell Publishing Ltd.
Alabama ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and freshwater fish species in Alabama. Vector polygons in this data set represent...
Maryland ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and freshwater fish species in Maryland. Vector polygons in this data...
Hawaii ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for reef, marine, estuarine, and native stream fish species in coastal Hawaii. Vector polygons in this data...
Hawaii ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of the U.S. Geological Survey 1:24,000 topographic maps and other map and digital data boundaries...
Alabama ESI: REPTILES (Reptile Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for threatened/endangered and rare reptiles in Alabama. Vector polygons in this data set represent the rare...
Alabama ESI: INVERT (Invertebrate Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species in Alabama. Vector polygons in this data set represent...
Virginia ESI: INVERT (Invertebrate Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and rare invertebrate species in Virginia. Vector polygons in this data set...
Control Point Generated PLS - polygons
Minnesota Department of Natural Resources — The Control Point Generated PLS layer contains line and polygon features to the 1/4 of 1/4 PLS section (approximately 40 acres) and government lot level. The layer...
Virginia ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Louisiana ESI: BIRDS (Bird Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for waterfowl species and shorebirds in coastal Louisiana. Vector polygons in this data set represent...
Model for polygonal hydraulic jumps
DEFF Research Database (Denmark)
Martens, Erik Andreas; Watanabe, Shinya; Bohr, Tomas
2012-01-01
We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard and co-workers [Nature (London) 392, 767 (1998); Nonlinearity 12, 1 (1999); Physica B 228, 1 (1996)], based on the known flow structure for the type-II hydraulic jumps with a "roller" (separation eddy...... nonhydrostatic pressure contributions from surface tension in light of recent observations by Bush and co-workers [J. Fluid Mech. 558, 33 (2006); Phys. Fluids 16, S4 (2004)]. The model can be analyzed by linearization around the circular state, resulting in a parameter relationship for nearly circular polygonal...... states. A truncated but fully nonlinear version of the model can be solved analytically. This simpler model gives rise to polygonal shapes that are very similar to those observed in experiments, even though surface tension is neglected, and the condition for the existence of a polygon with N corners...
Virginia ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and brackishwater fish species in Virginia. Vector polygons in this data...
Louisiana ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for freshwater (inland) fish species in coastal Louisiana. Vector polygons represent water-bodies and other...
Soils - Volusia County Soils (Polygons)
NSGIC Local Govt | GIS Inventory — Soils: 1:24000 SSURGO Map. Polygon boundaries of Soils in Volusia County, downloaded from SJRWMD and created by NRCS and SJRWMD. This data set is a digital version...
Invariant polygons in systems with grazing-sliding.
Szalai, R; Osinga, H M
2008-06-01
The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.
Inscribed polygons and Heron polynomials
International Nuclear Information System (INIS)
Varfolomeev, V V
2003-01-01
Heron's well-known formula expressing the area of a triangle in terms of the lengths of its sides is generalized in the following sense to polygons inscribed in a circle: it is proved that the area is an algebraic function of the lengths of the edges of the polygon. Similar results are proved for the diagonals and the radius of the circumscribed circle. The resulting algebraic equations are studied and elementary geometric applications of the algebraic results obtained are presented
Quantisation of monotonic twist maps
International Nuclear Information System (INIS)
Boasman, P.A.; Smilansky, U.
1993-08-01
Using an approach suggested by Moser, classical Hamiltonians are generated that provide an interpolating flow to the stroboscopic motion of maps with a monotonic twist condition. The quantum properties of these Hamiltonians are then studied in analogy with recent work on the semiclassical quantization of systems based on Poincare surfaces of section. For the generalized standard map, the correspondence with the usual classical and quantum results is shown, and the advantages of the quantum Moser Hamiltonian demonstrated. The same approach is then applied to the free motion of a particle on a 2-torus, and to the circle billiard. A natural quantization condition based on the eigenphases of the unitary time--development operator is applied, leaving the exact eigenvalues of the torus, but only the semiclassical eigenvalues for the billiard; an explanation for this failure is proposed. It is also seen how iterating the classical map commutes with the quantization. (authors)
Zernike-like systems in polygons and polygonal facets.
Ferreira, Chelo; López, José L; Navarro, Rafael; Sinusía, Ester Pérez
2015-07-20
Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit disk. In [Opt. Lett.32, 74 (2007)10.1364/OL.32.000074OPLEDP0146-9592] we introduced a new Zernike basis for elliptic and annular optical apertures based on an appropriate diffeomorphism between the unit disk and the ellipse and the annulus. Here, we present a generalization of this Zernike basis for a variety of important optical apertures, paying special attention to polygons and the polygonal facets present in segmented mirror telescopes. On the contrary to ad hoc solutions, most of them based on the Gram-Smith orthonormalization method, here we consider a piecewise diffeomorphism that transforms the unit disk into the polygon under consideration. We use this mapping to define a Zernike-like orthonormal system over the polygon. We also consider ensembles of polygonal facets that are essential in the design of segmented mirror telescopes. This generalization, based on in-plane warping of the basis functions, provides a unique solution, and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both the general form and the explicit expressions for a typical example of telescope optical aperture are provided.
Tessellating the Sphere with Regular Polygons
Soto-Johnson, Hortensia; Bechthold, Dawn
2004-01-01
Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.
On the size of monotone span programs
Nikov, V.S.; Nikova, S.I.; Preneel, B.; Blundo, C.; Cimato, S.
2005-01-01
Span programs provide a linear algebraic model of computation. Monotone span programs (MSP) correspond to linear secret sharing schemes. This paper studies the properties of monotone span programs related to their size. Using the results of van Dijk (connecting codes and MSPs) and a construction for
Edit Distance to Monotonicity in Sliding Windows
DEFF Research Database (Denmark)
Chan, Ho-Leung; Lam, Tak-Wah; Lee, Lap Kei
2011-01-01
Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space complexity of estimating the edit distance to monotonicity of a ...
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
Approximation algorithms for guarding holey polygons ...
African Journals Online (AJOL)
Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...
Triangulating and guarding realistic polygons
Aloupis, G.; Bose, P.; Dujmovic, V.; Gray, C.M.; Langerman, S.; Speckmann, B.
2008-01-01
We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards in the interior of the object. In this abstract, we describe a simple algorithm for triangulating k-guardable polygons. Our algorithm, which is easily implementable, takes
Triangulating and guarding realistic polygons
Aloupis, G.; Bose, P.; Dujmovic, V.; Gray, C.M.; Langerman, S.; Speckmann, B.
2014-01-01
We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards. We show that k-guardable polygons generalize two previously identified classes of realistic input. Following this, we give two simple algorithms for triangulating
Rotating Polygons on a Fluid Surface
DEFF Research Database (Denmark)
Bohr, Tomas; Jansson, Thomas; Haspang, Martin
spontaneously and the surface can take the shape of a rigidly rotating polygon. With water we have observed polygons with up to 6 corners. The rotation speed of the polygons does not coincide with that of the plate, but it is often mode-locked, such that the polygon rotates by one corner for each complete...... and R. Miraghaie, ”Symmetry breaking in free-surface cylinder flows”, J. Fluid Mech., 502, 99 (2004)). The polygons occur at much larger Reynolds numbers, for water around 500.000. Correspondingly, the dependence on viscosity is rather small....
Polygons, Stars, and Clusters; an Investigation of Polygon Displays
1988-01-01
variables were chosen, nine in each case , to give reasonably complex polygons without being too complex. I have seen no reported studies of the relation...Pont. Catalina C Datsun 210, Toyota Corolla, Dodge Colt, Honda Civic, Mazda GLC, Subaru, Ford Fiesta, Plym. Champ Figure 6. Clusters on the basis of...Merc. Marquis, Pont. Catalina, Pont. Grand Prix C Datsun 210, Toyota Corolla, Dodge Colt, Honda Civic, Mazda GLC, Subaru, Ford Fiesta, Plym. Champ
2015-01-01
There are many types of intersections in the Netherlands. In an inherently safe road traffic system, however, the number of intersection types needs to be limited, depending on the road types that intersect. The desired types of intersections do not always correspond with the recommendations in the
Directory of Open Access Journals (Sweden)
Chakkrid Klin-eam
2009-01-01
Full Text Available We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space.
Random walks and polygons in tight confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Ziegler, U
2014-01-01
We discuss the effect of confinement on the topology and geometry of tightly confined random walks and polygons. Here the walks and polygons are confined in a sphere of radius R ≥ 1/2 and the polygons are equilateral with n edges of unit length. We illustrate numerically that for a fixed length of random polygons the knotting probability increases to one as the radius decreases to 1/2. We also demonstrate that for random polygons (walks) the curvature increases to πn (π(n – 1)) as the radius approaches 1/2 and that the torsion decreases to ≈ πn/3 (≈ π(n – 1)/3). In addition we show the effect of length and confinement on the average crossing number of a random polygon
Lucchitta, B. K.
1984-01-01
Polygonal-fracture patterns on the martian surface were discovered on Viking Orbiter images. The polygons are 2-20 km in diameter, much larger than those of known patterned ground on Earth. New observations show, however, that polygons exist on Mars that have diameters similar to those of ice-wedge polygons on Earth (generally a few meters to more than 100 m). Various explanations for the origin of these crustal features are examined; seasonal desiccation and thermal-contraction cracking in ice-rich ground. It is difficult to ascertain whether the polygons are forming today or are relics from the past. The crispness of some crack suggests a recent origin. On the other hand the absence of upturned edges (indicating actively forming ice wedges), the locally disintegrating ground, and a few possible superposed rayed craters indicate that the polygons are not forming at the present.
Multipartite classical and quantum secrecy monotones
International Nuclear Information System (INIS)
Cerf, N.J.; Massar, S.; Schneider, S.
2002-01-01
In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or public classical communication. These 'secrecy monotones' therefore measure how much secret correlation is shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalizations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monotones allows us to show that in multipartite quantum cryptography the parties must make irreversible choices about which multipartite correlations they want to obtain. Secrecy monotones can be extended to the quantum domain and are then defined on density matrices. We illustrate this generalization by considering tripartite quantum cryptography based on the Greenberger-Horne-Zeilinger state. We show that before carrying out measurements on the state, the parties must make an irreversible decision about what probability distribution they want to obtain
Meter-scale thermal contraction crack polygons on the nucleus of comet 67P/Churyumov-Gerasimenko
Auger, A.-T.; Groussin, O.; Jorda, L.; El-Maarry, M. R.; Bouley, S.; Séjourné, A.; Gaskell, R.; Capanna, C.; Davidsson, B.; Marchi, S.; Höfner, S.; Lamy, P. L.; Sierks, H.; Barbieri, C.; Rodrigo, R.; Koschny, D.; Rickman, H.; Keller, H. U.; Agarwal, J.; A'Hearn, M. F.; Barucci, M. A.; Bertaux, J.-L.; Bertini, I.; Cremonese, G.; Da Deppo, V.; Debei, S.; De Cecco, M.; Fornasier, S.; Fulle, M.; Gutiérrez, P. J.; Güttler, C.; Hviid, S.; Ip, W.-H.; Knollenberg, J.; Kramm, J.-R.; Kührt, E.; Küppers, M.; Lara, L. M.; Lazzarin, M.; Lopez Moreno, J. J.; Marzari, F.; Massironi, M.; Michalik, H.; Naletto, G.; Oklay, N.; Pommerol, A.; Sabau, L.; Thomas, N.; Tubiana, C.; Vincent, J.-B.; Wenzel, K.-P.
2018-02-01
We report on the detection and characterization of more than 6300 polygons on the surface of the nucleus of comet 67P/Churyumov-Gerasimenko, using images acquired by the OSIRIS camera onboard Rosetta between August 2014 and March 2015. They are found in consolidated terrains and grouped in localized networks. They are present at all latitudes (from North to South) and longitudes (head, neck, and body), sometimes on pit walls or following lineaments. About 1.5% of the observed surface is covered by polygons. Polygons have an homogeneous size across the nucleus, with 90% of them in the size range 1 - 5 m and a mean size of 3.0 ± 1.4 m. They show different morphologies, depending on the width and depth of their trough. They are found in networks with 3- or 4-crack intersection nodes. The polygons observed on 67P are consistent with thermal contraction crack polygons formed by the diurnal or seasonal temperature variations in a hard (MPa) and consolidated sintered layer of water ice, located a few centimeters below the surface. Our thermal analysis shows an evolution of thermal contraction crack polygons according to the local thermal environment, with more evolved polygons (i.e. deeper and larger troughs) where the temperature and the diurnal and seasonal temperature range are the highest. Thermal contraction crack polygons are young surface morphologies that probably formed after the injection of 67P in the inner solar system, typically 100,000 years ago, and could be as young as a few orbital periods, following the decreasing of its perihelion distance in 1959 from 2.7 to 1.3 a.u. Meter scale thermal contraction crack polygons should be common features on the nucleus of Jupiter family comets.
Spatial database for intersections.
2015-08-01
Deciding which intersections in the state of Kentucky warrant safety improvements requires a comprehensive inventory : with information on every intersection in the public roadway network. The Kentucky Transportation Cabinet (KYTC) : had previously c...
Parcels and Land Ownership - Volusia County Parcels (Polygons)
NSGIC Local Govt | GIS Inventory — Parcel Ownership Polygon Layer: Polygons showing property ownership created from the "master" subdivision base map for Volusia County. Multiple lots and parcels...
Entanglement complexity of semiflexible lattice polygons
International Nuclear Information System (INIS)
Orlandini, E; Tesi, M C; Whittington, S G
2005-01-01
We use Monte Carlo methods to study knotting in polygons on the simple cubic lattice with a stiffness fugacity. We investigate how the knot probability depends on stiffness and how the relative frequency of trefoils and figure eight knots changes as the stiffness changes. In addition, we examine the effect of stiffness on the writhe of the polygons. (letter to the editor)
Computing nonsimple polygons of minimum perimeter
Fekete, S.P.; Haas, A.; Hemmer, M.; Hoffmann, M.; Kostitsyna, I.; Krupke, D.; Maurer, F.; Mitchell, J.S.B.; Schmidt, A.; Schmidt, C.; Troegel, J.
2018-01-01
We consider the Minimum Perimeter Polygon Problem (MP3): for a given set V of points in the plane, find a polygon P with holes that has vertex set V , such that the total boundary length is smallest possible. The MP3 can be considered a natural geometric generalization of the Traveling Salesman
Kink-free deformations of polygons
Vegter, Gert
1989-01-01
We consider a discrete version of the Whitney-Graustein theorem concerning regular equivalence of closed curves. Two regular polygons P and P’, i.e. polygons without overlapping adjacent edges, are called regularly equivalent if there is a continuous one-parameter family Ps, 0 ≤ s ≤ 1, of regular
Accelerating Generalized Polygon Beams and Their Propagation
International Nuclear Information System (INIS)
Zhang Yun-Tian; Zhang Zhi-Gang; Cheng Teng; Zhang Qing-Chuan; Wu Xiao-Ping
2015-01-01
Accelerating beams with intensity cusps and exotic topological properties are drawing increasing attention as they have extensive uses in many intriguing fields. We investigate the structural features of accelerating polygon beams, show their generalized mathematical form theoretically, and discuss the even-numbered polygon beams. Furthermore, we also carry out the experiment and observe the intensity evolution during their propagation
Monotonicity and bounds on Bessel functions
Directory of Open Access Journals (Sweden)
Larry Landau
2000-07-01
Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.
New concurrent iterative methods with monotonic convergence
Energy Technology Data Exchange (ETDEWEB)
Yao, Qingchuan [Michigan State Univ., East Lansing, MI (United States)
1996-12-31
This paper proposes the new concurrent iterative methods without using any derivatives for finding all zeros of polynomials simultaneously. The new methods are of monotonic convergence for both simple and multiple real-zeros of polynomials and are quadratically convergent. The corresponding accelerated concurrent iterative methods are obtained too. The new methods are good candidates for the application in solving symmetric eigenproblems.
INTERSECTIONAL DISCRIMINATION AGAINST CHILDREN
DEFF Research Database (Denmark)
Ravnbøl, Camilla Ida
This paper adds a perspective to existing research on child protection by engaging in a debate on intersectional discrimination and its relationship to child protection. The paper has a twofold objective, (1) to further establish intersectionality as a concept to address discrimination against...... children, and (2) to illustrate the importance of addressing intersectionality within rights-based programmes of child protection....
Perceptually stable regions for arbitrary polygons.
Rocha, J
2003-01-01
Zou and Yan have recently developed a skeletonization algorithm of digital shapes based on a regularity/singularity analysis; they use the polygon whose vertices are the boundary pixels of the image to compute a constrained Delaunay triangulation (CDT) in order to find local symmetries and stable regions. Their method has produced good results but it is slow since its complexity depends on the number of contour pixels. This paper presents an extension of their technique to handle arbitrary polygons, not only polygons of short edges. Consequently, not only can we achieve results as good as theirs for digital images, but we can also compute skeletons of polygons of any number of edges. Since we can handle polygonal approximations of figures, the skeletons are more resilient to noise and faster to process.
Does a point lie inside a polygon
International Nuclear Information System (INIS)
Milgram, M.S.
1988-01-01
A superficially simple problem in computational geometry is that of determining whether a query point P lies in the interior of a polygon if it lies in the polygon's plane. Answering this question is often required when tracking particles in a Monte Carlo program; it is asked frequently and an efficient algorithm is crucial. Littlefield has recently rediscovered Shimrat's algorithm, while in separate works, Wooff, Preparata and Shamos and Mehlhorn, as well as Yamaguchi, give other algorithms. A practical algorithm answering this question when the polygon's plane is skewed in space is not immediately evident from most of these methods. Additionally, all but one fails when two sides extend to infinity (open polygons). In this paper the author review the above methods and present a new, efficient algorithm, valid for all convex polygons, open or closed, and topologically connected in n-dimensional space (n ≥ 2)
Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons
Bae, Sang Won; Shin, Chan-Su; Vigneron, Antoine E.
2016-01-01
We establish tight bounds for beacon-based coverage problems. In particular, we show that $$\\lfloor \\frac{n}{6} \\rfloor $$⌊n6⌋ beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes $$\\lfloor \\frac{n+4}{8} \\rfloor $$⌊n+48⌋. We also present an optimal linear-time algorithm for computing the beacon kernel of P.
Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons
Bae, Sang Won
2016-03-21
We establish tight bounds for beacon-based coverage problems. In particular, we show that $$\\\\lfloor \\\\frac{n}{6} \\ floor $$⌊n6⌋ beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes $$\\\\lfloor \\\\frac{n+4}{8} \\ floor $$⌊n+48⌋. We also present an optimal linear-time algorithm for computing the beacon kernel of P.
Stretched polygons in a lattice tube
Energy Technology Data Exchange (ETDEWEB)
Atapour, M [Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3 (Canada); Soteros, C E [Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5E6 (Canada); Whittington, S G [Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6 (Canada)], E-mail: atapour@mathstat.yorku.ca, E-mail: soteros@math.usask.ca, E-mail: swhittin@chem.utoronto.ca
2009-08-14
We examine the topological entanglements of polygons confined to a lattice tube and under the influence of an external tensile force f. The existence of the limiting free energy for these so-called stretched polygons is proved and then, using transfer matrix arguments, a pattern theorem for stretched polygons is proved. Note that the tube constraint allows us to prove a pattern theorem for any arbitrary value of f, while without the tube constraint it has so far only been proved for large values of f. The stretched polygon pattern theorem is used first to show that the average span per edge of a randomly chosen n-edge stretched polygon approaches a positive value, non-decreasing in f, as n {yields} {infinity}. We then show that the knotting probability of an n-edge stretched polygon confined to a tube goes to one exponentially as n {yields} {infinity}. Thus as n {yields} {infinity} when polygons are influenced by a force f, no matter its strength or direction, topological entanglements, as defined by knotting, occur with high probability. (fast track communication)
Stretched polygons in a lattice tube
International Nuclear Information System (INIS)
Atapour, M; Soteros, C E; Whittington, S G
2009-01-01
We examine the topological entanglements of polygons confined to a lattice tube and under the influence of an external tensile force f. The existence of the limiting free energy for these so-called stretched polygons is proved and then, using transfer matrix arguments, a pattern theorem for stretched polygons is proved. Note that the tube constraint allows us to prove a pattern theorem for any arbitrary value of f, while without the tube constraint it has so far only been proved for large values of f. The stretched polygon pattern theorem is used first to show that the average span per edge of a randomly chosen n-edge stretched polygon approaches a positive value, non-decreasing in f, as n → ∞. We then show that the knotting probability of an n-edge stretched polygon confined to a tube goes to one exponentially as n → ∞. Thus as n → ∞ when polygons are influenced by a force f, no matter its strength or direction, topological entanglements, as defined by knotting, occur with high probability. (fast track communication)
A note on monotone real circuits
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Pudlák, Pavel
2018-01-01
Roč. 131, March (2018), s. 15-19 ISSN 0020-0190 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : computational complexity * monotone real circuit * Karchmer-Wigderson game Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.748, year: 2016 http ://www.sciencedirect.com/science/article/pii/S0020019017301965?via%3Dihub
A note on monotone real circuits
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Pudlák, Pavel
2018-01-01
Roč. 131, March (2018), s. 15-19 ISSN 0020-0190 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : computational complexity * monotone real circuit * Karchmer-Wigderson game Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.748, year: 2016 http://www.sciencedirect.com/science/article/pii/S0020019017301965?via%3Dihub
Polygons on a rotating fluid surface
DEFF Research Database (Denmark)
Jansson, Thomas R.N.; Haspang, Martin P.; Jensen, Kåre H.
2006-01-01
We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously break the axial symmetry and assume the form of a polygon...... rotating rigidly with a speed different from that of the plate. With water, we have observed polygons with up to 6 corners. It has been known for many years that such flows are prone to symmetry breaking, but apparently the polygonal surface shapes have never been observed. The creation of rotating...
Federal Geographic Data Committee — The SMA implementation is comprised of one feature dataset, with several polygon feature classes, rather than a single feature class. SurfaceManagementAgency: The...
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Hundsdorfer, W.; Mozartova, A.; Spijker, M. N.
2011-01-01
In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many
Columbia River ESI: INVERT (Invertebrate Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for clams, oysters, crabs, and other invertebrate species in Columbia River. Vector polygons in this data...
Louisiana ESI: REPTILES (Reptile and Amphibian Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for reptiles and amphibians in coastal Louisiana. Vector polygons represent reptile and amphibian habitats,...
Western Alaska ESI: BIOINDEX (Biological Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of the 1:250,000 map boundaries used in the creation of the Environmental Sensitivity Index (ESI)...
Comic image understanding based on polygon detection
Li, Luyuan; Wang, Yongtao; Tang, Zhi; Liu, Dong
2013-01-01
Comic image understanding aims to automatically decompose scanned comic page images into storyboards and then identify the reading order of them, which is the key technique to produce digital comic documents that are suitable for reading on mobile devices. In this paper, we propose a novel comic image understanding method based on polygon detection. First, we segment a comic page images into storyboards by finding the polygonal enclosing box of each storyboard. Then, each storyboard can be represented by a polygon, and the reading order of them is determined by analyzing the relative geometric relationship between each pair of polygons. The proposed method is tested on 2000 comic images from ten printed comic series, and the experimental results demonstrate that it works well on different types of comic images.
Western Alaska ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all the hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Columbia River ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and freshwater fish species in Columbia River. Vector polygons in this...
Infinite genus surfaces and irrational polygonal billiards
Valdez, Ferrán
2009-01-01
We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.
Western Alaska ESI: LAKES (Lake Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing lakes and land masses used in the creation of the Environmental Sensitivity Index (ESI) for Western Alaska. The...
Western Alaska ESI: HYDRO (Land Mass Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing coastal hydrography that defines the primary land masses used in the creation of the Environmental Sensitivity...
Southeast Alaska ESI: BIRDS (Bird Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for waterfowl in Southeast Alaska. Vector polygons in this data set represent locations of foraging and rafting...
Southeast Alaska ESI: MGT (Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains management area data for National Parks, Wildlife Refuges, and areas designated as Critical Habitat in Southeast Alaska. Vector polygons in...
Western Alaska ESI: MGT (Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains management area data for Designated Critical Habitats, Wildlife Refuges, Wild and Scenic Rivers, and State Parks. Vector polygons in this data...
From Newton's bucket to rotating polygons
DEFF Research Database (Denmark)
Bach, B.; Linnartz, E. C.; Vested, Malene Louise Hovgaard
2014-01-01
We present an experimental study of 'polygons' forming on the free surface of a swirling water flow in a partially filled cylindrical container. In our set-up, we rotate the bottom plate and the cylinder wall with separate motors. We thereby vary rotation rate and shear strength independently...... and move from a rigidly rotating 'Newton's bucket' flow to one where bottom and cylinder wall are rotating oppositely and the surface is strongly turbulent but flat on average. Between those two extremes, we find polygonal states for which the rotational symmetry is spontaneously broken. We investigate...... the phase diagram spanned by the two rotational frequencies at a given water filling height and find polygons in a regime, where the two frequencies are sufficiently different and, predominantly, when they have opposite signs. In addition to the extension of the family of polygons found with the stationary...
Hawaii ESI: REPTILES (Reptile and Amphibian Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for threatened/endangered sea turtles in coastal Hawaii. Vector polygons in this data set represent sea...
Virginia ESI: MGT (Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains boundaries for management areas, national parks, state and local parks, and wildlife refuges in Virginia. Vector polygons in this data set...
Western Alaska ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and anadromous fish species in Western Alaska. Vector polygons in this data set...
Columbia River ESI: MGT (Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive human-use data for Wildlife Refuges, National Forests, and State Parks for the Columbia River area. Vector polygons in this data set...
Louisiana ESI: MGT (Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains boundaries for managed lands in coastal Louisiana. Vector polygons in this data set represent the management areas. Location-specific type and...
Louisiana ESI: PARISH (Parish Management Area Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains boundaries for parishes in coastal Louisiana. Vector polygons in this data set represent parish management areas. Location-specific type and...
Virginia ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Virginia. The...
Southeast Alaska ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for estuarine, benthic, and pelagic fish in Southeast Alaska. Vector polygons in this data set represent locations of...
Anisotropic rectangular metric for polygonal surface remeshing
Pellenard, Bertrand
2013-06-18
We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity.
Anisotropic rectangular metric for polygonal surface remeshing
Pellenard, Bertrand; Morvan, Jean-Marie; Alliez, Pierre
2013-01-01
We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity.
Testing Manifest Monotonicity Using Order-Constrained Statistical Inference
Tijmstra, Jesper; Hessen, David J.; van der Heijden, Peter G. M.; Sijtsma, Klaas
2013-01-01
Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores,…
Generating equilateral random polygons in confinement II
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2012-01-01
In this paper we continue an earlier study (Diao et al 2011 J. Phys. A: Math. Theor. 44 405202) on the generation algorithms of random equilateral polygons confined in a sphere. Here, the equilateral random polygons are rooted at the center of the confining sphere and the confining sphere behaves like an absorbing boundary. One way to generate such a random polygon is the accept/reject method in which an unconditioned equilateral random polygon rooted at origin is generated. The polygon is accepted if it is within the confining sphere, otherwise it is rejected and the process is repeated. The algorithm proposed in this paper offers an alternative to the accept/reject method, yielding a faster generation process when the confining sphere is small. In order to use this algorithm effectively, a large, reusable data set needs to be pre-computed only once. We derive the theoretical distribution of the given random polygon model and demonstrate, with strong numerical evidence, that our implementation of the algorithm follows this distribution. A run time analysis and a numerical error estimate are given at the end of the paper. (paper)
Control of grinding polygonal surfaces
Directory of Open Access Journals (Sweden)
Юрій Володимирович Петраков
2017-12-01
Full Text Available Grinding of non-round surfaces, in particular polygonal surfaces of dies, is characterized by substantial non stationary. At different sections of the profile, the change in the main characteristic (Material Removal Rate – MRR process reaches tens of times. To stabilize the grinding process, it is recommended to control the spindle speed of the workpiece CNC grinding machine. Created software that allows to design the control program on the basis of mathematical model of the system. The determination of MRR is realized automatically in the simulation of the grinding process which uses the algorithm developed for solving problems in geometric interaction of the workpiece and the wheel. In forming the control program is possible takes into account the limitations on the maximum circumferential force of cutting, and the maximum allowable acceleration of the machine spindle. Practice has shown that full stabilization is not obtained, even though the performance is increased more than 2 times, while ensuring the quality of the surface. The developed block diagram of the grinding process can serve as a basis for further improvement in the solution of dynamic problems.
Monotone Comparative Statics for the Industry Composition
DEFF Research Database (Denmark)
Laugesen, Anders Rosenstand; Bache, Peter Arendorf
2015-01-01
We let heterogeneous firms face decisions on a number of complementary activities in a monopolistically-competitive industry. The endogenous level of competition and selection regarding entry and exit of firms introduces a wedge between monotone comparative statics (MCS) at the firm level and MCS...... for the industry composition. The latter phenomenon is defined as first-order stochastic dominance shifts in the equilibrium distributions of all activities across active firms. We provide sufficient conditions for MCS at both levels of analysis and show that we may have either type of MCS without the other...
EJWS retrospective on intersectionality
Davis, K.E.; Zarkov, Dubravka
2017-01-01
The EJWS has been at the forefront of debates about intersectionality in Europe. In the past two decades, the journal has published countless articles on intersectionality as theory, methodology, and political framework for doing critical feminist research. We have selected some of these articles
The Monotonicity Puzzle: An Experimental Investigation of Incentive Structures
Directory of Open Access Journals (Sweden)
Jeannette Brosig
2010-05-01
Full Text Available Non-monotone incentive structures, which - according to theory - are able to induce optimal behavior, are often regarded as empirically less relevant for labor relationships. We compare the performance of a theoretically optimal non-monotone contract with a monotone one under controlled laboratory conditions. Implementing some features relevant to real-world employment relationships, our paper demonstrates that, in fact, the frequency of income-maximizing decisions made by agents is higher under the monotone contract. Although this observed behavior does not change the superiority of the non-monotone contract for principals, they do not choose this contract type in a significant way. This is what we call the monotonicity puzzle. Detailed investigations of decisions provide a clue for solving the puzzle and a possible explanation for the popularity of monotone contracts.
Generating equilateral random polygons in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2011-01-01
One challenging problem in biology is to understand the mechanism of DNA packing in a confined volume such as a cell. It is known that confined circular DNA is often knotted and hence the topology of the extracted (and relaxed) circular DNA can be used as a probe of the DNA packing mechanism. However, in order to properly estimate the topological properties of the confined circular DNA structures using mathematical models, it is necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths that are confined in a volume such as a sphere of certain fixed radius. Finding efficient algorithms that properly sample the space of such confined equilateral random polygons is a difficult problem. In this paper, we propose a method that generates confined equilateral random polygons based on their probability distribution. This method requires the creation of a large database initially. However, once the database has been created, a confined equilateral random polygon of length n can be generated in linear time in terms of n. The errors introduced by the method can be controlled and reduced by the refinement of the database. Furthermore, our numerical simulations indicate that these errors are unbiased and tend to cancel each other in a long polygon. (paper)
Minimal knotted polygons in cubic lattices
International Nuclear Information System (INIS)
Van Rensburg, E J Janse; Rechnitzer, A
2011-01-01
In this paper we examine numerically the properties of minimal length knotted lattice polygons in the simple cubic, face-centered cubic, and body-centered cubic lattices by sieving minimal length polygons from a data stream of a Monte Carlo algorithm, implemented as described in Aragão de Carvalho and Caracciolo (1983 Phys. Rev. B 27 1635), Aragão de Carvalho et al (1983 Nucl. Phys. B 215 209) and Berg and Foester (1981 Phys. Lett. B 106 323). The entropy, mean writhe, and mean curvature of minimal length polygons are computed (in some cases exactly). While the minimal length and mean curvature are found to be lattice dependent, the mean writhe is found to be only weakly dependent on the lattice type. Comparison of our results to numerical results for the writhe obtained elsewhere (see Janse van Rensburg et al 1999 Contributed to Ideal Knots (Series on Knots and Everything vol 19) ed Stasiak, Katritch and Kauffman (Singapore: World Scientific), Portillo et al 2011 J. Phys. A: Math. Theor. 44 275004) shows that the mean writhe is also insensitive to the length of a knotted polygon. Thus, while these results for the mean writhe and mean absolute writhe at minimal length are not universal, our results demonstrate that these values are quite close the those of long polygons regardless of the underlying lattice and length
Generalized convexity, generalized monotonicity recent results
Martinez-Legaz, Juan-Enrique; Volle, Michel
1998-01-01
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized conve...
Two generalizations of column-convex polygons
International Nuclear Information System (INIS)
Feretic, Svjetlan; Guttmann, Anthony J
2009-01-01
Column-convex polygons were first counted by area several decades ago, and the result was found to be a simple, rational, generating function. In this work we generalize that result. Let a p-column polyomino be a polyomino whose columns can have 1, 2, ..., p connected components. Then column-convex polygons are equivalent to 1-convex polyominoes. The area generating function of even the simplest generalization, namely 2-column polyominoes, is unlikely to be solvable. We therefore define two classes of polyominoes which interpolate between column-convex polygons and 2-column polyominoes. We derive the area generating functions of those two classes, using extensions of existing algorithms. The growth constants of both classes are greater than the growth constant of column-convex polyominoes. Rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis.
Steady state of tapped granular polygons
International Nuclear Information System (INIS)
Carlevaro, Carlos M; Pugnaloni, Luis A
2011-01-01
The steady state packing fraction of a tapped granular bed is studied for different grain shapes via a discrete element method. Grains are monosized regular polygons, from triangles to icosagons. Comparisons with disc packings show that the steady state packing fraction as a function of the tapping intensity presents the same general trends in polygon packings. However, better packing fractions are obtained, as expected, for shapes that can tessellate the plane (triangles, squares and hexagons). In addition, we find a sharp transition for packings of polygons with more than 13 vertices signaled by a discontinuity in the packing fraction at a particular tapping intensity. Density fluctuations for most shapes are consistent with recent experimental findings in disc packing; however, a peculiar behavior is found for triangles and squares
Polygons on a rotating fluid surface.
Jansson, Thomas R N; Haspang, Martin P; Jensen, Kåre H; Hersen, Pascal; Bohr, Tomas
2006-05-05
We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously break the axial symmetry and assume the form of a polygon rotating rigidly with a speed different from that of the plate. With water, we have observed polygons with up to 6 corners. It has been known for many years that such flows are prone to symmetry breaking, but apparently the polygonal surface shapes have never been observed. The creation of rotating internal waves in a similar setup was observed for much lower rotation rates, where the free surface remains essentially flat [J. M. Lopez, J. Fluid Mech. 502, 99 (2004). We speculate that the instability is caused by the strong azimuthal shear due to the stationary walls and that it is triggered by minute wobbling of the rotating plate.
Exact generating function for 2-convex polygons
International Nuclear Information System (INIS)
James, W R G; Jensen, I; Guttmann, A J
2008-01-01
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their 'concavity index', m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure based on series expansions. We then proceed to prove this result for the more general case of the full anisotropic generating function, in which steps in the x and y directions are distinguished. In doing so, we develop tools that would allow for the case m > 2 to be studied
Generating equilateral random polygons in confinement III
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2012-01-01
In this paper we continue our earlier studies (Diao et al 2011 J. Phys. A: Math. Theor. 44 405202, Diao et al J. Phys. A: Math. Theor. 45 275203) on the generation methods of random equilateral polygons confined in a sphere. The first half of this paper is concerned with the generation of confined equilateral random walks. We show that if the selection of a vertex is uniform subject to the position of its previous vertex and the confining condition, then the distributions of the vertices are not uniform, although there exists a distribution such that if the initial vertex is selected following this distribution, then all vertices of the random walk follow this same distribution. Thus in order to generate a confined equilateral random walk, the selection of a vertex cannot be uniform subject to the position of its previous vertex and the confining condition. We provide a simple algorithm capable of generating confined equilateral random walks whose vertex distribution is almost uniform in the confinement sphere. In the second half of this paper we show that any process generating confined equilateral random walks can be turned into a process generating confined equilateral random polygons with the property that the vertex distribution of the polygons approaches the vertex distribution of the walks as the polygons get longer and longer. In our earlier studies, the starting point of the confined polygon is fixed at the center of the sphere. The new approach here allows us to move the starting point of the confined polygon off the center of the sphere. (paper)
Outlook from the intersections
International Nuclear Information System (INIS)
Haxton, W.C.
1995-01-01
I review a number of the physics themes of the Fifth Conference on the Intersections of Particle and Nuclear Physics, discussing the significance and promise of current work at the interface of these fields. copyright 1995 American Institute of Physics
Equipartitioning and balancing points of polygons
Directory of Open Access Journals (Sweden)
Shunmugam Pillay
2010-07-01
Full Text Available The centre of mass G of a triangle has the property that the rays to the vertices from G sweep out triangles having equal areas. We show that such points, termed equipartitioning points in this paper, need not exist in other polygons. A necessary and sufficient condition for a quadrilateral to have an equipartitioning point is that one of its diagonals bisects the other. The general theorem, namely, necessary and sufficient conditions for equipartitioning points for arbitrary polygons to exist, is also stated and proved. When this happens, they are in general, distinct from the centre of mass. In parallelograms, and only in them, do the two points coincide.
Slow relaxation in weakly open rational polygons.
Kokshenev, Valery B; Vicentini, Eduardo
2003-07-01
The interplay between the regular (piecewise-linear) and irregular (vertex-angle) boundary effects in nonintegrable rational polygonal billiards (of m equal sides) is discussed. Decay dynamics in polygons (of perimeter P(m) and small opening Delta) is analyzed through the late-time survival probability S(m) approximately equal t(-delta). Two distinct slow relaxation channels are established. The primary universal channel exhibits relaxation of regular sliding orbits, with delta=1. The secondary channel is given by delta>1 and becomes open when m>P(m)/Delta. It originates from vertex order-disorder dual effects and is due to relaxation of chaoticlike excitations.
Intersectionality - an intercategorical approach
DEFF Research Database (Denmark)
Emerek, Ruth
2017-01-01
The aim of this article is to demonstrate how to empirically uncover intersectional complexity by simple methods. The article is based on three examples of intercategorical complexity. Firstly, by discussing gender mainstreaming, it is shown that a narrow focus on categories without their interse...... of a study in partial analyses may reveal intersectionality. The examples show how interaction and interwoven categories can be included in intercategorical analyses of structural relationships....
Random packing of regular polygons and star polygons on a flat two-dimensional surface.
Cieśla, Michał; Barbasz, Jakub
2014-08-01
Random packing of unoriented regular polygons and star polygons on a two-dimensional flat continuous surface is studied numerically using random sequential adsorption algorithm. Obtained results are analyzed to determine the saturated random packing ratio as well as its density autocorrelation function. Additionally, the kinetics of packing growth and available surface function are measured. In general, stars give lower packing ratios than polygons, but when the number of vertexes is large enough, both shapes approach disks and, therefore, properties of their packing reproduce already known results for disks.
Type monotonic allocation schemes for multi-glove games
Brânzei, R.; Solymosi, T.; Tijs, S.H.
2007-01-01
Multiglove markets and corresponding games are considered.For this class of games we introduce the notion of type monotonic allocation scheme.Allocation rules for multiglove markets based on weight systems are introduced and characterized.These allocation rules generate type monotonic allocation schemes for multiglove games and are also helpful in proving that each core element of the corresponding game is extendable to a type monotonic allocation scheme.The T-value turns out to generate a ty...
Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions
Michel, Anthony N; Liu, Derong
2015-01-01
The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover the following four general topics: - Representation and modeling of dynamical systems of the types described above - Presentation of Lyapunov and Lagrange stability theory for dynamical sy...
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Hundsdorfer, W.
2011-04-29
In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.
Dilation-optimal edge deletion in polygonal cycles
Ahn, H.K.; Farshi, M.; Knauer, C.; Smid, M.H.M.; Wang, Y.; Tokuyama, T.
2007-01-01
Let C be a polygonal cycle on n vertices in the plane. A randomized algorithm is presented which computes in O(n log3 n) expected time, the edge of C whose removal results in a polygonal path of smallest possible dilation. It is also shown that the edge whose removal gives a polygonal path of
Calculating the Areas of Polygons with a Smartphone Light Sensor
Kapucu, Serkan; Simsek, Mertkan; Öçal, Mehmet Fatih
2017-01-01
This study explores finding the areas of polygons with a smartphone light sensor. A square and an irregular pentagon were chosen as our polygons. During the activity, the LED light was placed at the vertices of our polygons, and the illuminance values of this LED light were detected by the smartphone light sensor. The smartphone was placed on a…
Automatically repairing invalid polygons with a constrained triangulation
Ledoux, H.; Arroyo Ohori, K.; Meijers, M.
2012-01-01
Although the validation of single polygons has received considerable attention, the automatic repair of invalid polygons has not. Automated repair methods can be considered as interpreting ambiguous or ill-defined polygons and giving a coherent and clearly defined output. At this moment, automatic
Realistic roofs over a rectilinear polygon
Ahn, Heekap; Bae, Sangwon; Knauer, Christian; Lee, Mira; Shin, Chansu; Vigneron, Antoine E.
2013-01-01
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. According to this definition, some roofs may have faces
Exploring Nonconvex, Crossed and Degenerate Polygons
Contreras, Jose N.
2004-01-01
An exploration of nonconvex, crossed, and degenerate polygons (NCCDPs) are described with the help of examples with pedagogical tips and recommendations that are found useful when teaching the mathematical process of extending geometric patterns to NCCDPs. The study concludes that investigating such extensions with interactive geometry software…
Generating realistic roofs over a rectilinear polygon
Ahn, Heekap; Bae, Sangwon; Knauer, Christian; Lee, Mira; Shin, Chansu; Vigneron, Antoine E.
2011-01-01
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. In this paper, we introduce realistic roofs by imposing
The structure of near polygons with quads
Brouwer, A.E.; Wilbrink, H.A.
1983-01-01
We develop a structure theory for near polygons with quads. Main results are the existence of sub 2j-gons for 2jd and the nonexistence of regular sporadic 2d-gons for d4 with s>1 and t 2>1 and t 3t 2(t 2+1).
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Logarithmically completely monotonic functions involving the Generalized Gamma Function
Directory of Open Access Journals (Sweden)
Faton Merovci
2010-12-01
Full Text Available By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.
Logarithmically completely monotonic functions involving the Generalized Gamma Function
Faton Merovci; Valmir Krasniqi
2010-01-01
By a simple approach, two classes of functions involving generalization Euler's gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of functions involving the psi function is showed to be completely monotonic.
Testing manifest monotonicity using order-constrained statistical inference
Tijmstra, J.; Hessen, D.J.; van der Heijden, P.G.M.; Sijtsma, K.
2013-01-01
Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest
Intersectional embodiment and power
DEFF Research Database (Denmark)
Elg, Camilla; Jensen, Sune Qvotrup
Through almost two decades the term ‘intersectionality' has gained influence in post colonial studies, gender studies, feminist theory and other research fields occupied with how social differences are distributed and how individuals are socially constructed in stratified societies. The ‘interse......Through almost two decades the term ‘intersectionality' has gained influence in post colonial studies, gender studies, feminist theory and other research fields occupied with how social differences are distributed and how individuals are socially constructed in stratified societies...... not seem to gain much attention in social stratification research in general. In our paper we will present our work on an embodied approach to intersectionality, which is inspired by Pierre Bourdieu and other thinkers of embodiment. We will argue for the importance of a focus on the embodiment of social...
Some solvable, and as yet unsolvable, polygon and walk models
International Nuclear Information System (INIS)
Guttmann, Anthony J
2006-01-01
One partly solvable and two solvable models of polygons are discussed. Using a simple transfer matrix approach Iwan Jensen has derived very long series expansions for the perimeter generating function of both three-choice polygons and punctured staircase polygons. In both cases it is found that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We report on an analysis of the properties of the differential equations. Recently Enrica Duchi has discussed the problem of so-called prudent self-avoiding walks. We discuss the polygon analogue of this problem, and argue that the generating function for prudent polygons is unlikely to be differentiably finite, though a restricted version of the problem, called prudent polygons of the second type, is likely to be differentiably finite. The exact generating function for prudent polygons of the first type is also found
CERN PhotoLab
1974-01-01
The experimental apparatus used at intersection 1 by the CERN-Bologna Collaboration (experiment R105). It consists of two almost identical magnetic spectrometers centered at 90 degrees on opposite sides of the intersection region. In each spectrometer one can see magnetostrictive wire spark chambers, a magnet, more chambers and various hodoscopes of scintillation counters. Gas Cerenkov counters (almost invisible in the picture) are located in the gap of each magnet. On the left hand side, a matrix of 119 lead glass Cerenkov counters is located behind some concrete and iron shielding.
Intersection carbon monoxide modeling
International Nuclear Information System (INIS)
Zamurs, J.
1990-01-01
In this note the author discusses the need for better air quality mobile source models near roadways and intersections. To develop the improved models, a better understanding of emissions and their relation to ambient concentrations is necessary. The database for the modal model indicates that vehicles do have different emission levels for different engine operating modes. If the modal approach is used information is needed on traffic signal phasing, queue lengths, delay times, acceleration rates, deceleration rates, capacity, etc. Dispersion estimates using current air quality models may be inaccurate because the models do not take into account intersecting traffic streams, multiple buildings of varying setbacks, height, and spacing
Intersectionality and Liberal Education
Butler, Johnella E.
2017-01-01
Intersectionality--an integrated approach to analyzing the complex, matrix-like interconnections among patterns of discrimination based on race, gender, and other social identities, with the goal of highlighting how resulting inequalities are experienced--has many implications for exploring the relationship between knowledge and experience and for…
Particle-nuclear intersections
International Nuclear Information System (INIS)
Anon.
1994-01-01
With the traditional distinctions between particle and nuclear physics becoming increasing blurred, the Fifth Conference on the Intersections of Particle and Nuclear Physics, held from May 31 to June 6 in St. Petersburg, Florida, brought together particle and nuclear physicists to discuss common research efforts and to define and plan a united approach
Considering Intersectionality in Multiculturalism
Clark, Madeline
2015-01-01
The intersection of feminist theory and multiculturalism is discussed. Although Frisby makes several strong points, there are several aspects of his definition of multiculturalism that are simplistic. Expansion of ideas borrowed from feminism has potential to increase the nuance and accuracy of the conceptualization of multiculturalism.
Self-assembly of chiral molecular polygons.
Jiang, Hua; Lin, Wenbin
2003-07-09
Treatment of 2,2'-diacetyl-1,1'-binaphthyl-6,6'-bis(ethyne), L-H2, with 1 equiv of trans-Pt(PEt3)2Cl2 led to a mixture of different sizes of chiral metallocycles [trans-(PEt3)2Pt(L)]n (n = 3-8, 1-6). Each of the chiral molecular polygons 1-6 was purified by silica gel column chromatography and characterized by 1H, 13C{1H}, and 31P{1H} NMR spectroscopy, MS, IR, UV-vis, and circular dichroism spectroscopies, and microanalysis. The presence of tunable cavities (1.4-4.3 nm) and chiral functionalities in these molecular polygons promises to make them excellent receptors for a variety of guests.
Simulating 3D deformation using connected polygons
Tarigan, J. T.; Jaya, I.; Hardi, S. M.; Zamzami, E. M.
2018-03-01
In modern 3D application, interaction between user and the virtual world is one of an important factor to increase the realism. This interaction can be visualized in many forms; one of them is object deformation. There are many ways to simulate object deformation in virtual 3D world; each comes with different level of realism and performance. Our objective is to present a new method to simulate object deformation by using a graph-connected polygon. In this solution, each object contains multiple level of polygons in different level of volume. The proposed solution focusses on performance rather while maintaining the acceptable level of realism. In this paper, we present the design and implementation of our solution and show that this solution is usable in performance sensitive 3D application such as games and virtual reality.
Counting convex polygons in planar point sets
Mitchell, J.S.B.; Rote, G.; Sundaram, Gopalakrishnan; Woeginger, G.J.
1995-01-01
Given a set S of n points in the plane, we compute in time O(n3) the total number of convex polygons whose vertices are a subset of S. We give an O(m · n3) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3,…, m; previously known bounds were exponential
Non-convex polygons clustering algorithm
Directory of Open Access Journals (Sweden)
Kruglikov Alexey
2016-01-01
Full Text Available A clustering algorithm is proposed, to be used as a preliminary step in motion planning. It is tightly coupled to the applied problem statement, i.e. uses parameters meaningful only with respect to it. Use of geometrical properties for polygons clustering allows for a better calculation time as opposed to general-purpose algorithms. A special form of map optimized for quick motion planning is constructed as a result.
137Cs in Research Polygon 'Sumbar'
International Nuclear Information System (INIS)
Skoko, B.; Marovic, G.; Babic, D.; Vickovic, I.
2011-01-01
In 2009, Radiation Protection Unit of the Institute for Medical Reseach and Occupational Health started a radioactivity measurement programme in research polygon ''Sumbar''. The purpose of these investigations is to collect as many data as possible about the contamination of the polygon that is mainly covered by a forest of English oak (Quercus robur) and hornbeam (Carpinus betulus). Once contaminated, forests represent long-term sources of radiation exposure to specific population groups which are using them as a source of foodstuffs. After the Chernobyl accident, researchers have shown that there has been more variability in radionuclide activity concentration in forests than in agricultural ecosystems. In order to carry out a radioactivity screening of the polygon, we randomly chosed three sampling sites for collecting soil, grass and moss samples. Different species of mushrooms were collected over the whole polygon area. The average activity concentration of 137Cs in soil for two sampling sites is (123 @ 9) Bq kg -1 , while the result for the third site is lower by an order of magnitude ((16.1@0.5) Bq kg -1 ). The activity concentration of 137Cs in grass samples ranges from (0.43 @ 0.03) Bq kg -1 to (13.2 @ 0.1) Bq kg -1 , and in moss samples from (8.7 @ 0.2) Bq kg -1 to (57.8 @ 0.3) Bq kg - 1. In five collected mushroom species, the activity of 137Cs is in the range between (4.1 @ 0.5) Bq kg -1 and (610 @ 5) Bq kg -1 , the lowest and the highest values referreing to Clitocybe nebularis and Gymnopus dryophilus, respectively. Parasitic mushrooms exhibit activity below the minimum detection level. Our preliminary results show and confirm variability of the activity concentration of 137Cs in different parts of this ecosystem. (author)
Strong monotonicity in mixed-state entanglement manipulation
International Nuclear Information System (INIS)
Ishizaka, Satoshi
2006-01-01
A strong entanglement monotone, which never increases under local operations and classical communications (LOCC), restricts quantum entanglement manipulation more strongly than the usual monotone since the usual one does not increase on average under LOCC. We propose strong monotones in mixed-state entanglement manipulation under LOCC. These are related to the decomposability and one-positivity of an operator constructed from a quantum state, and reveal geometrical characteristics of entangled states. These are lower bounded by the negativity or generalized robustness of entanglement
Monotonicity-based electrical impedance tomography for lung imaging
Zhou, Liangdong; Harrach, Bastian; Seo, Jin Keun
2018-04-01
This paper presents a monotonicity-based spatiotemporal conductivity imaging method for continuous regional lung monitoring using electrical impedance tomography (EIT). The EIT data (i.e. the boundary current-voltage data) can be decomposed into pulmonary, cardiac and other parts using their different periodic natures. The time-differential current-voltage operator corresponding to the lung ventilation can be viewed as either semi-positive or semi-negative definite owing to monotonic conductivity changes within the lung regions. We used these monotonicity constraints to improve the quality of lung EIT imaging. We tested the proposed methods in numerical simulations, phantom experiments and human experiments.
Risk-Sensitive Control with Near Monotone Cost
International Nuclear Information System (INIS)
Biswas, Anup; Borkar, V. S.; Suresh Kumar, K.
2010-01-01
The infinite horizon risk-sensitive control problem for non-degenerate controlled diffusions is analyzed under a 'near monotonicity' condition on the running cost that penalizes large excursions of the process.
An Examination of Cooper's Test for Monotonic Trend
Hsu, Louis
1977-01-01
A statistic for testing monotonic trend that has been presented in the literature is shown not to be the binomial random variable it is contended to be, but rather it is linearly related to Kendall's tau statistic. (JKS)
A Survey on Operator Monotonicity, Operator Convexity, and Operator Means
Directory of Open Access Journals (Sweden)
Pattrawut Chansangiam
2015-01-01
Full Text Available This paper is an expository devoted to an important class of real-valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences. From the viewpoint of operator inequalities, various characterizations and the relationship between operator monotonicity and operator convexity are given by Hansen and Pedersen. In the viewpoint of measure theory, operator monotone functions on the nonnegative reals admit meaningful integral representations with respect to Borel measures on the unit interval. Furthermore, Kubo-Ando theory asserts the correspondence between operator monotone functions and operator means.
Completely monotonic functions related to logarithmic derivatives of entire functions
DEFF Research Database (Denmark)
Pedersen, Henrik Laurberg
2011-01-01
The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity...... of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given....
Monotonic Loading of Circular Surface Footings on Clay
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin
2011-01-01
Appropriate modeling of offshore foundations under monotonic loading is a significant challenge in geotechnical engineering. This paper reports experimental and numerical analyses, specifically investigating the response of circular surface footings during monotonic loading and elastoplastic...... behavior during reloading. By using the findings presented in this paper, it is possible to extend the model to simulate the vertical-load displacement response of offshore bucket foundations....
Electronic theodolite intersection systems
Bingley, R. M.
1990-01-01
The development of electronic surveying instruments, such as electronic theodolites, and concurrent advances in computer technology, has revolutionised engineering surveying; one of the more recent examples being the introduction of Electronic Theodolite Intersection Systems (ETISs). An ETIS consists of two or more electronic theodolites and a computer, with peripheral hardware and suitable software. The theoretical principles on which they are based have been known for a long time, but ...
Outlook from the intersections
International Nuclear Information System (INIS)
Haxton, W.C.
1994-01-01
I review a number of the physics themes of the Fifth Conference on the Intersections of Particle and Nuclear Physics, discussing the significance and promise of current work at the interface of these fields. Some of thee themes are: pattern of quark and boson masses; solar neutrino problem; lepton flavor violation tests; atomic dipole moments studies; Δs=0 weak interaction between nucleons; and strongly-interacting many-body problems
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Directory of Open Access Journals (Sweden)
Miroslav Krbec
2010-01-01
Full Text Available First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Köthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity δ^m,E. The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008 which establish that Banach lattices X with ε0,m(X<1 and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001.
Specific non-monotonous interactions increase persistence of ecological networks.
Yan, Chuan; Zhang, Zhibin
2014-03-22
The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.
Generating random walks and polygons with stiffness in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Saarinen, S; Ziegler, U
2015-01-01
The purpose of this paper is to explore ways to generate random walks and polygons in confinement with a bias toward stiffness. Here the stiffness refers to the curvature angle between two consecutive edges along the random walk or polygon. The stiffer the walk (polygon), the smaller this angle on average. Thus random walks and polygons with an elevated stiffness have lower than expected curvatures. The authors introduced and studied several generation algorithms with a stiffness parameter s>0 that regulates the expected curvature angle at a given vertex in which the random walks and polygons are generated one edge at a time using conditional probability density functions. Our generating algorithms also allow the generation of unconfined random walks and polygons with any desired mean curvature angle. In the case of random walks and polygons confined in a sphere of fixed radius, we observe that, as expected, stiff random walks or polygons are more likely to be close to the confinement boundary. The methods developed here require that the random walks and random polygons be rooted at the center of the confinement sphere. (paper)
The magnetic field generated by a rotating charged polygon
International Nuclear Information System (INIS)
Wan, Songlin; Chen, Xiangyu; Teng, Baohua; Fu, Hao; Li, Yefeng; Wu, Minghe; Wu, Shaoyi; Balfour, E A
2014-01-01
The magnetic field along the symmetry axis of a regular polygon carrying a uniform electric charge on its edges is calculated systematically when the polygon is rotated about this axis of symmetry. A group of circular current-carrying coils arranged concentrically about the axis of the polygon has been designed to simulate the magnetic field characteristics of the rotating charged polygon. The magnetic field of the simulated coils is measured using the PASCO magnetic field sensor. The results show that the theoretical calculation agrees well with the experimental results. (paper)
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1981-01-01
Properties of the subset of polygonal paths in the Hilbert space H of paths referring to a d-dimensional quantum-mechanical system are examined. Using the reproduction kernel technique we prove that each element of H is approximated by polygonal paths uniformly with respect to the ''norm'' of time-interval partitions. This result will be applied in the second part of the present paper to prove consistency of the uniform polygonal-path extension of the Feynman maps [ru
Finding the Maximal Area of Bounded Polygons in a Circle
Rokach, Arie
2005-01-01
The article deals with the area of polygons that are inscribed in a given circle. Naturally, the following question arises: Among all n-polygons that are inscribed in a given circle, which one has the biggest area? Intuitively, it may be guessed that is suitable for secondary students, and without any use id calculus, but only using very…
Beam envelope profile of non-centrosymmetric polygonal phase space
International Nuclear Information System (INIS)
Chen Yinbao; Xie Xi
1984-01-01
The general theory of beam envelope profile of non-centrosymmetric polygonal phase space is developed. By means of this theory the beam envelope profile of non-centrosymmetric polygonal phase space can be calculated directly. An example is carried out in detail to show the practical application of the theory
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
Intersectionality research in counseling psychology.
Grzanka, Patrick R; Santos, Carlos E; Moradi, Bonnie
2017-10-01
This article introduces the special section on intersectionality research in counseling psychology. Across the 4 manuscripts that constitute this special section, a clear theme emerges: a need to return to the roots and politics of intersectionality. Importantly, the 2 empirical articles in this special section (Jerald, Cole, Ward, & Avery, 2017; Lewis, Williams, Peppers, & Gadson, 2017) are studies of Black women's experiences: a return, so to speak, to the subject positions and social locations from which intersectionality emanates. Shin et al. (2017) explore why this focus on Black feminist thought and social justice is so important by highlighting the persistent weaknesses in how much research published in leading counseling psychology journals has tended to use intersectionality as a way to talk about multiple identities, rather than as a framework for critiquing systemic, intersecting forms of oppression and privilege. Shin and colleagues also point to the possibilities intersectionality affords us when scholars realize the transformative potential of this critical framework. Answers to this call for transformative practices are foregrounded in Moradi and Grzanka's (2017) contribution, which surveys the interdisciplinary literature on intersectionality and presents a series of guidelines for using intersectionality responsibly. We close with a discussion of issues concerning the applications of intersectionality to counseling psychology research that spans beyond the contributions of each manuscript in this special section. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Linking of uniform random polygons in confined spaces
Arsuaga, J.; Blackstone, T.; Diao, Y.; Karadayi, E.; Saito, M.
2007-03-01
In this paper, we study the topological entanglement of uniform random polygons in a confined space. We derive the formula for the mean squared linking number of such polygons. For a fixed simple closed curve in the confined space, we rigorously show that the linking probability between this curve and a uniform random polygon of n vertices is at least 1-O\\big(\\frac{1}{\\sqrt{n}}\\big) . Our numerical study also indicates that the linking probability between two uniform random polygons (in a confined space), of m and n vertices respectively, is bounded below by 1-O\\big(\\frac{1}{\\sqrt{mn}}\\big) . In particular, the linking probability between two uniform random polygons, both of n vertices, is bounded below by 1-O\\big(\\frac{1}{n}\\big) .
Linking of uniform random polygons in confined spaces
International Nuclear Information System (INIS)
Arsuaga, J; Blackstone, T; Diao, Y; Karadayi, E; Saito, M
2007-01-01
In this paper, we study the topological entanglement of uniform random polygons in a confined space. We derive the formula for the mean squared linking number of such polygons. For a fixed simple closed curve in the confined space, we rigorously show that the linking probability between this curve and a uniform random polygon of n vertices is at least 1-O(1/√n). Our numerical study also indicates that the linking probability between two uniform random polygons (in a confined space), of m and n vertices respectively, is bounded below by 1-O(1/√(mn)). In particular, the linking probability between two uniform random polygons, both of n vertices, is bounded below by 1-O(1/n)
Information flow in layered networks of non-monotonic units
Schittler Neves, Fabio; Martim Schubert, Benno; Erichsen, Rubem, Jr.
2015-07-01
Layered neural networks are feedforward structures that yield robust parallel and distributed pattern recognition. Even though much attention has been paid to pattern retrieval properties in such systems, many aspects of their dynamics are not yet well characterized or understood. In this work we study, at different temperatures, the memory activity and information flows through layered networks in which the elements are the simplest binary odd non-monotonic function. Our results show that, considering a standard Hebbian learning approach, the network information content has its maximum always at the monotonic limit, even though the maximum memory capacity can be found at non-monotonic values for small enough temperatures. Furthermore, we show that such systems exhibit rich macroscopic dynamics, including not only fixed point solutions of its iterative map, but also cyclic and chaotic attractors that also carry information.
Information flow in layered networks of non-monotonic units
International Nuclear Information System (INIS)
Neves, Fabio Schittler; Schubert, Benno Martim; Erichsen, Rubem Jr
2015-01-01
Layered neural networks are feedforward structures that yield robust parallel and distributed pattern recognition. Even though much attention has been paid to pattern retrieval properties in such systems, many aspects of their dynamics are not yet well characterized or understood. In this work we study, at different temperatures, the memory activity and information flows through layered networks in which the elements are the simplest binary odd non-monotonic function. Our results show that, considering a standard Hebbian learning approach, the network information content has its maximum always at the monotonic limit, even though the maximum memory capacity can be found at non-monotonic values for small enough temperatures. Furthermore, we show that such systems exhibit rich macroscopic dynamics, including not only fixed point solutions of its iterative map, but also cyclic and chaotic attractors that also carry information. (paper)
Estimating monotonic rates from biological data using local linear regression.
Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R
2017-03-01
Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.
Iterates of piecewise monotone mappings on an interval
Preston, Chris
1988-01-01
Piecewise monotone mappings on an interval provide simple examples of discrete dynamical systems whose behaviour can be very complicated. These notes are concerned with the properties of the iterates of such mappings. The material presented can be understood by anyone who has had a basic course in (one-dimensional) real analysis. The account concentrates on the topological (as opposed to the measure theoretical) aspects of the theory of piecewise monotone mappings. As well as offering an elementary introduction to this theory, these notes also contain a more advanced treatment of the problem of classifying such mappings up to topological conjugacy.
Wenrich, M. L.; Christensen, P. R.
1993-01-01
The mechanism for the genesis of the polygonal terrains in Acidalia and Utopia Planitia has long been sought: however, no completely satisfying model was put forth that characterizes the evolution of these complexly patterned terrains. The polygons are roughly hexagonal but some are not entirely enclosed by fractures. These polygonal features range in widths from approximately 5 to 20 km. Several origins were proposed that describe the polygon borders as desiccation cracks, columnar jointing in a cooled lava, or frost-wedge features. These tension-induced cracking hypotheses were addressed by Pechmann, who convincingly disputes these mechanisms of formation based on scale magnitude difficulties and morphology. Pechmann suggests instead that the cracks delineating the 5-20-km-wide polygons on the northern plains of Mars are graben resulting from deep-seated, uniform, horizontal tension. The difficulty with this hypothesis is that no analogous polygonal forms are known to have originated by tectonism on Earth. McGill and Hills propose that the polygonal terrains on Mars resulted from either rapid desiccation of sediments or cooling of volcanics coupled with differential compaction of the material over a buried irregular topographic surface. They suggest that fracturing was enhanced over the areas of positive relief and was suppressed above the topographic lows. McGill and Hills suggest that the spacing of the topographic highs primarily controls the size of the Martian polygons and the physics of the shrinkage process is a secondary concern. Ray et. al. conducted a terrestrial study of patterned ground in periglacial areas of the U.S. to determine the process responsible for polygonal ground formation. They developed a model for polygon formation in which convection of seasonal melt water above a permafrost layer, driven by an unstable density stratification, differentially melts the permafrost interface, causing it to become undulatory.
Uehara, Erica; Deguchi, Tetsuo
2017-12-07
We show that the average size of self-avoiding polygons (SAPs) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an "enhancement" of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the topological balance length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the topological balance length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.
Exploring Class-Based Intersectionality
Block, David; Corona, Victor
2014-01-01
This paper argues that language, culture and identity researchers need to take the intersectionality of identity inscriptions seriously and, further to this, that an intersectional approach which emanates from an interest in social class provides a productive way to examine the lives and experience of individuals living in multicultural societies.…
Intersectionality and Critical Race Parenting
DePouw, Christin
2018-01-01
This conceptual article employs critical race theory (CRT) as a theoretical framework to explore the importance of intersectionality in critical race parenting. In particular, I focus on intersectionality to understand better how Whiteness and racial power play out in intimate relationships within the family, particularly between White parents and…
Scattering Amplitudes from Intersection Theory.
Mizera, Sebastian
2018-04-06
We use Picard-Lefschetz theory to prove a new formula for intersection numbers of twisted cocycles associated with a given arrangement of hyperplanes. In a special case when this arrangement produces the moduli space of punctured Riemann spheres, intersection numbers become tree-level scattering amplitudes of quantum field theories in the Cachazo-He-Yuan formulation.
Simplest bifurcation diagrams for monotone families of vector fields on a torus
Baesens, C.; MacKay, R. S.
2018-06-01
In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
Generating realistic roofs over a rectilinear polygon
Ahn, Heekap
2011-01-01
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. In this paper, we introduce realistic roofs by imposing a few additional constraints. We investigate the geometric and combinatorial properties of realistic roofs, and show a connection with the straight skeleton of P. We show that the maximum possible number of distinct realistic roofs over P is ( ⌊(n-4)/4⌋ (n-4)/2) when P has n vertices. We present an algorithm that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n 4) preprocessing time. We also present an O(n 5)-time algorithm for computing a realistic roof with minimum height or volume. © 2011 Springer-Verlag.
Rotational Fourier tracking of diffusing polygons.
Mayoral, Kenny; Kennair, Terry P; Zhu, Xiaoming; Milazzo, James; Ngo, Kathy; Fryd, Michael M; Mason, Thomas G
2011-11-01
We use optical microscopy to measure the rotational Brownian motion of polygonal platelets that are dispersed in a liquid and confined by depletion attractions near a wall. The depletion attraction inhibits out-of-plane translational and rotational Brownian fluctuations, thereby facilitating in-plane imaging and video analysis. By taking fast Fourier transforms (FFTs) of the images and analyzing the angular position of rays in the FFTs, we determine an isolated particle's rotational trajectory, independent of its position. The measured in-plane rotational diffusion coefficients are significantly smaller than estimates for the bulk; this difference is likely due to the close proximity of the particles to the wall arising from the depletion attraction.
High speed printing with polygon scan heads
Stutz, Glenn
2016-03-01
To reduce and in many cases eliminate the costs associated with high volume printing of consumer and industrial products, this paper investigates and validates the use of the new generation of high speed pulse on demand (POD) lasers in concert with high speed (HS) polygon scan heads (PSH). Associated costs include consumables such as printing ink and nozzles, provisioning labor, maintenance and repair expense as well as reduction of printing lines due to high through put. Targets that are applicable and investigated include direct printing on plastics, printing on paper/cardboard as well as printing on labels. Market segments would include consumer products (CPG), medical and pharmaceutical products, universal ID (UID), and industrial products. In regards to the POD lasers employed, the wavelengths include UV(355nm), Green (532nm) and IR (1064nm) operating within the repetition range of 180 to 250 KHz.
Self-avoiding polygons and walks in slits
International Nuclear Information System (INIS)
Alvarez, J; Whittington, S G; Rensburg, E J Janse van; Soteros, C E
2008-01-01
A polymer in a confined geometry may be modeled by a self-avoiding walk or a self-avoiding polygon confined between two parallel walls. In two dimensions, this model involves self-avoiding walks or self-avoiding polygons in the square lattice between two parallel confining lines. Interactions of the polymer with the confining walls are introduced by energy terms associated with edges in the walk or polygon which are at or near the confining lines. We use transfer-matrix methods to investigate the forces between the walk or polygon and the confining lines, as well as to investigate the effects of the confining slit's width and of the energy terms on the thermodynamic properties of the walks or polygons in several models. The phase diagram found for the self-avoiding walk models is qualitatively similar to the phase diagram of a directed walk model confined between two parallel lines, as was previously conjectured. However, the phase diagram of one of our polygon models is found to be significantly different and we present numerical data to support this. For that particular model we prove that, for any finite values of the energy terms, there are an infinite number of slit widths where a polygon will induce a steric repulsion between the confining lines
The regularized monotonicity method: detecting irregular indefinite inclusions
DEFF Research Database (Denmark)
Garde, Henrik; Staboulis, Stratos
2018-01-01
inclusions, where the conductivity distribution has both more and less conductive parts relative to the background conductivity; one such method is the monotonicity method of Harrach, Seo, and Ullrich. We formulate the method for irregular indefinite inclusions, meaning that we make no regularity assumptions...
Generalized monotonicity from global minimization in fourth-order ODEs
M.A. Peletier (Mark)
2000-01-01
textabstractWe consider solutions of the stationary Extended Fisher-Kolmogorov equation with general potential that are global minimizers of an associated variational problem. We present results that relate the global minimization property to a generalized concept of monotonicity of the solutions.
Monotone difference schemes for weakly coupled elliptic and parabolic systems
P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)
2017-01-01
textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is
Pathwise duals of monotone and additive Markov processes
Czech Academy of Sciences Publication Activity Database
Sturm, A.; Swart, Jan M.
-, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf
Statistical analysis of sediment toxicity by additive monotone regression splines
Boer, de W.J.; Besten, den P.J.; Braak, ter C.J.F.
2002-01-01
Modeling nonlinearity and thresholds in dose-effect relations is a major challenge, particularly in noisy data sets. Here we show the utility of nonlinear regression with additive monotone regression splines. These splines lead almost automatically to the estimation of thresholds. We applied this
Interval Routing and Minor-Monotone Graph Parameters
Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van
2006-01-01
We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the
On monotonic solutions of an integral equation of Abel type
International Nuclear Information System (INIS)
Darwish, Mohamed Abdalla
2007-08-01
We present an existence theorem of monotonic solutions for a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar's integral equation is considered as a special case. The concept of measure of noncompactness and a fi xed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Rational functions with maximal radius of absolute monotonicity
Loczi, Lajos; Ketcheson, David I.
2014-01-01
-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend
POLARIZED LINE FORMATION IN NON-MONOTONIC VELOCITY FIELDS
Energy Technology Data Exchange (ETDEWEB)
Sampoorna, M.; Nagendra, K. N., E-mail: sampoorna@iiap.res.in, E-mail: knn@iiap.res.in [Indian Institute of Astrophysics, Koramangala, Bengaluru 560034 (India)
2016-12-10
For a correct interpretation of the observed spectro-polarimetric data from astrophysical objects such as the Sun, it is necessary to solve the polarized line transfer problems taking into account a realistic temperature structure, the dynamical state of the atmosphere, a realistic scattering mechanism (namely, the partial frequency redistribution—PRD), and the magnetic fields. In a recent paper, we studied the effects of monotonic vertical velocity fields on linearly polarized line profiles formed in isothermal atmospheres with and without magnetic fields. However, in general the velocity fields that prevail in dynamical atmospheres of astrophysical objects are non-monotonic. Stellar atmospheres with shocks, multi-component supernova atmospheres, and various kinds of wave motions in solar and stellar atmospheres are examples of non-monotonic velocity fields. Here we present studies on the effect of non-relativistic non-monotonic vertical velocity fields on the linearly polarized line profiles formed in semi-empirical atmospheres. We consider a two-level atom model and PRD scattering mechanism. We solve the polarized transfer equation in the comoving frame (CMF) of the fluid using a polarized accelerated lambda iteration method that has been appropriately modified for the problem at hand. We present numerical tests to validate the CMF method and also discuss the accuracy and numerical instabilities associated with it.
Modelling Embedded Systems by Non-Monotonic Refinement
Mader, Angelika H.; Marincic, J.; Wupper, H.
2008-01-01
This paper addresses the process of modelling embedded sys- tems for formal verification. We propose a modelling process built on non-monotonic refinement and a number of guidelines. The outcome of the modelling process is a model, together with a correctness argument that justifies our modelling
Conformal array design on arbitrary polygon surface with transformation optics
Energy Technology Data Exchange (ETDEWEB)
Deng, Li, E-mail: dengl@bupt.edu.cn; Hong, Weijun, E-mail: hongwj@bupt.edu.cn; Zhu, Jianfeng; Peng, Biao; Li, Shufang [Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, 100876 Beijing (China); Wu, Yongle, E-mail: wuyongle138@gmail.com [Beijing Key Laboratory of Work Safety Intelligent Monitoring, School of Electronic Engineering, Beijing University of Posts and Telecommunications, 100876 Beijing (China)
2016-06-15
A transformation-optics based method to design a conformal antenna array on an arbitrary polygon surface is proposed and demonstrated in this paper. This conformal antenna array can be adjusted to behave equivalently as a uniformly spaced linear array by applying an appropriate transformation medium. An typical example of general arbitrary polygon conformal arrays, not limited to circular array, is presented, verifying the proposed approach. In summary, the novel arbitrary polygon surface conformal array can be utilized in array synthesis and beam-forming, maintaining all benefits of linear array.
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2013-08-01
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.
Conformal array design on arbitrary polygon surface with transformation optics
International Nuclear Information System (INIS)
Deng, Li; Hong, Weijun; Zhu, Jianfeng; Peng, Biao; Li, Shufang; Wu, Yongle
2016-01-01
A transformation-optics based method to design a conformal antenna array on an arbitrary polygon surface is proposed and demonstrated in this paper. This conformal antenna array can be adjusted to behave equivalently as a uniformly spaced linear array by applying an appropriate transformation medium. An typical example of general arbitrary polygon conformal arrays, not limited to circular array, is presented, verifying the proposed approach. In summary, the novel arbitrary polygon surface conformal array can be utilized in array synthesis and beam-forming, maintaining all benefits of linear array.
Intersectional perspective in elderly care.
Cuesta, Marta; Rämgård, Margareta
2016-01-01
Earlier research has shown that power relationships at workplaces are constructed by power structures. Processes related to power always influence the working conditions for (in this study in elderly care) the working groups involved. Power structures are central for intersectional analysis, in the sense that the intersectional perspective highlights aspects such as gender and ethnicity (subjective dimensions) and interrelates them to processes of power (objective dimension). This qualitative study aims to explore in what way an intersectional perspective could contribute to increased knowledge of power structures in a nursing home where the employees were mostly immigrants from different countries. By using reflexive dialogues related to an intersectional perspective, new knowledge which contributes to the employees' well-being could develop. Narrative analysis was the method used to conduct this study. Through a multi-stage focus group on six occasions over 6 months, the staff were engaged in intersectional and critical reflections about power relationship with the researchers, by identifying patterns in their professional activities that could be connected to their subjectivities (gender, ethnicity, etc.). The result of this study presents three themes that express the staff's experiences and connect these experiences to structural discrimination. 1) Intersectionality, knowledge, and experiences of professionalism; 2) Intersectionality, knowledge, and experiences of collaboration; and 3) Intersectionality, knowledge, and experiences of discrimination. The result demonstrates that an intersectional perspective reinforces the involved abilities, during the conversations, into being clear about, for example, their experiences of discrimination, and consequently developing a better understanding of their professionalism and collaboration. Such deeper reflections became possible through a process of consciousness raising, strengthening the employee's self
Intersectional perspective in elderly care
Cuesta, Marta; Rämgård, Margareta
2016-01-01
Earlier research has shown that power relationships at workplaces are constructed by power structures. Processes related to power always influence the working conditions for (in this study in elderly care) the working groups involved. Power structures are central for intersectional analysis, in the sense that the intersectional perspective highlights aspects such as gender and ethnicity (subjective dimensions) and interrelates them to processes of power (objective dimension). This qualitative study aims to explore in what way an intersectional perspective could contribute to increased knowledge of power structures in a nursing home where the employees were mostly immigrants from different countries. By using reflexive dialogues related to an intersectional perspective, new knowledge which contributes to the employees’ well-being could develop. Narrative analysis was the method used to conduct this study. Through a multi-stage focus group on six occasions over 6 months, the staff were engaged in intersectional and critical reflections about power relationship with the researchers, by identifying patterns in their professional activities that could be connected to their subjectivities (gender, ethnicity, etc.). The result of this study presents three themes that express the staff's experiences and connect these experiences to structural discrimination. 1) Intersectionality, knowledge, and experiences of professionalism; 2) Intersectionality, knowledge, and experiences of collaboration; and 3) Intersectionality, knowledge, and experiences of discrimination. The result demonstrates that an intersectional perspective reinforces the involved abilities, during the conversations, into being clear about, for example, their experiences of discrimination, and consequently developing a better understanding of their professionalism and collaboration. Such deeper reflections became possible through a process of consciousness raising, strengthening the employee's self
Intersectional perspective in elderly care
Directory of Open Access Journals (Sweden)
Marta Cuesta
2016-05-01
Full Text Available Earlier research has shown that power relationships at workplaces are constructed by power structures. Processes related to power always influence the working conditions for (in this study in elderly care the working groups involved. Power structures are central for intersectional analysis, in the sense that the intersectional perspective highlights aspects such as gender and ethnicity (subjective dimensions and interrelates them to processes of power (objective dimension. This qualitative study aims to explore in what way an intersectional perspective could contribute to increased knowledge of power structures in a nursing home where the employees were mostly immigrants from different countries. By using reflexive dialogues related to an intersectional perspective, new knowledge which contributes to the employees’ well-being could develop. Narrative analysis was the method used to conduct this study. Through a multi-stage focus group on six occasions over 6 months, the staff were engaged in intersectional and critical reflections about power relationship with the researchers, by identifying patterns in their professional activities that could be connected to their subjectivities (gender, ethnicity, etc.. The result of this study presents three themes that express the staff's experiences and connect these experiences to structural discrimination. 1 Intersectionality, knowledge, and experiences of professionalism; 2 Intersectionality, knowledge, and experiences of collaboration; and 3 Intersectionality, knowledge, and experiences of discrimination. The result demonstrates that an intersectional perspective reinforces the involved abilities, during the conversations, into being clear about, for example, their experiences of discrimination, and consequently developing a better understanding of their professionalism and collaboration. Such deeper reflections became possible through a process of consciousness raising, strengthening the employee
Alabama ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for dolphins and manatees in Alabama. Vector polygons in this data set represent marine mammal distribution...
Western Alaska ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for seals, whales, dolphins, walruses, and Steller sea lions in Western Alaska. Vector polygons in this...
American Samoa ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for whales and dolphins in American Samoa. Vector polygons in this data set represent marine mammal...
Columbia River ESI: NWI (National Wetlands Inventory - Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the wetlands of Columbia River classified according to the Environmental Sensitivity Index (ESI) classification...
Coastal Resources Atlas: Long Island: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and freshwater fish species for Long Island, New York. Vector polygons...
Coastal Resources Atlas: Long Island: REPTILES (Reptile and Amphibian Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles, estuarine turtles, and amphibians for Long Island, New York. Vector polygons in this data...
Louisiana ESI: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for terrestrial mammals in Louisiana. Vector polygons in this data set represent terrestrial mammal...
North Slope, Alaska ESI: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for brown bears, caribou, and muskoxen for the North Slope, Alaska. Vector polygons in this data set...
Virginia ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for dolphin, seals, whales, and porpoise in Virginia. Vector polygons in this data set represent marine...
North Slope, Alaska ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for whales, seals, walruses, and polar bears for the North Slope of Alaska. Vector polygons in this data...
Shinarump Channel Polygons, North Central AUM Region, 1964, USDOE
U.S. Environmental Protection Agency — This is a polygon shapefile that provides Shinarump channels compiled and mapped by Young and Malan (1964) in the Monument Valley District, San Juan County, Utah,...
Cook Inlet and Kenai Peninsula, Alaska ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries used in the creation of the Environmental Sensitivity Index (ESI) for Cook Inlet and Kenai...
Southeast Alaska ESI: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for brown bears in Southeast Alaska. Vector polygons in this data set represent locations of bear concentrations....
American Samoa ESI: REPTILES (Reptile and Amphibian Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles in American Samoa. Vector polygons in this data set represent sea turtle nesting and...
Columbia River ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for Steller sea lions, harbor seals, and California sea lions in Columbia River. Vector polygons in this...
Coastal Resources Atlas: Long Island: INVERT (Invertebrate Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for coastal, estuarine, and marine invertebrate species for Long Island, New York. Vector polygons in this...
Cook Inlet and Kenai Peninsula, Alaska ESI: INVERT (Invertebrate Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for razor clams in Cook Inlet and Kenai Peninsula, Alaska. Vector polygons in this data set represent locations of...
Columbia River ESI: REPTILES (Reptile and Amphibian Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for western pond turtles and western painted turtles in Columbia River. Vector polygons in this data set...
Cook Inlet and Kenai Peninsula, Alaska ESI: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for herring spawning areas in Cook Inlet and Kenai Peninsula, Alaska. Vector polygons in this data set represent...
PNW River Reach Files -- 1:100k Waterbodies (polygons)
Pacific States Marine Fisheries Commission — This feature class includes the POLYGON waterbody features from the 2001 version of the PNW River Reach files Arc/INFO coverage. Separate, companion feature classes...
North Slope, Alaska ESI: BIOINDEX (Biological Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the quad boundaries of the 1:250,000 USGS topographic quadrangles. These boundaries represent the extent of the...
Louisiana ESI: LG_INDEX (Large Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all the hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Structural characterization of the packings of granular regular polygons.
Wang, Chuncheng; Dong, Kejun; Yu, Aibing
2015-12-01
By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.
Polygon formation and surface flow on a rotating fluid surface
DEFF Research Database (Denmark)
Bergmann, Raymond; Tophøj, Laust Emil Hjerrild; Homan, T. A. M.
2011-01-01
We present a study of polygons forming on the free surface of a water flow confined to a stationary cylinder and driven by a rotating bottom plate as described by Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, 174502). In particular, we study the case of a triangular structure, either completely...... there the symmetry breaking proceeds like a low-dimensional linear instability. We show that the circular state and the unstable manifold connecting it with the polygon solution are universal in the sense that very different initial conditions lead to the same circular state and unstable manifold. For a wet triangle......, we measure the surface flows by particle image velocimetry (PIV) and show that there are three vortices present, but that the strength of these vortices is far too weak to account for the rotation velocity of the polygon. We show that partial blocking of the surface flow destroys the polygons and re...
The unusual asymptotics of three-sided prudent polygons
International Nuclear Information System (INIS)
Beaton, Nicholas R; Guttmann, Anthony J; Flajolet, Philippe
2010-01-01
We have studied the area-generating function of prudent polygons on the square lattice. Exact solutions are obtained for the generating function of two-sided and three-sided prudent polygons, and a functional equation is found for four-sided prudent polygons. This is used to generate series coefficients in polynomial time, and these are analysed to determine the asymptotics numerically. A careful asymptotic analysis of the three-sided polygons produces a most surprising result. A transcendental critical exponent is found, and the leading amplitude is not quite a constant, but is a constant plus a small oscillatory component with an amplitude approximately 10 -8 times that of the leading amplitude. This effect cannot be seen by any standard numerical analysis, but it may be present in other models. If so, it changes our whole view of the asymptotic behaviour of lattice models. (fast track communication)
Average size of random polygons with fixed knot topology.
Matsuda, Hiroshi; Yao, Akihisa; Tsukahara, Hiroshi; Deguchi, Tetsuo; Furuta, Ko; Inami, Takeo
2003-07-01
We have evaluated by numerical simulation the average size R(K) of random polygons of fixed knot topology K=,3(1),3(1) musical sharp 4(1), and we have confirmed the scaling law R(2)(K) approximately N(2nu(K)) for the number N of polygonal nodes in a wide range; N=100-2200. The best fit gives 2nu(K) approximately 1.11-1.16 with good fitting curves in the whole range of N. The estimate of 2nu(K) is consistent with the exponent of self-avoiding polygons. In a limited range of N (N greater, similar 600), however, we have another fit with 2nu(K) approximately 1.01-1.07, which is close to the exponent of random polygons.
Bristol Bay, Alaska Subarea ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all the hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Maryland ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for seals, whales, porpoise, and dolphin in Maryland. Vector polygons in this data set represent marine...
Alabama ESI: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for Alabama and Perdido Key beach mice in Alabama. Vector polygons in this data set represent the rare...
Morphometric analysis of the arteries of Willis Polygon
Directory of Open Access Journals (Sweden)
Canaz Huseyin
2018-03-01
Full Text Available Objective: Willis polygon forms the basis of the arterial circulation of the cerebrum. Willis polygon is a vascular structure whom variations are not rare. Knowledge of the anatomy and preservation of its integrity is crucial for performing neurovascular surgery and intracranial tumour surgery. Because of the important vascular and neurological structures, approaches to this region are considered extremely risky. One of the main variations in-person basis is the diameter differences of the arteries, which forms Willis polygon, between the left and right hemispheres. About structure and variations, studies of Rhoton and Yasargil had formed the touchstone. Our aim is to contribute to the literature and clinical studies, to be done in the future, by comparing our results with previous studies about variations and morphometric features of Willis polygon.
Coastal Resources Atlas: Long Island: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Long Island,...
North Slope, Alaska ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for the North...
Columbia River ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Columbia...
Bristol Bay, Alaska Subarea ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for the Bristol...
Spectral segmentation of polygonized images with normalized cuts
Energy Technology Data Exchange (ETDEWEB)
Matsekh, Anna [Los Alamos National Laboratory; Skurikhin, Alexei [Los Alamos National Laboratory; Rosten, Edward [UNIV OF CAMBRIDGE
2009-01-01
We analyze numerical behavior of the eigenvectors corresponding to the lowest eigenvalues of the generalized graph Laplacians arising in the Normalized Cuts formulations of the image segmentation problem on coarse polygonal grids.
Rotating polygon instability of a swirling free surface flow
DEFF Research Database (Denmark)
Tophøj, Laust Emil Hjerrild; Bohr, Tomas; Mougel, J.
2013-01-01
We explain the rotating polygon instability on a swirling fluid surface [G. H. Vatistas, J. Fluid Mech. 217, 241 (1990)JFLSA70022-1120 and Jansson et al., Phys. Rev. Lett. 96, 174502 (2006)PRLTAO0031-9007] in terms of resonant interactions between gravity waves on the outer part of the surface...... behavior near the corners), and indeed we show that we can obtain the polygons transiently by violently stirring liquid nitrogen in a hot container....
NSGIC State | GIS Inventory — SILURIAN_REEF_POLYGONS_MM54_IN is a polygon shapefile that shows the general locations of Silurian rock reef bank formations in Indiana. These data include two major...
Image segmentation by hierarchial agglomeration of polygons using ecological statistics
Prasad, Lakshman; Swaminarayan, Sriram
2013-04-23
A method for rapid hierarchical image segmentation based on perceptually driven contour completion and scene statistics is disclosed. The method begins with an initial fine-scale segmentation of an image, such as obtained by perceptual completion of partial contours into polygonal regions using region-contour correspondences established by Delaunay triangulation of edge pixels as implemented in VISTA. The resulting polygons are analyzed with respect to their size and color/intensity distributions and the structural properties of their boundaries. Statistical estimates of granularity of size, similarity of color, texture, and saliency of intervening boundaries are computed and formulated into logical (Boolean) predicates. The combined satisfiability of these Boolean predicates by a pair of adjacent polygons at a given segmentation level qualifies them for merging into a larger polygon representing a coarser, larger-scale feature of the pixel image and collectively obtains the next level of polygonal segments in a hierarchy of fine-to-coarse segmentations. The iterative application of this process precipitates textured regions as polygons with highly convolved boundaries and helps distinguish them from objects which typically have more regular boundaries. The method yields a multiscale decomposition of an image into constituent features that enjoy a hierarchical relationship with features at finer and coarser scales. This provides a traversable graph structure from which feature content and context in terms of other features can be derived, aiding in automated image understanding tasks. The method disclosed is highly efficient and can be used to decompose and analyze large images.
Aberdeen polygons: computer displays of physiological profiles for intensive care.
Green, C A; Logie, R H; Gilhooly, K J; Ross, D G; Ronald, A
1996-03-01
The clinician in an intensive therapy unit is presented regularly with a range of information about the current physiological state of the patients under care. This information typically comes from a variety of sources and in a variety of formats. A more integrated form of display incorporating several physiological parameters may be helpful therefore. Three experiments are reported that explored the potential use of analogue, polygon diagrams to display physiological data from patients undergoing intensive therapy. Experiment 1 demonstrated that information can be extracted readily from such diagrams comprising 8- or 10-sided polygons, but with an advantage for simpler polygons and for information displayed at the top of the diagram. Experiment 2 showed that colour coding removed these biases for simpler polygons and the top of the diagram, together with speeding the processing time. Experiment 3 used polygons displaying patterns of physiological data that were consistent with typical conditions observed in the intensive care unit. It was found that physicians can readily learn to recognize these patterns and to diagnose both the nature and severity of the patient's physiological state. These polygon diagrams appear to have some considerable potential for use in providing on-line summary information of a patient's physiological state.
Water polygons in high-resolution protein crystal structures.
Lee, Jonas; Kim, Sung-Hou
2009-07-01
We have analyzed the interstitial water (ISW) structures in 1500 protein crystal structures deposited in the Protein Data Bank that have greater than 1.5 A resolution with less than 90% sequence similarity with each other. We observed varieties of polygonal water structures composed of three to eight water molecules. These polygons may represent the time- and space-averaged structures of "stable" water oligomers present in liquid water, and their presence as well as relative population may be relevant in understanding physical properties of liquid water at a given temperature. On an average, 13% of ISWs are localized enough to be visible by X-ray diffraction. Of those, averages of 78% are water molecules in the first water layer on the protein surface. Of the localized ISWs beyond the first layer, almost half of them form water polygons such as trigons, tetragons, as well as expected pentagons, hexagons, higher polygons, partial dodecahedrons, and disordered networks. Most of the octagons and nanogons are formed by fusion of smaller polygons. The trigons are most commonly observed. We suggest that our observation provides an experimental basis for including these water polygon structures in correlating and predicting various water properties in liquid state.
Vigorous convection as the explanation for Pluto's polygonal terrain.
Trowbridge, A J; Melosh, H J; Steckloff, J K; Freed, A M
2016-06-02
Pluto's surface is surprisingly young and geologically active. One of its youngest terrains is the near-equatorial region informally named Sputnik Planum, which is a topographic basin filled by nitrogen (N2) ice mixed with minor amounts of CH4 and CO ices. Nearly the entire surface of the region is divided into irregular polygons about 20-30 kilometres in diameter, whose centres rise tens of metres above their sides. The edges of this region exhibit bulk flow features without polygons. Both thermal contraction and convection have been proposed to explain this terrain, but polygons formed from thermal contraction (analogous to ice-wedges or mud-crack networks) of N2 are inconsistent with the observations on Pluto of non-brittle deformation within the N2-ice sheet. Here we report a parameterized convection model to compute the Rayleigh number of the N2 ice and show that it is vigorously convecting, making Rayleigh-Bénard convection the most likely explanation for these polygons. The diameter of Sputnik Planum's polygons and the dimensions of the 'floating mountains' (the hills of of water ice along the edges of the polygons) suggest that its N2 ice is about ten kilometres thick. The estimated convection velocity of 1.5 centimetres a year indicates a surface age of only around a million years.
Strongly Normal Sets of Convex Polygons or Polyhedra
National Research Council Canada - National Science Library
Saha, Punam
1997-01-01
...,...,Pn, if each Pi intersects P and I = P1 n...n Pn is nonempty, then I intersects P. The union of the Pi epsilon P that intersect P epsilon P is called the neighborhood of P in P and is denoted by Np(P...
Monotonicity properties of keff with shape change and with nesting
International Nuclear Information System (INIS)
Arzhanov, V.
2002-01-01
It was found that, contrary to expectations based on physical intuition, k eff can both increase and decrease when changing the shape of an initially regular critical system, while preserving its volume. Physical intuition would only allow for a decrease of k eff when the surface/volume ratio increases. The unexpected behaviour of increasing k eff was found through numerical investigation. For a convincing demonstration of the possibility of the non-monotonic behaviour, a simple geometrical proof was constructed. This latter proof, in turn, is based on the assumption that k eff can only increase (or stay constant) in the case of nesting, i.e. when adding extra volume to a system. Since we found no formal proof of the nesting theorem for the general case, we close the paper by a simple formal proof of the monotonic behaviour of k eff by nesting
A Hybrid Approach to Proving Memory Reference Monotonicity
Oancea, Cosmin E.
2013-01-01
Array references indexed by non-linear expressions or subscript arrays represent a major obstacle to compiler analysis and to automatic parallelization. Most previous proposed solutions either enhance the static analysis repertoire to recognize more patterns, to infer array-value properties, and to refine the mathematical support, or apply expensive run time analysis of memory reference traces to disambiguate these accesses. This paper presents an automated solution based on static construction of access summaries, in which the reference non-linearity problem can be solved for a large number of reference patterns by extracting arbitrarily-shaped predicates that can (in)validate the reference monotonicity property and thus (dis)prove loop independence. Experiments on six benchmarks show that our general technique for dynamic validation of the monotonicity property can cover a large class of codes, incurs minimal run-time overhead and obtains good speedups. © 2013 Springer-Verlag.
Rational functions with maximal radius of absolute monotonicity
Loczi, Lajos
2014-05-19
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.
Computation of Optimal Monotonicity Preserving General Linear Methods
Ketcheson, David I.
2009-07-01
Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.
Monotonicity and Logarithmic Concavity of Two Functions Involving Exponential Function
Liu, Ai-Qi; Li, Guo-Fu; Guo, Bai-Ni; Qi, Feng
2008-01-01
The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…
Estimation of Poisson-Dirichlet Parameters with Monotone Missing Data
Directory of Open Access Journals (Sweden)
Xueqin Zhou
2017-01-01
Full Text Available This article considers the estimation of the unknown numerical parameters and the density of the base measure in a Poisson-Dirichlet process prior with grouped monotone missing data. The numerical parameters are estimated by the method of maximum likelihood estimates and the density function is estimated by kernel method. A set of simulations was conducted, which shows that the estimates perform well.
Sampling from a Discrete Distribution While Preserving Monotonicity.
1982-02-01
in a table beforehand, this procedure, known as the inverse transform method, requires n storage spaces and EX comparisons on average, which may prove...limitations that deserve attention: a. In general, the alias method does not preserve a monotone relationship between U and X as does the inverse transform method...uses the inverse transform approach but with more information computed beforehand, as in the alias method. The proposed method is not new having been
On a strong law of large numbers for monotone measures
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Ouyang, Y.
2013-01-01
Roč. 83, č. 4 (2013), s. 1213-1218 ISSN 0167-7152 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : capacity * Choquet integral * strong law of large numbers Subject RIV: BA - General Mathematics Impact factor: 0.531, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-on a strong law of large numbers for monotone measures.pdf
Monotonous braking of high energy hadrons in nuclear matter
International Nuclear Information System (INIS)
Strugalski, Z.
1979-01-01
Propagation of high energy hadrons in nuclear matter is discussed. The possibility of the existence of the monotonous energy losses of hadrons in nuclear matter is considered. In favour of this hypothesis experimental facts such as pion-nucleus interactions (proton emission spectra, proton multiplicity distributions in these interactions) and other data are presented. The investigated phenomenon in the framework of the hypothesis is characterized in more detail
L'intersectionnalité contre l'intersection
Chauvin, S.; Jaunait, A.
2015-01-01
Intersectionality against intersection. Is the notion of intersectionality doomed to being part of the problem it designates? Intersectionality theory was not developed to merely point at intersections but to capture subject positions made invisible by dominant systems of normative representation.
Realistic roofs over a rectilinear polygon
Ahn, Heekap
2013-11-01
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. According to this definition, some roofs may have faces isolated from the boundary of P or even local minima, which are undesirable for several practical reasons. In this paper, we introduce realistic roofs by imposing a few additional constraints. We investigate the geometric and combinatorial properties of realistic roofs and show that the straight skeleton induces a realistic roof with maximum height and volume. We also show that the maximum possible number of distinct realistic roofs over P is ((n-4)(n-4)/4 /2⌋) when P has n vertices. We present an algorithm that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n4) preprocessing time. We also present an O(n5)-time algorithm for computing a realistic roof with minimum height or volume. © 2013 Elsevier B.V.
A new convexity measure for polygons.
Zunic, Jovisa; Rosin, Paul L
2004-07-01
Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.
Bifurcation of self-folded polygonal bilayers
Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy
2017-09-01
Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.
Directory of Open Access Journals (Sweden)
Feng Qi
2014-10-01
Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
Directory of Open Access Journals (Sweden)
Chowdhury Molhammad SR
2000-01-01
Full Text Available Results are obtained on existence theorems of generalized bi-quasi-variational inequalities for quasi-semi-monotone and bi-quasi-semi-monotone operators in both compact and non-compact settings. We shall use the concept of escaping sequences introduced by Border (Fixed Point Theorem with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, 1985 to obtain results in non-compact settings. Existence theorems on non-compact generalized bi-complementarity problems for quasi-semi-monotone and bi-quasi-semi-monotone operators are also obtained. Moreover, as applications of some results of this paper on generalized bi-quasi-variational inequalities, we shall obtain existence of solutions for some kind of minimization problems with quasi- semi-monotone and bi-quasi-semi-monotone operators.
International Nuclear Information System (INIS)
Mediavilla, E.; Lopez, P.; Mediavilla, T.; Ariza, O.; Muñoz, J. A.; Gonzalez-Morcillo, C.; Jimenez-Vicente, J.
2011-01-01
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previously reported N –3/4 dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.
A non-parametric test for partial monotonicity in multiple regression
van Beek, M.; Daniëls, H.A.M.
Partial positive (negative) monotonicity in a dataset is the property that an increase in an independent variable, ceteris paribus, generates an increase (decrease) in the dependent variable. A test for partial monotonicity in datasets could (1) increase model performance if monotonicity may be
In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements
Czech Academy of Sciences Publication Activity Database
Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
2016-01-01
Roč. 90, č. 1 (2016), s. 249-261 ISSN 0001-9054 Institutional support: RVO:67985840 Keywords : symmetric spaces * K-monotone symmetric Banach spaces * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2016 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6
Sequential and Parallel Algorithms for Finding a Maximum Convex Polygon
DEFF Research Database (Denmark)
Fischer, Paul
1997-01-01
This paper investigates the problem where one is given a finite set of n points in the plane each of which is labeled either ?positive? or ?negative?. We consider bounded convex polygons, the vertices of which are positive points and which do not contain any negative point. It is shown how...... such a polygon which is maximal with respect to area can be found in time O(n³ log n). With the same running time one can also find such a polygon which contains a maximum number of positive points. If, in addition, the number of vertices of the polygon is restricted to be at most M, then the running time...... becomes O(M n³ log n). It is also shown how to find a maximum convex polygon which contains a given point in time O(n³ log n). Two parallel algorithms for the basic problem are also presented. The first one runs in time O(n log n) using O(n²) processors, the second one has polylogarithmic time but needs O...
Non-monotonic behaviour in relaxation dynamics of image restoration
International Nuclear Information System (INIS)
Ozeki, Tomoko; Okada, Masato
2003-01-01
We have investigated the relaxation dynamics of image restoration through a Bayesian approach. The relaxation dynamics is much faster at zero temperature than at the Nishimori temperature where the pixel-wise error rate is minimized in equilibrium. At low temperature, we observed non-monotonic development of the overlap. We suggest that the optimal performance is realized through premature termination in the relaxation processes in the case of the infinite-range model. We also performed Markov chain Monte Carlo simulations to clarify the underlying mechanism of non-trivial behaviour at low temperature by checking the local field distributions of each pixel
An iterative method for nonlinear demiclosed monotone-type operators
International Nuclear Information System (INIS)
Chidume, C.E.
1991-01-01
It is proved that a well known fixed point iteration scheme which has been used for approximating solutions of certain nonlinear demiclosed monotone-type operator equations in Hilbert spaces remains applicable in real Banach spaces with property (U, α, m+1, m). These Banach spaces include the L p -spaces, p is an element of [2,∞]. An application of our results to the approximation of a solution of a certain linear operator equation in this general setting is also given. (author). 19 refs
A QUALITY ASSESSMENT METHOD FOR 3D ROAD POLYGON OBJECTS
Directory of Open Access Journals (Sweden)
L. Gao
2015-08-01
Full Text Available With the development of the economy, the fast and accurate extraction of the city road is significant for GIS data collection and update, remote sensing images interpretation, mapping and spatial database updating etc. 3D GIS has attracted more and more attentions from academics, industries and governments with the increase of requirements for interoperability and integration of different sources of data. The quality of 3D geographic objects is very important for spatial analysis and decision-making. This paper presents a method for the quality assessment of the 3D road polygon objects which is created by integrating 2D Road Polygon data with LiDAR point cloud and other height information such as Spot Height data in Hong Kong Island. The quality of the created 3D road polygon data set is evaluated by the vertical accuracy, geometric and attribute accuracy, connectivity error, undulation error and completeness error and the final results are presented.
Long-term repetition priming with symmetrical polygons and words.
Kersteen-Tucker, Z
1991-01-01
In two different tasks, subjects were asked to make lexical decisions (word or nonword) and symmetry judgments (symmetrical or nonsymmetrical) about two-dimensional polygons. In both tasks, every stimulus was repeated at one of four lags (0, 1, 4, or 8 items interposed between the first and second stimulus presentations). This paradigm, known as repetition priming, revealed comparable short-term priming (Lag 0) and long-term priming (Lags 1, 4, and 8) both for symmetrical polygons and for words. A shorter term component (Lags 0 and 1) of priming was observed for nonwords, and only very short-term priming (Lag 0) was observed for nonsymmetrical polygons. These results indicate that response facilitation accruing from repeated exposure can be observed for stimuli that have no preexisting memory representations and suggest that perceptual factors contribute to repetition-priming effects.
Experimental quantum control landscapes: Inherent monotonicity and artificial structure
International Nuclear Information System (INIS)
Roslund, Jonathan; Rabitz, Herschel
2009-01-01
Unconstrained searches over quantum control landscapes are theoretically predicted to generally exhibit trap-free monotonic behavior. This paper makes an explicit experimental demonstration of this intrinsic monotonicity for two controlled quantum systems: frequency unfiltered and filtered second-harmonic generation (SHG). For unfiltered SHG, the landscape is randomly sampled and interpolation of the data is found to be devoid of landscape traps up to the level of data noise. In the case of narrow-band-filtered SHG, trajectories are taken on the landscape to reveal a lack of traps. Although the filtered SHG landscape is trap free, it exhibits a rich local structure. A perturbation analysis around the top of these landscapes provides a basis to understand their topology. Despite the inherent trap-free nature of the landscapes, practical constraints placed on the controls can lead to the appearance of artificial structure arising from the resultant forced sampling of the landscape. This circumstance and the likely lack of knowledge about the detailed local landscape structure in most quantum control applications suggests that the a priori identification of globally successful (un)constrained curvilinear control variables may be a challenging task.
Positivity and monotonicity properties of C0-semigroups. Pt. 1
International Nuclear Information System (INIS)
Bratteli, O.; Kishimoto, A.; Robinson, D.W.
1980-01-01
If exp(-tH), exp(-tK), are self-adjoint, positivity preserving, contraction semigroups on a Hilbert space H = L 2 (X;dμ) we write esup(-tH) >= esup(-tK) >= 0 whenever exp(-tH) - exp(-tK) is positivity preserving for all t >= 0 and then we characterize the class of positive functions for which (*) always implies esup(-tf(H)) >= esup(-tf(K)) >= 0. This class consists of the f epsilon Csup(infinitely)(0, infinitely) with (-1)sup(n)fsup((n + 1))(x) >= 0, x epsilon(0, infinitely), n = 0, 1, 2, ... In particular it contains the class of monotone operator functions. Furthermore if exp(-tH) is Lsup(P)(X;dμ) contractive for all p epsilon[1, infinitely] and all t > 0 (or, equivalently, for p = infinitely and t > 0) then exp(-tf(H)) has the same property. Various applications to monotonicity properties of Green's functions are given. (orig.)
Theoretical and experimental study of non-monotonous effects
International Nuclear Information System (INIS)
Delforge, J.
1977-01-01
In recent years, the study of the effects of low dose rates has expanded considerably, especially in connection with current problems concerning the environment and health physics. After having made a precise definition of the different types of non-monotonous effect which may be encountered, for each the main experimental results known are indicated, as well as the principal consequences which may be expected. One example is the case of radiotherapy, where there is a chance of finding irradiation conditions such that the ratio of destructive action on malignant cells to healthy cells is significantly improved. In the second part of the report, the appearance of these phenomena, especially at low dose rates are explained. For this purpose, the theory of transformation systems of P. Delattre is used as a theoretical framework. With the help of a specific example, it is shown that non-monotonous effects are frequently encountered, especially when the overall effect observed is actually the sum of several different elementary effects (e.g. in survival curves, where death may be due to several different causes), or when the objects studied possess inherent kinetics not limited to restoration phenomena alone (e.g. cellular cycle) [fr
The Monotonic Lagrangian Grid for Rapid Air-Traffic Evaluation
Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay
2010-01-01
The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.
Agency for Toxic Substances and Disease Registry (ATSDR) Hazardous Waste Site Polygon Data, 1996
National Aeronautics and Space Administration — The Agency for Toxic Substances and Disease Registry (ATSDR) Hazardous Waste Site Polygon Data, 1996 consists of 2042 polygons for selected hazardous waste sites...
United States National Grid for New Mexico, UTM 12, (1000m X 1000m polygons )
Earth Data Analysis Center, University of New Mexico — This is a polygon feature data layer of United States National Grid (1000m x 1000m polygons ) constructed by the Center for Interdisciplinary Geospatial Information...
United States National Grid for New Mexico, UTM 13, (1000m X 1000m polygons )
Earth Data Analysis Center, University of New Mexico — This is a polygon feature data layer of United States National Grid (1000m x 1000m polygons ) constructed by the Center for Interdisciplinary Geospatial Information...
A fast direct sampling algorithm for equilateral closed polygons
International Nuclear Information System (INIS)
Cantarella, Jason; Duplantier, Bertrand; Shonkwiler, Clayton; Uehara, Erica
2016-01-01
Sampling equilateral closed polygons is of interest in the statistical study of ring polymers. Over the past 30 years, previous authors have proposed a variety of simple Markov chain algorithms (but have not been able to show that they converge to the correct probability distribution) and complicated direct samplers (which require extended-precision arithmetic to evaluate numerically unstable polynomials). We present a simple direct sampler which is fast and numerically stable, and analyze its runtime using a new formula for the volume of equilateral polygon space as a Dirichlet-type integral. (paper)
Polygons of global undersea features for geographic searches
Hartwell, Stephen R.; Wingfield, Dana K.; Allwardt, Alan O.; Lightsom, Frances L.; Wong, Florence L.
2018-01-01
A shapefile of 311 undersea features from all major oceans and seas has been created as an aid for retrieving georeferenced information resources. Geospatial information systems with the capability to search user-defined, polygonal geographic areas will be able to utilize this shapefile or secondary products derived from it, such as linked data based on well-known text representations of the individual polygons within the shapefile. Version 1.1 of this report also includes a linked data representation of 299 of these features and their spatial extents.
Congestion analysis of unsignalized intersections
Abhishek,; Mandjes, M.R.H.; Boon, M.A.A.; Nunez Queija, R.
2016-01-01
This paper considers an unsignalized intersection used by two traffic streams. A stream of cars is using a primary road, and has priority over the other, low-priority, stream. Cars belonging to the latter stream cross the primary road if the gaps between two subsequent cars on the primary road is
Intersectionality in European Union policymaking
DEFF Research Database (Denmark)
Lombardo, Emanuela; Agustin, Lise Rolandsen
2016-01-01
is particularly apt to deal with equality and diversity in policymaking. By analysing a selection of European Union policy documents on gender-based violence in the period 2000–2014, we attend to the question of what intersectionality can bring to policymaking in terms of strengthening inclusiveness and address...
Decomposition of orthogonal polygons in a set of rectanglеs
Shestakov, E.; Voronov, A.
2009-01-01
Algorithm for covering orthogonal integrated circuit layout objects is considered. Objects of the research are special single-connected orthogonal polygons which are generated during decomposition of any multiply connected polygon in a set of single-connected orthogonal polygons. Developed algorithm for covering polygons based on the mathematical techinque of logic matrix transformation. Results described in this paper, can be applied in computer geometry and image analysis.
Using Intersectionality in Student Affairs Research
Strayhorn, Terrell L.
2017-01-01
This chapter presents intersectionality as a useful heuristic for conducting research in higher education and student affairs contexts. Much more than just another theory, intersectionality can powerfully shape student affairs research in both obvious and tacit ways.
Authenticity in Leadership: Intersectionality of Identities.
Jones, Susan R
2016-12-01
This chapter situates leadership and the process of becoming a leader within an understanding of identity, particularly intersecting social identities and intersectionality. © 2016 Wiley Periodicals, Inc., A Wiley Company.
Speetjens, M.F.M.; Meleshko, V.V.; Heijst, van G.J.F.
2014-01-01
The present study addresses the classical problem of the dynamics and stability of a cluster of N point vortices of equal strength arranged in a polygonal configuration ("N-vortex polygons"). In unbounded domains, such N-vortex polygons are unconditionally stable for N
International Nuclear Information System (INIS)
Chenal, C.
1996-01-01
Semipalatinsk in Kazakhstan was one of the nuclear weapons polygon for atmospheric, excavation and underground tests. After a description of the actual state of the polygon, a dosimetric approach inside and outside the polygon is presented from 1949 to 1989. (A.B.). 5 refs., 3 figs., 5 tabs
Multipartite entangled quantum states: Transformation, Entanglement monotones and Application
Cui, Wei
Entanglement is one of the fundamental features of quantum information science. Though bipartite entanglement has been analyzed thoroughly in theory and shown to be an important resource in quantum computation and communication protocols, the theory of entanglement shared between more than two parties, which is called multipartite entanglement, is still not complete. Specifically, the classification of multipartite entanglement and the transformation property between different multipartite states by local operators and classical communications (LOCC) are two fundamental questions in the theory of multipartite entanglement. In this thesis, we present results related to the LOCC transformation between multipartite entangled states. Firstly, we investigate the bounds on the LOCC transformation probability between multipartite states, especially the GHZ class states. By analyzing the involvement of 3-tangle and other entanglement measures under weak two-outcome measurement, we derive explicit upper and lower bound on the transformation probability between GHZ class states. After that, we also analyze the transformation between N-party W type states, which is a special class of multipartite entangled states that has an explicit unique expression and a set of analytical entanglement monotones. We present a necessary and sufficient condition for a known upper bound of transformation probability between two N-party W type states to be achieved. We also further investigate a novel entanglement transformation protocol, the random distillation, which transforms multipartite entanglement into bipartite entanglement ii shared by a non-deterministic pair of parties. We find upper bounds for the random distillation protocol for general N-party W type states and find the condition for the upper bounds to be achieved. What is surprising is that the upper bounds correspond to entanglement monotones that can be increased by Separable Operators (SEP), which gives the first set of
Intersectionality, Race-Gender Subordination, and Education
Harris, Angela; Leonardo, Zeus
2018-01-01
In this chapter, we unpack "intersectionality as an analytical framework." First, we cite Black Lives Matter as an impetus for discussing intersectionality's current traction. Second, we review the genealogy of "intersectionality" beginning with Kimberlé Crenshaw's formulation, which brought a Black Studies provocation into…
30 CFR 57.7055 - Intersecting holes.
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Intersecting holes. 57.7055 Section 57.7055... Jet Piercing Drilling-Surface and Underground § 57.7055 Intersecting holes. Holes shall not be drilled where there is a danger of intersecting a misfired hole or a hole containing explosives, blasting agents...
30 CFR 56.7055 - Intersecting holes.
2010-07-01
... 30 Mineral Resources 1 2010-07-01 2010-07-01 false Intersecting holes. 56.7055 Section 56.7055... Piercing Drilling § 56.7055 Intersecting holes. Holes shall not be drilled where there is a danger of intersecting a misfired hole or a hole containing explosives blasting agents, or detonators. [56 FR 46508, Sept...
Sampling dynamics: an alternative to payoff-monotone selection dynamics
DEFF Research Database (Denmark)
Berkemer, Rainer
payoff-monotone nor payoff-positive which has interesting consequences. This can be demonstrated by application to the travelers dilemma, a deliberately constructed social dilemma. The game has just one symmetric Nash equilibrium which is Pareto inefficient. Especially when the travelers have many......'' of the standard game theory result. Both, analytical tools and agent based simulation are used to investigate the dynamic stability of sampling equilibria in a generalized travelers dilemma. Two parameters are of interest: the number of strategy options (m) available to each traveler and an experience parameter...... (k), which indicates the number of samples an agent would evaluate before fixing his decision. The special case (k=1) can be treated analytically. The stationary points of the dynamics must be sampling equilibria and one can calculate that for m>3 there will be an interior solution in addition...
Modeling non-monotonic properties under propositional argumentation
Wang, Geng; Lin, Zuoquan
2013-03-01
In the field of knowledge representation, argumentation is usually considered as an abstract framework for nonclassical logic. In this paper, however, we'd like to present a propositional argumentation framework, which can be used to closer simulate a real-world argumentation. We thereby argue that under a dialectical argumentation game, we can allow non-monotonic reasoning even under classical logic. We introduce two methods together for gaining nonmonotonicity, one by giving plausibility for arguments, the other by adding "exceptions" which is similar to defaults. Furthermore, we will give out an alternative definition for propositional argumentation using argumentative models, which is highly related to the previous reasoning method, but with a simple algorithm for calculation.
Monotonic childhoods: representations of otherness in research writing
Directory of Open Access Journals (Sweden)
Denise Marcos Bussoletti
2011-12-01
Full Text Available This paper is part of a doctoral thesis entitled “Monotonic childhoods – a rhapsody of hope”. It follows the perspective of a critical psychosocial and cultural study, and aims at discussing the other’s representation in research writing, electing childhood as an allegorical and refl ective place. It takes into consideration, by means of analysis, the drawings and poems of children from the Terezin ghetto during the Second World War. The work is mostly based on Serge Moscovici’s Social Representation Theory, but it is also in constant dialogue with other theories and knowledge fi elds, especially Walter Benjamin’s and Mikhail Bakhtin’s contributions. At the end, the paper supports the thesis that conceives poetics as one of the translation axes of childhood cultures.
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Expert system for failures detection and non-monotonic reasoning
International Nuclear Information System (INIS)
Assis, Abilio de; Schirru, Roberto
1997-01-01
This paper presents the development of a shell denominated TIGER that has the purpose to serve as environment to the development of expert systems in diagnosis of faults in industrial complex plants. A model of knowledge representation and an inference engine based on non monotonic reasoning has been developed in order to provide flexibility in the representation of complex plants as well as performance to satisfy restrictions of real time. The TIGER is able to provide both the occurred fault and a hierarchical view of the several reasons that caused the fault to happen. As a validation of the developed shell a monitoring system of the critical safety functions of Angra-1 has been developed. 7 refs., 7 figs., 2 tabs
Determination of wave direction from linear and polygonal arrays
Digital Repository Service at National Institute of Oceanography (India)
Fernandes, A.A; Gouveia, A; Nagarajan, R.
documentation of Borgman (1974) in case of linear arrays; and the second issue being the failure of Esteva (1976, 1977) to correctly determine wave directions over the design range 25 to 7 sec of his polygonal array. This paper presents requisite documentation...
Vibrational resonances of nonrigid vehicles: Polygonization and ripple patterns
Dekker, H.
2009-01-01
The well-known phenomenon of ripples on roads has its modern counterpart in ripple patterns on railroads and polygonization of wheels on state-of-the-art lightrail streetcars. Here we study an idealized mechanical suspension model for the vibrational frequency response of a buggy with a nonrigid
design chart procedures for polygonal concrete-filled steel columns
African Journals Online (AJOL)
ADMIN
hexagonal and octagonal steel-concrete composite columns subjected to ... This paper also outlines procedures that will enable preparation of ... buildings and in a variety of large-span building ... Likewise, hot-rolled steel tubes are used while ... small moderate large. Fig. 2. Possible arrangement of composite polygonal ...
A Teaching Polygon Makes Learning a Community Enterprise
Colgan, Mark; DeLong, Matt
2015-01-01
In order to strengthen departmental collegiality and improve teaching, our mathematics department instituted a Teaching Polygon. Building on the faculty development idea of Teaching Squares, each member of our department visited one class taught by every other department member in a round-robin fashion during the school year. The visits were…
Sub-wavelength resonances in polygonal metamaterial cylinders
DEFF Research Database (Denmark)
Arslanagic, Samel; Breinbjerg, Olav
2008-01-01
It has been shown that the sub-wavelength resonances of circular MTM cylinders also occur for polygonal MTM cylinders. This is the case for lossless and non-dispersive cylinders as well as lossy and dispersive cylinders. The sub-wavelength resonances are thus not limited to structures of canonical...
Polygons, Pillars and Pavilions: Discovering Connections between Geometry and Architecture
Madden, Sean Patrick
2017-01-01
Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical…
Computing the Fréchet distance between folded polygons
Cook IV, A.F.; Driemel, A.; Sherette, J.; Wenk, C.
2015-01-01
Computing the Fréchet distance for surfaces is a surprisingly hard problem and the only known polynomial-time algorithm is limited to computing it between flat surfaces. We study the problem of computing the Fréchet distance for a class of non-flat surfaces called folded polygons. We present a
Monotonicity of fitness landscapes and mutation rate control.
Belavkin, Roman V; Channon, Alastair; Aston, Elizabeth; Aston, John; Krašovec, Rok; Knight, Christopher G
2016-12-01
A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.
Modeling of chromosome intermingling by partially overlapping uniform random polygons.
Blackstone, T; Scharein, R; Borgo, B; Varela, R; Diao, Y; Arsuaga, J
2011-03-01
During the early phase of the cell cycle the eukaryotic genome is organized into chromosome territories. The geometry of the interface between any two chromosomes remains a matter of debate and may have important functional consequences. The Interchromosomal Network model (introduced by Branco and Pombo) proposes that territories intermingle along their periphery. In order to partially quantify this concept we here investigate the probability that two chromosomes form an unsplittable link. We use the uniform random polygon as a crude model for chromosome territories and we model the interchromosomal network as the common spatial region of two overlapping uniform random polygons. This simple model allows us to derive some rigorous mathematical results as well as to perform computer simulations easily. We find that the probability that one uniform random polygon of length n that partially overlaps a fixed polygon is bounded below by 1 − O(1/√n). We use numerical simulations to estimate the dependence of the linking probability of two uniform random polygons (of lengths n and m, respectively) on the amount of overlapping. The degree of overlapping is parametrized by a parameter [Formula: see text] such that [Formula: see text] indicates no overlapping and [Formula: see text] indicates total overlapping. We propose that this dependence relation may be modeled as f (ε, m, n) = [Formula: see text]. Numerical evidence shows that this model works well when [Formula: see text] is relatively large (ε ≥ 0.5). We then use these results to model the data published by Branco and Pombo and observe that for the amount of overlapping observed experimentally the URPs have a non-zero probability of forming an unsplittable link.
Conformational analysis by intersection: CONAN.
Smellie, Andrew; Stanton, Robert; Henne, Randy; Teig, Steve
2003-01-15
As high throughput techniques in chemical synthesis and screening improve, more demands are placed on computer assisted design and virtual screening. Many of these computational methods require one or more three-dimensional conformations for molecules, creating a demand for a conformational analysis tool that can rapidly and robustly cover the low-energy conformational spaces of small molecules. A new algorithm of intersection is presented here, which quickly generates (on average heuristics are applied after intersection to generate a small representative collection of conformations that span the conformational space. In a study of approximately 97,000 randomly selected molecules from the MDDR, results are presented that explore these conformations and their ability to cover low-energy conformational space. Copyright 2002 Wiley Periodicals, Inc. J Comput Chem 24: 10-20, 2003
Avoided intersections of nodal lines
International Nuclear Information System (INIS)
Monastra, Alejandro G; Smilansky, Uzy; Gnutzmann, Sven
2003-01-01
We consider real eigenfunctions of the Schroedinger operator in 2D. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wavefunctions of non-integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in this work. We define a measure for the avoidance range and compute its distribution for the random wave ensemble. We show that the avoidance range distribution of wavefunctions of chaotic systems follows the expected random wave distributions, whereas for wavefunctions of classically integrable but quantum non-separable systems, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random wave ensemble
Technology in Intersecting Figured Worlds.
Esbensen, Gertrud Lynge; Hasse, Cathrine
2015-01-01
In this chapter we analyze aspects of how Danish student nurses acquire technological literacy during their clinical internship at a Danish hospital. The argument is supported by several cases from Esbensen's empirical work. We focus on a Techno-Anthropological study of how student nurses learn to engage in technological mediated relations, and discuss how we think the ideas of intersecting worlds help to analyze some of the difficulties, student's experience.
Log-supermodularity of weight functions and the loading monotonicity of weighted insurance premiums
Hristo S. Sendov; Ying Wang; Ricardas Zitikis
2010-01-01
The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called loading monotonicity, is satisfied by premiums that appear in the literature. The increased interest in constructing new insurance premiums has raised a question as to what weight functions would produce loading-monotonic premiums. In this paper we demonstrate a...
A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces
Directory of Open Access Journals (Sweden)
Jinlin Guan
2013-01-01
Full Text Available We introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012, and we generalize the variational inclusion involving the -monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012 with the mapping studied by Lan et al. (2011 and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.
Obliquely Propagating Non-Monotonic Double Layer in a Hot Magnetized Plasma
International Nuclear Information System (INIS)
Kim, T.H.; Kim, S.S.; Hwang, J.H.; Kim, H.Y.
2005-01-01
Obliquely propagating non-monotonic double layer is investigated in a hot magnetized plasma, which consists of a positively charged hot ion fluid and trapped, as well as free electrons. A model equation (modified Korteweg-de Vries equation) is derived by the usual reductive perturbation method from a set of basic hydrodynamic equations. A time stationary obliquely propagating non-monotonic double layer solution is obtained in a hot magnetized-plasma. This solution is an analytic extension of the monotonic double layer and the solitary hole. The effects of obliqueness, external magnetic field and ion temperature on the properties of the non-monotonic double layer are discussed
Surfactants non-monotonically modify the onset of Faraday waves
Strickland, Stephen; Shearer, Michael; Daniels, Karen
2017-11-01
When a water-filled container is vertically vibrated, subharmonic Faraday waves emerge once the driving from the vibrations exceeds viscous dissipation. In the presence of an insoluble surfactant, a viscous boundary layer forms at the contaminated surface to balance the Marangoni and Boussinesq stresses. For linear gravity-capillary waves in an undriven fluid, the surfactant-induced boundary layer increases the amount of viscous dissipation. In our analysis and experiments, we consider whether similar effects occur for nonlinear Faraday (gravity-capillary) waves. Assuming a finite-depth, infinite-breadth, low-viscosity fluid, we derive an analytic expression for the onset acceleration up to second order in ɛ =√{ 1 / Re } . This expression allows us to include fluid depth and driving frequency as parameters, in addition to the Marangoni and Boussinesq numbers. For millimetric fluid depths and driving frequencies of 30 to 120 Hz, our analysis recovers prior numerical results and agrees with our measurements of NBD-PC surfactant on DI water. In both case, the onset acceleration increases non-monotonically as a function of Marangoni and Boussinesq numbers. For shallower systems, our model predicts that surfactants could decrease the onset acceleration. DMS-0968258.
Dynamical zeta functions for piecewise monotone maps of the interval
Ruelle, David
2004-01-01
Consider a space M, a map f:M\\to M, and a function g:M \\to {\\mathbb C}. The formal power series \\zeta (z) = \\exp \\sum ^\\infty _{m=1} \\frac {z^m}{m} \\sum _{x \\in \\mathrm {Fix}\\,f^m} \\prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0,1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of \\zeta (z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M,f,g).
The resource theory of quantum reference frames: manipulations and monotones
International Nuclear Information System (INIS)
Gour, Gilad; Spekkens, Robert W
2008-01-01
Every restriction on quantum operations defines a resource theory, determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection rule (SSR) is a restriction that arises through the lack of a classical reference frame and the states that circumvent it (the resource) are quantum reference frames. We consider the resource theories that arise from three types of SSRs, associated respectively with lacking: (i) a phase reference, (ii) a frame for chirality, and (iii) a frame for spatial orientation. Focusing on pure unipartite quantum states (and in some cases restricting our attention even further to subsets of these), we explore single-copy and asymptotic manipulations. In particular, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the maximum rate of conversion. A comparison of the three resource theories demonstrates that the extent to which resources can be interconverted decreases as the strength of the restriction increases. Along the way, we introduce several measures of frameness and prove that these are monotonically non-increasing under various classes of operations that are permitted by the SSR
The Marotto Theorem on planar monotone or competitive maps
International Nuclear Information System (INIS)
Yu Huang
2004-01-01
In 1978, Marotto generalized Li-Yorke's results on the criterion for chaos from one-dimensional discrete dynamical systems to n-dimensional discrete dynamical systems, showing that the existence of a non-degenerate snap-back repeller implies chaos in the sense of Li-Yorke. This theorem is very useful in predicting and analyzing discrete chaos in multi-dimensional dynamical systems. Yet, besides it is well known that there exists an error in the conditions of the original Marotto Theorem, and several authors had tried to correct it in different way, Chen, Hsu and Zhou pointed out that the verification of 'non-degeneracy' of a snap-back repeller is the most difficult in general and expected, 'almost beyond reasonable doubt', that the existence of only degenerate snap-back repeller still implies chaotic, which was posed as a conjecture by them. In this paper, we shall give necessary and sufficient conditions of chaos in the sense of Li-Yorke for planar monotone or competitive discrete dynamical systems and solve Chen-Hsu-Zhou Conjecture for such kinds of systems
The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation
Alexandrov, Natalia; Kaplan, Carolyn; Oran, Elaine; Boris, Jay
2010-01-01
This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.
Exact moduli space metrics for hyperbolic vortex polygons
International Nuclear Information System (INIS)
Krusch, S.; Speight, J. M.
2010-01-01
Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as Σ n,m , are spaces of C n -invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of Σ n,m are investigated, and it is found that Σ n,n-1 is isometric to the hyperbolic plane of curvature -(3πn) -1 . The geodesic flow on Σ n,m and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys. Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.
Electron localization and optical absorption of polygonal quantum rings
Sitek, Anna; Serra, Llorenç; Gudmundsson, Vidar; Manolescu, Andrei
2015-06-01
We investigate theoretically polygonal quantum rings and focus mostly on the triangular geometry where the corner effects are maximal. Such rings can be seen as short core-shell nanowires, a generation of semiconductor heterostructures with multiple applications. We show how the geometry of the sample determines the electronic energy spectrum, and also the localization of electrons, with effects on the optical absorption. In particular, we show that irrespective of the ring shape low-energy electrons are always attracted by corners and are localized in their vicinity. The absorption spectrum in the presence of a magnetic field shows only two peaks within the corner-localized state domain, each associated with different circular polarization. This picture may be changed by an external electric field which allows previously forbidden transitions, and thus enables the number of corners to be determined. We show that polygonal quantum rings allow absorption of waves from distant ranges of the electromagnetic spectrum within one sample.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Selection of industrial robots using the Polygons area method
Directory of Open Access Journals (Sweden)
Mortaza Honarmande Azimi
2014-08-01
Full Text Available Selection of robots from the several proposed alternatives is a very important and tedious task. Decision makers are not limited to one method and several methods have been proposed for solving this problem. This study presents Polygons Area Method (PAM as a multi attribute decision making method for robot selection problem. In this method, the maximum polygons area obtained from the attributes of an alternative robot on the radar chart is introduced as a decision-making criterion. The results of this method are compared with other typical multiple attribute decision-making methods (SAW, WPM, TOPSIS, and VIKOR by giving two examples. To find similarity in ranking given by different methods, Spearman’s rank correlation coefficients are obtained for different pairs of MADM methods. It was observed that the introduced method is in good agreement with other well-known MADM methods in the robot selection problem.
Extending backward polygon beam tracing to glossy scattering surfaces
CSIR Research Space (South Africa)
Duvenhage, B
2011-05-01
Full Text Available to render caustics that could not otherwise be sim- ulated efficiently using the high fidelity forward raytracing and radiosity rendering techniques of the time. Similar to what Heckbert and Hanrahan proposed, Watt [Wat90] used backward polygon beam....: Adaptive radiosity textures for bidi- rectional ray tracing. In SIGGRAPH ?90: Proceedings of the 17th Annual Conference on Computer graphics and Interactive Techniques (New York, NY, USA, 1990), ACM Press, New York, pp. 145?154. [HH84] HECKBERT P. S...
Fat polygonal partitions with applications to visualization and embeddings
Directory of Open Access Journals (Sweden)
Mark de Berg
2013-12-01
Full Text Available Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high.We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes.We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in ℝd. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a polylog(Δ-approximation algorithm for embedding n-point ultrametrics into ℝd with minimum distortion, where Δ denotes the spread of the metric. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.
Measured Hydrologic Storage Characteristics of Three Major Ice Wedge Polygon Types, Barrow, Alaska
Chamberlain, A. J.; Liljedahl, A.; Wilson, C. J.; Cable, W.; Romanovsky, V. E.
2014-12-01
Model simulations have suggested that the hydrologic fluxes and stores of Arctic wetlands are constrained by the micro-topographical features of ice wedge polygons, which are abundant in lowland tundra landscapes. Recently observed changes in ice wedge polygon landscapes - in particular, ice wedge degradation and trough formation - emphasize the need to better understand how differing ice wedge polygon morphologies affect the larger hydrologic system. Here we present three seasons of measured end-of-winter snow accumulation, continuous soil moisture and water table elevations, and repeated frost table mapping. Together, these describe the hydrologic characteristics of three main ice wedge polygon types: low centered polygons with limited trough development (representative of a ~500 year old vegetated drained thaw lake basin), and low- and high-centered polygons with well-defined troughs. Dramatic spatiotemporal variability exists both between polygon types and between the features of an individual polygon (e.g. troughs, centers, rims). Landscape-scale end-of-winter snow water equivalent is similar between polygon types, while the sub-polygon scale distribution of the surface water differs, both as snow and as ponded water. Some sub-polygon features appear buffered against large variations in water levels, while others display periods of prolonged recessions and large responses to rain events. Frost table elevations in general mimic the ground surface topography, but with spatiotemporal variability in thaw rate. The studied thaw seasons represented above long-term average rainfall, and in 2014, record high June precipitation. Differing ice wedge polygon types express dramatically different local hydrology, despite nearly identical climate forcing and landscape-scale snow accumulation, making ice wedge polygons an important component when describing the Arctic water, nutrient and energy system.
Intersecting Branes Flip SU(5)
Ellis, Jonathan Richard; Nanopoulos, Dimitri V; Ellis, John
2002-01-01
Within a toroidal orbifold framework, we exhibit intersecting brane-world constructions of flipped SU(5) \\times U(1) GUT models with various numbers of generations, other chiral matter representations and Higgs representations. We exhibit orientifold constructions with integer winding numbers that yield 8 or more conventional SU(5) generations, and orbifold constructions with fractional winding numbers that yield flipped SU(5) \\times U(1) models with just 3 conventional generations. Some of these models have candidates for the 5 and {\\bar 5} Higgs representations needed for electroweak symmetry breaking, but not for the 10 and {\\bar 10} representations needed for GUT symmetry breaking, or vice-versa.
Projective modules and complete intersections
Mandal, Satya
1997-01-01
In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions". These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel.
Singular moduli and Arakelov intersection
International Nuclear Information System (INIS)
Weng Lin.
1994-05-01
The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs
On a correspondence between regular and non-regular operator monotone functions
DEFF Research Database (Denmark)
Gibilisco, P.; Hansen, Frank; Isola, T.
2009-01-01
We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....
Tijs, S.H.; Moretti, S.; Brânzei, R.; Norde, H.W.
2005-01-01
A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems
An analysis of the stability and monotonicity of a kind of control models
Directory of Open Access Journals (Sweden)
LU Yifa
2013-06-01
Full Text Available The stability and monotonicity of control systems with parameters are considered.By the iterative relationship of the coefficients of characteristic polynomials and the Mathematica software,some sufficient conditions for the monotonicity and stability of systems are given.
A Novel Polygonal Finite Element Method: Virtual Node Method
Tang, X. H.; Zheng, C.; Zhang, J. H.
2010-05-01
Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.
Properties of regular polygons of coupled microring resonators.
Chremmos, Ioannis; Uzunoglu, Nikolaos
2007-11-01
The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.
Fast incorporation of optical flow into active polygons.
Unal, Gozde; Krim, Hamid; Yezzi, Anthony
2005-06-01
In this paper, we first reconsider, in a different light, the addition of a prediction step to active contour-based visual tracking using an optical flow and clarify the local computation of the latter along the boundaries of continuous active contours with appropriate regularizers. We subsequently detail our contribution of computing an optical flow-based prediction step directly from the parameters of an active polygon, and of exploiting it in object tracking. This is in contrast to an explicitly separate computation of the optical flow and its ad hoc application. It also provides an inherent regularization effect resulting from integrating measurements along polygon edges. As a result, we completely avoid the need of adding ad hoc regularizing terms to the optical flow computations, and the inevitably arbitrary associated weighting parameters. This direct integration of optical flow into the active polygon framework distinguishes this technique from most previous contour-based approaches, where regularization terms are theoretically, as well as practically, essential. The greater robustness and speed due to a reduced number of parameters of this technique are additional and appealing features.
PolyRES: A polygon-based Richards equation solver
International Nuclear Information System (INIS)
Hills, R.G.
1995-12-01
This document describes the theory, implementation, and use of a software package designed to solve the transient, two-dimensional, Richards equation for water flow in unsaturated-saturated soils. This package was specifically designed to model complex geometries with minimal input from the user and to simulate groundwater flow related to assessment of low-level radioactive waste disposal sites and engineered facilities. The spatial variation of the hydraulic properties can be defined across individual polygon-shaped subdomains, called objects. These objects combine to form a polygon-shaped model domain. Each object can have its own distribution of hydraulic parameters. The resulting model domain and polygon-shaped internal objects are mapped onto a rectangular, finite-volume, computational grid by a preprocessor. This allows the user to specify model geometry independently of the underlying grid and greatly simplifies user input for complex geometries. In addition, this approach significantly reduces the computational requirements since complex geometries are actually modeled on a rectangular grid. This results in well-structured, finite difference-like systems of equations that require minimal storage and are very efficient to solve. The documentation for this software package includes a user's manual, a detailed description of the underlying theory, and a detailed discussion of program flow. Several example problems are presented that show the use and features of the software package. The water flow predictions for several of these example problems are compared to those of another algorithm to test for prediction equivalency
A model of anelastic relaxation associated with polygonization boundary
International Nuclear Information System (INIS)
Yan, S.C.
1990-01-01
A model of anelastic relaxation associated with polygonization boundary is proposed in order to explain internal friction peaks and other experimental phenomena observed recently. The model, which is referred to as vacancy-thermal jog model, shows that under conditions of high temperature and low applied stress with lower frequencies of vibration, thermal jog pairs are generated on dislocation segments of the boundaries. These jogs are in saturation with vacancies in the vicinity of them, and the vacancy current due to the concentration gradient of vacancy drifts among the boundaries. As a result, a diffusional creep is produced and a part of energy is dissipated. For vacancy drift, it is required that the thermal jogs emit (absorb) vacancies, which brings climbing bow of segments into operation, and another part of energy is dissipated so that there are two parts of energy dissipated in the strain process connected with polygonization boundary. Based on this point of view, the mathematical expressions of internal friction and modulus defect associated with polygonization boundary were subsequently derived and found to be in satisfactory agreement with experiments. (author). 13 refs, 6 figs
Curvature of random walks and random polygons in confinement
International Nuclear Information System (INIS)
Diao, Y; Ernst, C; Montemayor, A; Ziegler, U
2013-01-01
The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to π. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. (paper)
Electronic properties of carbon nanotubes with polygonized cross sections
International Nuclear Information System (INIS)
Charlier, J.; Lambin, P.; Ebbesen, T.
1996-01-01
The electronic properties of carbon nanotubes having polygonized cross sections instead of purely circular ones, such as recently observed using transmission electron microscopy, are investigated with plane-wave ab initio pseudopotential local-density-functional calculations and simple tight-binding models. Strong σ * -π * hybridization effects occur in zigzag nanotubes due to the high curvature located near the edges of the polygonal cross-section prism. These effects, combined with a lowering of symmetry, dramatically affect the electronic properties of the nanotubes. It is found that modified low-lying conduction-band states are introduced either into the bandgap of insulating nanotubes, or below the degenerate states that form the top of the valence band of metallic nanotubes, leading the corresponding nanostructures to be metals, semimetals, or at least very-small-gap semiconductors. The degree of the polygon representing the cross section of the tube, and the sharpness of the edge angles, are found to be major factors in the hybridization effect, and consequently govern the electronic behavior at the Fermi level. copyright 1996 The American Physical Society
Framing Gender Intersections in the European Union
DEFF Research Database (Denmark)
Lombardo, Emanuela; Agustin, Lise Rolandsen
2012-01-01
are increasingly present but they are treated implicitly and from a separate perspective, and the inclusion of a wide range of inequalities often implies a degendering of the policy content. We assess the implications of the identified intersectionality trends for the quality of intersectionality in gender...... equality policies, and we suggest the practice of an “intersectionality impact assessment” as a way to improve the quality of EU policy-making....
Generalized Yosida Approximations Based on Relatively A-Maximal m-Relaxed Monotonicity Frameworks
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Heng-you Lan
2013-01-01
Full Text Available We introduce and study a new notion of relatively A-maximal m-relaxed monotonicity framework and discuss some properties of a new class of generalized relatively resolvent operator associated with the relatively A-maximal m-relaxed monotone operator and the new generalized Yosida approximations based on relatively A-maximal m-relaxed monotonicity framework. Furthermore, we give some remarks to show that the theory of the new generalized relatively resolvent operator and Yosida approximations associated with relatively A-maximal m-relaxed monotone operators generalizes most of the existing notions on (relatively maximal monotone mappings in Hilbert as well as Banach space and can be applied to study variational inclusion problems and first-order evolution equations as well as evolution inclusions.
DESIGNING AN EFFECTIVE INTERSECTION USING CAD ENVIRONMENT
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CRISAN George-Horea
2017-05-01
Full Text Available Ensuring the safety and streamline in road traffic are very important aims, with regard to the nowadays people mobility level. Road infrastructure is an essential element that can meet these requirements. Thus, it is proposed to develop an effective model of intersection by using CAD software tools. This type of intersection can be successfully used on almost any category of roads, increasing road traffic safety, reducing passing times through the intersection and in the same time, reducing conflict points and increase the intersection capacity.
Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups
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Francesco Paolo Montefalcone
2010-12-01
Full Text Available Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S. We stress that S and @S are endowed with the homogeneous measures n????1 H and n????2 H , respectively, which are actually equivalent to the intrinsic (Q - 1-dimensional and (Q - 2-dimensional Hausdor measures with respect to a given homogeneous metric % on G. This result generalizes a classical inequality, involving the mean curvature of the hypersurface, proven by Michael and Simon [29] and Allard [1], independently. One may also deduce some related Sobolev-type inequalities. The strategy of the proof is inspired by the classical one and will be discussed at the rst section. After reminding some preliminary notions about Carnot groups, we shall begin by proving a linear isoperimetric inequality. The second step is a local monotonicity formula. Then we may achieve the proof by a covering argument.We stress however that there are many dierences, due to our non-Euclidean setting.Some of the tools developed ad hoc are, in order, a \\blow-up" theorem, which holds true also for characteristic points, and a smooth Coarea Formula for the HS-gradient. Other tools are the horizontal integration by parts formula and the 1st variation formula for the H-perimeter n????1H already developed in [30, 31] and then generalized to hypersurfaces having non-empty characteristic set in [32]. These results can be useful in the study of minimal and constant horizontal mean curvature hypersurfaces in Carnot groups.
Small-Scale Polygons and the History of Ground Ice on Mars
Mellon, Michael T.
2000-01-01
This research has laid a foundation for continued study of permafrost polygons on Mars using the models and understanding discussed here. Further study of polygonal patterns on Mars is proceeding (under new funding) which is expected to reveal more results about the origin of observed martian polygons and what information they contain regarding the recent history of tile martian climate and of water ice on Mars.
Material parameters characterization for arbitrary N-sided regular polygonal invisible cloak
International Nuclear Information System (INIS)
Wu Qun; Zhang Kuang; Meng Fanyi; Li Lewei
2009-01-01
Arbitrary N-sided regular polygonal cylindrical cloaks are proposed and designed based on the coordinate transformation theory. First, the general expressions of constitutive tensors of the N-sided regular polygonal cylindrical cloaks are derived, then there are some full-wave simulations of the cloaks that are composed of inhomogeneous and anisotropic metamaterials, which will bend incoming electromagnetic waves and guide them to propagate around the inner region; such electromagnetic waves will return to their original propagation directions without distorting the waves outside the polygonal cloak. The results of full-wave simulations validate the general expressions of constitutive tensors of the N-sided regular polygonal cylindrical cloaks we derived.
A numerical investigation of sub-wavelength resonances in polygonal metamaterial cylinders
DEFF Research Database (Denmark)
Arslanagic, Samel; Breinbjerg, Olav
2009-01-01
The sub-wavelength resonances, known to exist in metamaterial radiators and scatterers of circular cylindrical shape, are investigated with the aim of determining if these resonances also exist for polygonal cylinders and, if so, how they are affected by the shape of the polygon. To this end, a set...... of polygonal cylinders excited by a nearby electric line current is analyzed numerically and it is shown, through detailed analysis of the near-field distribution and radiation resistance, that these polygonal cylinders do indeed support sub-wavelength resonances similar to those of the circular cylinders...
Intersectionality and Educational Leadership: A Critical Review
Agosto, Vonzell; Roland, Ericka
2018-01-01
In this review of research, we explore intersectionality in the literature on K-12 educational leadership. We seek to understand how researchers have used intersectionality and what their findings or arguments reveal about the work of leading to reduce inequities in education. We ask, What traditions and trends associated with intersectionality…
Traffic monitoring and modeling for Intersection Safety
Pyykönen, P.; Molinier, M.; Klunder, G.A.
2010-01-01
The INTERSAFE-2 project aims to develop and demonstrate a Cooperative Intersection Safety System that is able to significantly reduce injury and fatal accidents at intersections. The cooperative sensor data fusion is based on state-of-the-art and advanced on-board sensors for object recognition and
Rank 2 fusion rings are complete intersections
DEFF Research Database (Denmark)
Andersen, Troels Bak
We give a non-constructive proof that fusion rings attached to a simple complex Lie algebra of rank 2 are complete intersections.......We give a non-constructive proof that fusion rings attached to a simple complex Lie algebra of rank 2 are complete intersections....
UpSet: Visualization of Intersecting Sets
Lex, Alexander; Gehlenborg, Nils; Strobelt, Hendrik; Vuillemot, Romain; Pfister, Hanspeter
2016-01-01
Understanding relationships between sets is an important analysis task that has received widespread attention in the visualization community. The major challenge in this context is the combinatorial explosion of the number of set intersections if the number of sets exceeds a trivial threshold. In this paper we introduce UpSet, a novel visualization technique for the quantitative analysis of sets, their intersections, and aggregates of intersections. UpSet is focused on creating task-driven aggregates, communicating the size and properties of aggregates and intersections, and a duality between the visualization of the elements in a dataset and their set membership. UpSet visualizes set intersections in a matrix layout and introduces aggregates based on groupings and queries. The matrix layout enables the effective representation of associated data, such as the number of elements in the aggregates and intersections, as well as additional summary statistics derived from subset or element attributes. Sorting according to various measures enables a task-driven analysis of relevant intersections and aggregates. The elements represented in the sets and their associated attributes are visualized in a separate view. Queries based on containment in specific intersections, aggregates or driven by attribute filters are propagated between both views. We also introduce several advanced visual encodings and interaction methods to overcome the problems of varying scales and to address scalability. UpSet is web-based and open source. We demonstrate its general utility in multiple use cases from various domains. PMID:26356912
Appropriate Pupilness: Social Categories Intersecting in School
Kofoed, Jette
2008-01-01
The analytical focus in this article is on how social categories intersect in daily school life and how intersections intertwine with other empirically relevant categories such as normality, pupilness and (in)appropriatedness. The point of empirical departure is a daily ritual where teams for football are selected. The article opens up for a…
Directory of Open Access Journals (Sweden)
Mervan Pašić
2016-10-01
Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.
Engaging student expeditionary units to land work at aerospace polygons
Directory of Open Access Journals (Sweden)
Ирина Жемерова
2016-10-01
Full Text Available To organize the aerospace polygon it is necessary to conduct a large number of measurement and descriptive works. First and foremost is working with the fund and cartographic material. The map of the landfill shows the most important objects and phenomena: quarries, sinkholes, deep ravines, industrial, residential and protected areas. Organization of the aerospace polygon operation involves large labour costs. To train professionals on the ground research of the earth’s cover remote sensing, we have organized a permanent student expedition. Prior to the start of work, students listen to a series of introductory lectures on remote sensing, principles of ground work, methods of statistical evaluation, basic methods of data collection and processing. This article covers one direction of work - collecting and processing of phytometric data of crops and steppe vegetation in the Streletskaya steppe in the Central Chernozem nature reserve. The work is carried out on the test area of Kursk aerospace polygon, organized on the basis of Kursk biospheric station of the Institute of Geography RAS. A generally accepted method of test platforms is used on the routes. The results of measurements and observations are recorded in a field book. Species diversity, plant height, projective cover and crops density are determined on the sample area by the instrumental and visual methods. The rest phytometric indexes are calculated in laboratory conditions. The students can use the resulting material when writing articles, course and degree works. At the site, students acquire skills of working in field conditions with natural objects, collecting and processing of information by various methods, expanding understanding of the need and importance of the earth surface study by remote sensing methods.
The Knot Spectrum of Confined Random Equilateral Polygons
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Diao Y.
2014-01-01
Full Text Available It is well known that genomic materials (long DNA chains of living organisms are often packed compactly under extreme confining conditions using macromolecular self-assembly processes but the general DNA packing mechanism remains an unsolved problem. It has been proposed that the topology of the packed DNA may be used to study the DNA packing mechanism. For example, in the case of (mutant bacteriophage P4, DNA molecules packed inside the bacteriophage head are considered to be circular since the two sticky ends of the DNA are close to each other. The DNAs extracted from the capsid without separating the two ends can thus preserve the topology of the (circular DNAs. It turns out that the circular DNAs extracted from bacteriophage P4 are non-trivially knotted with very high probability and with a bias toward chiral knots. In order to study this problem using a systematic approach based on mathematical modeling, one needs to introduce a DNA packing model under extreme volume confinement condition and test whether such a model can produce the kind of knot spectrum observed in the experiments. In this paper we introduce and study a model of equilateral random polygons con_ned in a sphere. This model is not meant to generate polygons that model DNA packed in a virus head directly. Instead, the average topological characteristics of this model may serve as benchmark data for totally randomly packed circular DNAs. The difference between the biologically observed topological characteristics and our benchmark data might reveal the bias of DNA packed in the viral capsids and possibly lead to a better understanding of the DNA packing mechanism, at least for the bacteriophage DNA. The purpose of this paper is to provide information about the knot spectrum of equilateral random polygons under such a spherical confinement with length and confinement ratios in a range comparable to circular DNAs packed inside bacteriophage heads.
Giant polygons and mounds in the lowlands of Mars: signatures of an ancient ocean?
Oehler, Dorothy Z; Allen, Carlton C
2012-06-01
This paper presents the hypothesis that the well-known giant polygons and bright mounds of the martian lowlands may be related to a common process-a process of fluid expulsion that results from burial of fine-grained sediments beneath a body of water. Specifically, we hypothesize that giant polygons and mounds in Chryse and Acidalia Planitiae are analogous to kilometer-scale polygons and mud volcanoes in terrestrial, marine basins and that the co-occurrence of masses of these features in Chryse and Acidalia may be the signature of sedimentary processes in an ancient martian ocean. We base this hypothesis on recent data from both Earth and Mars. On Earth, 3-D seismic data illustrate kilometer-scale polygons that may be analogous to the giant polygons on Mars. The terrestrial polygons form in fine-grained sediments that have been deposited and buried in passive-margin, marine settings. These polygons are thought to result from compaction/dewatering, and they are commonly associated with fluid expulsion features, such as mud volcanoes. On Mars, in Chryse and Acidalia Planitiae, orbital data demonstrate that giant polygons and mounds have overlapping spatial distributions. There, each set of features occurs within a geological setting that is seemingly analogous to that of the terrestrial, kilometer-scale polygons (broad basin of deposition, predicted fine-grained sediments, and lack of significant horizontal stress). Regionally, the martian polygons and mounds both show a correlation to elevation, as if their formation were related to past water levels. Although these observations are based on older data with incomplete coverage, a similar correlation to elevation has been established in one local area studied in detail with newer higher-resolution data. Further mapping with the latest data sets should more clearly elucidate the relationship(s) of the polygons and mounds to elevation over the entire Chryse-Acidalia region and thereby provide more insight into this
Logarithmically complete monotonicity of a function related to the Catalan-Qi function
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Qi Feng
2016-08-01
Full Text Available In the paper, the authors find necessary and sufficient conditions such that a function related to the Catalan-Qi function, which is an alternative generalization of the Catalan numbers, is logarithmically complete monotonic.
Monotone matrix transformations defined by the group inverse and simultaneous diagonalizability
International Nuclear Information System (INIS)
Bogdanov, I I; Guterman, A E
2007-01-01
Bijective linear transformations of the matrix algebra over an arbitrary field that preserve simultaneous diagonalizability are characterized. This result is used for the characterization of bijective linear monotone transformations . Bibliography: 28 titles.
Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables
Chikalov, Igor; Hussain, Shahid; Moshkov, Mikhail
2013-01-01
In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization
Monotone methods for solving a boundary value problem of second order discrete system
Directory of Open Access Journals (Sweden)
Wang Yuan-Ming
1999-01-01
Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
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Kalabušić S
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.
Reduction theorems for weighted integral inequalities on the cone of monotone functions
International Nuclear Information System (INIS)
Gogatishvili, A; Stepanov, V D
2013-01-01
This paper surveys results related to the reduction of integral inequalities involving positive operators in weighted Lebesgue spaces on the real semi-axis and valid on the cone of monotone functions, to certain more easily manageable inequalities valid on the cone of non-negative functions. The case of monotone operators is new. As an application, a complete characterization for all possible integrability parameters is obtained for a number of Volterra operators. Bibliography: 118 titles
Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables
Chikalov, Igor
2013-01-01
In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.
Directory of Open Access Journals (Sweden)
Heinz Werner Höppel
2012-02-01
Full Text Available The monotonic and cyclic deformation behavior of ultrafine-grained metastable austenitic steel AISI 304L, produced by severe plastic deformation, was investigated. Under monotonic loading, the martensitic phase transformation in the ultrafine-grained state is strongly favored. Under cyclic loading, the martensitic transformation behavior is similar to the coarse-grained condition, but the cyclic stress response is three times larger for the ultrafine-grained condition.
International Nuclear Information System (INIS)
Duan Shukai; Liao Xiaofeng
2007-01-01
A new chaotic delayed neuron model with non-monotonously increasing transfer function, called as chaotic Liao's delayed neuron model, was recently reported and analyzed. An electronic implementation of this model is described in detail. At the same time, some methods in circuit design, especially for circuit with time delayed unit and non-monotonously increasing activation unit, are also considered carefully. We find that the dynamical behaviors of the designed circuits are closely similar to the results predicted by numerical experiments
A fast ergodic algorithm for generating ensembles of equilateral random polygons
Varela, R.; Hinson, K.; Arsuaga, J.; Diao, Y.
2009-03-01
Knotted structures are commonly found in circular DNA and along the backbone of certain proteins. In order to properly estimate properties of these three-dimensional structures it is often necessary to generate large ensembles of simulated closed chains (i.e. polygons) of equal edge lengths (such polygons are called equilateral random polygons). However finding efficient algorithms that properly sample the space of equilateral random polygons is a difficult problem. Currently there are no proven algorithms that generate equilateral random polygons with its theoretical distribution. In this paper we propose a method that generates equilateral random polygons in a 'step-wise uniform' way. We prove that this method is ergodic in the sense that any given equilateral random polygon can be generated by this method and we show that the time needed to generate an equilateral random polygon of length n is linear in terms of n. These two properties make this algorithm a big improvement over the existing generating methods. Detailed numerical comparisons of our algorithm with other widely used algorithms are provided.
Development of polygon elements based on the scaled boundary finite element method
International Nuclear Information System (INIS)
Chiong, Irene; Song Chongmin
2010-01-01
We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.
System and method for the adaptive mapping of matrix data to sets of polygons
Burdon, David (Inventor)
2003-01-01
A system and method for converting bitmapped data, for example, weather data or thermal imaging data, to polygons is disclosed. The conversion of the data into polygons creates smaller data files. The invention is adaptive in that it allows for a variable degree of fidelity of the polygons. Matrix data is obtained. A color value is obtained. The color value is a variable used in the creation of the polygons. A list of cells to check is determined based on the color value. The list of cells to check is examined in order to determine a boundary list. The boundary list is then examined to determine vertices. The determination of the vertices is based on a prescribed maximum distance. When drawn, the ordered list of vertices create polygons which depict the cell data. The data files which include the vertices for the polygons are much smaller than the corresponding cell data files. The fidelity of the polygon representation can be adjusted by repeating the logic with varying fidelity values to achieve a given maximum file size or a maximum number of vertices per polygon.
Decompositions, partitions, and coverings with convex polygons and pseudo-triangles
Aichholzer, O.; Huemer, C.; Kappes, S.; Speckmann, B.; Tóth, Cs.D.
2007-01-01
We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex
Origin of the Polygons and Underground Structures in Western Utopia Planitia on Mars
Yoshikawa, K.
2002-01-01
The area of lower albedo (Hvm) has a higher density of polygonal patterns. These patterns potentially suggest that 1) the polygonal pattern is caused primarily by ground heaving and collapsing, 2) lower albedo materials had higher tensile strength. Additional information is contained in the original extended abstract.
Analysis of the Misconceptions of 7th Grade Students on Polygons and Specific Quadrilaterals
Ozkan, Mustafa; Bal, Ayten Pinar
2017-01-01
Purpose: This study will find out student misconceptions about geometrical figures, particularly polygons and quadrilaterals. Thus, it will offer insights into teaching these concepts. The objective of this study, the question of "What are the misconceptions of seventh grade students on polygons and quadrilaterals?" constitutes the…
International Nuclear Information System (INIS)
Yu Yunhan; Xia Yan; Liu Yaqiang; Wang Shi; Ma Tianyu; Chen Jing; Hong Baoyu
2013-01-01
To achieve a maximum compression of system matrix in positron emission tomography (PET) image reconstruction, we proposed a polygonal image pixel division strategy in accordance with rotationally symmetric PET geometry. Geometrical definition and indexing rule for polygonal pixels were established. Image conversion from polygonal pixel structure to conventional rectangular pixel structure was implemented using a conversion matrix. A set of test images were analytically defined in polygonal pixel structure, converted to conventional rectangular pixel based images, and correctly displayed which verified the correctness of the image definition, conversion description and conversion of polygonal pixel structure. A compressed system matrix for PET image recon was generated by tap model and tested by forward-projecting three different distributions of radioactive sources to the sinogram domain and comparing them with theoretical predictions. On a practical small animal PET scanner, a compress ratio of 12.6:1 of the system matrix size was achieved with the polygonal pixel structure, comparing with the conventional rectangular pixel based tap-mode one. OS-EM iterative image reconstruction algorithms with the polygonal and conventional Cartesian pixel grid were developed. A hot rod phantom was detected and reconstructed based on these two grids with reasonable time cost. Image resolution of reconstructed images was both 1.35 mm. We conclude that it is feasible to reconstruct and display images in a polygonal image pixel structure based on a compressed system matrix in PET image reconstruction. (authors)
Origami tubes with reconfigurable polygonal cross-sections.
Filipov, E T; Paulino, G H; Tachi, T
2016-01-01
Thin sheets can be assembled into origami tubes to create a variety of deployable, reconfigurable and mechanistically unique three-dimensional structures. We introduce and explore origami tubes with polygonal, translational symmetric cross-sections that can reconfigure into numerous geometries. The tubular structures satisfy the mathematical definitions for flat and rigid foldability, meaning that they can fully unfold from a flattened state with deformations occurring only at the fold lines. The tubes do not need to be straight and can be constructed to follow a non-linear curved line when deployed. The cross-section and kinematics of the tubular structures can be reprogrammed by changing the direction of folding at some folds. We discuss the variety of tubular structures that can be conceived and we show limitations that govern the geometric design. We quantify the global stiffness of the origami tubes through eigenvalue and structural analyses and highlight the mechanical characteristics of these systems. The two-scale nature of this work indicates that, from a local viewpoint, the cross-sections of the polygonal tubes are reconfigurable while, from a global viewpoint, deployable tubes of desired shapes are achieved. This class of tubes has potential applications ranging from pipes and micro-robotics to deployable architecture in buildings.
Origami tubes with reconfigurable polygonal cross-sections
Filipov, E. T.; Paulino, G. H.; Tachi, T.
2016-01-01
Thin sheets can be assembled into origami tubes to create a variety of deployable, reconfigurable and mechanistically unique three-dimensional structures. We introduce and explore origami tubes with polygonal, translational symmetric cross-sections that can reconfigure into numerous geometries. The tubular structures satisfy the mathematical definitions for flat and rigid foldability, meaning that they can fully unfold from a flattened state with deformations occurring only at the fold lines. The tubes do not need to be straight and can be constructed to follow a non-linear curved line when deployed. The cross-section and kinematics of the tubular structures can be reprogrammed by changing the direction of folding at some folds. We discuss the variety of tubular structures that can be conceived and we show limitations that govern the geometric design. We quantify the global stiffness of the origami tubes through eigenvalue and structural analyses and highlight the mechanical characteristics of these systems. The two-scale nature of this work indicates that, from a local viewpoint, the cross-sections of the polygonal tubes are reconfigurable while, from a global viewpoint, deployable tubes of desired shapes are achieved. This class of tubes has potential applications ranging from pipes and micro-robotics to deployable architecture in buildings. PMID:26997894
Transit Traffic Analysis Zone Delineating Method Based on Thiessen Polygon
Directory of Open Access Journals (Sweden)
Shuwei Wang
2014-04-01
Full Text Available A green transportation system composed of transit, busses and bicycles could be a significant in alleviating traffic congestion. However, the inaccuracy of current transit ridership forecasting methods is imposing a negative impact on the development of urban transit systems. Traffic Analysis Zone (TAZ delineating is a fundamental and essential step in ridership forecasting, existing delineating method in four-step models have some problems in reflecting the travel characteristics of urban transit. This paper aims to come up with a Transit Traffic Analysis Zone delineation method as supplement of traditional TAZs in transit service analysis. The deficiencies of current TAZ delineating methods were analyzed, and the requirements of Transit Traffic Analysis Zone (TTAZ were summarized. Considering these requirements, Thiessen Polygon was introduced into TTAZ delineating. In order to validate its feasibility, Beijing was then taken as an example to delineate TTAZs, followed by a spatial analysis of office buildings within a TTAZ and transit station departure passengers. Analysis result shows that the TTAZs based on Thiessen polygon could reflect the transit travel characteristic and is of in-depth research value.
Polygonal patterned peatlands of the White Sea islands
Kutenkov, S. A.; Kozhin, M. N.; Golovina, E. O.; Kopeina, E. I.; Stoikina, N. V.
2018-03-01
The summits and slopes of some islands along the northeastern and northern coasts of the White Sea are covered with dried out peatlands. The thickness of the peat deposit is 30–80 cm and it is separated by troughs into gently sloping polygonal peat blocks up to 20 m2 in size. On some northern islands the peat blocks have permafrost cores. The main components of the dried out peatlands vegetation are dwarf shrubs and lichens. The peat stratigraphy reveals two stages of peatland development. On the first stage, the islands were covered with wet cottongrass carpets, which repeated the convex relief shape. On the second stage, they were occupied by the xeromorphic vegetation. We suggest that these polygonal patterned peatlands are the remnants of blanket bogs, the formation of which assumes the conditions of a much more humid climate in the historical past. The time of their active development was calculated according to the White Sea level changes and radiocarbon dates from 1000–4000 BP.
A discrete wavelet spectrum approach for identifying non-monotonic trends in hydroclimate data
Sang, Yan-Fang; Sun, Fubao; Singh, Vijay P.; Xie, Ping; Sun, Jian
2018-01-01
The hydroclimatic process is changing non-monotonically and identifying its trends is a great challenge. Building on the discrete wavelet transform theory, we developed a discrete wavelet spectrum (DWS) approach for identifying non-monotonic trends in hydroclimate time series and evaluating their statistical significance. After validating the DWS approach using two typical synthetic time series, we examined annual temperature and potential evaporation over China from 1961-2013 and found that the DWS approach detected both the warming and the warming hiatus in temperature, and the reversed changes in potential evaporation. Further, the identified non-monotonic trends showed stable significance when the time series was longer than 30 years or so (i.e. the widely defined climate timescale). The significance of trends in potential evaporation measured at 150 stations in China, with an obvious non-monotonic trend, was underestimated and was not detected by the Mann-Kendall test. Comparatively, the DWS approach overcame the problem and detected those significant non-monotonic trends at 380 stations, which helped understand and interpret the spatiotemporal variability in the hydroclimatic process. Our results suggest that non-monotonic trends of hydroclimate time series and their significance should be carefully identified, and the DWS approach proposed has the potential for wide use in the hydrological and climate sciences.
A discrete wavelet spectrum approach for identifying non-monotonic trends in hydroclimate data
Directory of Open Access Journals (Sweden)
Y.-F. Sang
2018-01-01
Full Text Available The hydroclimatic process is changing non-monotonically and identifying its trends is a great challenge. Building on the discrete wavelet transform theory, we developed a discrete wavelet spectrum (DWS approach for identifying non-monotonic trends in hydroclimate time series and evaluating their statistical significance. After validating the DWS approach using two typical synthetic time series, we examined annual temperature and potential evaporation over China from 1961–2013 and found that the DWS approach detected both the warming and the warming hiatus in temperature, and the reversed changes in potential evaporation. Further, the identified non-monotonic trends showed stable significance when the time series was longer than 30 years or so (i.e. the widely defined climate timescale. The significance of trends in potential evaporation measured at 150 stations in China, with an obvious non-monotonic trend, was underestimated and was not detected by the Mann–Kendall test. Comparatively, the DWS approach overcame the problem and detected those significant non-monotonic trends at 380 stations, which helped understand and interpret the spatiotemporal variability in the hydroclimatic process. Our results suggest that non-monotonic trends of hydroclimate time series and their significance should be carefully identified, and the DWS approach proposed has the potential for wide use in the hydrological and climate sciences.
Kang, Hyeon-Ah; Su, Ya-Hui; Chang, Hua-Hua
2018-03-08
A monotone relationship between a true score (τ) and a latent trait level (θ) has been a key assumption for many psychometric applications. The monotonicity property in dichotomous response models is evident as a result of a transformation via a test characteristic curve. Monotonicity in polytomous models, in contrast, is not immediately obvious because item response functions are determined by a set of response category curves, which are conceivably non-monotonic in θ. The purpose of the present note is to demonstrate strict monotonicity in ordered polytomous item response models. Five models that are widely used in operational assessments are considered for proof: the generalized partial credit model (Muraki, 1992, Applied Psychological Measurement, 16, 159), the nominal model (Bock, 1972, Psychometrika, 37, 29), the partial credit model (Masters, 1982, Psychometrika, 47, 147), the rating scale model (Andrich, 1978, Psychometrika, 43, 561), and the graded response model (Samejima, 1972, A general model for free-response data (Psychometric Monograph no. 18). Psychometric Society, Richmond). The study asserts that the item response functions in these models strictly increase in θ and thus there exists strict monotonicity between τ and θ under certain specified conditions. This conclusion validates the practice of customarily using τ in place of θ in applied settings and provides theoretical grounds for one-to-one transformations between the two scales. © 2018 The British Psychological Society.
Brooker, L. M.; Balme, M. R.; Conway, S. J.; Hagermann, A.; Barrett, A. M.; Collins, G. S.; Soare, R. J.
2018-03-01
Polygonal networks of patterned ground are a common feature in cold-climate environments. They can form through the thermal contraction of ice-cemented sediment (i.e. formed from fractures), or the freezing and thawing of ground ice (i.e. formed by patterns of clasts, or ground deformation). The characteristics of these landforms provide information about environmental conditions. Analogous polygonal forms have been observed on Mars leading to inferences about environmental conditions. We have identified clastic polygonal features located around Lyot crater, Mars (50°N, 30°E). These polygons are unusually large (>100 m diameter) compared to terrestrial clastic polygons, and contain very large clasts, some of which are up to 15 metres in diameter. The polygons are distributed in a wide arc around the eastern side of Lyot crater, at a consistent distance from the crater rim. Using high-resolution imaging data, we digitised these features to extract morphological information. These data are compared to existing terrestrial and Martian polygon data to look for similarities and differences and to inform hypotheses concerning possible formation mechanisms. Our results show the clastic polygons do not have any morphometric features that indicate they are similar to terrestrial sorted, clastic polygons formed by freeze-thaw processes. They are too large, do not show the expected variation in form with slope, and have clasts that do not scale in size with polygon diameter. However, the clastic networks are similar in network morphology to thermal contraction cracks, and there is a potential direct Martian analogue in a sub-type of thermal contraction polygons located in Utopia Planitia. Based upon our observations, we reject the hypothesis that polygons located around Lyot formed as freeze-thaw polygons and instead an alternative mechanism is put forward: they result from the infilling of earlier thermal contraction cracks by wind-blown material, which then became
Intersection numbers of spectral curves
Eynard, B.
2011-01-01
We compute the symplectic invariants of an arbitrary spectral curve with only 1 branchpoint in terms of integrals of characteristic classes in the moduli space of curves. Our formula associates to any spectral curve, a characteristic class, which is determined by the laplace transform of the spectral curve. This is a hint to the key role of Laplace transform in mirror symmetry. When the spectral curve is y=\\sqrt{x}, the formula gives Kontsevich--Witten intersection numbers, when the spectral curve is chosen to be the Lambert function \\exp{x}=y\\exp{-y}, the formula gives the ELSV formula for Hurwitz numbers, and when one chooses the mirror of C^3 with framing f, i.e. \\exp{-x}=\\exp{-yf}(1-\\exp{-y}), the formula gives the Marino-Vafa formula, i.e. the generating function of Gromov-Witten invariants of C^3. In some sense this formula generalizes ELSV, Marino-Vafa formula, and Mumford formula.
A Polygon and Point-Based Approach to Matching Geospatial Features
Directory of Open Access Journals (Sweden)
Juan J. Ruiz-Lendínez
2017-12-01
Full Text Available A methodology for matching bidimensional entities is presented in this paper. The matching is proposed for both area and point features extracted from geographical databases. The procedure used to obtain homologous entities is achieved in a two-step process: The first matching, polygon to polygon matching (inter-element matching, is obtained by means of a genetic algorithm that allows the classifying of area features from two geographical databases. After this, we apply a point to point matching (intra-element matching based on the comparison of changes in their turning functions. This study shows that genetic algorithms are suitable for matching polygon features even if these features are quite different. Our results show up to 40% of matched polygons with differences in geometrical attributes. With regards to point matching, the vertex from homologous polygons, the function and threshold values proposed in this paper show a useful method for obtaining precise vertex matching.
The average inter-crossing number of equilateral random walks and polygons
International Nuclear Information System (INIS)
Diao, Y; Dobay, A; Stasiak, A
2005-01-01
In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = 3ln2/8 ∼ 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance ρ apart and ρ is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of ρ. Our simulation result shows that the model in fact works very well for the entire range of ρ. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well
Rural expressway intersection safety toolbox : desktop reference.
2011-06-01
This document is intended to be a guide for planning-level decisions concerning safety : issues and subsequent potential improvements at rural expressway intersections. It is : NOT a design guide. It simply presents the gamut of safety treatment opti...
Optimising Signalised Intersection Using Wireless Vehicle Detectors
DEFF Research Database (Denmark)
Adjin, Daniel Michael Okwabi; Torkudzor, Moses; Asare, Jack
Traffic congestion on roads wastes travel times. In this paper, we developed a vehicular traffic model to optimise a signalised intersection in Accra, using wireless vehicle detectors. Traffic volume gathered was extrapolated to cover 2011 and 2016 and were analysed to obtain the peak hour traffic...... volume causing congestion. The intersection was modelled and simulated in Synchro7 as an actuated signalised model using results from the analysed data. The model for morning peak periods gave optimal cycle lengths of 100s and 150s with corresponding intersection delay of 48.9s and 90.6s in 2011 and 2016...... respectively while that for the evening was 55s giving delay of 14.2s and 16.3s respectively. It is shown that the model will improve traffic flow at the intersection....
Gender Equality, Intersectionality and Diversity in Europe
DEFF Research Database (Denmark)
Agustin, Lise Rolandsen
. Drawing on discursive policy analysis, it addresses the interaction between policies, institutions and civil society actors in relation to gender equality, diversity and intersectionality at the European level. Rolandsen Agustín successfully integrates the concepts of diversity and gender equality...... into a contextualized approach to analyzing transnational intersectionality. This unique approach focuses on processes of institutionalization and mobilization, which are addressed in relation to the institutional setup of the EU, its policies and policymaking structures, as well as transnational civil society...
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Self-Localization at Street Intersections.
Fusco, Giovanni; Shen, Huiying; Coughlan, James M
2014-05-01
There is growing interest among smartphone users in the ability to determine their precise location in their environment for a variety of applications related to wayfinding, travel and shopping. While GPS provides valuable self-localization estimates, its accuracy is limited to approximately 10 meters in most urban locations. This paper focuses on the self-localization needs of blind or visually impaired travelers, who are faced with the challenge of negotiating street intersections. These travelers need more precise self-localization to help them align themselves properly to crosswalks, signal lights and other features such as walk light pushbuttons. We demonstrate a novel computer vision-based localization approach that is tailored to the street intersection domain. Unlike most work on computer vision-based localization techniques, which typically assume the presence of detailed, high-quality 3D models of urban environments, our technique harnesses the availability of simple, ubiquitous satellite imagery (e.g., Google Maps) to create simple maps of each intersection. Not only does this technique scale naturally to the great majority of street intersections in urban areas, but it has the added advantage of incorporating the specific metric information that blind or visually impaired travelers need, namely, the locations of intersection features such as crosswalks. Key to our approach is the integration of IMU (inertial measurement unit) information with geometric information obtained from image panorama stitchings. Finally, we evaluate the localization performance of our algorithm on a dataset of intersection panoramas, demonstrating the feasibility of our approach.
Deformations of polyhedra and polygons by the unitary group
Energy Technology Data Exchange (ETDEWEB)
Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d' Italie, Lyon 69007, France and Perimeter Institute, 31 Caroline St N, Waterloo, Ontario N2L 2Y5 (Canada)
2013-12-15
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in
A polygon soup representation for free viewpoint video
Colleu, T.; Pateux, S.; Morin, L.; Labit, C.
2010-02-01
This paper presents a polygon soup representation for multiview data. Starting from a sequence of multi-view video plus depth (MVD) data, the proposed representation takes into account, in a unified manner, different issues such as compactness, compression, and intermediate view synthesis. The representation is built in two steps. First, a set of 3D quads is extracted using a quadtree decomposition of the depth maps. Second, a selective elimination of the quads is performed in order to reduce inter-view redundancies and thus provide a compact representation. Moreover, the proposed methodology for extracting the representation allows to reduce ghosting artifacts. Finally, an adapted compression technique is proposed that limits coding artifacts. The results presented on two real sequences show that the proposed representation provides a good trade-off between rendering quality and data compactness.
PATTERN CLASSIFICATION APPROACHES TO MATCHING BUILDING POLYGONS AT MULTIPLE SCALES
Directory of Open Access Journals (Sweden)
X. Zhang
2012-07-01
Full Text Available Matching of building polygons with different levels of detail is crucial in the maintenance and quality assessment of multi-representation databases. Two general problems need to be addressed in the matching process: (1 Which criteria are suitable? (2 How to effectively combine different criteria to make decisions? This paper mainly focuses on the second issue and views data matching as a supervised pattern classification. Several classifiers (i.e. decision trees, Naive Bayes and support vector machines are evaluated for the matching task. Four criteria (i.e. position, size, shape and orientation are used to extract information for these classifiers. Evidence shows that these classifiers outperformed the weighted average approach.
Treks into intuitive geometry the world of polygons and polyhedra
Akiyama, Jin
2015-01-01
This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was ...
Reachability by paths of bounded curvature in a convex polygon
Ahn, Heekap; Cheong, Otfried; Matoušek, Jiřǐ; Vigneron, Antoine E.
2012-01-01
Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n2) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment. © 2011 Elsevier B.V.
Vortex breakdown in closed containers with polygonal cross sections
International Nuclear Information System (INIS)
Naumov, I. V.; Dvoynishnikov, S. V.; Kabardin, I. K.; Tsoy, M. A.
2015-01-01
The vortex breakdown bubble in the confined flow generated by a rotating lid in closed containers with polygonal cross sections was analysed both experimentally and numerically for the height/radius aspect ratio equal to 2. The stagnation point locations of the breakdown bubble emergence and the corresponding Reynolds number were determined experimentally and in addition computed numerically by STAR-CCM+ CFD software for square, pentagonal, hexagonal, and octagonal cross section configurations. The flow pattern and the velocity were observed and measured by combining the seeding particle visualization and the temporal accuracy of laser Doppler anemometry. The vortex breakdown size and position on the container axis were determined for Reynolds numbers, ranging from 1450 to 2400. The obtained results were compared with the flow structure in the closed container of cubical and cylindrical configurations. It is shown that the measured evolution of steady vortex breakdown is in close agreement with the numerical results
Convergence of Wachspress coordinates: from polygons to curved domains
Kosinka, Jiří
2014-08-08
Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases. © 2014 Springer Science+Business Media New York.
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
Convergence of Wachspress coordinates: from polygons to curved domains
Kosinka, Jiří
2014-01-01
Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases. © 2014 Springer Science+Business Media New York.
Generalized Swept Mid-structure for Polygonal Models
Martin, Tobias; Chen, Guoning; Musuvathy, Suraj; Cohen, Elaine; Hansen, Charles
2012-01-01
We introduce a novel mid-structure called the generalized swept mid-structure (GSM) of a closed polygonal shape, and a framework to compute it. The GSM contains both curve and surface elements and has consistent sheet-by-sheet topology, versus triangle-by-triangle topology produced by other mid-structure methods. To obtain this structure, a harmonic function, defined on the volume that is enclosed by the surface, is used to decompose the volume into a set of slices. A technique for computing the 1D mid-structures of these slices is introduced. The mid-structures of adjacent slices are then iteratively matched through a boundary similarity computation and triangulated to form the GSM. This structure respects the topology of the input surface model is a hybrid mid-structure representation. The construction and topology of the GSM allows for local and global simplification, used in further applications such as parameterization, volumetric mesh generation and medical applications.
Generalized Swept Mid-structure for Polygonal Models
Martin, Tobias
2012-05-01
We introduce a novel mid-structure called the generalized swept mid-structure (GSM) of a closed polygonal shape, and a framework to compute it. The GSM contains both curve and surface elements and has consistent sheet-by-sheet topology, versus triangle-by-triangle topology produced by other mid-structure methods. To obtain this structure, a harmonic function, defined on the volume that is enclosed by the surface, is used to decompose the volume into a set of slices. A technique for computing the 1D mid-structures of these slices is introduced. The mid-structures of adjacent slices are then iteratively matched through a boundary similarity computation and triangulated to form the GSM. This structure respects the topology of the input surface model is a hybrid mid-structure representation. The construction and topology of the GSM allows for local and global simplification, used in further applications such as parameterization, volumetric mesh generation and medical applications.
An electrophysiological study of the mental rotation of polygons.
Pierret, A; Peronnet, F; Thevenet, M
1994-05-09
Reaction times and event-related potentials (ERPs) were recorded during a task requiring subjects to decide whether two sequentially presented polygons had the same shape regardless of differences in orientation. Reaction times increased approximately linearly with angular departure from upright orientation, which suggests that mental rotation was involved in the comparison process. The ERPs showed, between 665 and 1055 ms, a late posterior negativity also increasing with angular disparity from upright, which we assumed to reflect mental rotation. Two other activities were exhibited, from 265 to 665 ms, which may be related either to an evaluation of the stimulus or a predetermination of its orientation, and from 1055 to 1600 ms attributed to the decision process.
Experimental investigation into the mechanism of the polygonal wear of electric locomotive wheels
Tao, Gongquan; Wang, Linfeng; Wen, Zefeng; Guan, Qinghua; Jin, Xuesong
2018-06-01
Experiments were conducted at field sites to investigate the mechanism of the polygonal wear of electric locomotive wheels. The polygonal wear rule of electric locomotive wheels was obtained. Moreover, two on-track tests have been carried out to investigate the vibration characteristics of the electric locomotive's key components. The measurement results of wheels out-of-round show that most electric locomotive wheels exhibit polygonal wear. The main centre wavelength in the 1/3 octave bands is 200 mm and/or 160 mm. The test results of vibration characteristics indicate that the dominating frequency of the vertical acceleration measured on the axle box is approximately equal to the passing frequency of a polygonal wheel, and does not vary with the locomotive speed during the acceleration course. The wheelset modal analysis using the finite element method (FEM) indicates that the first bending resonant frequency of the wheelset is quite close to the main vibration frequency of the axle box. The FEM results are verified by the experimental modal analysis of the wheelset. Moreover, different plans were designed to verify whether the braking system and the locomotive's adhesion control have significant influence on the wheel polygon or not. The test results indicate that they are not responsible for the initiation of the wheel polygon. The first bending resonance of the wheelset is easy to be excited in the locomotive operation and it is the root cause of wheel polygon with centre wavelength of 200 mm in the 1/3 octave bands.
Failure mechanisms of closed-cell aluminum foam under monotonic and cyclic loading
International Nuclear Information System (INIS)
Amsterdam, E.; De Hosson, J.Th.M.; Onck, P.R.
2006-01-01
This paper concentrates on the differences in failure mechanisms of Alporas closed-cell aluminum foam under either monotonic or cyclic loading. The emphasis lies on aspects of crack nucleation and crack propagation in relation to the microstructure. The cell wall material consists of Al dendrites and an interdendritic network of Al 4 Ca and Al 22 CaTi 2 precipitates. In situ scanning electron microscopy monotonic tensile tests were performed on small samples to study crack nucleation and propagation. Digital image correlation was employed to map the strain in the cell wall on the characteristic microstructural length scale. Monotonic tensile tests and tension-tension fatigue tests were performed on larger samples to observe the overall fracture behavior and crack path in monotonic and cyclic loading. The crack nucleation and propagation path in both loading conditions are revealed and it can be concluded that during monotonic tension cracks nucleate in and propagate partly through the Al 4 Ca interdendritic network, whereas under cyclic loading cracks nucleate and propagate through the Al dendrites
A Polygon Model for Wireless Sensor Network Deployment with Directional Sensing Areas
Wu, Chun-Hsien; Chung, Yeh-Ching
2009-01-01
The modeling of the sensing area of a sensor node is essential for the deployment algorithm of wireless sensor networks (WSNs). In this paper, a polygon model is proposed for the sensor node with directional sensing area. In addition, a WSN deployment algorithm is presented with topology control and scoring mechanisms to maintain network connectivity and improve sensing coverage rate. To evaluate the proposed polygon model and WSN deployment algorithm, a simulation is conducted. The simulation results show that the proposed polygon model outperforms the existed disk model and circular sector model in terms of the maximum sensing coverage rate. PMID:22303159
On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement
International Nuclear Information System (INIS)
Ikehata, M; Itou, H
2011-01-01
In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation.
The generation algorithm of arbitrary polygon animation based on dynamic correction
Directory of Open Access Journals (Sweden)
Hou Ya Wei
2016-01-01
Full Text Available This paper, based on the key-frame polygon sequence, proposes a method that makes use of dynamic correction to develop continuous animation. Firstly we use quadratic Bezier curve to interpolate the corresponding sides vector of polygon sequence consecutive frame and realize the continuity of animation sequences. And then, according to Bezier curve characteristic, we conduct dynamic regulation to interpolation parameters and implement the changing smoothness. Meanwhile, we take use of Lagrange Multiplier Method to correct the polygon and close it. Finally, we provide the concrete algorithm flow and present numerical experiment results. The experiment results show that the algorithm acquires excellent effect.
Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
Mozartova, A.; Savostianov, I.; Hundsdorfer, W.
2015-01-01
© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
Energy Technology Data Exchange (ETDEWEB)
Erol, V. [Department of Computer Engineering, Institute of Science, Okan University, Istanbul (Turkey); Netas Telecommunication Inc., Istanbul (Turkey)
2016-04-21
Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.
Bornkamp, Björn; Ickstadt, Katja
2009-03-01
In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.
Comparison of boundedness and monotonicity properties of one-leg and linear multistep methods
Mozartova, A.
2015-05-01
© 2014 Elsevier B.V. All rights reserved. One-leg multistep methods have some advantage over linear multistep methods with respect to storage of the past results. In this paper boundedness and monotonicity properties with arbitrary (semi-)norms or convex functionals are analyzed for such multistep methods. The maximal stepsize coefficient for boundedness and monotonicity of a one-leg method is the same as for the associated linear multistep method when arbitrary starting values are considered. It will be shown, however, that combinations of one-leg methods and Runge-Kutta starting procedures may give very different stepsize coefficients for monotonicity than the linear multistep methods with the same starting procedures. Detailed results are presented for explicit two-step methods.
Watching Electrons at Conical Intersections and Funnels
Jonas, David M.; Smith, Eric R.; Peters, William K.; Kitney, Katherine A.
2009-06-01
The electronic motion at conical intersections and funnels is probed after polarized excitation of aligned electronic wavepackets. The pulses have bandwidth sufficient to observe vibrations mainly through their effect on the electrons. Vibrational symmetry can be identified by the polarization anisotropy of vibrational quantum beats. The polarized transients show signatures of electronic wavepacket motion (due to the energy gaps) and of electron transfer between orbitals (due to the couplings) driven by the conical intersection. For a conical intersection in a four-fold symmetric symmetry silicon naphthalocyanine molecule, electronic motions on a 100 fs timescale are driven by couplings of 1 meV. In the lower symmetry free-base naphthalocyanine, the conical intersection may be missed or missing (conical funnel), and the motions are nearly as rapid, but electronic equilibration is incomplete for red-edge excitation. These experiments probe non-adiabatic electronic dynamics with near-zero nuclear momentum - the electronic motions are determined by the principal slopes of the conical intersection and the width of the vibrational wavepacket.
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.; Saude, Joao
2017-01-01
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models
International Nuclear Information System (INIS)
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng
2013-01-01
The purpose of this work is to investigate the existence, uniqueness, monotonicity and asymptotic behaviour of travelling wave solutions for a general epidemic model arising from the spread of an epidemic by oral–faecal transmission. First, we apply Schauder's fixed point theorem combining with a supersolution and subsolution pair to derive the existence of positive monotone monostable travelling wave solutions. Then, applying the Ikehara's theorem, we determine the exponential rates of travelling wave solutions which converge to two different equilibria as the moving coordinate tends to positive infinity and negative infinity, respectively. Finally, using the sliding method, we prove the uniqueness result provided the travelling wave solutions satisfy some boundedness conditions. (paper)
Monotone numerical methods for finite-state mean-field games
Gomes, Diogo A.
2017-04-29
Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard conditions are the main difficulty in the numerical approximation of solutions. Using the monotonicity condition, we build a flow that is a contraction and whose fixed points solve the MFG, both for stationary and time-dependent problems. We illustrate our methods in a MFG modeling the paradigm-shift problem.
Masuyama, Hiroyuki
2014-01-01
In this paper we study the augmented truncation of discrete-time block-monotone Markov chains under geometric drift conditions. We first present a bound for the total variation distance between the stationary distributions of an original Markov chain and its augmented truncation. We also obtain such error bounds for more general cases, where an original Markov chain itself is not necessarily block monotone but is blockwise dominated by a block-monotone Markov chain. Finally,...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and anadromous fish species in Central California. Vector polygons in this data set...
Sensitivity of Coastal Environments and Wildlife to Spilled Oil: Hudson River: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and freshwater fish species in the Hudson River. Vector polygons in this...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for amphibians and reptiles in Central California. Vector polygons in this data set represent sea turtle...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains management area data for National Wildlife Refuges in the Aleutian Islands, Alaska. Vector polygons in this data set represent management...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles, estuarine turtles, and gopher tortoise in Mississippi. Vector polygons in this data set...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Abandoned Uranium Mine (AUM) Region Polygons, Navajo Nation, 2016, US EPA Region 9
U.S. Environmental Protection Agency — This GIS dataset contains polygon features representing the boundaries of the six Abandoned Uranium Mines (AUM) Regions, including the: Central, Eastern, Northern,...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, freshwater, and anadromous fish species in Northwest Arctic, Alaska. Vector polygons...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing coastal wetlands classified according to the Environmental Sensitivity Index (ESI) classification system for...
Cook Inlet and Kenai Peninsula, Alaska ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains biological resource data for marine mammals in Cook Inlet and Kenai Peninsula, Alaska. Vector polygons in this data set represent locations of...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species for the Hudson River. Vector polygons in this data set...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for dolphin and manatees in Mississippi. Vector polygons in this data set represent marine mammal...
U.S. Environmental Protection Agency — This is a polygon feature dataset with areas along the shoreline of the Hawaiian islands. The National Coastal Condition Assessment (NCCA) is a national coastal...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for endangered plants for the Upper Coast of Texas. Vector polygons in this data set represent occurrence...
Sensitivity of Coastal Environments and Wildlife to Spilled Oil: South Florida: FISH (Fish Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine fish species in South Florida. Vector polygons in this data set represent fish...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for South...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains benthic habitats, including coral reef and hardbottom, seagrass, algae, and others in [for] South Florida. Vector polygons in the data set...
National Oceanic and Atmospheric Administration, Department of Commerce — The ESIP data set contains vector polygons representing the shoreline and coastal habitats of South Florida classified according to the Environmental Sensitivity...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles and estuarine frogs and turtles in Northern California. Vector polygons in this data set...
National Priorities List (NPL) Site Polygons, Region 9, 2012, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
National Priorities List (NPL) Site Polygons, Region 9, 2010, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
AMCO Off-Site Air Monitoring Polygons, Oakland CA, 2017, US EPA Region 9
U.S. Environmental Protection Agency — This feature class was developed to support the AMCO Chemical Superfund Site air monitoring process and depicts a single polygon layer, Off-Site Air Monitors,...
National Priorities List (NPL) Site Polygons, Region 9, 2014, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
National Priorities List (NPL) Site Polygons, Region 9, 2013, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
National Priorities List (NPL) Site Polygons, Region 9, 2015, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
Guam and the Northern Mariana Islands ESI: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for dolphins in Guam and the Northern Mariana Islands. Vector polygons in this data set represent marine...
Coastal Resources Atlas: Long Island: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for northern river otter, mink, muskrat, and beaver for Long Island, New York. Vector polygons in this data...
National Priorities List (NPL) Site Polygons, Region 9, 2017, US EPA Region 9
U.S. Environmental Protection Agency — NPL site POLYGON locations for the US EPA Region 9. NPL (National Priorities List) sites are hazardous waste sites that are eligible for extensive long-term cleanup...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species in Northwest Arctic, Alaska. Vector polygons in this data set...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and brackish water invertebrate species in Mississippi. Vector polygons in this data...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles and select estuarine/freshwater reptiles for the Florida Panhandle. Vector polygons in this...
Rhode Island, Connecticut, New York, and New Jersey ESI: INDEX (Index Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of the U.S. Geological Survey 1:24,000 topographic maps and other map and digital data boundaries...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, and estuarine invertebrate species in New Hampshire. Vector polygons in this data set represent...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species for the Upper Coast of Texas. Vector polygons in this data...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, and freshwater fish species for the Upper Coast of Texas. Vector polygons in this...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species in South Florida. Vector polygons in this data set represent...
Coastal Resources Atlas: Long Island: M_MAMMAL (Marine Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for seals, whales, and porpoises for Long Island, New York. Vector polygons in this data set represent...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine and estuarine invertebrate species in North Carolina. Vector polygons in this data set represent...
Quasi regular polygons and their duals with Coxeter symmetries Dn represented by complex numbers
International Nuclear Information System (INIS)
Koca, M; Koca, N O
2011-01-01
This paper deals with tiling of the plane by quasi regular polygons and their duals. The problem is motivated from the fact that the graphene, infinite number of carbon molecules forming a honeycomb lattice, may have states with two bond lengths and equal bond angles or one bond length and different bond angles. We prove that the Euclidean plane can be tiled with two tiles consisting of quasi regular hexagons with two different lengths (isogonal hexagons) and regular hexagons. The dual lattice is constructed with the isotoxal hexagons (equal edges but two different interior angles) and regular hexagons. We also give similar tilings of the plane with the quasi regular polygons along with the regular polygons possessing the Coxeter symmetries D n , n=2,3,4,5. The group elements as well as the vertices of the polygons are represented by the complex numbers.
The packing of two species of polygons on the square lattice
International Nuclear Information System (INIS)
Dei Cont, David; Nienhuis, Bernard
2004-01-01
We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24-vertex model which is known in the literature as the fully packed double loop model (FPL 2 ). In the particular case in which the fugacities of the polygons are the same, the model admits an exact solution. The solution is obtained using coordinate Bethe ansatz and provides a closed expression for the free energy. In particular, we find the free energy of the four-colouring model and the double Hamiltonian walk and recover the known entropy of the Ice model. When both fugacities are set equal to 2 the model undergoes an infinite-order phase transition
Supramolecule-to-supramolecule transformations of coordination-driven self-assembled polygons.
Zhao, Liang; Northrop, Brian H; Stang, Peter J
2008-09-10
Two types of supramolecular transformations, wherein a self-assembled Pt(II)-pyridyl metal-organic polygon is controllably converted into an alternative polygon, have been achieved through the reaction between cobalt carbonyl and the acetylene moiety of a dipyridyl donor ligand. A [6 + 6] hexagon is transformed into two [3 + 3] hexagons, and a triangle-square mixture is converted into [2 + 2] rhomboids. 1H and 31P NMR spectra are used to track the transformation process and evaluate the yield of new self-assembled polygons. Such transformed species are identified by electrospray ionization (ESI) mass spectrometry. This new kind of supramolecule-to-supramolecule transformations provides a viable means for constructing, and then converting, new self-assembled polygons.
Convex lattice polygons of fixed area with perimeter-dependent weights.
Rajesh, R; Dhar, Deepak
2005-01-01
We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a critical exponent which does not change with t. Using heuristic arguments, we find that theta(conv) is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected nonuniversality of theta(conv) is traced to existence of sharp corners in the asymptotic shape of these polygons.
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing the boundaries of all hardcopy cartographic products produced as part of the Environmental Sensitivity Index...
Virginia ESI: ESI (Environmental Sensitivity Index Shoreline Types - Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing the shoreline and coastal habitats for Virginia, classified according to the Environmental Sensitivity...
Maryland ESI: ESI (Environmental Sensitivity Index Shoreline Types - Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing the shoreline and coastal habitats for Maryland, classified according to the Environmental Sensitivity...
Rhode Island, Connecticut, New York, and New Jersey ESI: T_MAMMAL (Terrestrial Mammal Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for small mammal species in coastal Rhode Island, Connecticut, New York, and New Jersey. Vector polygons in...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for marine, estuarine, anadromous, and brackish/freshwater fish species in North Carolina. Vector polygons...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Southern...
Guam and the Northern Mariana Islands ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Guam and the...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Central...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector polygons representing management area data for Designated Critical Habitats, National Park Service properties, Wildlife Refuges, and...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Northern...
Rhode Island, Connecticut, New York, and New Jersey ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Rhode Island,...
Cook Inlet and Kenai Peninsula, Alaska ESI: HYDRO (Hydrography Lines and Polygons)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for Cook Inlet...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing coastal hydrography used in the creation of the Environmental Sensitivity Index (ESI) for New...
U.S. Environmental Protection Agency — This feature class contains the 64 tax map key polygons across the state of Hawaii that have been inspected by US EPA Pacific Southwest Enforcement Division as of...
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains vector lines and polygons representing the shoreline and coastal habitats of Cook Inlet and Kenai Peninsula, Alaska, classified according to...
Switching Exciton Pulses Through Conical Intersections
Leonhardt, K.; Wüster, S.; Rost, J. M.
2014-11-01
Exciton pulses transport excitation and entanglement adiabatically through Rydberg aggregates, assemblies of highly excited light atoms, which are set into directed motion by resonant dipole-dipole interaction. Here, we demonstrate the coherent splitting of such pulses as well as the spatial segregation of electronic excitation and atomic motion. Both mechanisms exploit local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The intersection provides a sensitive knob controlling the propagation direction and coherence properties of exciton pulses. The fundamental ideas discussed here have general implications for excitons on a dynamic network.
Model of Random Polygon Particles for Concrete and Mesh Automatic Subdivision
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In order to study the constitutive behavior of concrete in mesoscopic level, a new method is proposed in this paper. This method uses random polygon particles to simulate full grading broken aggregates of concrete. Based on computational geometry, we carry out the automatic generation of the triangle finite element mesh for the model of random polygon particles of concrete. The finite element mesh generated in this paper is also applicable to many other numerical methods.
In-gap corner states in core-shell polygonal quantum rings.
Sitek, Anna; Ţolea, Mugurel; Niţă, Marian; Serra, Llorenç; Gudmundsson, Vidar; Manolescu, Andrei
2017-01-10
We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of corner-side-localized states. We specify conditions allowing optical excitation to those states.
In-gap corner states in core-shell polygonal quantum rings
Sitek, Anna; Ţolea, Mugurel; Niţă, Marian; Serra, Llorenç; Gudmundsson, Vidar; Manolescu, Andrei
2017-01-01
We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of corner-side-localized states. We specify conditions allowing optical excitation to those states.
On the mean and variance of the writhe of random polygons
International Nuclear Information System (INIS)
Portillo, J; Scharein, R; Arsuaga, J; Vazquez, M; Diao, Y
2011-01-01
We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe. Suppose that we are dealing with a set of random polygons with the same length and knot type, which could be the model of some circular DNA with the same topological property. In general, a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons; if the mean writhe is non-zero then the knot is chiral. How accurate is this method? For example, if for a specific knot type K the mean writhe decreased to zero as the length of the polygons increased, then this method would be limited in the case of long polygons. Furthermore, we conjecture that the sign of the mean writhe is a topological invariant of chiral knots. This sign appears to be the same as that of an 'ideal' conformation of the knot. We provide numerical evidence to support these claims, and we propose a new nomenclature of knots based on the sign of their expected writhes. This nomenclature can be of particular interest to applied scientists. The second part of our study focuses on the variance of the writhe, a problem that has not received much attention in the past. In this case, we focused on the equilateral random polygons. We give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons (of length n) behaves as a linear function of the length of the equilateral random polygon.
On the mean and variance of the writhe of random polygons.
Portillo, J; Diao, Y; Scharein, R; Arsuaga, J; Vazquez, M
We here address two problems concerning the writhe of random polygons. First, we study the behavior of the mean writhe as a function length. Second, we study the variance of the writhe. Suppose that we are dealing with a set of random polygons with the same length and knot type, which could be the model of some circular DNA with the same topological property. In general, a simple way of detecting chirality of this knot type is to compute the mean writhe of the polygons; if the mean writhe is non-zero then the knot is chiral. How accurate is this method? For example, if for a specific knot type K the mean writhe decreased to zero as the length of the polygons increased, then this method would be limited in the case of long polygons. Furthermore, we conjecture that the sign of the mean writhe is a topological invariant of chiral knots. This sign appears to be the same as that of an "ideal" conformation of the knot. We provide numerical evidence to support these claims, and we propose a new nomenclature of knots based on the sign of their expected writhes. This nomenclature can be of particular interest to applied scientists. The second part of our study focuses on the variance of the writhe, a problem that has not received much attention in the past. In this case, we focused on the equilateral random polygons. We give numerical as well as analytical evidence to show that the variance of the writhe of equilateral random polygons (of length n ) behaves as a linear function of the length of the equilateral random polygon.
International Nuclear Information System (INIS)
Mori, N.; Kobayashi, K.
1996-01-01
A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)
Identifying Conventionally Sub-Seismic Faults in Polygonal Fault Systems
Fry, C.; Dix, J.
2017-12-01
Polygonal Fault Systems (PFS) are prevalent in hydrocarbon basins globally and represent potential fluid pathways. However the characterization of these pathways is subject to the limitations of conventional 3D seismic imaging; only capable of resolving features on a decametre scale horizontally and metres scale vertically. While outcrop and core examples can identify smaller features, they are limited by the extent of the exposures. The disparity between these scales can allow for smaller faults to be lost in a resolution gap which could mean potential pathways are left unseen. Here the focus is upon PFS from within the London Clay, a common bedrock that is tunnelled into and bears construction foundations for much of London. It is a continuation of the Ieper Clay where PFS were first identified and is found to approach the seafloor within the Outer Thames Estuary. This allows for the direct analysis of PFS surface expressions, via the use of high resolution 1m bathymetric imaging in combination with high resolution seismic imaging. Through use of these datasets surface expressions of over 1500 faults within the London Clay have been identified, with the smallest fault measuring 12m and the largest at 612m in length. The displacements over these faults established from both bathymetric and seismic imaging ranges from 30cm to a couple of metres, scales that would typically be sub-seismic for conventional basin seismic imaging. The orientations and dimensions of the faults within this network have been directly compared to 3D seismic data of the Ieper Clay from the offshore Dutch sector where it exists approximately 1km below the seafloor. These have typical PFS attributes with lengths of hundreds of metres to kilometres and throws of tens of metres, a magnitude larger than those identified in the Outer Thames Estuary. The similar orientations and polygonal patterns within both locations indicates that the smaller faults exist within typical PFS structure but are
Co-evolution of polygonal and scalloped terrains, southwestern Utopia Planitia, Mars
Haltigin, T. W.; Pollard, W. H.; Dutilleul, P.; Osinski, G. R.; Koponen, L.
2014-02-01
Thermal contraction crack polygons and scalloped depressions, two of the most common landforms found in Utopia Planitia, Mars, have previously been linked to the presence of ice-rich deposits in the subsurface. Although the formation and evolution of these features individually are relatively well understood, little to no effort has been directed towards elucidating possible interactions that occur between them during their development. Thus, the overarching goal of this research was to investigate if there is an evolutionary link between polygonal and scalloped terrains by correlating metrics representing polygon and scallop maturity. A variety of statistical analyses were performed using HiRISE and MOLA datasets to quantify interactions between four sets of polygonal and scalloped terrains. Our results demonstrate the existence of a negative relationship between polygonal subdivision and surface elevation, indicating that polygon networks become more ‘evolved’ as the surface subsides. These results suggest that the permafrost landscape in Utopia Planitia may once have been extremely ice-rich, and that multiple geomorphic processes may be responsible for its evolution. Ultimately, this work demonstrates that landscape reconstruction is more complete when a system approach is followed, quantifying interactions between landforms as opposed to examining an individual landform in isolation.