The image presents a network graph and specific tasks related to the spread of behaviors within the network.### Problem Statement:1. **Network Overview (Figure 1):** - Each node in the network initially exhibits behavior B. - Nodes switch to behavior A if at least half (`q = 1/2`) of their neighbors have adopted behavior A.2. **Tasks:** a. **Initial Adoption:** - Nodes `e` and `f` are initial adopters of behavior A, forming a set S. - Determine which additional nodes switch to behavior A under the threshold rule. b. **Blocking Cluster:** - Identify a cluster outside S with density greater than `1 - q = 1/2` that prevents the spread of behavior A to all nodes.### Graph Description:The graph consists of 11 nodes connected by edges as follows:- Node `e` connects to nodes `c`, `f`, and `i`.- Node `f` connects to nodes `c`, `g`, and `i`.- Node `g` connects to nodes `f`, `d`, and `j`.- Node `d` connects to nodes `g` and `h`.- Node `h` connects to node `j`.- Node `j` connects to nodes `g`, `h`, and `k`.- Node `i` connects to nodes `e`, `f`, and `k`.- Node `k` connects to nodes `i` and `j`.### Figure Caption:**Figure 1:** Starting from nodes `e` and `f`, the new behavior A fails to spread to the entire graph.In summary, the nodes `e` and `f` are initial adopters, and the goal is to assess which other nodes switch to behavior A and identify a dense cluster to block its spread.

Network diffusion is a mechanism of propagation of events in a complex network. It indicates the…

Answered: Consider the network depicted in Figure…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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g) Show the residual graph for the network flow given in answer to part (c). What is the bottleneck edge of the path (?, ?2, ?3, ?1, ?4, ?) in the residual graph you have given in answer to part (g) ? Show the network with the flow that results from augmenting the flow based on the path (?, ?2, ?3, ?1, ?4, ?) of the residual graph you have given in answer to part (g).
Determine the minimum size of a maximal matching in the cycle Cn.
What type of algorithm can be used to solve the basic network model for the critical path method? Label Setting Algorithm Dantzig's Algorithm Dijkstra's Algorithm Label Correcting Algorithm
1. Consider the generalization of stable matching problem where a certain man-woman pairs are forbidden. The set of forbidden pairs is denoted as F. Each man m ranks all the woman w for which (m, w) ¢ F and each woman w ranks all the man m for which (m, w) ¢ F. Consider the following algorithm for finding a stable matching that consists of only unforbidden pairs: Initially all mE M and w e W are free; S = Ø While there is a man m who is free and hasn't proposed to every woman w for which (m, w) ¢ F Choose such a man m Let w be the highest-ranked woman in m's preference list to which m has not yet proposed If w is free: Add (m, w) to solution S Else (w is current matched with m'): If w prefers m' to m m remains free Else Replace (m', w) by (m, w) in S Return solution S Answer true or false for the following questions: (a) Any woman w remains engaged from the point at which she receives her first proposal, and the se- quence of partners to which she is engaged get better and better. (b)…
Suppose you are fitting a neural network with one hidden layer to a training set. You find that the cross validation error Jcv (0) is much larger than the training error Jtrain (0). Is increasing the number of hidden units likely to help? CV Yes, because it is currently suffering from high bias. Ob. Yes, because this increases the number of parameters and lets the network represent more complex functions. Oc. No, because it is currently suffering from high variance, so adding hidden units is unlikely to help. Od. No, because it is currently suffering from high bias, so adding hidden units is unlikely to help.
Consider a prize-collecting TSP we discussed as the subproblem for VRP: there is no constraint requiring every node to be on the tour, but there is a reward πi for visiting node i. The objective is to minimize the total tour length minus the total rewards for nodes visited. (a) Formulate the prize-collecting TSP as a linear integer programming problem. (b) Propose a heuristic for the prize-collecting TSP. Explain your heuristic in word. This question is open-ended.
Computer Science Suppose that the family is a (d1, d2, p1, p2)-sensitive LSH family. What does this mean specifically with respect to the distance parameters d1 < d2 and the probability parameters p1 > p2? What is the false positive rate and the false positive rate of the family?
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Exercise 3 Consider calculation of PageRank for a directed graph. Consider two jumping probabilities a and B such that a > B. For every node u, let Pa(u) be the PageRank of u calculated using a and let Pg (u) be the PageRank of u calculated using B. For each of the following statements, indicate whether the statement is true or false and provide a brief explanation for your answer. 1. The inequality Pa (u) > Pg (u) must hold for all nodes u. 2. The inequality Pa(u) > Pg (u) must hold for at least one node u.
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Suppose we have two industrial control systems S1 and S2 that are workingconcurrently. We need to forbid some sequence of actions from taking placebetween the two systems. One such action is allowing S1 and S2 to be onat the same time. Consider the alphabet:Σ = {On(S1), On(S2), Off(S1), Off(S2)}A sequence of actions is a word over Σ∗.i. Convert the property on sequences given above into a language, andthen define an NFA that accepts it.ii. A second property is that S2 must power off after S1, but S2 mustpower on before S1. Define a language which captures this property(and this property only), and then define a NFA that accepts it.

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