Because ZCTAs and metro areas do not always conform to county -- or even state -- lines, CNN then grouped applications by county and Core-Based Statistical Area based on which counties and CBSAs contained each ZCTA's centroid.
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Political scientists at the University of California, Davis, have found that most state capitals were located near what was then the population centroid of each state — typically closer to the geographical center of the state, and not the place where the most people already lived, breaking with how much of the world sited its capitals.
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Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value.
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Beginning in 2005, geocoding platforms included parcel-centroid geocoding. Parcel-centroid geocoding allowed for a lot of precision in geocoding an address. For example, parcel-centroid allowed a geocoder to determine the centroid of a specific building or lot of land. Platforms were now also able to determine the elevation of specific parcels.
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The centroid of a pyramid is located on the line segment that connects the apex to the centroid of the base. For a solid pyramid, the centroid is 1/4 the distance from the base to the apex.
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Both sets of coordinates must be translated first, so that their centroid coincides with the origin of the coordinate system. This is done by subtracting from the point coordinates the coordinates of the respective centroid.
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The figures to which they apply require also an areal center (Greek kentron), today called a centroid, serving as a center of symmetry in two directions. These figures are the circle, ellipse, and two-branched hyperbola. There is only one centroid, which must not be confused with the foci. A diameter is a chord passing through the centroid, which always bisects it.
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If g is large enough, then this becomes an edge detector. For corner detection, two further steps are used. Firstly, the centroid of the SUSAN is found. A proper corner will have the centroid far from the nucleus.
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The center of a general polygon can be defined in several different ways. The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual center, called just the centroid (center of area) comes from considering the surface of the polygon as having constant density.
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The centers of the in- and excircles form an orthocentric system. The intersection of the medians is the centroid. A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas. The three medians intersect in a single point, the triangle's centroid or geometric barycenter, usually denoted by G. The centroid of a rigid triangular object (cut out of a thin sheet of uniform density) is also its center of mass: the object can be balanced on its centroid in a uniform gravitational field.
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The centroid cuts every median in the ratio 2:1, i.e. the distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side. Nine-point circle demonstrates a symmetry where six points lie on the edge of the triangle. The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine-point circle.
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53–54 As in the two-dimensional case, the centroid of the tetrahedron is the center of mass. However contrary to the two-dimensional case the centroid divides the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem).
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The x = y = z = 1 case implies that the three medians are concurrent (through the centroid).
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The tetrahedron's center of mass computes as the arithmetic mean of its four vertices, see Centroid.
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The mean center, or centroid, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of equal mass. Mathematically, the centroid is the point to which the population has the smallest possible sum of squared distances. It is easily found by taking the arithmetic mean of each coordinate. If defined in the three-dimensional space, the centroid of points on the Earth's surface is actually inside the Earth.
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Using only the centroid to redistribute the data has problems when clusters lack uniform sizes and shapes.
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Methods of dot placement include by areal unit centroid, random dispersement, and uniform (evenly spaced) placement, among others.
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The coordinate-wise mean of a point set is the centroid, which solves the same variational problem in the plane (or higher-dimensional Euclidean space) that the familiar average solves on the real line -- that is, the centroid has the smallest possible average squared distance to all points in the set.
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Cluster-internal labeling selects labels that only depend on the contents of the cluster of interest. No comparison is made with the other clusters. Cluster-internal labeling can use a variety of methods, such as finding terms that occur frequently in the centroid or finding the document that lies closest to the centroid.
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Australia's centre of population in June 2016 was approximately east of the town of Ivanhoe in western New South Wales. Australia has not seen its population centroid move drastically since the creation of the country. In 1911, the centroid was in central New South Wales; in 1996, it was only slightly further northwest.
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Machine Learning, volume 20, pp. 97–112, 2011.M. Kloft and P. Laskov. "Security analysis of online centroid anomaly detection".
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For a particular cluster of documents, we can calculate the centroid by finding the arithmetic mean of all the document vectors. If an entry in the centroid vector has a high value, then the corresponding term occurs frequently within the cluster. These terms can be used as a label for the cluster. One downside to using centroid labeling is that it can pick up words like "place" and "word" that have a high frequency in written text, but have little relevance to the contents of the particular cluster.
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Each of the three medians of a triangle is a line segment going through one vertex and the midpoint of the opposite side, so it bisects that side (though not in general perpendicularly). The three medians intersect each other at the centroid of the triangle, which is its center of mass if it has uniform density; thus any line through a triangle's centroid and one of its vertices bisects the opposite side. The centroid is twice as close to the midpoint of any one side as it is to the opposite vertex.
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The Conway operation of dual interchanges faces and vertices. In Archimedean solids and k-uniform tilings alike, the new vertex coincides with the center of each regular face, or the centroid. In the Euclidean (plane) case; in order to make new faces around each original vertex, the centroids must be connected by new edges, each of which must intersect exactly one of the original edges. Since regular polygons have dihedral symmetry, we see that these new centroid- centroid edges must be perpendicular bisectors of the common original edges (e.g.
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Especially useful for quality checking on machined products. For calculating the area or centroid of a polygon that contains circular segments.
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This point could then be projected back to the surface. Alternatively, one could define the centroid directly on a flat map projection; this is, for example, the definition that the US Census Bureau uses. Contrary to a common misconception, the centroid does not minimize the average distance to the population. That property belongs to the geometric median.
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More generally, all triangle centers are also equivariant under similarity transformations (combinations of translation, rotation, and scaling),. "Similar triangles have similarly situated centers", p. 164. and the centroid is equivariant under affine transformations.The centroid is the only affine equivariant center of a triangle, but more general convex bodies can have other affine equivariant centers; see e.g. .
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The centroid of a triangle (where the three red segments meet) is equivariant under affine transformations: the centroid of a transformed triangle is the same point as the transformation of the centroid of the triangle. In the geometry of triangles, the area and perimeter of a triangle are invariants: translating or rotating a triangle does not change its area or perimeter. However, triangle centers such as the centroid, circumcenter, incenter and orthocenter are not invariant, because moving a triangle will also cause its centers to move. Instead, these centers are equivariant: applying any Euclidean congruence (a combination of a translation and rotation) to a triangle, and then constructing its center, produces the same point as constructing the center first, and then applying the same congruence to the center.
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Australia's population centroid is in central New South Wales. By 1996 it had moved only a little to the north-west since 1911.
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Let DEF be the Morley triangle of triangle ABC. The centroid of triangle DEF is called the first Morley center of triangle ABC.
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The parallel axes rule also applies to the second moment of area (area moment of inertia) for a plane region D: :I_z = I_x + Ar^2, where is the area moment of inertia of D relative to the parallel axis, is the area moment of inertia of D relative to its centroid, is the area of the plane region D, and is the distance from the new axis to the centroid of the plane region D. The centroid of D coincides with the centre of gravity of a physical plate with the same shape that has uniform density.
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Let G be the centroid of a triangle with vertices A, B, and C, and let P be any interior point. Then the distances between the points are related by :(PA)^2 + (PB)^2 +(PC)^2 =(GA)^2 + (GB)^2 + (GC)^2 +3(PG)^2. \, The sum of the squares of the triangle's sides equals three times the sum of the squared distances of the centroid from the vertices: :AB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2). Let qa, qb, and qc be the distances from the centroid to the sides of lengths a, b, and c.
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One method is to fix the coordinates of two points to (0,0) and (0,1), which are the two ends of a baseline. In one step, the shapes are translated to the same position (the same two coordinates are fixed to those values), the shapes are scaled (to unit baseline length) and the shapes are rotated. An alternative, and preferred method, is Procrustes superimposition. This method translates the centroid of the shapes to (0,0); the x coordinate of the centroid is the average of the x coordinates of the landmarks, and the y coordinate of the centroid is the average of the y-coordinates.
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Its centroid bisects the segment between vertices. There is room for one more diameter-like line: let a grid of lines parallel to the diameter cut both branches of the hyperbola. These lines are chord-like except that they do not terminate on the same continuous curve. A conjugate diameter can be drawn from the centroid to bisect the chord-like lines.
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Centroid Motion Capture Limited, a motion capture studio, was acquired by TT Games on 31 May 2007. Its assets, including 10 employees in its England headquarters, plus another 12 employees in its subsidiary studio in Serbia, were absorbed by a new entity, TT Centroid Limited and the company moved to Pinewood Studios in Buckinghamshire, England. The deal was overseen by Farleys Solicitors.
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Hence there are four medians and three bimedians in a tetrahedron. These seven line segments are all concurrent at a point called the centroid of the tetrahedron.Leung, Kam-tim; and Suen, Suk-nam; "Vectors, matrices and geometry", Hong Kong University Press, 1994, pp. 53–54 In addition the four medians are divided in a 3:1 ratio by the centroid (see Commandino's theorem).
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Euler showed in 1765 that in any triangle, the orthocenter, circumcenter and centroid are collinear. Reprinted in Opera Omnia, ser. I, vol. XXVI, pp.
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Over any horizontal interval, the ratio of the area under the catenary to its length equals , independent of the interval selected. The catenary is the only plane curve other than a horizontal line with this property. Also, the geometric centroid of the area under a stretch of catenary is the midpoint of the perpendicular segment connecting the centroid of the curve itself and the -axis.
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Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from.
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A CCD camera integrated into the guidance system is useful as it is hard to jam. The initial guidance is provided by area correlation around the target, to which is added a centroid tracking mechanism. Homing in the terminal phase is done by area correlation around the centroid. The Nag rises upwards suddenly and then bends at a steep angle to aim for the target.
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The second theorem states that the volume V of a solid of revolution generated by rotating a plane figure F about an external axis is equal to the product of the area A of F and the distance d traveled by the geometric centroid of F. (The centroid of F is usually different from the centroid of its boundary curve C.) That is: : V = Ad. For example, the volume of the torus with minor radius r and major radius R is : V = (\pi r^2)(2\pi R) = 2\pi^2 R r^2. This special case was derived by Johannes Kepler using infinitesimals.
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UCLUST is an algorithm designed to cluster nucleotide or amino-acid sequences into clusters based on sequence similarity. The algorithm was published in 2010 and implemented in a program also named UCLUST. The algorithm is described by the author as following two simple clustering criteria, in regard to the requested similarity threshold T. The first criterion states that any given cluster's centroid sequence will have a similarity smaller than T to any other clusters' centroid sequence. The second criterion states that each member sequence in a given cluster will have similarity to the cluster's centroid sequence that is equal or greater than T. UCLUST algorithm is a greedy one.
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The centroid terms are part of this graph, and they thus can be interpreted and scored by inspecting the terms that surround them in the graph.
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The second step insists that all points on the line from the nucleus through the centroid out to the edge of the mask are in the SUSAN.
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In a convex quadrilateral, the quasiorthocenter H, the "area centroid" G, and the quasicircumcenter O are collinear in this order on the Euler line, and HG = 2GO..
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The most important of details include: mass, center of mass, moment of inertia, thruster positions, thrust vectors, thrust curves, specific impulse, thrust centroid offsets, and fuel consumption.
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If a line segment connecting the diagonals of a quadrilateral bisects both diagonals, then this line segment (the Newton Line) is itself bisected by the vertex centroid.
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The theorems can be generalized for arbitrary curves and shapes, under appropriate conditions. Goodman & Goodman generalize the second theorem as follows. If the figure F moves through space so that it remains perpendicular to the curve L traced by the centroid of F, then it sweeps out a solid of volume V = Ad, where A is the area of F and d is the length of L. (This assumes the solid does not intersect itself.) In particular, F may rotate about its centroid during the motion. However, the corresponding generalization of the first theorem is only true if the curve L traced by the centroid lies in a plane perpendicular to the plane of C.
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The Global Centroid Moment Tensor Database shows a NNW strike on a nearly vertical fault, with a rake angle that is within 25 degrees of being pure strike-slip.
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1, (2016), Issue 3, page 76-79, If OH is any line through the centroid of triangle ABC, this problem is the Yiu's generalization of the Gossard perspector theorem.
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It has been asserted that the relaxed solution of -means clustering, specified by the cluster indicators, is given by the principal components, and the PCA subspace spanned by the principal directions is identical to the cluster centroid subspace. However, that PCA is a useful relaxation of -means clustering was not a new result, and it is straightforward to uncover counterexamples to the statement that the cluster centroid subspace is spanned by the principal directions.
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For each animal, the angular difference between its orientation and the group orientation is then found. The group polarity is then the average of these differences (Viscido 2004). Nearest Neighbor Distance: The nearest neighbor distance (NND) describes the distance between the centroid of one animal (the focal animal) and the centroid of the animal nearest to the focal animal. This parameter can be found for each animal in an aggregation and then averaged.
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The triangle medians and the centroid. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.
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Shapes are scaled to unit centroid size, which is the square root of the summed squared distances of each landmark to the centroid. The configuration is rotated to minimize the deviation between it and a reference, typically the mean shape. In the case of semi-landmarks, variation in position along the curve is also removed. Because shape space is curved, analyses are done by projecting shapes onto a space tangent to shape space.
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Combining these characteristics produces a basic Weeble. In theory, it is not possible to have a Weeble with a centroid that is too low to achieve a stable mechanical equilibrium.
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Cluster centroids is a method that replaces cluster of samples by the cluster centroid of a K-means algorithm, where the number of clusters is set by the level of undersampling.
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A tetrahedron is a three-dimensional object bounded by four triangular faces. Seven lines associated with a tetrahedron are concurrent at its centroid; its six midplanes intersect at its Monge point; and there is a circumsphere passing through all of the vertices, whose center is the circumcenter. These points define the "Euler line" of a tetrahedron analogous to that of a triangle. The centroid is the midpoint between its Monge point and circumcenter along this line.
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An alternative to centroid labeling is title labeling. Here, we find the document within the cluster that has the smallest Euclidean distance to the centroid, and use its title as a label for the cluster. One advantage to using document titles is that they provide additional information that would not be present in a list of terms. However, they also have the potential to mislead the user, since one document might not be representative of the entire cluster.
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The unsupervised approach to summarization is also quite similar in spirit to unsupervised keyphrase extraction and gets around the issue of costly training data. Some unsupervised summarization approaches are based on finding a "centroid" sentence, which is the mean word vector of all the sentences in the document. Then the sentences can be ranked with regard to their similarity to this centroid sentence. A more principled way to estimate sentence importance is using random walks and eigenvector centrality.
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For s=t=\tfrac 1 2 the points of contact U,V,W are the midpoints of the sides and the inellipse is the Steiner inellipse (its center is the triangle's centroid).
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Prototype methods are machine learning methods that use data prototypes. A data prototype is a data value that reflects other values in its class, e.g., the centroid in a K-means clustering problem.
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Since the sum of a positive number and its reciprocal is at least 2 by AM–GM inequality, we are finished. Equality holds only for the equilateral triangle, where P is its centroid.
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The associated resolution loss from sharing the synthetic aperture among different swaths is compensated by collecting radar echoes with multiple displaced azimuth apertures. A possible drawback of multichannel ScanSAR or TOPS approaches is the rather high Doppler centroid,Cafforio C, Guccione P, Guarnieri A M. Doppler centroid estimation for ScanSAR data[J]. IEEE transactions on geoscience and remote sensing, 2004, 42(1): 14-23. which is one of the most important parameters need to be estimated in computing SAR images.
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The first step is translation and rotation to minimize the squared and summed differences (squared Procrustes distance) between landmarks on each specimen. Then the landmarks are individually scaled to the same unit Centroid size. Centroid size is the square root of the sum of squared distances of the landmarks in configuration to their mean location. The translation, rotation, and scaling bring the landmark configurations for all specimens into a common coordinate system so that the only differing variables are based on shape alone.
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The center of the nine-point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter. The center of the incircle is not in general located on Euler's line. If one reflects a median in the angle bisector that passes through the same vertex, one obtains a symmedian. The three symmedians intersect in a single point, the symmedian point of the triangle.
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With these, samples from outside the pixel being processed are weighted linearly based upon their distance from the centroid of that pixel, with the linear function adjusted based on the wide or narrow filter chosen.
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The following is a list of centroids of various two-dimensional and three- dimensional objects. The centroid of an object X in n-dimensional space is the intersection of all hyperplanes that divide X into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of X. For an object of uniform composition, the centroid of a body is also its center of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines.
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Rotating a curve. The surface formed is a surface of revolution; it encloses a solid of revolution. Matemateca Ime-Usp) In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the axis of revolution) that lies on the same plane. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area (Pappus's second centroid Theorem).
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The Petr–Douglas–Neumann theorem asserts the following. :If isosceles triangles with apex angles 2kπ/n are erected on the sides of an arbitrary n-gon A0, and if this process is repeated with the n-gon formed by the free apices of the triangles, but with a different value of k, and so on until all values 1 ≤ k ≤ n − 2 have been used (in arbitrary order), then a regular n-gon An−2 is formed whose centroid coincides with the centroid of A0.
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Nathan Altshiller Court: Notes on the centroid. The Mathematics Teacher, Vol. 53, No. 1 (JANUARY 1960), pp. 34 (JSTOR) Other scholars have speculated that the result may have already been known to Greek mathematicians during antiquity.
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However, Below 110 K, ferrocene crystallizes in an orthorhombic crystal lattice in which the Cp rings are ordered and eclipsed, so that the molecule has symmetry group D5h. In the gas phase, electron diffraction and computational studies show that the Cp rings are eclipsed. The Cp rings rotate with a low barrier about the Cp(centroid)–Fe–Cp(centroid) axis, as observed by measurements on substituted derivatives of ferrocene using 1H and 13C nuclear magnetic resonance spectroscopy. For example, methylferrocene (CH3C5H4FeC5H5) exhibits a singlet for the C5H5 ring.
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The cubical cells to be meshed can also be sliced into 5 tetrahedra, using a (Diamond cubic) lattice as a basis. Cubes are mated on each side with another that has an opposite alignment of the tetrahedron around the centroid of the cube. Alternating vertices have a different number of tetrahedra intersecting on it, resulting in a slightly different mesh depending on position. When sliced this way, additional planes of symmetry are provided; having a tetrahedron around the centroid of the cube also generates very open spaces around points that are outside of the surface.
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In additive number theory, Kemnitz's conjecture states that every set of lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autumn of 2003 by Christian Reiher and Carlos di Fiore. The exact formulation of this conjecture is as follows: :Let n be a natural number and S a set of 4n − 3 lattice points in plane. Then there exists a subset S_1 \subseteq S with n points such that the centroid of all points from S_1 is also a lattice point.
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There are an infinitude of lines that bisect the area of a triangle. Three of them are the medians of the triangle (which connect the sides' midpoints with the opposite vertices), and these are concurrent at the triangle's centroid; indeed, they are the only area bisectors that go through the centroid. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle.
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Texels can also be described by image regions that are obtained through simple procedures such as thresholding. Voronoi tesselation can be used to define their spatial relationships—divisions are made at the midpoints between the centroids of each texel and the centroids of every surrounding texel for the entire texture. This results in each texel centroid having a Voronoi polygon surrounding it, which consists of all points that are closer to its own texel centroid than any other centroid.Linda G. Shapiro and George C. Stockman, Computer Vision, Upper Saddle River: Prentice-Hall, 2001.
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A triangle that is itself equilateral has a unique isodynamic point, at its centroid; every non-equilateral triangle has two isodynamic points. Isodynamic points were first studied and named by .For the credit to Neuberg, see e.g. and .
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Although Pappus's Theorem usually refers to Pappus's hexagon theorem, it may also refer to Pappus's centroid theorem. He also gives his name to the Pappus chain and to the Pappus configuration and Pappus graph arising from his hexagon theorem.
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Ellipses appear in triangle geometry as # Steiner ellipse: ellipse through the vertices of the triangle with center at the centroid, # inellipses: ellipses which touch the sides of a triangle. Special cases are the Steiner inellipse and the Mandart inellipse.
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A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet.
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Naukati Bay is located at , elevation: (Section 18, Township 069 South, Range 080 East, Copper River Meridian) between a pair of sheltered bays (Little Naukati Bay and Naukati Bay) on the West coast of Prince of Wales Island in South-East Alaska. Naukati Bay is located in the Ketchikan Recording District. Naukati Bay, census-designated place (CDP) tract's Centroid is at , elevation: The United States Census Bureau adjusted the census-designated place tract's boundaries from 1990 to 2008, resulting in the shift of the CDP's Centroid coordinates seen above, i.e. the ground has not moved, but the places where the Census counts has.
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Vector quantization is used for lossy data compression, lossy data correction, pattern recognition, density estimation and clustering. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm).
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The remaining three points for which it is named are the midpoints of the portion of altitude between the vertices and the orthocenter. The radius of the nine-point circle is half that of the circumcircle. It touches the incircle (at the Feuerbach point) and the three excircles. Euler's line is a straight line through the orthocenter (blue), center of the nine- point circle (red), centroid (orange), and circumcenter (green) The orthocenter (blue point), center of the nine-point circle (red), centroid (orange), and circumcenter (green) all lie on a single line, known as Euler's line (red line).
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On the other hand, centroid-centroid connecting only yields interior planigons (with variable translation and scale), but this construction is nonetheless equivalent in the interior. If the original k-uniform tiling fills the entire frame, then so will the k-dual uniform lattice by the first construction, and the boundary line segments can be ignored (equivalent to second construction). As seen below, some types of vertex polygons are different from their mirror images and are listed twice. For example, a triangle \triangle ABC,\triangle CBA are mirror images if \angle A,\angle B,\angle C are all unique.
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Medoids are representative objects of a data set or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images and 3-D trajectories and gene expression (where while the data is sparse the medoid need not be).
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The D86 width is defined as the diameter of the circle that is centered at the centroid of the beam profile and contains 86% of the beam power. The solution for D86 is found by computing the area of increasingly larger circles around the centroid until the area contains 0.86 of the total power. Unlike the previous beam width definitions, the D86 width is not derived from marginal distributions. The percentage of 86, rather than 50, 80, or 90, is chosen because a circular Gaussian beam profile integrated down to 1/e2 of its peak value contains 86% of its total power.
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The midpoint of the segment (1, 1) to (2, 2) In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
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The John Hancock Center is a braced tube structure. Most braced frames are concentric. This means that, where members intersect at a node, the centroid of each member passes through the same point. Concentrically braced frames can further be classified as either ordinary or special.
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International Journal of Pharmacy and Biological Sciences 2011, 1 (3), 103-116.Rispoli, F. J.; Badia, D.; Shah, V., Optimization of the fermentation media for sophorolipid production from Candida bombicola ATCC 22214 using a simplex centroid design. Biotechnology Progress 2010, 26 (4), 938-944.
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The Kiepert hyperbola is the unique conic which passes through the triangle's three vertices, its centroid, and its circumcenter. Of all triangles contained in a given convex polygon, there exists a triangle with maximal area whose vertices are all vertices of the given polygon.
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Euler's line (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red). In geometry, the Euler line, named after Leonhard Euler (), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. The concept of a triangle's Euler line extends to the Euler line of other shapes, such as the quadrilateral and the tetrahedron.
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Lego Star Wars was released in 2005 to positive reviews and strong sales, wherefore Traveller's Tales acquired Giant Interactive in April, forming TT Games. TT Games continued to produce Lego games to considerable success; Lego Star Wars II: The Original Trilogy received several awards and nominations in 2006, including the Best Gameplay Award at the British Academy of Film and Television Arts' 3rd British Academy Games Awards. In 2007, under advise from Farleys Solicitors, TT Games acquired developer Embryonic Studios and motion capture studio Centroid, which became TT Fusion and TT Centroid, respectively. On 8 November 2007, TT Games was acquired by Warner Bros.
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Clustering of similar fragments. Centroid is shown in blue. Libraries of these fragments are constructed from an analysis of the Protein Data Bank (PDB). First, a representative subset of the PDB is chosen which should cover a diverse array of structures, preferably at a good resolution.
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The centroid of population of Japan is in Gifu Prefecture, almost directly north of Nagoya city, and has been moving east-southeast for the past few decades. More recently, the only large regions in Japan with significant population growth have been in Greater Nagoya and Greater Tokyo.
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On average, internal noise up to about 7dB can be reduced. Robots may interpret strayed noise as speech instructions. Current voice activity detection (VAD) system uses the complex spectrum circle centroid (CSCC) method and a maximum signal-to-noise ratio (SNR) beamformer.Kim HD, et al (2009).
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The simplest training algorithm for vector quantization is: # Pick a sample point at random # Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance # Repeat A more sophisticated algorithm reduces the bias in the density matching estimation, and ensures that all points are used, by including an extra sensitivity parameter : # Increase each centroid's sensitivity s_i by a small amount # Pick a sample point P at random # For each quantization vector centroid c_i, let d(P, c_i) denote the distance of P and c_i # Find the centroid c_i for which d(P, c_i) - s_i is the smallest # Move c_i towards P by a small fraction of the distance # Set s_i to zero # Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another (simpler) method is LBG which is based on K-Means. The algorithm can be iteratively updated with 'live' data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples.
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If the set of fixed points of the symmetry group of an object is a line or plane then the centroid and centre of mass of the object, if defined, and any other point that has unique properties with respect to the object, are on this line or plane.
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Further optimization can be performed to ensure that the centroid possesses ideal bond geometry, as it was derived by averaging other geometries. Kolodny, R., Koehl, P., Guibas, L., and Levitt, M. (2005). Small Libraries of Protein Fragments Model Native Protein Structures Accurately. J Mol Biol 323, 297-307.
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The Nagel point is the isotomic conjugate of the Gergonne point. The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line. The incenter is the Nagel point of the medial triangle; equivalently, the Nagel point is the incenter of the anticomplementary triangle.
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Transylvania is located at 32.66° north, 91.25° west (ZIP Code centroid). It is approximately south of Lake Providence on U.S. Highway 65, at the junction with SR 581, near the Mississippi River. The U.S. Census Bureau lacks statistics for the total area, land and water areas of Transylvania.
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9, M. C. Mozer, M. I. Jordan, and T. Petsche, Eds. Cambridge, Massachusetts: MIT Press, 1997, pp. 368-374. is a cluster analysis algorithm. It is a variation of k-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median.
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A pair of cyclopentadienyl ligands can be covalently linked giving rise to so-call ansa metallocenes. The angle between the two Cp rings is fixed. Rotation of the rings about the metal-centroid axis is stopped as well. A related class of derivatives give rise to the constrained geometry complexes.
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In order to understand the tooth movement, Stanton used the theory of least squares and was able to compute the least possible sum of total tooth movements necessary in treatment to change the positions of all teeth from existing malocclusion. Therefore he computed an imaginary point called centroid for each map.
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Therefore, the nearest-neighbor chain algorithm will not necessarily find the same clustering as the greedy algorithm. Nevertheless, writes that the nearest-neighbor chain algorithm provides "a good heuristic" for the centroid method. A different algorithm by can be used to find the greedy clustering in time for this distance measure.
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For example, two half-moon shaped clusters intertwined in space do not separate well when projected onto PCA subspace. k-means should not be expected to do well on this data. It is straightforward to produce counterexamples to the statement that the cluster centroid subspace is spanned by the principal directions.
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In: Bergmann G, Kölbel R, Rohlmann A (Editors). Biomechanics: Basic and Applied Research. Springer, pp 121-128. full text In any single plane, the path formed by the locations of the moving instantaneous axis of rotation (IAR) is known as the 'centroid', and is used in the description of joint motion.
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This window of azimuth values is then divided by two to give the calculated "centroid" azimuth. The errors in this algorithm cause the aircraft to jitter across the controllers scope, and is referred to as "track jitter." The jitter problem makes software tracking algorithms problematic, and is the reason why monopulse was implemented.
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There are infinitely many lines that bisect the area of a triangle.Dunn, J.A., and Pretty, J.E., "Halving a triangle," Mathematical Gazette 56, May 1972, 105–108. Three of them are the medians, which are the only area bisectors that go through the centroid. Three other area bisectors are parallel to the triangle's sides.
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There are now a number of commonly used condensed matter computer simulation techniques that make use of the path integral formulation including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD), and the Feynman-Kleinert Quasi-Classical Wigner (FK-QCW) method. The same techniques are also used in path integral Monte Carlo (PIMC).
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That larger area would include part of the Kerkennah Islands and the coast around Sfax. The centroid for the smaller gulf is at , and the distance across is , with a depth of . The larger gulf is acrossIt is 150 km from the northwestern point of Djerba Island to the coast just above Sfax, but only 81 km to the island, which comports with the distances from Pliny the Elder, above. with a depth of , and the centroid is at . The entire Gulf of Gabes, both larger and smaller versions, is underlain by the continental shelf of the African Plate,International Court of Justice (1984) Case concerning the continental shelf (Tunisia/Libya) International Court of Justice, The Hague, Netherlands, and is nowhere deeper than 200 meters.
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The optics term encircled energy refers to a measure of concentration of energy in an optical image, or projected laser at a given range. If a single star is brought to its sharpest focus by a lens giving the smallest image possible with that given lens (called a point spread function or PSF), calculation of the encircled energy of the resulting image gives the distribution of energy in that PSF. Encircled energy is calculated by first determining the total energy of the PSF over the full image plane, then determining the centroid of the PSF. Circles of increasing radius are then created at that centroid and the PSF energy within each circle is calculated and divided by the total energy.
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The USGS Domestic GeoNames resource has two listings for Decatur: "City of Decatur", which is a Civil-class designation, and "Decatur", which is a Populated Place designation, which have slightly different coordinate centroids: "City of Decatur" centroid is located at , while the "Decatur" centroid is at . Decatur is 180 miles southwest of Chicago, 40 miles east of Springfield, the state capital, and 115 miles northeast of St. Louis. According to the 2010 census, consisted of land and of water, together amounting to a total area of , consisting of 90% land and 10% water. Lakes include Lake Decatur, an 11 km2 reservoir formed in 1923 by the damming of the Sangamon River, accounting for >90% of the state's census-designated water area.
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A simplicial polytope is a polytope whose facets are all simplices. For example, every polygon is a simplicial polytope. The Euler line associated to such a polytope is the line determined by its centroid and circumcenter of mass. This definition of an Euler line generalizes the ones above.. Suppose that P is a polygon.
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I ++ for j=1:1:spnum2 % From first pixel of previous frame to the last one pixel. J++ posdiff(i,j) = sum((regstats1(j).Centroid’-mupwtd(:,i))); % Calculate the color distance. end end After this two process, we will get a saliency map, and then store all of these maps into a new FileFolder.
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It touches the sides at its midpoints. There is no other (non-degenerate) conic section with the same properties, because a conic section is determined by 5 points/tangents. b) By a simple calculation. c) The circumcircle is mapped by a scaling, with factor 1/2 and the centroid as center, onto the incircle.
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Ramgha is a former village development committee now changed into MadhyaNepal Municipality in Lamjung District in the Gandaki Zone of northern-central Nepal. According to Geologist Dr.Harka Gurung this area lies in the centroid of Nepal.At the time of the 1991 Nepal census it had a population of 2327 people living in 446 individual households..
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Spieker circles also have relations to Nagel points. The incenter of the triangle and the Nagel point form a line within the Spieker circle. The middle of this line segment is the Spieker center. The Nagel line is formed by the incenter of the triangle, the Nagel point, and the centroid of the triangle.
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From a projective point of view the two triangles P_1P_3P_5 and P_2P_4P_6 lie perspectively with center B. That means there exists a central collineation, which maps the one onto the other triangle. But only in special cases this collineation is an affine scaling. For example for a Steiner inellipse, where the Brianchon point is the centroid.
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In geometry, a centroidal Voronoi tessellation (CVT) is a special type of Voronoi tessellation or Voronoi diagram. A Voronoi tessellation is called centroidal when the generating point of each Voronoi cell is also its centroid, i.e. the arithmetic mean or center of mass. It can be viewed as an optimal partition corresponding to an optimal distribution of generators.
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The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at a point called the "vertex centroid" and are all bisected by this point.Altshiller-Court, Nathan, College Geometry, Dover Publ., 2007.
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Nagel line of triangle ABC is the line passing through the centroid, the incenter, the Spieker center and the Nagel point of triangle ABC. The trilinear equation of the Nagel line is : x a ( b − c ) + y b ( c − a ) + z c ( a − b ) = 0. This is the central line associated with the triangle center X649.
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Most processes have employed two-bearing screens. Two- bearing circular vibrating screens with a screen box weight of 35 kN and speed of 1200 RPM were common. The centroid axis of the screen box and unbalanced load does not change during rotation. A four-bearing vibrating screen (F- Class) was developedCanada’s National Equipment Newspaper Equipment Journals, No. 4, pp.
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The term "brightness" is also used in discussions of sound timbres, in a rough analogy with visual brightness. Timbre researchers consider brightness to be one of the perceptually strongest distinctions between sounds , and formalize it acoustically as an indication of the amount of high-frequency content in a sound, using a measure such as the spectral centroid.
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A midplane is defined as a plane that is orthogonal to an edge joining any two vertices that also contains the centroid of an opposite edge formed by joining the other two vertices. If the tetrahedron's altitudes do intersect, then the Monge point and the orthocenter coincide to give the class of orthocentric tetrahedron. An orthogonal line dropped from the Monge point to any face meets that face at the midpoint of the line segment between that face's orthocenter and the foot of the altitude dropped from the opposite vertex. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median and a line segment joining the midpoints of two opposite edges is called a bimedian of the tetrahedron.
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In 2005 J. A. ScottJ. A. Scott (2005) "A Nine-point Hyperbola", The Mathematical Gazette 89:93–6 (#514) used the unit hyperbola as the circumconic of triangle ABC and found conditions for it to include six triangle centers: the centroid X(2), the orthocenter X(4), the Fermat points X(13) and X(14), and the Napoleon points X(17) and X(18) as listed in the Encyclopedia of Triangle Centers. Scott’s hyperbola is a Kiepert hyperbola of the triangle. Christopher BathChristopher Bath (2010) A Nine Point Rectangular Hyperbola describes a nine-point rectangular hyperbola passing through these centers: incenter X(1), the three excenters, the centroid X(2), the de Longchamps point X(20), and the three points obtained by extending the triangle medians to twice their cevian length.
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Sentiment and emotion characteristics are prominent in different phonetic and prosodic properties contained in audio features. Some of the most important audio features employed in multimodal sentiment analysis are mel-frequency cepstrum (MFCC), spectral centroid, spectral flux, beat histogram, beat sum, strongest beat, pause duration, and pitch. OpenSMILE and Praat are popular open-source toolkits for extracting such audio features.
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Niederdorla claims to be the most central municipality in Germany. A plaque was erected and a lime tree planted at after the 1990 German reunification.Niederdorla, German Wikipedia Retrieved 1 Nov 2011 The point was confirmed as the centroid of the extreme coordinates by the Dresden University of Technology. Niederdorla also comprises the centre of gravity (equilibrium point) about to the southwest.
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Given a point P in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when P is the centroid. In no other triangle is there a point for which this ratio is as small as 2.
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The word 'Ilanji' has a number of meanings including a water body. The village has three lakes very close to it. This is the only place which receives both south-west and north-east monsoon. Geographically, Ilanji is the centroid of a triangle whose three corners are the towns of Senkottai, Courtallam and Tenkasi, each of which is located approximately from Ilanji.
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For many years, the village of Piątek, Łódź Voivodeship has been claimed the "geometrical centre" (not the exact geographical centre) of Poland. In 2018, the exact locations of the geodetic center (centroid) of the whole territory of Poland has been marked in the village of Nowa Wieś, 16 km north-west from Piątek. Its coordinates are 52°11'27.95" N and 19°21'19.46" E.
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If the four faces of a tetrahedron have the same perimeter, then the tetrahedron is a disphenoid. If the four faces of a tetrahedron have the same area, then it is a disphenoid. The centers in the circumscribed and inscribed spheres coincide with the centroid of the disphenoid. The bimedians are perpendicular to the edges they connect and to each other.
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"Identifying Lenses with Small-Scale Structure II. Fold Lenses," C. Keeton, S. Gaudi, and A. O. Petters, Astrophys. J., 635, 35 (2005); . classify the local astrometric (centroid) and photometric curves of an extended source when it crosses fold and cusp caustics due to generic lenses;"Gravitational Microlensing Near Caustics I: Folds," B. S. Gaudi and A. O. Petters, Astrophys. J., 574, 970 (2002); .
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In one technique called shift-and-add (also called image stacking), the short exposure images are aligned by using the brightest speckle and averaged to give a single output image. In the lucky imaging approach, only the best short exposures are selected for averaging. Early shift-and-add techniques aligned images according to the image centroid, giving a lower overall Strehl ratio.
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Let f be a triangle center function. If two sides of a triangle are equal (say a = b) then so two components of the associated triangle center are always equal. Therefore all triangle centers of an isosceles triangle must lie on its line of symmetry. For an equilateral triangle all three components are equal so all centers coincide with the centroid.
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The algorithm has a loose relationship to the k-nearest neighbor classifier, a popular machine learning technique for classification that is often confused with k-means due to the name. Applying the 1-nearest neighbor classifier to the cluster centers obtained by k-means classifies new data into the existing clusters. This is known as nearest centroid classifier or Rocchio algorithm.
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Paul Yiu's generalisation of Gossard triangle. This generalisation is due to Paul Yiu. Let P be any point in the plane of the triangle ABC different from its centroid G. :Let the line PG meet the sidelines BC, CA and AB at X, Y and Z respectively. :Let the centroids of the triangles AYZ, BZX and CXY be Ga, Gb and Gc respectively.
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The midpoint polygon of a triangle is called the medial triangle. It shares the same centroid and medians with the original triangle. The perimeter of the medial triangle equals the semiperimeter of the original triangle, and the area is one quarter of the area of the original triangle. This can be proven by the midpoint theorem of triangles and Heron's formula.
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Where there is doubt about the meaning of "volume of fluid displaced", this should be interpreted as the overflow from a full container when the object is floated in it, or as the volume of the object below the average level of the fluid. The center of buoyancy of an object is the centroid of the displaced volume of fluid.
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Euler line of triangle ABC is the line passing through the centroid, the circumcenter, the orthocenter and the nine-point center of triangle ABC. The trilinear equation of the Euler line is : x sin 2A sin ( B − C ) + y sin 2B sin ( C − A ) + z sin 2C sin ( C − A ) = 0. This is the central line associated with the triangle center X647.
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Nowa Wieś is a village in the administrative district of Gmina Kutno, within Kutno County, Łódź Voivodeship, in central Poland. It lies approximately south of Kutno and north of the regional capital Łódź. The village has an approximate population of 150. In Nowa Wieś is located the exact geodetic center of Poland - a centroid of the entire territory of Poland.
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A right bipyramid has two points above and below the centroid of its base. Nonright bipyramids are called oblique bipyramids. A regular bipyramid has a regular polygon internal face and is usually implied to be a right bipyramid. A right bipyramid can be represented as for internal polygon P, and a regular n-bipyramid A concave bipyramid has a concave interior polygon.
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The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are concurrent at (all intersect at)a point called the "vertex centroid", which is the midpoint of all three of these segments.Altshiller- Court, Nathan, College Geometry, Dover Publ., 2007.
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Jockers, M. L., D. M. Witten, and C. S. Criddle, 2008. "Reassessing authorship of the Book of Mormon using delta and nearest shrunken centroid classification". Literary and Linguistic Computing (2008) 23(4): 465–91. However, this study only examined the relative likelihood of the five above- mentioned authors writing the Book of Mormon, not the possibility of an author or authors outside the five-person pool.
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Ilanji as said is the centroid of Tenkasi, Senkottai and Courtalam triangle, finds all the buses (that is from Tenkasi to Senkottai) to stop. There are two stops namely Chowkai (buses not going via Courtallam from Tenkasi to Shencottah stop here), West Ilanji bus stop (buses going via Courtallam from Tenkasi to Senkottai stop here) which serve as the North and South extremes of the village.
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The second major improvement is increased azimuth accuracy. With PSRs and old SSRs, azimuth of the aircraft is determined by the half split (centroid) method. The half split method is computed by recording the azimuth of the first and last replies from the aircraft, as the radar beam sweeps past its position. Then the midpoint between the start and stop azimuth is used for aircraft position.
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In the past, alignment of laser beams was done with irises. Two irises uniquely defined a beam path; the farther apart the irises and the smaller the iris holes, the better the path was defined. The smallest aperture that an iris can define is about 0.8 mm. In comparison, the centroid of a laser beam can be determined to sub-micrometre accuracy with a laser beam profiler.
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The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation.
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In computer science and information theory, set redundancy compression are methods of data compression that exploits redundancy between individual data groups of a set, usually a set of similar images. It is wide used on medical and satellital images. Ph.D. thesis, Department of Computer Science, Louisiana State University, Baton Rouge, La, USA The main methods are min-max differential, mín-máx predictive and centroid method.
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The central point shifted several times during the country's eventful history. Today Niederdorla in the state of Thuringia claims to be the most central municipality in Germany. A plaque was erected and a lime tree planted at after the 1990 German reunification.Niederdorla, German Wikipedia Retrieved 1 Nov 2011 The point was confirmed as the centroid of the extreme coordinates by the Dresden University of Technology.
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The two diagonals of a convex quadrilateral are the line segments that connect opposite vertices. The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides. They intersect at the "vertex centroid" of the quadrilateral (see below). The four maltitudes of a convex quadrilateral are the perpendiculars to a side—through the midpoint of the opposite side.
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Note that a medoid is not equivalent to a median, a geometric median, or centroid. A median is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for metrics induced by a norm (such as the Manhattan distance or Euclidean distance). A geometric median is defined in any dimension, but is not necessarily a point from within the original dataset.
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For each context window, MSSA calculates the centroid of each word sense definition by averaging the word vectors of its words in WordNet's glosses (i.e., short defining gloss and one or more usage example) using a pre-trained word embeddings model. These centroids are later used to select the word sense with the highest similarity of a target word to its immediately adjacent neighbors (i.e., predecessor and successor words).
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This method is useful when one wishes to find the location of the centroid or center of mass of an object that is easily divided into elementary shapes, whose centers of mass are easy to find (see List of centroids). Here the center of mass will only be found in the x direction. The same procedure may be followed to locate the center of mass in the y direction. The shape.
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The BFR algorithm, named after its inventors Bradley, Fayyad and Reina, is a variant of k-means algorithm that is designed to cluster data in a high- dimensional Euclidean space. It makes a very strong assumption about the shape of clusters: they must be normally distributed about a centroid. The mean and standard deviation for a cluster may differ for different dimensions, but the dimensions must be independent.
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Phylogenetic studies suggest these are indicative of ancestral qualities. Morpho menelaus is part of the achilles subclade of Morpho. Within this species, there are no differences between males and females regarding forewing length, aspect ratio and wing centroid measurement which may be indicative of morphological homogeneity. Despite the popularity of the genus Morpho, there is not a general consensus on the number of species or on how these species are defined.
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Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms.
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The rhodium–centroid distance is 1.904 Å and the rhodium–carbon bond lengths average 2.26 Å; the carbon–carbon bond lengths average 1.44 Å. These distances are all similar to those found in the 1,2,3-tri-tert- butylrhodocenium cation described above, with the one difference that the effective size of the rhodium centre appears larger, an observation consistent with the expanded ionic radius of rhodium(II) compared with rhodium(III).
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An automedian triangle is one whose medians are in the same proportions as its sides (though in a different order). If ABC is an automedian triangle in which vertex A stands opposite the side a, G is the centroid (where the three medians of ABC intersect), and AL is one of the extended medians of ABC with L lying on the circumcircle of ABC, then BGCL is a parallelogram.
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The B9077 road is a public highway in Aberdeenshire, Scotland that connects the city of Aberdeen to the southern part of Banchory.United Kingdom Ordnance Survey Map. 2004 The two lane road lies entirely on the south side of the River Dee and in many places provides good views of that river. The road is also a centroid for accessing a number of historic and prehistoric features in the south DeesideArchibald Watt.
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The barrier for the rotation of the alkene about the M-centroid vector is a measure of the strength of the M-alkene pi-bond. Low symmetry complexes of ethylene, e.g. CpRh(C2H4)2, are suitable for analysis of the rotational barriers associated with the metal- ethylene bond. In Zeise's anion ([PtCl3(C2H4)]−) this rotational barrier cannot be assessed by NMR spectroscopy because all four protons are equivalent.
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The chemical isomer shift and quadrupole splitting are generally evaluated with respect to a reference material. For example, in iron compounds, the Mössbauer parameters were evaluated using iron foil (thickness less than 40 micrometers). The centroid of the six lines spectrum from metallic iron foil is −0.1 mm/s (for Co/Rh source). All shifts in other iron compounds are computed relative to this −0.10 mm/s (at room temperature), i.e.
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Like other oceanic dolphins, pygmy killer whales use echolocation. The centroid of echolocation frequencies is between 70–85 kHz and can range from 32 to 100 kHz. This is similar to the range of other odontocetes such as the bottlenose dolphin but is slightly higher than false killer whales. While echolocating, they produce 8-20 clicks per second with a 197-223 decibel sound level at the production source.
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The system calculates a distance from a fire station or AVL location to a centroid point. The closest fire station, according to CAD system rules, would be assigned. Systems may use centroids that are not exactly centered in order to skew or weight system decisions. Staff based at a fire station that is physically closer by drawing a straight line on the map may be slower to reach a zone.
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This can occur because responding units must drive around freeways, lakes, or terrain obstructions in order to reach a zone. A centroid may be moved because 200-car freight trains often block a railroad crossing used to access a particular zone. This is the cheapest system to develop because it requires the least detailed geographic information and the simplest calculations. Another problem occurs where several services use the same system.
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In image processing, computer vision and related fields, an image moment is a certain particular weighted average (moment) of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation. Image moments are useful to describe objects after segmentation. Simple properties of the image which are found via image moments include area (or total intensity), its centroid, and information about its orientation.
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The output fuzzy sets for all the rules are then aggregated into a single fuzzy set. This group encompasses a range of output values, and is de-fuzzified in order to resolve a single crisp output value from the group (i.e. a value between 0 and 1). This approach uses the centroid method to obtain the representative non-fuzzy value for the output, as commonly adopted in the Sugeno-type systems.
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He is known for his hexagon theorem and centroid theorem, as well as the Pappus configuration and Pappus graph. His Collection is a major source of knowledge on Greek mathematics as most of it has survived. Pappus is considered the last major innovator in Greek mathematics, with subsequent work consisting mostly of commentaries on earlier work. The first woman mathematician recorded by history was Hypatia of Alexandria (AD 350–415).
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A typical radar produces a beam that is several degrees wide. The pattern is non-linear; the antenna is most sensitive at the center of the beam, also known as the boresight or centroid, and its sensitivity drops off at greater angles. This pattern is typically represented by measuring the angle where it has one-half the sensitivity as it does on the boresight. This is known as the half power point.
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Such a point needs not be unique; if it is not, there is translational symmetry, hence there are infinitely many of such points. On the other hand, in the cases of e.g. C3h and D2 symmetry there is a centre of symmetry in the first sense, but no inversion. If the symmetry group of an object has no fixed points then the object is infinite and its centroid and centre of mass are undefined.
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The previous theorem has further interesting consequences other than the aforementioned generalization of Commandino's theorem. It can be used to prove the following theorem about the centroid of a tetrahedron, first described in the Mathematische Unterhaltungen by the German physicist Friedrich Eduard Reusch:Friedrich Joseph Pythagoras Riecke (Hrsg.): Mathematische Unterhaltungen. Zweites Heft. 1973, S. 100, 128In den Mathematische Unterhaltungen (Zweites Heft, S. 128) wird auf die S. 36 von Reuschs Abhandlung Der Spitzbogen verwiesen.
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A specific case of Reusch's theorem where all four vertices of a tetrahedron are coplanar and lie on a single plane, thereby degenerating into a quadrilateral, Varignon's theorem, named after Pierre Varignon, states the following:Coxeter, op. cit., S. 242DUDEN: Rechnen und Mathematik. 1985, S. 652 :Let a quadrilateral in \R^2 be given. Then the two midlines connecting opposite edge midpoints intersect in the centroid of the quadrilateral and are divided in half by it.
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The three lines connecting the excenters of the given triangle to the corresponding edge midpoints all meet at the mittenpunkt; thus, it is the center of perspective of the excentral triangle and the median triangle, with the corresponding axis of perspective being the trilinear polar of the Gergonne point.. The mittenpunkt is also the centroid of the Mandart inellipse of the given triangle, the ellipse tangent to the triangle at its extouch points..
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Camp Carroll (also known as Artillery Plateau, Firebase Tan Lam and Hill 241) was a United States Marine Corps and Army of the Republic of Vietnam (ARVN) artillery base during the Vietnam War. It was located 8 km southwest of Cam Lộ, Quang Tri Province. Camp Carroll was also at the centroid of a large arc of the strategic Highway 9 corridor south of the Vietnamese Demilitarized Zone (DMZ), which made it a key facility.
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An operational definition was proposed in 2017, where a 'living fossil' lineage has a slow rate of evolution and occurs close to the middle of morphological variation (the centroid of morphospace) among related taxa (i.e. a species is morphologically conservative among relatives). The scientific accuracy of the morphometric analyses used to classify tuatara as a living fossil under this definition have been criticised however, which prompted a rebuttal from the original authors.
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The mean center of the United States population (using the centroid definition) has been calculated for each U.S. Census since 1790. Over the last two centuries, it has progressed westward and, since 1930, southwesterly, reflecting population drift. For example, in 2010, the mean center was located near Plato, Missouri, in the south-central part of the state, whereas, in 1790, it was in Kent County, Maryland, east-northeast of the future federal capital, Washington, D.C.
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Niederdorla also comprises the centre of gravity (equilibrium point) about to the southwest. Other municipalities competing are Krebeck in Lower Saxony and Edermünde in Hesse, as well as the village of Landstreit near Eisenach. The geographical centre of the German Empire from 1871 to 1919 was located at Spremberg in the Prussian Province of Brandenburg. The centroid of East Germany until 1990 was located between the villages of Verlorenwasser and Weitzgrund near Belzig.
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The tetrahedron has many properties analogous to those of a triangle, including an insphere, circumsphere, medial tetrahedron, and exspheres. It has respective centers such as incenter, circumcenter, excenters, Spieker center and points such as a centroid. However, there is generally no orthocenter in the sense of intersecting altitudes. Gaspard Monge found a center that exists in every tetrahedron, now known as the Monge point: the point where the six midplanes of a tetrahedron intersect.
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The first is an orthogonal line passing through the corresponding Euler point to the chosen face. The second is an orthogonal line passing through the centroid of the chosen face. This orthogonal line through the twelve-point center lies midway between the Euler point orthogonal line and the centroidal orthogonal line. Furthermore, for any face, the twelve-point center lies at the midpoint of the corresponding Euler point and the orthocenter for that face.
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This invariance is the defining property of a triangle center. It rules out other well-known points such as the Brocard points which are not invariant under reflection and so fail to qualify as triangle centers. All centers of an equilateral triangle coincide at its centroid, but they generally differ from each other on scalene triangles. The definitions and properties of thousands of triangle centers have been collected in the Encyclopedia of Triangle Centers.
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The grayscale value of each pixel can be used to provide sub-pixel accuracy by finding the centroid of the Gaussian. An object with markers attached at known positions is used to calibrate the cameras and obtain their positions and the lens distortion of each camera is measured. If two calibrated cameras see a marker, a three-dimensional fix can be obtained. Typically a system will consist of around 2 to 48 cameras.
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These are also of interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings). For some data sets there may be more than one medoid, as with medians. A common application of the medoid is the k-medoids clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows.
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Rotational stability depends on the relative lines of action of forces on an object. The upward buoyancy force on an object acts through the center of buoyancy, being the centroid of the displaced volume of fluid. The weight force on the object acts through its center of gravity. A buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment'.
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More importantly, the Nagel point N, the "area centroid" G, and the incenter I are collinear in this order, and NG = 2GI. This line is called the Nagel line of a tangential quadrilateral.. In a tangential quadrilateral ABCD with incenter I and where the diagonals intersect at P, let HX, HY, HZ, HW be the orthocenters of triangles AIB, BIC, CID, DIA. Then the points P, HX, HY, HZ, HW are collinear.
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For the circle and ellipse, let a grid of parallel chords be superimposed over the figure such that the longest is a diameter and the others are successively shorter until the last is not a chord, but is a tangent point. The tangent must be parallel to the diameter. A conjugate diameter bisects the chords, being placed between the centroid and the tangent point. Moreover, both diameters are conjugate to each other, being called a conjugate pair.
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In most Kaleidica Studios the same brush appears multiple times on the screen, each brush exactly mimicking the others. The brush appears as many times as the user specifies, each radiating from the central point called a "centroid" which can be placed anywhere inside or outside the screen. Users may retrieve content from the program by capturing the screen. As well, users can record their actions on the screen in real time to be later replayed.
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A simple, cost-effective way of overcoming the above limitation is to embed the centroid terms with the highest weight in a graph structure that provides a context for their interpretation and selection.Francois Role, Moahmed Nadif. Beyond cluster labeling: Semantic interpretation of clusters’ contents using a graph representation. Knowledge-Based Systems, Volume 56, January, 2014: 141-155 In this approach, a term-term co-occurrence matrix referred as T_k is first built for each cluster S_k.
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The village is located at approximately -84.739 Longitude and 43.002 Latitude in Dallas Township on M-21 about west of St. Johns and about east of Grand Rapids. It is about north of I-96 via county roads. The 48835 ZIP code centroid is located at -84.749958 longitude, 43.010137 Latitude, somewhat outside the incorporated city limits. According to the United States Census Bureau, the village has a total area of , of which is land and is water.
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In geometry, the Exeter point is a special point associated with a plane triangle. The Exeter point is a triangle center and is designated as the center X(22) in Clark Kimberling's Encyclopedia of Triangle Centers. This was discovered in a computers-in-mathematics workshop at Phillips Exeter Academy in 1986. This is one of the recent triangle centers, having been discovered only in 1986, unlike the classical triangle centers like centroid, incenter, and Steiner point.
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Sholl analysis is used to measure the number of crossings processes make at different distances from the centroid, and is a type of morphometic analysis. It is primarily used to measure arbour complexity. Certain morphologies cannot however be indexed using Sholl alone. For instance it may not make sense to compare neurons with arbors that take up small volumes to those that take up large volumes, and instead an analysis like 'complexity index' could be used.
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Through this correspondence, more accuracy is obtained, and a statistical assessment of the results becomes possible. In this case, the calculation is adjusted with the Gaussian least squares method. A numerical value for the accuracy of the transformation parameters is obtained by calculating the values at the reference points, and weighting the results relative to the centroid of the points. While the method is mathematically rigorous, it is entirely dependent on the accuracy of the parameters that are used.
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Multiple plume sprays are routinely used in automotive injectors. The multiple plumes are primarily used to provide for the optimal mixing of fuel and air so as to reduce pollutant emission under different operating conditions. The multiple plume automotive injectors can have anywhere from 2 to 8 plumes. The precise location of the centroid of these plumes, the individual plume angles, and the percentage split of the liquid amongst the plumes are normally obtained using an optical patternator.
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The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. The theorems are attributed to Pappus of Alexandria and Paul Guldin.
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Brennand Farm, Bowland Brennand Farm is often claimed to be the true centre of Great Britain. This is about seven kilometres north-west of Dunsop Bridge - which has the nearest BT phone box to the 'true centre'. A plaque reads “You are calling from the BT payphone that marks the centre of Great Britain”. The location was calculated by Ordnance Survey as the centroid of the two- dimensional shape of Great Britain, including all its islands.
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In statistics, the relationship square is a graphical representation for use in the factorial analysis of a table individuals x variables. This representation completes classical representations provided by principal component analysis (PCA) or multiple correspondence analysis (MCA), namely those of individuals, of quantitative variables (correlation circle) and of the categories of qualitative variables (at the centroid of the individuals who possess them). It is especially important in factor analysis of mixed data (FAMD) and in multiple factor analysis (MFA).
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Dayton is within Ohio's Miami Valley region, just north of Greater Cincinnati. Ohio's borders are within of roughly 60 percent of the country's population and manufacturing infrastructure, making the Dayton area a logistical centroid for manufacturers, suppliers, and shippers.Doug Page,"Dayton Region a Crucial Hub for Supply Chain Management", Dayton Daily News, 2009-12-21. Dayton also hosts significant research and development in fields like industrial, aeronautical, and astronautical engineering that have led to many technological innovations.
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Each median divides the area of the triangle in half; hence the name, and hence a triangular object of uniform density would balance on any median. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.)Dunn, J. A., and Pretty, J. E., "Halving a triangle," Mathematical Gazette 56, May 1972, 105-108. DOI 10.2307/3615256 The three medians divide the triangle into six smaller triangles of equal area.
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This scheme is essentially a list of spatial cells occupied by the solid. The cells, also called voxels are cubes of a fixed size and are arranged in a fixed spatial grid (other polyhedral arrangements are also possible but cubes are the simplest). Each cell may be represented by the coordinates of a single point, such as the cell's centroid. Usually a specific scanning order is imposed and the corresponding ordered set of coordinates is called a spatial array.
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Put simply, the centroid is the point at which a cardboard cut-out of the area could be perfectly balanced on the tip of a pencil. Islands are assumed fixed to the mainland in their precise position by invisible rigid weightless wires. A mathematical method is used to do the balancing to a much greater accuracy than the practical method could achieve. Unless stated, positions are the centroids of the two-dimensional shapes made by the countries.
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Columns at the Airavatesvara Temple, India Compression members are structural elements that are pushed together or carry a load, more technically they are subjected only to axial compressive forces. That is, the loads are applied on the longitudinal axis through the centroid of the member cross section, and the load over the cross sectional area gives the stress on the compressed member. In buildings, posts and columns are almost always compression members as are the top chord of trusses.
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The centers of both the inner and outer Napoleon triangles coincide with the centroid of the original triangle. This coincidence was noted in Chambers's Encyclopaedia in 1867, as quoted above. The entry there is unsigned. P. G. Tait, then Professor of Natural Philosophy in the University of Edinburgh, is listed amongst the contributors, but J. U. Hillhouse, Mathematical Tutor also at the University of Edinburgh, appears amongst other literary gentlemen connected for longer or shorter times with the regular staff of the Encyclopaedia.
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A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space. For an object, any unique centre and, more generally, any point with unique properties with respect to the object is a fixed point of its symmetry group. In particular this applies for the centroid of a figure, if it exists.
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In the case of a physical body, if for the symmetry not only the shape but also the density is taken into account, it applies to the centre of mass. If the set of fixed points of the symmetry group of an object is a singleton then the object has a specific centre of symmetry. The centroid and centre of mass, if defined, are this point. Another meaning of "centre of symmetry" is a point with respect to which inversion symmetry applies.
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One method of forming the Kleetope of a polytope is to place a new vertex outside , near the centroid of each facet. If all of these new vertices are placed close enough to the corresponding centroids, then the only other vertices visible to them will be the vertices of the facets from which they are defined. In this case, the Kleetope of is the convex hull of the union of the vertices of and the set of new vertices., p. 217.
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Life On Gold Plates: A New Book of Mormon Wordprint Analysis. Another study was published in the same journal that critiqued the methodology used in the earlier study and, using Smith's personal writings written in his own handwriting, concluded that stylometric evidence supports neither Smith nor a Spalding–Rigdon authorship.Schaalje, G. Bruce, Paul J. Fields, Matthew Roper, Gregory L. Snow. "Extended nearest shrunken centroid classification: A new method for open-set authorship attribution of texts of varying sizes", Literary and Linguistic Computing (2011).
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Beam with neutral axis (x). The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.
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A Nodal Point in UK school admissions over-subscription criteria is a geographical location, used to specify a school's catchment. If a school is oversubscribed, the distance from applicants' homes to the nodal point can be used for prioritising admissions. This can ensure the school not only serves pupils closest to it but also those living in other areas, for example areas that have more limited access to school places. Nodal points are sometimes known as Admissions Points or Centroid Points.
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The first moment of area is based on the mathematical construct moments in metric spaces. It is a measure of the spatial distribution of a shape in relation to an axis. The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis [Σ(a × d)]. First moment of area is commonly used to determine the centroid of an area.
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As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype. By aiming to minimize the expected squared quantization error and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of k-means clustering algorithm in an incremental manner.
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The attention given to surface runoff contaminant models has not matched the emphasis on pure hydrology models, in spite of their role in the generation of stream loading contaminant data. In the United States the EPA has had difficulty interpretingSteven Grant, I K Iskandar , Contaminant Hydrology, CRC Press (2000) diverse proprietary contaminant models and has to develop its own models more often than conventional resource agencies, who, focused on flood forecasting, have had more of a centroid of common basin models.
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Paul Guldin (original name Habakkuk Guldin; 12 June 1577 (Mels) – 3 November 1643 (Graz)) was a Swiss Jesuit mathematician and astronomer. He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution. (This theorem is also known as the Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria.) Guldin was noted for his association with the German mathematician and astronomer Johannes Kepler. Guldin composed a critique of Cavalieri's method of Indivisibles.
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The following image shows the data set from the previous clustering, but now fuzzy c-means clustering is applied. First, a new threshold value defining two clusters may be generated. Next, new membership coefficients for each data point are generated based on clusters centroids, as well as distance from each cluster centroid. frameless As one can see, the middle data point belongs to cluster A and cluster B. the value of 0.3 is this data point's membership coefficient for cluster A .
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The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to the product of the arc length s of C and the distance d traveled by the geometric centroid of C: : A = sd. For example, the surface area of the torus with minor radius r and major radius R is : A = (2\pi r)(2\pi R) = 4\pi^2 R r.
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By the Gauss–Lucas theorem, the root of the double derivative must be the average of the two foci, which is the center point of the ellipse and the centroid of the triangle. In the special case that the triangle is equilateral (as happens, for instance, for the polynomial ) the inscribed ellipse degenerates to a circle, and the derivative of has a double root at the center of the circle. Conversely, if the derivative has a double root, then the triangle must be equilateral .
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The Office for National Statistics also produces postcode directories, under similar licence terms to the OS product. Both the ONSPD and NSPL contain Northern Ireland postcodes, with centroid coordinates in the OSI grid as opposed to the OSGB grid, although Northern Ireland postcodes are subject to a more restrictive licence permitting internal business use only. Postcodes for the Crown Dependences are also included, without co-ordinates. A further difference is that non-current postcodes and dates of introduction and withdrawal of postcodes are included.
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In soil mechanics, the volumetric strain associated with shearing is known as Reynolds' dilation if it increases the volume, or compaction if it decreases the volume. The shear center (also known as the elastic axis or torsional axis) is an imaginary point on a section, where a shear force can be applied without inducing any torsion. In general, the shear center is not the centroid. For cross-sectional areas having one axis of symmetry, the shear center is located on the axis of symmetry.
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During acquisition, a guide star is first centred in an 8 × 8 pixel window. Small angle manoeuvres are then executed to translate this window to a pre-specified location within the field of view, so that an observation with one of the science instruments will be oriented correctly. Finally, the third is to provide the ACS with centroid measurements of the guide stars at a rate of 16 times per second. These measurements will be used to enable stable pointing at the milli-arc-second level.
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Each is focused onto a photon sensor (typically a CCD array or CMOS array or quad-cell ). If the sensor is placed at the geometric focal plane of the lenslet, and is uniformly illuminated, then, the integrated gradient of the wavefront across the lenslet is proportional to the displacement of the centroid. Consequently, any phase aberration can be approximated by a set of discrete tilts. By sampling the wavefront with an array of lenslets, all of these local tilts can be measured and the whole wavefront reconstructed.
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It contains the first exposition of the theory of potential. In physics, Green's theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows at any point inside a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter. It is in this essay that the term 'potential function' first occurs.
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The results of a factor analysis can be used to estimate each individual's score on the primary abilities based upon the individual's scores on the tests. Chapter X presents a method for obtaining the regression weights for estimating primary abilities from subject scores, and well as for estimating subjects scores from the primary traits (for estimating the components of variance of the subject scores). Appendices. I: Outline of Calculations for the Centroid Method with Unknown Diagonals. II: A Method of Finding the Roots of a Polynomial.
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A dancer wearing a suit used in an optical motion capture system Markers are placed at specific points on an actor's face during facial optical motion capture. Passive optical systems use markers coated with a retroreflective material to reflect light that is generated near the cameras lens. The camera's threshold can be adjusted so only the bright reflective markers will be sampled, ignoring skin and fabric. The centroid of the marker is estimated as a position within the two- dimensional image that is captured.
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Computer processing of modulated IDs allows less hand cleanup or filtered results for lower operational costs. This higher accuracy and resolution requires more processing than passive technologies, but the additional processing is done at the camera to improve resolution via a subpixel or centroid processing, providing both high resolution and high speed. These motion capture systems are typically $20,000 for an eight camera, 12 megapixel spatial resolution 120 hertz system with one actor. IR sensors can compute their location when lit by mobile multi-LED emitters, e.g.
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Local search that incorporates internal or external social signals could be considered social local search- driven. The first site to incorporate this type of search was Explore To Yellow Pages. Explore To uses Facebook Likes as one of the signals to increase the ranking of listings where other factors may be equal or almost equal. Typical ranking signals in local searches, such as keyword relevancy and distance from centroid can, therefore, be layered with these social signals to give a better crowdsourced experience for users.
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Permutational multivariate analysis of variance (PERMANOVA), is a non- parametric multivariate statistical test. PERMANOVA is used to compare groups of objects and test the null hypothesis that the centroids and dispersion of the groups as defined by measure space are equivalent for all groups. A rejection of the null hypothesis means that either the centroid and/or the spread of the objects is different between the groups. Hence the test is based on the prior calculation of the distance between any two objects included to the experiment.
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Multiple or multivariate regression is an approach to look at the relationship between several independent or predictor variables and a dependent or influential variable. It is best used in geometric morphometrics when analyzing shape variables based on an external influence. For example, it can be used in studies with attached functional or environmental variables like age or the development over time in certain environments. The multivariate regression of shape based on the logarithm of centroid size (square root of the sum of squared distances of landmarks) is ideal for allometric studies.
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The perpendicular bisector of a side of a triangle is the line that is perpendicular to that side and passes through its midpoint. The three perpendicular bisectors of a triangle's three sides intersect at the circumcenter (the center of the circle through the three vertices). The median of a triangle's side passes through both the side's midpoint and the triangle's opposite vertex. The three medians of a triangle intersect at the triangle's centroid (the point on which the triangle would balance if it were made of a thin sheet of uniform-density metal).
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The medial triangle of a given triangle has vertices at the midpoints of the given triangle's sides, therefore its sides are the three midsegments of the given triangle. It shares the same centroid and medians with the given triangle. The perimeter of the medial triangle equals the semiperimeter (half the perimeter) of the original triangle, and its area is one quarter of the area of the original triangle. The orthocenter (intersection of the altitudes) of the medial triangle coincides with the circumcenter (center of the circle through the vertices) of the original triangle.
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Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross- sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example.
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Next, the shape must be filled with two basic types of unmixed solids, and the volume of the lighter solid must be greater than that of the heavier solid. Next, the overall shape must have constant positive curvature. Next, the relationship between the heavy solid and the light solid must be such that any orientation of the object off of the vertical axis line must cause the object's centroid to raise and to become offset. Lastly, the object must have only one position in which it can achieve stable mechanical equilibrium.
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Ferdinand Wittenbauer also discovered an easy method to calculate the centroid (centre of mass) of any quadrangle, known as Wittenbauer Theorem or Wittenbauer's Parallelogram. In addition, Wittenbauer is known for his Aufgaben aus der technischen Mechanik, a collection of exercises in technical mechanics including solutions published in three volumes. Co-author was mathematician and engineer Theodor Pöschl (son to Jakob Pöschl Nikola Tesla’s teacher). Finished in 1911, it served as very first and then most prominent set of problems in the fields of mechanics in the German- speaking area for some decades.
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The D4σ width is sensitive to the beam energy or noise in the tail of the pulse because the pixels that are far from the beam centroid contribute to the D4σ width as the distance squared. To reduce the error in the D4σ width estimate, the baseline pixel values are subtracted from the measured signal. The baseline values for the pixels are measured by recording the values of the CCD pixels with no incident light. The finite value is due to dark current, readout noise, and other noise sources.
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After the release of Escape from Butcher Bay, Starbreeze again encountered financial difficulties after having not received a significant royalty payment from Vivendi. It sold part of its motion capture and animation department to a British company, Centroid. However, the game helped set Starbreeze's reputation as a studio capable of making good licensed titles. With the help of Union Entertainment, an intermediary company, Starbreeze signed an agreement with Majesco Entertainment for a new title set within The Darkness universe owned by Top Cow Comics on July 16, 2004.
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When P is chosen as the centroid G, then α = −1/3. When P is chosen as the circumcenter O, then α = −1 and the generated orthocentric system is congruent to the original system as well as being a reflection of it about the nine-point center. In this configuration PA, PB, PC form a Johnson triangle of the original reference triangle ABC. Consequently the circumcircles of the four triangles ABC, ABH, ACH, BCH are all equal and form a set of Johnson circles as shown in the diagram adjacent.
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For those having two axes of symmetry, the shear center lies on the centroid of the cross-section. In some materials such as metals, plastics, or granular materials like sand or soils, the shearing motion rapidly localizes into a narrow band, known as a shear band. In that case, all the sliding occurs within the band while the blocks of material on either side of the band simply slide past one another without internal deformation. A special case of shear localization occurs in brittle materials when they fracture along a narrow band.
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Three commonly used (but different) center points are: # the mean center, also known as the centroid or center of gravity; # the median center, which is the intersection of the median longitude and median latitude; # the geometric median, also known as Weber point, Fermat–Weber point, or point of minimum aggregate travel. A further complication is caused by the curved shape of the Earth. Different center points are obtained depending on whether the center is computed in three-dimensional space, or restricted to the curved surface, or computed using a flat map projection.
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In fact, standard factor analysis brings this issue to the fore. In either centroid or principal components analysis (PCA) the first factor scores are created by multiplying each rating by the correlation of the factor (usually the mean of all standardized ratings for each person) against each item's ratings. This multiplication weights each item by the correlation of the pattern of individual differences on each item (the component scores). If consensus is unevenly distributed over these items, some items may be more focused on the overall issues of the common factor.
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The centroid of a tetrahedron is the midpoint between its Monge point and circumcenter. These points define the Euler line of the tetrahedron that is analogous to the Euler line of a triangle. The nine-point circle of the general triangle has an analogue in the circumsphere of a tetrahedron's medial tetrahedron. It is the twelve-point sphere and besides the centroids of the four faces of the reference tetrahedron, it passes through four substitute Euler points, one third of the way from the Monge point toward each of the four vertices.
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The tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices. As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the perpendicular bisectors of the triangle's sides. Further, every triangle has a unique Steiner circumellipse, which passes through the triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area.
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The task of factor analysis is to find a factor matrix of the lowest possible rank (the least number of factors) that can reproduce the off-diagonal members of the observed correlation matrix as close as can be expected, allowing for sample variation. The bulk of the chapter considers mathematical issues, including the rank of a matrix and methods for estimating the commonalities of the correlation matrix (the diagonal elements). Chapter III: The Centroid Method. A computation method is developed for factoring a correlation matrix, which is a symmetric matrix of real elements.
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Trilinear equation: [cyclic sum (cos A)x(b2y2 − c2z2)] = 0 Barycentric equation: [cyclic sum (b2 \+ c2 − a2)x(y2 − z2)] = 0 The Lucas cubic is the locus of a point X such that the cevian triangle of X is the pedal triangle of some point; the point lies on the Darboux cubic. The Lucas cubic passes through the centroid, orthocenter, Gergonne point, Nagel point, de Longchamps point, other triangle centers, the vertices of the anticomplementary triangle, and the foci of the Steiner circumellipse. For graphics and properties, see K007 at Cubics in the Triangle Plane.
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In geometry, an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular. It is also known as an orthogonal tetrahedron since orthogonal means perpendicular. It was first studied by Simon Lhuilier in 1782, and got the name orthocentric tetrahedron by G. de Longchamps in 1890.. In an orthocentric tetrahedron the four altitudes are concurrent. This common point is called the orthocenter, and it has the property that it is the symmetric point of the center of the circumscribed sphere with respect to the centroid.
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Zirconocene dichloride may be prepared from zirconium(IV) chloride-THF complex and sodium cyclopentadienide: :ZrCl4(THF)2 \+ 2 NaCp -> Cp2ZrCl2 \+ 2 NaCl + 2 THF The closely related compound Cp2ZrBr2 was first described by Birmingham and Wilkinson. The compound is a bent metallocene: the Cp rings are not parallel, the average Cp(centroid)-M-Cp angle being 128°. The Cl-Zr-Cl angle of 97.1° is wider than in niobocene dichloride (85.6°) and molybdocene dichloride (82°). This trend helped to establish the orientation of the HOMO in this class of complex.
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Every triangle has an inscribed ellipse, called its Steiner inellipse, that is internally tangent to the triangle at the midpoints of all its sides. This ellipse is centered at the triangle's centroid, and it has the largest area of any ellipse inscribed in the triangle. In a right triangle, the circumcenter is the midpoint of the hypotenuse. In an isosceles triangle, the median, altitude, and perpendicular bisector from the base side and the angle bisector of the apex coincide with the Euler line and the axis of symmetry, and these coinciding lines go through the midpoint of the base side.
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Island Mountain is named peak in the Island Mountain range which covers an area from Mendocino County into Trinity County. The highest point of this range, and its official centroid, is a benchmark called "South Peak" on the unnamed tallest point which is in Mendocino County. Island Mountain in Trinity County was named by settlers in the 1850s because it is nearly isolated by water from two creeks and the Eel River. Due to the resistance of the rock to erosion, the Eel River makes an abrupt "S" curve around Island Mountain in its otherwise north-northwesterly flow between the California Coast Ranges.
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The first schedule of indoor shooting started with Rajinikanth's base actions being filmed as per the motion capturing norms. The film was launched with a formal puja on 19 January 2012 at the Ganesha temple located inside AVM Studios in Vadapalani, Chennai. The first phase of production began in Chennai on 15 March 2012. It was then moved to London on 17 March 2012, where motion capture filming was done at Centroid Motion Picture lab in Pinewood Studios Production in London lasted for 15 days, during which, Rajinikanth announced that the film might be released for Diwali 2012.
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If the total mass and center of mass can be determined for each area, then the center of mass of the whole is the weighted average of the centers. This method can even work for objects with holes, which can be accounted for as negative masses. A direct development of the planimeter known as an integraph, or integerometer, can be used to establish the position of the centroid or center of mass of an irregular two-dimensional shape. This method can be applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult.
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K-means clustering can be used to group an unlabeled set of inputs into k clusters, and then use the centroids of these clusters to produce features. These features can be produced in several ways. The simplest is to add k binary features to each sample, where each feature j has value one iff the jth centroid learned by k-means is the closest to the sample under consideration. It is also possible to use the distances to the clusters as features, perhaps after transforming them through a radial basis function (a technique that has been used to train RBF networks).
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In 1965, the NBS published Centroid Color Charts made up of color samples demonstrating the central color in each category, as a physical representation of the system usable by the public, and also published The Universal Color Language, a more general system for color designation with various degrees of precision from completely generic (13 broad categories) to extremely precise (numeric values from spectrophotometric measurement). In 1976, The Color Names Dictionary and The Universal Color Language were combined and updated with the publication of Color: Universal Language and Dictionary of Names, the definitive source on the ISCC–NBS system.
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Experimental laser systems benefit from the use of multiple laser beam profilers to characterize the pump beam, the output beam, and the beam shape at intermediate locations in the laser system, for example, after a Kerr-lens modelocker. Changes in the pump laser beam profile indicate the health of the pump laser, which laser modes are excited in the gain crystal, and also determine whether the laser is warmed up by locating the centroid of the beam relative to the breadboard. The output beam profile is often a strong function of pump power due to thermo- optical effects in the gain medium.
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This means that if more than one photon comes back in a single pulse, a conventional single-photon detector would only record the arrival time of the first photon. However, the important quantity is the centroid of the time of all returned photons (assuming the pulse and reflectors are symmetrical), so any system that can return multiple photons per pulse must record the arrival times of each photon. In APOLLO, the incoming photons are spread over an array of independent detectors, which reduces the chance that two or more photons hit any one of the detectors.
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The restriction of this projective transformation to the midsphere is a Möbius transformation.. There is a unique way of performing this transformation so that the midsphere is the unit sphere and so that the centroid of the points of tangency is at the center of the sphere; this gives a representation of the given polyhedron that is unique up to congruence, the canonical polyhedron.. Alternatively, a transformed polyhedron that maximizes the minimum distance of a vertex from the midsphere can be found in linear time; the canonical polyhedron chosen in this way has maximal symmetry among all choices of the canonical polyhedron..
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102 This conclusion was later supported by observations of GRB 970508, the first burst to have its redshift determined.Reichart 1998 The position of the burst's afterglow was measurably offset from the centroid of the host galaxy, effectively ruling out the possibility that the burst originated in an active galactic nucleus. The redshift of the galaxy was later determined to be z = 0.695,Bloom 2001 which corresponds to a distance of approximately .Converting of the redshift into the distance done by on-line tools: At this distance, the burst would have released a total of assuming isotropic emission.
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This arrangement has only m ordinary lines, the lines that connect a vertex v with the point at infinity collinear with the two neighbors of v. As with any finite configuration in the real projective plane, this construction can be perturbed so that all points are finite, without changing the number of ordinary lines. For odd n, only two examples are known that match Dirac's lower bound conjecture, that is, with t_2(n)=(n-1)/2 One example, by , consists of the vertices, edge midpoints, and centroid of an equilateral triangle; these seven points determine only three ordinary lines.
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ASAS-SN discovery image and 2 more epochs of Comet ASASSN1. During the ongoing ASAS-SN survey, using data from the quadruple 14-cm "Cassius" telescope on Cerro Tololo, Chile, a possible new moving transient source was detected on July 19, 2017; the team gave it the designation ASASSN1. In the discovery images, ASASSN1 had a V band magnitude of 15.3. The centroid was moving between the ASAS-SN three 90 second, dithered discovery images with no counterpart in the Minor Planet Center database. Follow-up images from the Savannah Skies Observatory recovered ASASSN1 9.7 hours later 0.21 degrees away.
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He also expresses appreciation to his computer (a person, Leone Chesire), who also wrote the appendix on the calculations used in the centroid method. He foresees a bright future for the use of factor analysis and expects to see the simplification of the computational methods. He expects factor analysis to become an important technique int the early stages of science. For example, the laws of classical mechanics could have been revealed by a factor analysis, by analyzing a great many attributes of objects that are dropped or thrown from an elevated point, with the time of fall factor uncorrelated with the weight factor.
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Trilinear equation: [cyclic sum bc(a4 − b2c2)x(y2 \+ z2] = 0 Barycentric equation: [cyclic sum (a4 − b2c2)x(c2y2 \+ b2z2] = 0 Let A′B′C′ be the 1st Brocard triangle. For arbitrary point X, let XA, XB, XC be the intersections of the lines XA′, XB′, XC′ with the sidelines BC, CA, AB, respectively. The 1st Brocard cubic is the locus of X for which the points XA, XB, XC are collinear. The 1st Brocard cubic passes through the centroid, symmedian point, Steiner point, other triangle centers, and the vertices of the 1st and 3rd Brocard triangles.
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The 1.3 m dome itself is compact, owing to the fast overall optics at f/4. It is located near by and southwest of, the very large 61-inch dome. In addition to astrometric studies (such as for Space Situational Awareness, SDSS and SST), research on this telescope includes the study of blue and K-Giant stars, celestial mechanics and dynamics of multiple star systems, characterizations of artificial satellites, and the astrometry and transit photometry of exoplanets. Astrometrically, exoplanets also confuse centroid of a parent star's PSF – and there are many exoplanets – so the impact of their not-bland dynamics must be understood.
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The received backscatter signal produces a linear fringe whose position is directly linked to the wind velocity; the wind speed is determined by the fringe centroid position to better than a tenth of the resolution (1.8 m/s). The Rayleigh receiver employs a dual-filter Fabry–Pérot interferometer with a 2 GHz resolution and 5 GHz spacing. It analyzes the wings of the Rayleigh spectrum with a CCD; the etalon is split into two zones, which are imaged separately on the detector. The lidar is aimed 35° from nadir and 90° to the satellite track (on the side away from the Sun).
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Kepler-14 is a binary star system, which means that it is actually composed of two gravitationally bound stars that orbit a common point in space. The system is composed of a primary star, Kepler-14A, and a dimmer companion star, Kepler-14B. When the stars were observed, while searching for the planet Kepler-14b, the angular separation of the binary system made it extremely difficult to note the dimmer companion star. The stars have such a wide orbit that it takes approximately 2800 years for each star to complete a revolution around the centroid. The two stars are located approximately 980 parsecs (3,196 light years) from Earth.
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CGC complexes feature a pi-bonded moiety (e.g. cyclopentadienyl) linked to one of the other ligands on the same metal centre in such a way that the angle at this metal between the centroid of the pi-system and the additional ligand is smaller than in comparable unbridged complexes. More specifically, the term CGC was used for ansa-bridged cyclopentadienyl amido complexes, although the definition goes far beyond this class of compounds. The term CGC is frequently used in connection with other more or less related ligand systems that may or may not be isolobal and/or isoelectronic with the ansa-bridged cyclopentadienyl amido ligand system.
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A stable horizontal trim requires that diver's centre of gravity is directly below the centre of buoyancy (the centroid). Small errors can be compensated fairly easily, but large offsets may make it necessary for the diver to constantly exert significant effort towards maintaining the desired attitude, if it is actually possible. The position of the centre of buoyancy is largely beyond the control of the diver, though the cylinder(s) may be shifted in the harness by a small amount, and the volume distribution of the buoyancy compensator has a large influence when inflated. Most of the control of trim available to the diver is in the positioning of ballast weights.
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The same technique can be used for any other quantitative pixel attribute, such as luminance, gradient, apparent motion in a video frame, etc.. More generally, the EMD is used in pattern recognition to compare generic summaries or surrogates of data records called signatures. A typical signature consists of list of pairs ((x1,m1), ... (xn,mn)), where each xi is a certain "feature" (e.g., color in an image, letter in a text, etc.), and mi is "mass" (how many times that feature occurs in the record). Alternatively, xi may be the centroid of a data cluster, and mi the number of entities in that cluster.
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There were tentergrounds (or tenter-fields), large open spaces full of tenters, wherever cloth was made, and as a result the word "tenter" is found in place names throughout the United Kingdom and its empire, for example several streets in Spitalfields, London.Approximate centroid of North-, South-, West-, and East- Tenter Street, and Tenter Passage, in Spitalfields, London: and Tenterfield House in Haddington, East Lothian, Scotland, which in turn gave its name to Tenterfield in New South Wales, Australia. The word tenter is still used today to refer to production line machinery employed to stretch polyester films and similar fabrics. The spelling stenter is also found.
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The work was originally thought to be lost, but in 1906 was rediscovered in the celebrated Archimedes Palimpsest. The palimpsest includes Archimedes' account of the "mechanical method", so-called because it relies on the law of the lever, which was first demonstrated by Archimedes, and of the center of mass (or centroid), which he had found for many special shapes. Archimedes did not admit the method of indivisibles as part of rigorous mathematics, and therefore did not publish his method in the formal treatises that contain the results. In these treatises, he proves the same theorems by exhaustion, finding rigorous upper and lower bounds which both converge to the answer required.
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Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set. Our first step would be to find the centroid or center of mass of the sample points. Intuitively, the closer the point in question is to this center of mass, the more likely it is to belong to the set. However, we also need to know if the set is spread out over a large range or a small range, so that we can decide whether a given distance from the center is noteworthy or not.
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MACS J0025.4-1222 is a galaxy cluster created by the collision of two galaxy clusters, and is part of the MAssive Cluster Survey (MACS). Like the earlier discovered Bullet Cluster, this cluster shows a clear separation between the centroid of the intergalactic gas (of majority of the normal, or baryonic, mass) and the colliding clusters. In the image, intergalactic gas is shown in pink and the mass centroids of the colliding clusters in blue, showing the separation of the two, similar to the Bullet Cluster. It provides independent, direct evidence for dark matter and supports the view that dark matter particles interact with each other only very weakly.
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Common nine-point circle, where O, O4 and A4 are the nine- point center, circumcenter, and orthocenter respectively of the triangle formed from the other three orthocentric points A1, A2 and A3. The center of this common nine-point circle lies at the centroid of the four orthocentric points. The radius of the common nine-point circle is the distance from the nine-point center to the midpoint of any of the six connectors that join any pair of orthocentric points through which the common nine-point circle passes. The nine-point circle also passes through the three orthogonal intersections at the feet of the altitudes of the four possible triangles.
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The compound has Cs symmetry, with a mirror plane intersecting one carbon of the Cp ring as well as the iron and iodide centre. The compound adopts a piano stool structure: the cyclopentadienyl ligand is the "seat" and three other ligands are "legs". Such compounds are members of the half-sandwich family of compounds, which is a subgroup of the metallocenes. X-ray crystallography shows the following features: Fe-Cp centroid = 1.72, Fe-I = 2.61, and Fe-CO = 1.78 Å. Electron counting of this ferrous complex indicates 5 electrons from the cyclopentadienyl anion, 2 electrons from each of the carbonyls, and 1 electron from the iodide.
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Sometimes the term "barycentric subdivision" is improperly used for any subdivision of a polytope P into simplices that have one vertex at the centroid of P, and the opposite facet on the boundary of P. While this property holds for the true barycentric subdivision, it also holds for other subdivisions which are not the BCS. For example, if one makes a straight cut from the barycenter of a triangle to each of its three corners, one obtains a subdivision into three triangles. Generalizing this idea, one obtains a schema for subdividing an n-dimensional simplex into n+1 simplices. However, this subdivision is not the BCS.
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This implies that the points at infinity have their last coordinate equal to zero, and that the projective coordinates of a point of the affine space are obtained by completing its affine coordinates by one as th coordinate. When one has points in an affine space that define a barycentric coordinate system, this is another projective frame of the projective completion that is convenient to choose. This frame consists of these points and their centroid, that is the point that has all its barycentric coordinates equal. In this case, the homogeneous barycentric coordinates of a point in the affine space are the same as the projective coordinates of this point.
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A number of major systemic changes were introduced in this version with the use of a new parametrized energy model (Turner 2004), restructuring of the RNAlib to support concurrent computations in thread-safe manner, improvements to the API, and inclusion of several new auxiliary tools. For example, tools to assess RNA-RNA interactions and restricted ensembles of structures. Furthermore, other features included additional output information such as centroid structures and maximum expected accuracy structures derived from base pairing probabilities, or z-scores for locally stable secondary structures, and support for input in FASTA format. The updates, however, are compatible with earlier versions without affecting the computational efficiency of the core algorithms.
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The centroid of the first Morley triangle is given in trilinear coordinates by : Morley center = X(356) = cos(A/3) + 2 cos(B/3)cos(C/3) : cos(B/3) + 2 cos(C/3)cos(A/3) : cos(C/3) + 2 cos(A/3)cos(B/3). The first Morley triangle is perspective to triangle ABC:Fox, M. D.; and Goggins, J. R. "Morley's diagram generalised", Mathematical Gazette 87, November 2003, 453–467. the lines each connecting a vertex of the original triangle with the opposite vertex of the Morley triangle concur at the point : 1st Morley–Taylor–Marr center = X(357) = sec(A/3) : sec(B/3) : sec(C/3).
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A stable horizontal trim requires that diver's centre of gravity is directly below the centre of buoyancy (the centroid). Small errors can be compensated fairly easily, but large offsets may make it necessary for the diver to constantly exert significant effort towards maintaining the desired attitude, if it is actually possible. The position of the centre of buoyancy is largely beyond the control of the diver, though the cylinder(s) may be shifted in the harness by a small amount, and the volume distribution of the buoyancy compensator has a large influence when inflated. Most of the control of trim available to the diver is in the positioning of ballast weights.
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On August 7, 2010, the Infrared Array Camera aboard the Spitzer Space Telescope was used to find the centroid, the point in space around which both of the Kepler-14 stars orbit. Analysis of the collected data determined which component of the binary star system was the site of the transit signal, and, additionally, that the transit signal came from the primary star in the system (as opposed to the fainter, less prominent star). Using the spectral data collected by HIRES and FIES, the Kepler team derived the characteristics of the host star. The HIRES and FIES results agreed on every aspect of the star that had been derived except for the star's radial velocity.
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In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
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The WHOIS protocol is still widely used to allow domain ownership records in the Internet to be easily queried. WHOIS++ attempted to address some of the short comings in the original WHOIS protocol that had become apparent over the years. It supported multiple languages and character sets to help with I18N issues, had a more advanced query syntax, and the ability to generate "forward knowledge" in the form of 'centroid' data structures that could be used to route queries from one server to another. The protocol was designed to be backward compatible with the older WHOIS standard, so that WHOIS++ clients could still extract meaningful information from the already deployed WHOIS servers.
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The location of a single source can be determined by computing the "center of gravity" (centroid) of the light distribution extending over several adjacent pixels (see figure on the left). Provided that there is enough light, this can be achieved with arbitrary precision, very much better than pixel width of the detecting apparatus and the resolution limit for the decision of whether the source is single or double. This technique, which requires the presupposition that all the light comes from a single source, is at the basis of what has become known as super-resolution microscopy, e.g. stochastic optical reconstruction microscopy (STORM), where fluorescent probes attached to molecules give nanoscale distance information.
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A slight head down trim is recommended to reduce downthrust during finning, and this reduces silting and fin impact with the bottom. The free-swimming diver may need to trim erect or inverted at times, but in general, a horizontal trim has advantages both for reduction of drag when swimming horizontally, and for observing the bottom. A horizontal trim allows the diver to direct propulsive thrust from the fins directly to the rear, which minimises disturbance of sediments on the bottom, and reduces the risk of striking delicate benthic organisms with the fins. A stable horizontal trim requires that diver's centre of gravity is directly below the centre of buoyancy (the centroid).
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The van Lamoen circle through six circumcenters A_b, A_c, B_c, B_a, C_a, C_b In Euclidean plane geometry, the van Lamoen circle is a special circle associated with any given triangle T. It contains the circumcenters of the six triangles that are defined inside T by its three medians. Specifically, let A, B, C be the vertices of T, and let G be its centroid (the intersection of its three medians). Let M_a, M_b, and M_c be the midpoints of the sidelines BC, CA, and AB, respectively. It turns out that the circumcenters of the six triangles AGM_c, BGM_c, BGM_a, CGM_a, CGM_b, and AGM_b lie on a common circle, which is the van Lamoen circle of T.
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A "physical color" is a combination of pure spectral colors (in the visible range). In principle there exist infinitely many distinct spectral colors, and so the set of all physical colors may be thought of as an infinite-dimensional vector space (a Hilbert space). This space is typically notated Hcolor. More technically, the space of physical colors may be considered to be the topological cone over the simplex whose vertices are the spectral colors, with white at the centroid of the simplex, black at the apex of the cone, and the monochromatic color associated with any given vertex somewhere along the line from that vertex to the apex depending on its brightness.
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The Vectors of Mind presents Thurstone's methods for conducting a factor analysis on a set of variables that allow for more than one factor, an important extension of Spearman's unifactor method. Having multiple factors adds significant complications and much of the book is focussed on the problem of rotation. It attempts to solve this problem by providing an objective basis for the rotation factors, called simple structure, and advocates the use of oblique (correlated) factors to achieve a simple structure. The book utilizes his centroid method of factor extraction, which made it feasible to complete the arduous calculations necessary for a factor analysis at a time when fast electronic computers had not even been imagined.
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Hotelling's method was also limited by the fact that it required too much calculation to be useable with more than about ten variables. A year after Hotelling's paper, Thurstone presented a more efficient way of extracting factors, called the centroid method, which allowed the factor analysis of a far larger number of variables. Later that year he gave his presidential address to the American Psychological Association wherein he presented the results of several factor analyses, including a factor analysis of 60 adjectives describing personality traits, showing how they could be reduced to five personality traits. He also presented analyses of 37 mental health symptoms, of attitudes towards 12 controversial social issues, and of 9 IQ tests.
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Likewise, neither compares homologous points, and global change is always given more weight than local variation (which may have large biological consequences). Eigenshape analysis requires an equivalent starting point to be set for each specimen, which can be a source of error EFA also suffers from redundancy in that not all variables are independent. On the other hand, it is possible to apply them to complex curves without having to define a centroid; this makes removing the effect of location, size and rotation much simpler. The perceived failings of outline morphometrics are that it doesn't compare points of a homologous origin, and that it oversimplifies complex shapes by restricting itself to considering the outline and not internal changes.
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Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then : where the path of integration along C is anticlockwise. In physics, Green's theorem finds many applications. One is solving two-dimensional flow integrals, stating that the sum of fluid outflowing from a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter.
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Corvus offers distraction and centroid operating modes, with the two differing from one another in the azimuth angle at firing and the range at which chaff is released. The equipment's firing and control panel is ideally located in the host vessel's combat information centre and has a maximum load of 16 chaff rockets provides protection against three missile attacks before reloading. Physically, Corvus features a cylindrical rotating structure that carries eight launching tubes mounted in two sets of three (one above the other) and crossed at 90° in azimuth. Two further tubes are set above this arrangement and are aligned midway between the other tubes, all at a fixed elevation of 30°.
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A map of the volcanic systems of Iceland Hekla has a morphological type between that of a crater row and stratovolcano (built from mixed lava and tephra eruptions) sited at a rift-transform junction in the area where the south Iceland seismic zone and eastern volcanic zone meet. The unusual form of Hekla is found on very few volcanoes around the world, notably Callaqui in Chile. Hekla is situated on a long volcanic ridge of which the 5.5 km Heklugjá fissure is considered Hekla proper. This fissure opens along its entire length during major eruptions and is fed by a magma reservoir estimated to have a top 4 km below the surface with centroid 2.5 km lower.
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However, the project was put on hold after Rajinkanth fell ill and uncertainty remained whether Rana would resume. In the meantime, producer Dr. J. Murali Manohar felt impressed by Soundarya's draft work on Sultan and persuaded her to materialise her directorial ambitions with Kochadaiiyaan, featuring a plot which leads itself up to the events of Rana, which was later deciphered as a sequel script to Kochadaiiyaan. The team agreed and completed filming in two years with Centroid Motion Capture at Pinewood Studios in the United Kingdom using motion capture technology, after which animation work and post-production ensued in the United States, Hong Kong, and China for a year.Rajinikanth's magnum opus Kochadaiiyaan coming to screens on May 23 – Official press release. Twitter.
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Stochastic optical reconstruction microscopy (STORM), photo activated localization microscopy (PALM), and fluorescence photo-activation localization microscopy (FPALM) are super-resolution imaging techniques that utilize sequential activation and time-resolved localization of photoswitchable fluorophores to create high resolution images. During imaging, only an optically resolvable subset of fluorophores is activated to a fluorescent state at any given moment, such that the position of each fluorophore can be determined with high precision by finding the centroid positions of the single-molecule images of a particular fluorophore. One subset of fluorophores is subsequently deactivated, and another subset is activated and imaged. Iteration of this process allows numerous fluorophores to be localized and a super-resolution image to be constructed from the image data.
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A tenterground, tenter ground or teneter-field was an area used for drying newly manufactured cloth after fulling. The wet cloth was hooked onto frames called tenters and stretched taut so that the cloth would dry flat and square. It is from this process that some have the expression "on tenterhooks", meaning in a state of nervous tension. There were tentergrounds wherever cloth was made, and as a result the word "tenter" is found in place names throughout the United Kingdom and its empire, for example several streets in Spitalfields, LondonApproximate centroid of North-, South-, West-, and East- Tenter Street, and Tenter Passage, in Spitalfields, London: and Tenterfield House in Haddington, East Lothian, Scotland, which is turn gave its name to Tenterfield in New South Wales, Australia.
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In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, that is, a point that is in the middle of the figure by some measure. For example the centroid, circumcenter, incenter and orthocenter were familiar to the ancient Greeks, and can be obtained by simple constructions. Each of these classical centers has the property that it is invariant (more precisely equivariant) under similarity transformations. In other words, for any triangle and any similarity transformation (such as a rotation, reflection, dilation, or translation), the center of the transformed triangle is the same point as the transformed center of the original triangle.
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His other research direction systematically determined the orientation and magnitude of the deformation for most of the significant earthquakes that have been well-recorded. These results are known as the Harvard CMTs (centroid moment tensor solutions) and are continued today at Lamont-Doherty Earth Observatory by Göran Ekström and Meredith Nettles as the Global CMT Project. Dziewonski received numerous honours and awards for his scientific achievements, among them the Gold Medal of Ettore Majorana Foundation and Centre for Scientific Culture (1999), the Harry Fielding Reid Medal of the Seismological Society of America (1999),The Harry Fielding Reid Medal. Seismological Society of America. Accessed September 12, 2008 the Crafoord Prize of the Royal Swedish Academy of Sciences (1998),The Crafoord Prize 1998.
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Trilinear equation: (bz + cx)(cx + ay)(ay + bz) = (bx + cy)(cy + ax)(az + bx) Barycentric equation: [cyclic sum a(a2 − bc)x(c3y2 − b3z2)] = 0 For any point X = x:y:z (trilinears), let XY = y:z:x and XZ = z:x:y. The 2nd equal areas cubic is the locus of X such that the area of the cevian triangle of XY equals the area of the cevian triangle of XZ. The 2nd equal areas cubic passes through the incenter, centroid, symmedian point, and points in Encyclopedia of Triangle Centers indexed as X(31), X(105), X(238), X(292), X(365), X(672), X(1453), X(1931), X(2053), and others. For a graphics and properties, see K155 at Cubics in the Triangle Plane.
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Scientists with the Institut de recherche pour le développement in New Caledonia investigated the extent of the aftershock zone and estimated that the rupture area was about , but an inversion of GPS-based displacement data showed a smaller rupture area of . It was also described as an intraplate event that occurred away from the east-dipping subduction interface on a west- dipping fault in an area with an uncertain type of convergence (either subduction or crustal thickening). The Harvard Centroid Moment Tensor project lists the slip vector as 67°, indicating that the mechanism was mostly thrust, with a significant amount of left-lateral strike-slip motion. Their submission for other fault parameters showed that the north-striking fault dipped shallowly at 30°.
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The Bou'in-Zahra earthquake was located in an area of active thrust faulting and folding, parallel and south of the southern edge of the Alborz mountain range, and was the 11th rupture in the previous two months in central Iran. A seismic inversion of long-period P and SH body-wave seismograms indicated a rupture on a thrust fault that dips 49 degrees to the southwest and had a centroid depth of roughly . The rupture's mechanism of faulting was reverse. Multiple-event relocation of the main shock and aftershock epicenters and discontinuous surface ruptures recorded after the earthquake are compatible with northeastward movement on a southwest-dipping thrust, although maximum recorded displacements were less than would have been expected from the observed magnitude.
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Wolfram Demonstrations Project, Volume and Surface Area of the Menger SpongeUniversity of British Columbia Science and Mathematics Education Research Group, Mathematics Geometry: Menger Sponge Therefore the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues, so that the limit is neither a solid nor a surface; it has a topological dimension of 1 and is accordingly identified as a curve. Each face of the construction becomes a Sierpinski carpet, and the intersection of the sponge with any diagonal of the cube or any midline of the faces is a Cantor set. The cross section of the sponge through its centroid and perpendicular to a space diagonal is a regular hexagon punctured with hexagrams arranged in six-fold symmetry.
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For positive stability in missiles, the total vehicle center of pressure defined as given above must be further from the nose of the vehicle than the center of gravity. In missiles at lower angles of attack, the contributions to the center of pressure are dominated by the nose, wings, and fins. The normalized normal force coefficient derivative with respect to the angle of attack of each component multiplied by the location of the center of pressure can be used to compute a centroid representing the total center of pressure. The center of pressure of the added flow field is behind the center of gravity and the additional force "points" in the direction of the added angle of attack; this produces a moment that pushes the vehicle back to the trim position.
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Schematic representation of the reconstruction of a high resolution image by localizing the centroid of many low-resolution images of point-like light emitters Conventional fluorescence microscopy is performed by selectively staining the sample with fluorescent molecules, either linked to antibodies as in immunohistochemistry or using fluorescent proteins genetically fused to the genes of interest. Typically, the more concentrated the fluorophores, the better the contrast of the fluorescence image. A single fluorophore can be visualized under a microscope (or even under the naked eye) if the number of photons emitted is sufficiently high, and in contrast the background is low enough. The two dimensional image of a point source observed under a microscope is an extended spot, corresponding to the Airy disk (a section of the point spread function) of the imaging system.
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Some very frequently considered segments in a triangle to include the three altitudes (each perpendicularly connecting a side or its extension to the opposite vertex), the three medians (each connecting a side's midpoint to the opposite vertex), the perpendicular bisectors of the sides (perpendicularly connecting the midpoint of a side to one of the other sides), and the internal angle bisectors (each connecting a vertex to the opposite side). In each case, there are various equalities relating these segment lengths to others (discussed in the articles on the various types of segment), as well as various inequalities. Other segments of interest in a triangle include those connecting various triangle centers to each other, most notably the incenter, the circumcenter, the nine-point center, the centroid and the orthocenter.
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A scaled version of the curve is the probability density function of the Cauchy distribution. This is the probability distribution on the random variable x determined by the following random experiment: for a fixed point p above the x-axis, choose uniformly at random a line through p, and let x be the coordinate of the point where this random line crosses the axis. The Cauchy distribution has a peaked distribution visually resembling the normal distribution, but its heavy tails prevent it from having an expected value by the usual definitions, despite its symmetry. In terms of the witch itself, this means that the x-coordinate of the centroid of the region between the curve and its asymptotic line is not well-defined, despite this region's symmetry and finite area.
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The distance between the mass centroid of the car and the suspension roll centre were designed to be the same front and rear to avoid unwanted weight transfer effects. Computer controlled dynamic suspension were considered but not applied due to the inherent increase in weight, increased complexity and loss of predictability of the vehicle. Damper and spring specifications: bump, rebound with bounce frequency at 1.43 Hz at front and 1.80 Hz at the rear. Despite being sports oriented, these figures imply a soft ride and inherently decrease track performance. As can be seen from the McLaren F1 LM and the McLaren F1 GTR track variants, the track performance potential is much higher than that in the standard F1 road car due to fact that car should be comfortable and usable in everyday conditions.
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The center of the van Lamoen circle is point X(1153) in Clark Kimberling's comprehensive list of triangle centers. In 2003, Alexey Myakishev and Peter Y. Woo proved that the converse of the theorem is nearly true, in the following sense: let P be any point in the triangle's interior, and AA', BB', and CC' be its cevians, that is, the line segments that connect each vertex to P and are extended until each meets the opposite side. Then the circumcenters of the six triangles APB', APC', BPC', BPA', CPA', and CPB' lie on the same circle if and only if P is the centroid of T or its orthocenter (the intersection of its three altitudes). A simpler proof of this result was given by Nguyen Minh Ha in 2005.
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The radar element provides very accurate, real-time, all weather slope movement measurements with sub millimetre detection ability, and is able to provide an alarm if the detected movement reaches a predetermined level, thereby permitting evacuation of the unstable area, and enhancing safety. All radar measurements are fully geo-referenced to an accuracy that allows easy integration with standard digital terrain mapping (DTM) tools. A second function of the Movement and Surveying Radar is to determine the absolute range to the electromagnetic reflective centroid of an area on a body of material or geographical feature. This functionality, combined with the accurately surveyed position of the measurement origin of the Movement and Surveying Radar and the positioning system’s angular measurement information, may be used to generate survey data of geographical features such as mine walls and rubble dumps.
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Chevreul's 1855 "chromatic diagram" based on the RYB color model, showing complementary colors and other relationships For the mixing of colored light, Newton's color wheel is often used to describe complementary colors, which are colors that cancel each other's hue to produce an achromatic (white, gray or black) light mixture. Newton offered as a conjecture that colors exactly opposite one another on the hue circle cancel out each other's hue; this concept was demonstrated more thoroughly in the 19th century. A key assumption in Newton's hue circle was that the "fiery" or maximum saturated hues are located on the outer circumference of the circle, while achromatic white is at the center. Then the saturation of the mixture of two spectral hues was predicted by the straight line between them; the mixture of three colors was predicted by the "center of gravity" or centroid of three triangle points, and so on.
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Chevreul's 1855 "chromatic diagram" based on the RYB color model, showing complementary colors and other relationships For the mixing of colored light, Isaac Newton's color wheel is often used to describe complementary colors, which are colors that cancel each other's hue to produce an achromatic (white, gray or black) light mixture. Newton offered as a conjecture that colors exactly opposite one another on the hue circle cancel out each other's hue; this concept was demonstrated more thoroughly in the 19th century. A key assumption in Newton's hue circle was that the "fiery" or maximum saturated hues are located on the outer circumference of the circle, while achromatic white is at the center. Then the saturation of the mixture of two spectral hues was predicted by the straight line between them; the mixture of three colors was predicted by the "center of gravity" or centroid of three triangle points, and so on.
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To illustrate the potential of the k-means algorithm to perform arbitrarily poorly with respect to the objective function of minimizing the sum of squared distances of cluster points to the centroid of their assigned clusters, consider the example of four points in R2 that form an axis-aligned rectangle whose width is greater than its height. If k = 2 and the two initial cluster centers lie at the midpoints of the top and bottom line segments of the rectangle formed by the four data points, the k-means algorithm converges immediately, without moving these cluster centers. Consequently, the two bottom data points are clustered together and the two data points forming the top of the rectangle are clustered together--a suboptimal clustering because the width of the rectangle is greater than its height. Now, consider stretching the rectangle horizontally to an arbitrary width.
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As built, the decoy system comprises two BAE Systems Shield Mark 2 decoy launchers which fire chaff to and infrared rockets to in distraction, confusion and centroid seduction modes. The torpedo decoy is the AN/SLQ-25A Nixie towed acoustic decoy from Argon ST. The ship's radar warning receiver, the CANEWS (Canadian Electronic Warfare System), SLQ-501, and the radar jammer, SLQ-505, were developed by Thorn and Lockheed Martin Canada. Two Thales Nederland (formerly Signaal) SPG-503 (STIR 1.8) fire control radars are installed one on the roof of the bridge and one on the raised radar platform immediately forward of the helicopter hangar. The ship is also fitted with Raytheon AN/SPS-49(V)5 long-range active air search radar operating at C and D bands, Ericsson HC150 Sea Giraffe medium-range air and surface search radar operating at G and H bands, and Kelvin Hughes Type 1007 I-band navigation radar.
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As built, the decoy system comprises Two BAE Systems Shield Mark 2 decoy launchers which fire chaff to and infrared rockets to in distraction, confusion and centroid seduction modes. The torpedo decoy is the AN/SLQ-25A Nixie towed acoustic decoy from Argon ST. The ship's radar warning receiver, the CANEWS (Canadian Electronic Warfare System), SLQ-501, and the radar jammer, SLQ-505, were developed by Thorn and Lockheed Martin Canada. Two Thales Nederland (formerly Signaal) SPG-503 (STIR 1.8) fire control radars are installed one on the roof of the bridge and one on the raised radar platform immediately forward of the helicopter hangar. The ship is also fitted with Raytheon AN/SPS-49(V)5 long-range active air search radar operating at C and D bands, Ericsson HC150 Sea Giraffe medium-range air and surface search radar operating at G and H bands, and Kelvin Hughes Type 1007 I-band navigation radar.
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As built, the decoy system comprises Two BAE Systems Shield Mark 2 decoy launchers which fire chaff to and infrared rockets to in distraction, confusion and centroid seduction modes. The torpedo decoy is the AN/SLQ-25A Nixie towed acoustic decoy from Argon ST. The ship's radar warning receiver, the CANEWS (Canadian Electronic Warfare System), SLQ-501, and the radar jammer, SLQ-505, were developed by Thorn and Lockheed Martin Canada. Two Thales Nederland (formerly Signaal) SPG-503 (STIR 1.8) fire control radars are installed one on the roof of the bridge and one on the raised radar platform immediately forward of the helicopter hangar. The ship is also fitted with Raytheon AN/SPS-49(V)5 long-range active air search radar operating at C and D bands, Ericsson HC150 Sea Giraffe medium-range air and surface search radar operating at G and H bands, and Kelvin Hughes Type 1007 I-band navigation radar.
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The centroid (geographical center) of the city is at , southeast of 28th and Leavitt Streets in an industrial area near the Chicago Sanitary and Ship Canal. (Before annexations in the 1950s, notably for O'Hare International Airport, references placed the geographical center near 37th and Honore Streets.) Chicago, along with New York City and Los Angeles, California are the three most populous cities of the U.S., yet Chicago is only half the other two cities' individual land areas. Chicago's nickname, "The Windy City," actually acquired from a political op-ed piece, fits the city well as its location on Lake Michigan moderates the climate and often provides a breeze. The Chicago Metropolitan Statistical Area (MSA) consists of Cook county and five surrounding Illinois counties as well as the Chicago–Gary–Kenosha Combined Statistical Area (CSA) which is made up of nine counties, two of them in northwestern Indiana and one in southeastern Wisconsin.
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As built, the decoy system comprises Two BAE Systems Shield Mark 2 decoy launchers which fire chaff to and infrared rockets to in distraction, confusion and centroid seduction modes. The torpedo decoy is the AN/SLQ-25A Nixie towed acoustic decoy from Argon ST. The ship's radar warning receiver, the CANEWS (Canadian Electronic Warfare System), SLQ-501, and the radar jammer, SLQ-505, were developed by Thorn and Lockheed Martin Canada. Two Thales Nederland (formerly Signaal) SPG-503 (STIR 1.8) fire control radars are installed one on the roof of the bridge and one on the raised radar platform immediately forward of the helicopter hangar. The ship is also fitted with Raytheon AN/SPS-49(V)5 long-range active air search radar operating at C and D bands, Ericsson HC150 Sea Giraffe medium-range air and surface search radar operating at G and H bands, and Kelvin Hughes Type 1007 I-band navigation radar.
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This stake is one of several way markers that mark the location of variously calculated geographic centres of Britain. It is located just to the west of Whitendale Hanging Stones in Lancashire at SD 64188 56541. Whalley, Lancashire at Grid Ref SD 72321.72 36671.1 (approximately), in December 2005 There has long been debate over the exact location of the geographical centre of the United Kingdom, and its constituent countries, due to the complexity and method of the calculation, such as whether to include offshore islands, and the fact that erosion will cause the position to change over time. There are two main methods of calculating this "centre": either as the centroid of the two-dimensional shape made by the country (projected to the Airy ellipsoid then flattened using the Transverse Mercator projection), or as the point farthest from the boundary of the country (either the sea, or, in the case of constituent countries, a land border).
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The recursive subdivision of triangles into three smaller triangles was investigated as an image segmentation technique in computer vision by ; in this context, they called it the ternary scalene triangle decomposition. They observed that, by placing each new vertex at the centroid of its enclosing triangle, the triangulation could be chosen in such a way that all triangles have equal areas, although they do not all have the same shape. More generally, Apollonian networks may be drawn in the plane with any prescribed area in each face; if the areas are rational numbers, so are all of the vertex coordinates.. It is also possible to carry out the process of subdividing a triangle to form an Apollonian network in such a way that, at every step, the edge lengths are rational numbers; it is an open problem whether every planar graph has a drawing with this property.For subdividing a triangle with rational side lengths so that the smaller triangles also have rational side lengths, see .
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In natural language processing and information retrieval, explicit semantic analysis (ESA) is a vectoral representation of text (individual words or entire documents) that uses a document corpus as a knowledge base. Specifically, in ESA, a word is represented as a column vector in the tf–idf matrix of the text corpus and a document (string of words) is represented as the centroid of the vectors representing its words. Typically, the text corpus is English Wikipedia, though other corpora including the Open Directory Project have been used. ESA was designed by Evgeniy Gabrilovich and Shaul Markovitch as a means of improving text categorization and has been used by this pair of researchers to compute what they refer to as "semantic relatedness" by means of cosine similarity between the aforementioned vectors, collectively interpreted as a space of "concepts explicitly defined and described by humans", where Wikipedia articles (or ODP entries, or otherwise titles of documents in the knowledge base corpus) are equated with concepts.
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On September 22, although the structure remained asymmetric with a fully exposed LLCC under easterly moderate vertical wind shear, the system still intensified into a tropical storm late on the same day and received the name Dujuan from the JMA. Tropical Storm Dujuan with a fully exposed LLCC on September 23 Many meteorological agencies initially forecasted a recurving track south of Japan to Dujuan, but those agencies changed it to a west-northwest track pointing to Taiwan after 24 hours. Dujuan developed smaller vortices rotating around a larger circulation centroid with deep convection along the western periphery on September 23; however, right after the storm entered the Philippine Area of Responsibility and was named Jenny by PAGASA, there was only one partially exposed LLCC within the consolidating structure in the afternoon, leading more model guidances to show a stairstep track vice a recurve scenario. When moving and organizing slowly on September 24, Dujuan was upgraded to a severe tropical storm early on that day, with an apparent eye revealed by a microwave imagery.
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In 1965, at the suggestion of Frank McDonald, Elihu Boldt initiated Goddard's program in X-ray astronomy with a series of balloon-borne experiments. At an early stage he was joined by Peter Serlemitsos, who had just completed his PhD space physics thesis on magnetospheric electrons, and by Guenter Riegler, a University of Maryland physics graduate student interested in doing his dissertation research in astrophysics. From 1965 to 1972 there were over a dozen balloon-borne experiments (mostly from New Mexico), including the first such to take place from Australia (1966), one in which hard X-ray emission was discovered (albeit with crude angular resolution) from a region towards the Galactic Center whose centroid is located among subsequently identified sources GX1+4, GX3+1, and GX5-1. A balloon-borne experiment in 1968 was based on the multi-anode multi-layer xenon gas proportional chamber that had recently been developed in our lab and represented the first use of such a high performance instrument for X-ray astronomy.
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As the reflection of the orthocenter around the circumcenter, the de Longchamps point belongs to the line through both of these points, which is the Euler line of the given triangle. Thus, it is collinear with all the other triangle centers on the Euler line, which along with the orthocenter and circumcenter include the centroid and the center of the nine-point circle... See in particular Section 5, "Six notable points on the Euler line", pp. 380–383. The de Longchamp point is also collinear, along a different line, with the incenter and the Gergonne point of its triangle.. The three circles centered at A, B, and C, with radii s-a, s-b, and s-c respectively (where s is the semiperimeter) are mutually tangent, and there are two more circles tangent to all three of them, the inner and outer Soddy circles; the centers of these two circles also lie on the same line with the de Longchamp point and the incenter. The de Longchamp point is the point of concurrence of this line with the Euler line, and with three other lines defined in a similar way as the line through the incenter but using instead the three excenters of the triangle.
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