Network layer      transport segment from sending to receiving host on sending side encapsulates segments into datagrams on receiving side, delivers segments to transport layer network layer protocols in every host, router router examines header fields in all IP datagrams passing through it application transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical application transport network data link physical Network Layer 4-4
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Network layer  transport segment from sending to receiving hosts  on sending side encapsulates segments into datagrams  on receiving side, delivers segments to transport layer  network layer protocols in every host & router  router examines application transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical application transport network data link physical Network Layer: Data 4-3 Plane
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Network layer      transport segment from sending to receiving host on sending side encapsulates segments into datagrams on rcving side, delivers segments to transport layer network layer protocols in every host, router router examines header fields in all IP applicatio n transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network network data link data link physical physical network data link physical network data link physical network data link physical network data link physical Network Layer applicatio n transport network data link physical 4-4
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Network Layer      transport segment from sending to receiving host. on sending side, encapsulates segments into datagram packets. on receiving side, delivers segments to transport layer. network layer protocols in every host, router. router examines Things header fieldsInternet in allofIP applicatio n transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network network data link data link physical physical network data link physical network data link physical network data link physical network data link physical applicatio n transport network data link physical K&R Routing Primer 6
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Network Layer      transport segment from sending to receiving host. on sending side, encapsulates segments into datagram packets. on receiving side, delivers segments to transport layer. network layer protocols in every host, router. router examines Advanced header fields inComputer all IP Networks applicatio n transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network network data link data link physical physical network data link physical network data link physical network data link physical network data link physical applicatio n transport network data link physical K&R Routing Primer 6
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Network Layer      transport segment from sending to receiving host. on sending side, encapsulates segments into datagram packets. on receiving side, delivers segments to transport layer. network layer protocols in every host and router. router examines Computer header fields inNetworks all IP applicatio n transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network network data link data link physical physical network data link physical network data link physical network data link physical network data link physical applicatio n transport network data link physical K&R Distance Vector Routing 9
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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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Comparison with other methods Recently, Tjong and Zhou (2007) developed a neural network method for predicting DNA-binding sites. In their method, for each surface residue, the PSSM and solvent accessibilities of the residue and its 14 neighbors were used as input to a neural network in the form of vectors. In their publication, Tjong and Zhou showed that their method achieved better performance than other previously published methods. In the current study, the 13 test proteins were obtained from the study of Tjong and Zhou. Thus, we can compare the method proposed in the current study with Tjong and Zhou’s neural network method using the 13 proteins. Figure 1. Tradeoff between coverage and accuracy In their publication, Tjong and Zhou also used coverage and accuracy to evaluate the predictions. However, they defined accuracy using a loosened criterion of “true positive” such that if a predicted interface residue is within four nearest neighbors of an actual interface residue, then it is counted as a true positive. Here, in the comparison of the two methods, the strict definition of true positive is used, i.e., a predicted interface residue is counted as true positive only when it is a true interface residue. The original data were obtained from table 1 of Tjong and Zhou (2007), the accuracy for the neural network method was recalculated using this strict definition (Table 3). The coverage of the neural network was directly taken from Tjong and Zhou (2007). For each protein, Tjong and Zhou’s method reported one coverage and one accuracy. In contrast, the method proposed this study allows the users to tradeoff between coverage and accuracy based on their actual need. For the purpose of comparison, for each test protein, topranking patches are included into the set of predicted interface residues one by one in the decreasing order of ranks until coverage is the same as or higher than the coverage that the neural network method achieved on that protein. Then the coverage and accuracy of the two methods are compared. On a test protein, method A is better than B, if accuracy(A)>accuracy(B) and coverage (A)≥coverage(B). Table 3 shows that the graph kernel method proposed in this study achieves better results than the neural network method on 7 proteins (in bold font in table 3). On 4 proteins (shown in gray shading in table 3), the neural network method is better than the graph kernel method. On the remaining 2 proteins (in italic font in table 3), conclusions can be drawn because the two conditions, accuracy(A)>accuracy(B) and coverage (A)≥coverage(B), never become true at the same time, i.e., when coverage (graph kernel)>coverage(neural network), we have accuracy(graph kernel)accuracy(neural network). Note that the coverage of the graph kernel method increases in a discontinuous fashion as we use more patches to predict DNA-binding sites. One these two proteins, we were not able to reach at a point where the two methods have identical coverage. Given these situations, we consider that the two methods tie on these 2 proteins. Thus, these comparisons show that the graph kernel method can achieves better results than the neural network on 7 of the 13 proteins (shown in bold font in Table 3). Additionally, on another 4 proteins (shown in Italic font in Table 3), the graph kernel method ties with the neural network method. When averaged over the 13 proteins, the coverage and accuracy for the graph kernel method are 59% and 64%. It is worth to point out that, in the current study, the predictions are made using the protein structures that are unbound with DNA. In contrast, the data we obtained from Tjong and Zhou’s study were obtained using proteins structures bound with DNA. In their study, Tjong and Zhou showed that when unbound structures were used, the average coverage decreased by 6.3% and average accuracy by 4.7% for the 14 proteins (but the data for each protein was not shown).
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Network layer  transport segment from sending to receiving host  on sending side encapsulates segments into datagrams  on rcving side, delivers segments to transport layer  network layer protocols in every host, router  Router examines header fields in all IP datagrams passing through it application transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical application transport network data link physical Network Layer 4-2
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Network layer functions • transport packet from sending to receiving hosts • network layer protocols in every host, router three important functions: • path determination: route taken by packets from source to dest. Routing algorithms • switching: move packets from router’s input to appropriate router output • call setup: some network architectures require router call setup along path before data flows applicatio n transport network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical network data link physical applicatio n transport network data link physical
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