Leading Edge Extensions David Gallagher Adam Entsminger Will Graf AOE 4124 3/26/2004 1
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An Issue of Controversy - Abortion Biblical source: In covenant with Noah & descendants, Genesis 9:6: “Whoso sheds the blood of ha-adam b’adam his blood shall be shed….”    ha-adam b’adam 1: a man, by a man ha-adam b’adam 2: lit., “the person in a person” – a fetus Symmetric wording of Hebrew: Shofeich dam ha-adam b’adam damo y’shafeich – don’t take seriously as legislation; rather, as ironic social comment
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Here Comes the Story… Adam, Bob, Carl, David Geeta, Heiki, Irina, Fran Adam Fran Carl, David, Bob, Adam Irina, Fran, Heiki, Geeta Geeta Bob Geeta, Fran, Heiki, Irina Carl, Bob, David, Adam Heiki Carl Irina, Heiki, Geeta, Fran David Adam, Carl, David, Bob Irina
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Sub-band Allocation Department of Electrical and Computer Engineering Adam, Bob, Carl, David Geeta, Heiki, Irina, Fran Adam Fran Carl, David, Bob, Adam Bob USER Irina, Fran, Heiki, Geeta SUB-BAND Geeta Carl, Bob, David, Adam Geeta, Fran, Heiki, Irina Carl Heiki Adam, Carl, David, Bob David Irina, Heiki, Geeta, Fran Irina 30
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A graph is a set of vertices, V, and a set of edges, E, each connecting a pair of those vertices. An edge from vertex h to vertex k is realized as the unordered set, {h,k} (or just hk), and can be viewed as an undirected line from h to k. We can either list the edges in a two column table (the Edge Table) or we can use a 3 column table in which the first 2 columns list all possible vertex pairs (in raster order) and the third column is a bit map indicating with a 1-bit the pairs that are edges and with a 0-bit the pairs that are not edges. This second option is called the edge map or edge mask and is shown below for a small graph, G1. The edge map obviously has |V| 2 rows. If the raster ordering is always assumed, the edge map is just a single column of bits. The edge map can be compressed into a pTree (predicate Tree) by dividing the bits up into “strides” of |V| bits each (4 for G1). This forms the lowest level of the pTree (level_0) and an upper level (level_1), indicates the truth of the predicate, “Not Purely Zeros” for the respective level_0 pTrees, and can be used to avoid retrieving level_0 pTrees that are purely zeros. We use the notation Ek for the kth level_0 pTree (which bitmaps the endpoints of the edges adjacent to vertex k.) and call it the Edge pTree of k A Path is a sequence of edges connecting a sequence of vertices, distinct, except for endpts. A Simple Path (assumed throughout) disallows simple loops, (v,v) Next we build a ShortestPathtree, SPG1 for G1 M M M It starts with Level_0 of the EdgeTree.  vertex, k, this gives us a mask, Sk, of M 1 0 0 Vertex Masks Edge Map Edges V1 V2 1 2 3 4 1,1 1,2 1,3 1,4_ 2,1 2,2 2,3 2,4_ 3,1 3,2 3,3 3,4_ 4,1 4,2 4,3 4,4 2-Level Stride=4, Edge pTree E 0 0 1 1_ 0 0 0 1_ 1 0 0 1_ 1 1 1 0 1 the end pts of edges adjacent to vertex k (shortest path of Length 1 starting at k). Level1 1 1 1 1 E1 0 0 1 1 E2 0 0 0 1 E3 1 0 0 1 E4 1 1 1 0 S2 0 0 0 1 S3 1 0 0 1 S4 1 1 1 0 2 1 2 3 N11 0 1 0 0 N12 1 0 1 0 N13 0 1 0 0 N14 0 0 0 0 1 2 1 0 We can avoid these calculations by noting Ct(N14 )=0. 0 S14 =N11&E4 0 1 0 0 S24 =N12&E4 1 0 1 0 1 2 S31 =N13&E1 0 0 0 0 0 S34 =N13&E4 0 1 0 0 1 S142 =N21&E2 0 0 0 0 S241 =N22&E1 0 0 0 0 S243 =N22&E3 0 0 0 0 S312 =N23&E1 0 0 0 0 S342 =N23&E2 0 0 0 0 0 0 0 0 0 Btwn =1 Btwn =2 Btwn =1 2 1 0 0 4 3 0 0 1 0 0 0 1 The complement of Ek (with k turned off) gives us the endpoints that never need to be considered again (since all shortest paths from k to these vertices hve been found). We call these pTrees the “Not Reached Yet masks” or “N masks”. S1 0 0 1 1 S13 =N11&E3 0 0 0 0 0 0 0 S41 =N14&E1 0 0 0 0 S42 =N14&E2 0 0 0 0 S43 =N14&E3 0 0 0 0 0 0 0 We use the notation, Shk for the map of the endpts of Shortest Paths thru h then k (obviously of length=2) and NLv for the map of vertices not reached by lengthL shortest paths from vertex v N21=N11& (S13|S14)’ 0 0 0 0 N22=N12& (S24)’ 0 0 0 0 N23=N13& (S31|S34)’ 0 0 0 0 N24=N14& (S41|S42|S43)’ 0 0 0 0 0 0 0 0 This entire level is unnecessary to construct since |N2 k|=0 k. The SPTree is shown by the green links. The connectivity components can be deduced from the zero set of the final NL ks. Girvan and Newman started a flurry of research by suggesting the graph could be edge labelled by an edge_between-ness measurement (which counts the shortest path participations of the edge) and that a graph could be usefully partitioned (into strongly connected components) by the divisive hierarchical clustering of removing edges in desc order of between-ness.
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Pig in the Python -rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r--rw-r--r-- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow netflow afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser afsuser 2019685 2031767 2032419 2072933 2062822 2120842 7013906 11331622 15607255 15748046 14216272 12008287 9972353 8973700 9042363 8017690 8109288 7301829 7175834 7029650 7063063 May May May May May May May May May May May May May May May May May May May May May 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 15:21 15:26 15:31 15:36 15:41 15:46 15:51 15:56 16:01 16:06 16:11 16:16 16:21 16:26 16:31 16:36 16:41 16:46 16:51 16:56 17:01 ft-v07.2004-10-02.151649-0500 ft-v07.2004-10-02.152148-0500 ft-v07.2004-10-02.152647-0500 ft-v07.2004-10-02.153145-0500 ft-v07.2004-10-02.153645-0500 ft-v07.2004-10-02.154144-0500 ft-v07.2004-10-02.154643-0500 ft-v07.2004-05-02.155141-0500 ft-v07.2004-05-02.155640-0500 ft-v07.2004-05-02.160139-0500 ft-v07.2004-05-02.160638-0500 ft-v07.2004-05-02.161137-0500 ft-v07.2004-05-02.161636-0500 ft-v07.2004-05-02.162135-0500 ft-v07.2004-05-02.162635-0500 ft-v07.2004-05-02.163133-0500 ft-v07.2004-05-02.163632-0500 ft-v07.2004-05-02.164131-0500 ft-v07.2004-05-02.164630-0500 ft-v07.2004-05-02.165129-0500 ft-v07.2004-05-02.165628-0500 35
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Polygonal Iso-Surfaces: Algorithm Strategy in DrawCubeTriangles(): 1. Look through the FoundEdgeConnection[][] array for a Cube Edge #A and a Cube Edge #B that have a connection between them. 2. If can’t find one, then you are done with this cube. 3. Now look through the FoundEdgeConnection[][] array for a Cube Edge #C that is connected to Cube Edge #B. If you can’t find one, something is wrong. 4. Draw a triangle using the EdgeIntersection[] nodes from Cube Edges #A, #B, and #C. Be sure to use glNormal3f() in addition to glVertex3f(). 5. Turn to false the FoundEdgeConnection[][]entries from Cube Edge #A to Cube Edge #B. 6. Turn to false the FoundEdgeConnection[][]entries from Cube Edge #B to Cube Edge #C. 7. Toggle the FoundEdgeConnection[][]entries from Cube Edge #C to Cube Edge #A. If this connection was there before, we don’t need it anymore. If it was not there before, then we just invented it and we will need it again.
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Conclusions • Leading edge extensions are more beneficial for combat fighter aircraft because these aircraft are more often in the flight conditions where a leading edge extension is most useful, such as high angle of attack maneuvers • However, strakes (as shown in the previous slide) are used on some general aviation aircraft to reduce the abruptness of stall onset and provide better landing capabilities • Leading edge extensions have their drawbacks, including pitchup at high angles of attack, and should only be used when additional maneuverability is necessary 3/26/2004 11
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Brand Extensions  Pertain to the approach the firm uses to launch new offerings by leveraging an existing brand, whether through line or category extensions  Brand line extensions (often called simply line extensions), the new offering is in the same product category but targets a different segment of customers, usually with a slightly different set of attributes  Brand category extensions, the new offering instead moves to a completely different product category  The key benefits that brand extensions offer a firm are:  Accelerates new product acceptance by reducing customers’ perceived risk.  Lowers the cost of new product launches by building on the established brand.  Reduces the time needed to build the new product’s brand by leveraging existing brand characteristics.  Increases the probability of gaining channel access by reducing perceived risk.  Helps enhance the image of the parent brand by linking it to newer and/or emerging product features. Expands the size of the market that the firm can access, by serving additional © Palmatiersubsegments with new offerings.  18
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Brand Extensions  Not all brand extensions achieve all these benefits  The many examples of unsuccessful brand extensions (e.g., Kleenex diapers, BenGay aspirin, Smucker’s ketchup) highlight the limits on a firm’s ability to stretch its brand into new segments and categories  Over time, researchers have developed some guidelines for improving the chances of success for brand extensions:   There must be perceived fit between the parent brand’s image and the extension on a dimension that is relevant to the customer  Brand extensions can be stretched farther if done incrementally  Higher quality brands generally can be extended further Vertical extensions of brands to lower priced markets often undermine the image of the parent brands © Palmatier 19
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Weak-to-Moderate Shear Case - Mature Stage • As the squall line matures (t=2-6h), it develops a mesoscale organization, characterized by a primarily solid line of strong convective cells at the leading edge, with an extensive surface cold pool extending from the leading edge rearward. • A region of lighter, stratiform precipitation now also extends well to the rear of the leading-line convection. • A narrow region of very light precipitation, referred to as a weak echo channel or transition zone, is often observed between the leading line convection and the stratiform precipitation region. • The wind field at the surface is characterized by diverging flow within the cold pool and strongly converging flow at the leading edge of the cold pool, especially on its downshear side.
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