1. Consider the Bayes network given below: Is the set (W)d-separated from Mand (X) d-separated from (Y) given {E}? Justify your answer? El w/
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A: Here is the solution to given question:-
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A: below is the transformation to FS relationship
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A: Given data, In the Erdös-Rényi random network model, N=101 and p=1/20, that is, there are 101…
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A: Answer is given below-
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A: The answer is in step 2:
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A: Solution :- (a) Complete f and c such that f is an admissible flow from S to T. Justify your answer.…
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A:
Q: (3) Show that if n 2 4 is even, then any pairwise stable network in the co-author model [JW(1996)]…
A: Answer: I have given answered in the handwritten format
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A: Answer is in given below- How big B MUST be: B = n(n-1)/2
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A: Lets see the solution.
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A: Given The answer is given below.
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A: The answer as given below steps:
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A: The figure of the network is as follows:
Q: Find the total number Q of tunable parameters in a general L-hidden-layer neural network, in terms…
A: Answer:- a feedforward neural network is the simplest type of artificial neural network in which…
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A: Actually, given question regarding networking.
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A: The Answer start from step-2.
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A: Answer:-
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A: The Answer is in Below Steps
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A: Answer to 1,2,3 are below:
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A: Answer :- Solution 1:- Introduction Depth First Search finds the lexicographical first path in the…
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Q: o 14. A complete network is one in which there is a link between every pair of nodes. Find a formula…
A: answer is given below-
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A: Given
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- Consider an arbitrary connected undirected graph network, with unique identifiers for nodes. We run a deterministic distributed algorithm, such that each node retains an edge only to its lowest indexed neighbour. An edge is retained, if at least one of its two endpoints retains it. A node communicates to that neighbour with which it is retaining its edge, to that effect. Then, the retained sub networkLet G = (V, E) be a connected, undirected graph, and let s be a fixed vertex in G. Let TB be the spanning tree of G found by a bread first search starting from s, and similarly TD the spanning tree found by depth first search, also starting at s. (As in problem 1, these trees are just sets of edges; the order in which they were traversed by the respective algorithms is irrelevant.) Using facts, prove that TB = TD if and only if TB = TD = E, i.e., G is itself a tree.let us take any standard graph G=(v,e) and let us pretend each edge is the same exact weight. let us think about a minimum spanning tree of the graph G, called T = (V, E' ). under each part a and b illustrate then show that a) s a unique path between u and v in T for all u, v ∈ V . b) tree T is not unique. provide proof
- Consider the following generalization of the maximum matching problem, which we callStrict-Matching. Recall that a matching in an undirected graph G = (V, E) is a setof edges such that no distinct pair of edges {a, b} and {c, d} have endpoints that areequal: {a, b} ∩ {c, d} = ∅. Say that a strict matching is matching with the propertythat no pair of distinct edges have endpoints that are connected by an edge: {a, c} ̸∈ E,{a, d} ̸∈ E, {b, c} ̸∈ E, and {b, d} ̸∈ E. (Since a strict matching is also a matching, wealso require {a, b} ∩ {c, d} = ∅.) The problem Strict-Matching is then given a graphG and an integer k, does G contain a strict matching with at least k edges.Prove that Strict-Matching is NP-complete.For each pair of graphs G1 = <V1, E1> and G2 = <V2, E2> a) determine if they are isomorphic or not. b) Determine a function that can be isomorphic between them if they are isomorphic. Otherwise you should justify why they are not isomorphic. c) is there an Euler road or an Euler bike in anyone graph? Is Hamilton available? You should draw if the answer is yes and reason if your answer is no.The Barabasi and Albert model ´• A discrete time network evolution process,relating the graph G(t + 1) to G(t).• Start at t=0 with a single isolated node.• At each discrete time step, a new node arrives.• This new node makes m edges to already existing nodes.(Why m edges? i.e., what happens if m = 1?)• The likelihood of a new edge to connect to an existing node jis proportional to the degree of node j, denoted dj.• We are interested in the limit of large graph size, n → ∞.Visualizing a PA graph (m = 1) at n = 5000Probabilistic treatment (kinetic theory)• Start at t = 0 with one isolated node (or a small core set).– At time t the total number of nodes added n = t.– At time t the total number of edges added is mt.• Let dj(t) denote the degree of node j at time t.• Probability an edge added at t + 1 connects to node j:P r(t + 1 → j) = dj(t)/Pjdj(t).• Normalization constant easy (but time dependent):Pjdj(t) = 2mt(Each node 1 through t, contributes m edges.)(Each edge augments the degree of…
- You are given a graph G = (V, E) with positive edge weights, and a minimum spanning tree T = (V, E') with respect to these weights; you may assume G and T are given as adjacency lists. Now suppose the weight of a particular edge e in E is modified from w(e) to a new value w̃(e). You wish to quickly update the minimum spanning tree T to reflect this change, without recomputing the entire tree from scratch. There are four cases. In each case give a linear-time algorithm for updating the tree. Note, you are given the tree T and the edge e = (y, z) whose weight is changed; you are told its old weight w(e) and its new weight w~(e) (which you type in latex by widetilde{w}(e) surrounded by double dollar signs). In each case specify if the tree might change. And if it might change then give an algorithm to find the weight of the possibly new MST (just return the weight or the MST, whatever's easier). You can use the algorithms DFS, Explore, BFS, Dijkstra's, SCC, Topological Sort as…Given the adjacency matrix of an undirected simple graph G = (V, E) mapped in a naturalfashion onto a mesh of size n2, in Θ(n) time a directed breadth-first spanning forest T = (V, A) can becreated. As a byproduct, the undirected breadth-first spanning forest edge set EA can also be created,where EA consists of the edges of A and the edges of A directed in the opposite direction.Is it conceivable for the following network to be effective and productive? Do not generalize; rather, provide an instance.
- Question 1: In graph theory, a graph X is a "complement" of a graph F if which of the following is true? Select one: a. If X is isomorph to F, then X is a complement of F. b. If X has half of the vertices of F (or if F has half of the vertices of X) then X is a complement of F. c. If X has the same vertex set as F, and as its edges ONLY all possible edges NOT contained in F, then X is a complement of F. d. If X is NOT isomorph to F, then X is a complement of F. Question 2: Which statement is NOT true about Merge Sort Algorithm: Select one: a. Merge Sort time complexity for worst case scenarios is: O(n log n) b. Merge Sort is a quadratic sorting algorithm c. Merge Sort key disadvantage is space overhead as compared to Bubble Sort, Selection Sort and Insertion Sort. d. Merge Sort adopts recursive approachSuppose you are given a directed graph G = (V, E) with a positive integer capacity ?? on each edge e, a designated source s ∈ V, and a designated sink t ∈ V. You are also given an integer maximum s-t flow value ?? on each edge e. Now suppose we pick a specific edge e belongs E and increase its capacity by one unit. Show how to find a maximum flow in the resulting capacitated graph in O(m + n), where m is the number of edges in G and n is the number on nodes.Please solve and show all work. 21.1-2 Professor Sabatier conjectures the following converse of Theorem 21.1. Let G = (V, E) be a connected, undirected graph with a real-valued weight function w defined on E. Let A be a subset of E that is included in some minimum spanning tree for G, let (S, V – S) be any cut of G that respects A, and let (u, v) be a safe edge for A crossing (S, V – S). Then, (u, v) is a light edge for the cut. Show that the professor’s conjecture is incorrect by giving a counterexample.