Control Limits The control limits for the x-chart are: UCL–x = =x + A2R and LCLx–= x=- A2R Where = X = central line of the chart, which can be either the average of past sample means or a target value set for the process. A2 = constant to provide three-sigma limits for the sample mean. The control limits for the R-chart are UCLR = D4R and LCLR = D3R where R = average of several past R values and the central line of the chart. D3,D4 = constants that provide 3 standard deviations (three-sigma) limits for a given sample size. © 2007 Pearson Education
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Control Charts for Variables Control Charts - Special Metal Screw R - Charts UCLR = D4R LCLR = D3R R = 0.0020 D4 = 2.282 D3 = 0 UCLR = 2.282 (0.0020) = 0.00456 in. LCLR = 0 (0.0020) = 0 in.
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NeMoFinder adapts SPIN [27] to extract frequent trees and expands them into non-isomorphic graphs.[8] NeMoFinder utilizes frequent size-n trees to partition the input network into a collection of size-n graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-n graph Kn. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, NeMoFinder is an exact enumeration algorithm and is not based on a sampling method. As Chen et al. claim, NeMoFinder is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole S. cerevisiae (yeast) PPI network as the authors claimed.[28] NeMoFinder consists of three main steps. First, finding frequent size-n trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-n graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.[26] In the first step, the algorithm detects all non-isomorphic size-n trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between NeMoFinder and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. NeMoFinder exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from preceding steps. The main advantage is in third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-n sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called cousin sub-graphs. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. NeMoFinder is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of NeMoFinder is shown here: NeMoFinder Input: G - PPI network; N - Number of randomized networks; K - Maximal network motif size; F - Frequency threshold; S - Uniqueness threshold; Output: U - Repeated and unique network motif set; D ← ∅; for motif-size k from 3 to K do T ← FindRepeatedTrees(k); GDk ← GraphPartition(G, T) D ← D ∪ T; D′ ← T; i ← k; while D″ = ∅ and i ≤ k × (k - 1) / 2 do D′ ← FindRepeatedGraphs(k, i, D′); D ← D ∪ D′; i ← i + 1; end while end for for counter i from 1 to N do Grand ← RandomizedNetworkGeneration(); for each g ∈ D do GetRandFrequency(g, Grand); end for end for U ← ∅; for each g ∈ D do s ← GetUniqunessValue(g); if s ≥ S then U ← U ∪ {g}; end if end for return U Grochow and Kellis [29] proposed an exact alg for enumerating sub-graph appearances, which is based on a motif-centric approach, which means that the frequency of a given sub-graph,called the query graph, is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed [29] that a motif-centric method in comparison to network-centric methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the alg, since it is an inefficient exact enumeration alg, the authors introduced a fast method which is called symmetry-breaking conditions. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In Grochow-Kellis alg symmetrybreaking is used to avoid such multiple mappings. GK alg and symmetry-breaking condition which eliminates redundant isomorphism tests. (a) graph G, (b) illustration of all automorphisms of G that is showed in (a). From set AutG we can obtain a set of symmetrybreaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; so, by applying SymG in Isomorphism Extension module alg only enumerate each match-able sub-graph to G once. Note that SynG is not a unique set for an arbitrary graph G. The GK alg discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, alg tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. Computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay’s tools.[24][25] As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in [29][30] that using (a) graph G, (b) illustration of all automorphisms of G that is showed in (a). From set AutG we can obtain a set the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected of symmetry-breaking conditions of G given by SymG networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ESU algorithm in (c). Only the first mapping in AutG satisfies the applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a SynG conditions; as a result, by applying SymG in the given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm Isomorphism Extension module the algorithm only performance. Also, GK alg is 1 of the known algorithms having no limitation for motif size in implementation and potentially enumerate each match-able sub-graph in network to G once. SynG is not a unique set for an arbitrary graph G. it can find motifs of any size.
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Communication In a parallel implementation of simple search, tasks can execute independently and need communicate only to report solutions. Chip Chip Size: Size: 25 25 Chip Chip Size: Size: 54 54 Chip Chip Size: Size: 55 55 Chip Chip Size: Size: 64 64 Chip Chip Size: Size: 144 144 Chip Chip Size: Size: 174 174 CS 340 Chip Chip Size: Size: 84 84 Chip Chip Size: Size: 130 130 Chip Chip Size: Size: 140 140 Chip Chip Size: Size: 143 143 Chip Chip Size: Size: 85 85 Chip Chip Size: Size: 65 65 Chip Chip Size: Size: 114 114 Chip Chip Size: Size: 200 200 The parallel algorithm for this problem will also need to keep track of the bounding value (i.e., the smallest chip area found so far), which must be accessed by every task. One possibility would be to encapsulate the bounding value maintenance in a single centralized task with which the other tasks will communicate. This approach is inherently unscalable, since the processor handling the centralized task can only service requests from the other tasks at a particular rate, thus bounding the number of tasks that can execute concurrently. Chip Chip Size: Size: 112 112 Chip Chip Size: Size: 220 220 Chip Chip Size: Size: 150 150 Chip Chip Size: Size: 234 234 Chip Chip Size: Size: 102 102 Page 6
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set 51 35 14 00010 set 49 30 14 00010 set 47 32 13 00010 set 46 31 15 00010 set 50 36 14 00010 set 54 39 17 00100 set 46 34 14 00011 set 50 34 15 00010 set 44 29 14 00010 set 49 31 15 00001 set 54 37 15 00010 set 48 34 16 00010 set 48 30 14 00001 set 43 30 11 00001 set 58 40 12 00010 set 57 44 15 00100 set 54 39 13 00100 set 51 35 14 00011 set 57 38 17 00011 set 51 38 15 00011 set 54 34 17 00010 set 51 37 15 00100 set 46 36 10 00010 set 51 33 17 00101 set 48 34 19 00010 set 50 30 16 00010 set 50 34 16 00100 set 52 35 15 00010 set 52 34 14 00010 set 47 32 16 00010 set 48 31 16 00010 set 54 34 15 00100 set 52 41 15 00001 ver 56 42 30 14 45 set 55 001 011 01 ver 58 31 27 15 41 set 49 001 0010 ver 62 32 22 12 45 set 50 001 011 01 ver 56 35 25 13 39 set 55 001 00 11 01 ver 59 31 32 15 48 set 49 01 00010 ver 61 30 28 13 40 set 44 001 0101 ver 63 34 25 15 49 set 51 001 011 01 ver 61 35 28 13 47 set 50 001 010 10 ver 64 23 29 13 43 set 45 001 010 11 ver 66 32 30 13 44 set 44 001 011 00 ver 68 35 28 16 48 set 50 00111 00 ver 67 38 30 19 50 set 51 01 00 1001 ver 60 30 29 14 45 set 48 001 0111 57 38 35 ver 58 26 16 40 set 51 00001 010 111 0000 55 32 24 14 38 ver 50 23 33 set 46 00001 010 101 0110 55 37 24 15 37 ver 56 27 42 set 53 00001 010 111 0001 58 33 27 14 39 ver 57 30 42 set 50 ID PL PW SL DPP 2 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1s1 1 151 0 35 0 14 2 60 0 1 1 1 100 2 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1s2 1 149 0 30 0 14 2 59 0 1 1 1 011 2 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1s3 1 047 1 32 0 13 2 60 0 1 1 1 100 2 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1s4 1 146 1 31 0 15 2 58 0 1 1 1 010 2 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1s5 1 150 0 36 0 14 2 60 0 1 1 1 100 4 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0s6 0 054 1 39 0 17 4 58 0 1 1 1 010 3 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1s7 1 146 0 34 0 14 3 60 0 1 1 1 100 2 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1s8 1 150 1 34 0 15 2 59 0 1 1 1 011 2 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1s9 1 144 0 29 0 14 2 59 0 1 1 1 011 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1s10 1 149 1 31 0 15 1 58 0 1 1 1 010 2 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1s11 1 154 1 37 0 15 2 60 0 1 1 1 100 2 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0s12 0 048 0 34 0 16 2 58 0 1 1 1 010 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1s13 1 148 0 30 0 14 1 59 0 1 1 1 011 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1s14 0 143 1 30 0 11 1 62 0 1 1 1 110 2 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1s15 1 058 0 40 0 12 2 63 0 1 1 1 111 4 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1s16 1 157 1 44 0 15 4 61 0 1 1 1 101 4 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1s17 1 054 1 39 0 13 4 61 0 1 1 1 101 3 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1s18 1 151 0 35 0 14 3 60 0 1 1 1 100 3 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0s19 0 057 1 38 0 17 3 58 0 1 1 1 010 3 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1s20 1 151 1 38 0 15 3 60 0 1 1 1 100 2 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0s21 0 054 1 34 0 17 2 57 0 1 1 1 001 4 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1s22 1 151 1 37 0 15 4 59 0 1 1 1 011 2 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1s23 0 146 0 36 0 10 2 64 1 0 0 0 000 5 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0s24 0 051 1 33 0 17 5 56 0 1 1 1 000 2 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0s25 0 148 1 34 0 19 2 56 0 1 1 1 000 2 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0s26 0 050 0 30 0 16 2 57 0 1 1 1 001 4 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0s27 0 050 0 34 0 16 4 57 0 1 1 1 001 2 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1s28 1 152 1 35 0 15 2 59 0 1 1 1 011 2 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1s29 1 152 0 34 0 14 2 60 0 1 1 1 100 2 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0s30 0 047 0 32 0 16 2 58 0 1 1 1 010 2 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0s31 0 048 0 31 0 16 2 57 0 1 1 1 001 4 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1s32 1 154 1 34 0 15 4 58 0 1 1 1 010 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1s33 1 152 1 41 0 15 1 61 0 1 1 1 101 15 1111055 2 00111101101010 100111011100 0001001s34 01 42 0 14 2 62 0 1 1 1 110 10 1101049 1 00111101000110 001111101111 0001001s35 11 31 0 15 1 58 0 1 1 1 010 15 1110050 2 00111101011100 100100010100 0001001s36 01 32 0 12 2 61 0 1 1 1 101 11 0110155 2 00111101101010 100101001011 0001001s37 11 35 0 13 2 61 0 1 1 1 101 18 0101049 1 00111101000111 011010101010 0001011s38 10 31 0 15 1 58 0 1 1 1 e26 66 01 0 1 30 44 14 27 0 0 1 001 13 0 0 2 00110111110001 001111111000 00010011 s39 1 44 1 30 0 2 60 e27 28 13 48 14 230010111 11 01 068 1 34 15 0 0 2 00111101011111 100101001001 00010110 s40 1 1 51 1 0 15 2 59 e28 30 50 17 210010111 0 1 167 100 1 35 12 1 1 3 00111101011001 100101011010 00010010 s41 1 50 1 0 3 61 e29 29 13 45 15 260010111 1 0 160 13 1 23 3 01100010100010 001101111011 00010011 s42 100145 10 0 13 3 57 e30 57 26 35 10 360011101 00 10 100 14 1 2 01100010100100 100101010100 00010010 s43 1 44 1 32 0 13 2 60 e31 24 38 11 320011101 1 0 055 000 0 35 14 6 01101000011000 100101011010 00011100 s44 0 50 0 0 6 57 e32 24 16 37 10 330011101 0 0 155 17 151 0 38 4 01101000001111 100101111100 00011100 s45 0010 11 0 19 4 56 e33 58 27 39 12 320011101 00 00 0 0 15 1 1 1 3 00111101010000 001111111001 00010010 s46 1 1 48 0 30 0 14 3 58 e34 27 51 16 200010111 0 1 060 1 0 0 10 010 1 100101101100 00011000 1 1 12 1 0 2 001111010011 s47 0 0 51 0 38 0 2 59 e35 30 16 45 15 270010111 0 11 154 11 11100 1 100100 101 001 001 0 00010011 11046 0 32 10 010 2 0011011010 s48 01 0 14 2 59 e36 60 34 45 16 270010111 01 11 0 1 10 010 100 110 1 1001011001 011 0 00010011 0 1 0 13 0 2 00111101 s49 1 1 53 1 37 0 15 2 60 e37 31 47 15 240010111 1 00 067 101 0 10010101 00110 1 00010011 010 11150 1 33 12 2 001111010010 s50 00 0 14 2 60 0 1 1 1 IRIS(SL,SW,PL,PW)  DPPMinVec,MaxVEC vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 00 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 00 vir 00 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 63 33 60 1001 58 27 51 0011 71 30 59 0101 63 29 56 0010 65 30 58 0110 76 30 66 0101 49 25 45 0001 73 29 63 0010 67 25 58 0010 72 36 61 1001 65 32 51 0100 64 27 53 0011 68 30 55 0101 57 25 50 0100 58 28 51 1000 64 32 53 0111 65 30 55 0010 77 38 67 0110 77 26 69 0111 60 22 50 1111 69 32 57 0111 56 28 49 0100 77 28 67 0100 63 27 49 0010 67 33 57 0101 72 32 60 0010 62 28 48 0010 61 30 49 0010 64 28 56 0101 72 30 58 0000 74 28 61 0011 79 38 64 0100 64 28 56 0110 63 28 51 1111 61 26 56 1110 77 30 61 0111 63 34 56 1000 64 31 55 0010 60 30 18 0010 69 31 54 0101 67 31 56 1000 69 31 51 0111 58 27 51 0011 68 32 59 25 19 21 18 22 21 17 18 18 25 20 19 21 20 24 23 18 22 23 15 23 20 20 18 21 18 18 18 21 16 19 20 22 15 14 23 24 18 18 21 24 23 19 23 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 i1 1 163 00 33 60 25 10 0 0 0 1010 1 i2 0 058 11 27 51 19 19 0 0 1 0011 1 i3 1 071 11 30 59 21 11 0 0 0 1011 1 i4 1 063 00 29 56 18 15 0 0 0 1111 1 i5 1 065 10 30 58 22 12 0 0 0 1100 0 i6 0 076 10 30 66 21 5 0 0 0 0101 0 i7 1 149 01 25 45 17 24 0 0 1 1000 1 i8 1 173 11 29 63 18 8 0 0 0 1000 1 i9 1 067 10 25 58 18 12 0 0 0 1100 1 i10 1 172 0 136 61 25 10 0 0 01010 1 i11 0 065 1 132 51 20 19 0 0 10011 1 i12 0 164 0 127 53 19 16 0 0 10000 1 i13 0 168 1 130 55 21 15 0 0 01111 1 i14 0 057 1 025 50 20 19 0 0 10011 1 i15 0 058 1 128 51 24 17 0 0 10001 1 i16 0 164 0 132 53 23 17 0 0 10001 1 i17 0 165 1 130 55 18 16 0 0 10000 0 i18 0 077 1 138 67 22 6 0 0 0 0110 0 i19 0 177 0 126 69 23 0 0 0 0 0000 1 e50 001 57028 41 13 30 0 0 11110 1 i1 1 063 01 33 60 25 10 0 0 0 1010 1 i2 0 058 01 27 51 19 19 0 0 1 0011 0 i3 0 071 11 30 59 21 11 0 0 0 1011 1 i4 0 063 01 29 56 18 15 0 0 0 1111 1 i5 1 065 01 30 58 22 12 0 0 0 1100 1 i6 1 176 00 30 66 21 5 0 0 0 0101 1 i7 0 049 00 25 45 17 24 0 0 1 1000 1 i8 0 073 01 29 63 18 8 0 0 0 1000 1 i9 1 067 00 25 58 18 12 0 0 0 1100 1 i10 1 072 1 036 61 25 10 0 0 01010 1 i11 1 165 0 132 51 20 19 0 0 10011 0 i12 0 064 0 027 53 19 16 0 0 10000 1 i13 1 068 0 030 55 21 15 0 0 01111 1 i14 0 057 1 125 50 20 19 0 0 10011 1 i15 1 058 0 028 51 24 17 0 0 10001 1 i16 1 164 0 132 53 23 17 0 0 10001 1 i17 1 065 0 030 55 18 16 0 0 10000 1 i18 0 177 1 138 67 22 6 0 0 0 0110 1 i19 0 077 1 026 69 23 0 0 0 0 0000 1 i40 0 169 1 031 54 21 16 0 0 10000 1 i41 1 067 0 031 56 24 13 0 0 01101 1 i42 0 069 1 131 51 23 18 0 0 10010 1 i43 0 058 1 127 51 19 19 0 0 10011 1 i44 1 068 1 132 59 23 11 0 0
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Partitioning There is no obvious data structure that could be used to perform a decomposition of this problem’s domain into components that could be mapped to separate processors. Chip Chip Size: Size: 25 25 Chip Chip Size: Size: 54 54 Chip Chip Size: Size: 55 55 Chip Chip Size: Size: 64 64 Chip Chip Size: Size: 85 85 Chip Chip Size: Size: 65 65 Chip Chip Size: Size: 84 84 Chip Chip Size: Size: 114 114 Chip Chip Size: Size: 144 144 Chip Chip Size: Size: 200 200 Chip Chip Size: Size: 174 174 Chip Chip Size: Size: 130 130 Chip Chip Size: Size: 140 140 Chip Chip Size: Size: 143 143 Chip Chip Size: Size: 112 112 Chip Chip Size: Size: 220 220 Chip Chip Size: Size: 150 150 Chip Chip Size: Size: 234 234 Chip Chip Size: Size: 102 102 A fine-grained functional decomposition is therefore needed, where the exploration of each search tree node is handled by a separate task. CS 340 This means that new tasks will be created in a wavefront as the search progresses down the search tree, which will be explored in a breadthfirst fashion. Notice that only tasks on the wavefront will be able to execute concurrently. Page 5
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West Allis Industries R-chart Control Chart Factors Example 6.1 Factor Size of for Sample Charts (n) Factor for UCL Factor for and LCL for LCL for x-Charts R-Charts (A2) (D3) 2 1.880 0 3.267 3 1.023 0 R = 0.0021 2.575 4 0.729 0 D4 = 2.282 2.282 5 0.577 0 UCLR = D4R = 2.282 (0.0021) = 0.00479 in. D3 = 0 2.115 LCLR = D3R 0.483 0 (0.0021) = 0 in. 0 © 2007 Pearson Education 6 2.004 UCL R(D4)
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set 0 set 0 set 0 set 0 set 0 set 0 set 1 set 0 set 0 set 1 set 0 set 0 set 1 set 1 set 0 set 0 set 0 set 1 set 1 set 1 set 0 set 0 set 0 set 1 set 0 set 0 set 0 set 0 set 0 set 0 set 0 set 0 set 1 set 0 set 1 set 0 set 0 set 1 set 0 set 0 set 1 set 1 set 0 set 0 set 0 set 1 SL 51 49 47 46 50 54 46 50 44 49 54 48 48 43 58 57 54 51 57 51 54 51 46 51 48 50 50 52 52 47 48 54 52 55 49 50 55 49 44 51 50 45 44 50 51 48 SW 35 30 32 31 36 39 34 34 29 31 37 34 30 30 40 44 39 35 38 38 34 37 36 33 34 30 34 35 34 32 31 34 41 42 31 32 35 31 30 34 35 23 32 35 38 30 PL PW 14 2 0 1 1 0 0 1 1 14 2 0 1 1 0 0 0 1 13 2 0 1 0 1 1 1 1 15 2 0 1 0 1 1 1 0 14 2 0 1 1 0 0 1 0 17 4 0 1 1 0 1 1 0 14 3 0 1 0 1 1 1 0 15 2 0 1 1 0 0 1 0 14 2 0 1 0 1 1 0 0 15 1 0 1 1 0 0 0 1 15 2 0 1 1 0 1 1 0 16 2 0 1 1 0 0 0 0 14 1 0 1 1 0 0 0 0 11 1 0 1 0 1 0 1 1 12 2 0 1 1 1 0 1 0 15 4 0 1 1 1 0 0 1 13 4 0 1 1 0 1 1 0 14 3 0 1 1 0 0 1 1 17 3 0 1 1 1 0 0 1 15 3 0 1 1 0 0 1 1 17 2 0 1 1 0 1 1 0 15 4 0 1 1 0 0 1 1 10 2 0 1 0 1 1 1 0 17 5 0 1 1 0 0 1 1 19 2 0 1 1 0 0 0 0 16 2 0 1 1 0 0 1 0 16 4 0 1 1 0 0 1 0 15 2 0 1 1 0 1 0 0 14 2 0 1 1 0 1 0 0 16 2 0 1 0 1 1 1 1 16 2 0 1 1 0 0 0 0 15 4 0 1 1 0 1 1 0 15 1 0 1 1 0 1 0 0 14 2 0 1 1 0 1 1 1 15 1 0 1 1 0 0 0 1 12 2 0 1 1 0 0 1 0 13 2 0 1 1 0 1 1 1 15 1 0 1 1 0 0 0 1 13 2 0 1 0 1 1 0 0 15 2 0 1 1 0 0 1 1 13 3 0 1 1 0 0 1 0 13 3 0 1 0 1 1 0 1 13 2 0 1 0 1 1 0 0 16 6 0 1 1 0 0 1 0 19 4 0 1 1 0 0 1 1 14 3 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 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1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 ver 0 ver 0 ver 0 ver 1 ver 0 ver 1 ver 1 ver 1 ver 1 vir 1 vir 1 vir 1 vir 0 vir 0 vir 1 vir 1 vir 0 vir 0 vir 1 vir 0 vir 1 vir 1 vir 0 vir 0 vir 1 vir 0 vir 0 vir 1 vir 1 vir 1 vir 0 vir 0 vir 0 vir 1 vir 0 vir 0 vir 0 vir 1 vir 0 vir 1 vir 0 vir 0 vir 1 vir 0 vir 1 vir 0 SL 61 58 50 56 57 57 62 51 57 63 58 71 63 65 76 49 73 67 72 65 64 68 57 58 64 65 77 77 60 69 56 77 63 67 72 62 61 64 72 74 79 64 63 61 77 63 SW 30 26 23 27 30 29 29 25 28 33 27 30 29 30 30 25 29 25 36 32 27 30 25 28 32 30 38 26 22 32 28 28 27 33 32 28 30 28 30 28 38 28 28 26 30 34 PL 46 40 33 42 42 42 43 30 41 60 51 59 56 58 66 45 63 58 61 51 53 55 50 51 53 55 67 69 50 57 49 67 49 57 60 48 49 56 58 61 64 56 51 56 61 56 PW 14 12 10 13 12 13 13 11 13 25 19 21 18 22 21 17 18 18 25 20 19 21 20 24 23 18 22 23 15 23 20 20 18 21 18 18 18 21 16 19 20 22 15 14 23 24 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 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Constants Lesson Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. Constants Lesson Outline What is a Constant? The Difference Between a Variable and a Constant Categories of Constants: Literal & Named Literal Constants Literal Constant Example Program Named Constants Name Constant Example Program The Value of a Named Constant Can’t Be Changed 10. 11. 12. 13. 14. 15. Why Literal Constants Are BAD BAD BAD 1997 Tax Program with Numeric Literal Constants 1999 Tax Program with Numeric Literal Constants Why Named Constants Are Good 1997 Tax Program with Named Constants 1999 Tax Program with Named Constants Constants Lesson CS1313 Spring 2019 1
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Control Charts for Variables Control Charts - Special Metal Screw R - Charts UCLR = D4R LCLR = D3R R = 0.0020
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Schreiber, Schwöbbermeyer [12] proposed flexible pattern finder (FPF) in a system Mavisto.[23] It exploits downward closure , applicable for frequency concepts F2 and F3. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; but it does not hold necessarily for frequency concept F1. FPF is based on a pattern tree (see figure) consisting of nodes that represents different graphs (or patterns), where the parent is a sub-graph of its children nodes; i.e., corresp. graph of each pattern tree’s node is expanded by adding a new edge of its parent node. At first, FPF enumerates and maintains info of all matches of a sub-graph at the root of the pattern tree. Then builds child nodes of previous node by adding 1 edge supported by a matching edge in target graph, tries to expand all of previous info about matches to the new sub-graph (child node).[In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse. It does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. But, FPF is most useful for frequency concepts F2 and F3, because downward closure is not applicable to F1. Still the pattern tree is still practical for F1 if the algorithm runs in parallel. It has no limitation on motif size, which makes it more amenable to improvements. ESU (FANMOD) Sampling bias of Kashtan et al. [9] provided great impetus for designing better algs for NM discovery, Even after weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated impl. It supports visual options and is time efficient. But it doesn’t allow searching for motifs of size 9. Wernicke [10] RAND-ESU is better than jfinder, based on the exact enumeration algorithm ESU, has been implemented as an app called FANMOD.[10] Rand-esu is a discovery alg applicable for both directed and undirected networks. It effectively exploits an unbiased node sampling, and prevents overcounting sub-graphs. RAND-ESU uses DIRECT for determining sub-graph significance instead of an ensemble of random networks as a Null-model. DIRECT estimates sub-graph # w/oexplicitly generating random networks.[10] Empirically, DIRECT is more efficient than random network ensemble for sub-graphs with a very low concentration. But classical Null-model is faster than DIRECT for highly concentrated sub-graphs.[3][10] ESU alg: We show how this exact algorithm can be modified efficiently to RAND-ESU that estimates sub-graphs concentrations. The algorithms ESU and RAND-ESU are fairly simple, and hence easy to implement. ESU first finds the set of all induced sub-graphs of size k, let Sk be this set. ESU can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth k, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size |SUB|≤k. If |SUB|=k, alg has found induced complete sub-graph, Sk=SUB ∪Sk. If |SUB|v} graphs of size 3 in the target graph. call ExtendSubgraph({v}, VExtension, v) endfor Leaves: set S3 or all of size-3 induced sub-graphs of the target graph (a). ESUtree nodes incl 2 adjoining sets: adjacent ExtendSubgraph(VSubgraph, VExtension, v) nodes called SUB and EXT=all adjacent if |VSubG|=k output G[VSubG] return 1 SUB node and where their numerical While VExt≠∅ do Remove arbitrary vertex w from VExt labels > SUB nodes labels. EXT set is VExtension′←VExtension∪{u∈Nexcl(w,VSubgraph)|u>v} utilized by the alg to expand a SUB set call ExtendSubgraph(VSubgraph ∪ {w}, VExtension′, v) until it reaches a desired size placed at return lowest level of ESU-Tree (or its leaves).
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