Consider the directed network G = (V,E) with N = 5 nodes and L = 8 links, in which node 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and 4, node 4 points to node 2, and node 5 points to nodes 3 and 4. 3 4 Lin Lin (c) Determine the in-degree sequence {kin, k, k, kin, k} and the out-degree sequence {kout,kout, kout kout, kout of the network. Write down the average node in-degree, the average node out-degree, the node in-degree distribution Pin (k) and the node out-degree distribution Pout (k).

. You are traveling on a grid from (2, 2) to (18, 18). The only steps you can make are either to increase the first number by 1, or to increase the second number by 1, which you can think of as unit steps that either go up or to the right. (a) Identify a bijection between the paths from (2, 2) to (18, 18) and bit sequences with a certain number of ones. Hint: there are two types of steps, so let one of these be a zero, and the other a one. (b) How many paths are there from (2, 2) to (18, 18)? (c) How many of these paths do not pass through (10, 10)? (d) How many of these paths do not pass through (7,7) or (10, 10)? (Note: this can also be phrased as paths that avoid both (7,7) and (10, 10), using De Morgan's Law to negate the or notice this is a time where "and" does not mean multiply in counting).

In R, with the code below: We create a new object a as a numeric sequence (1, 2, ..., 10), and a second new object b as a vector of characters (`a', `b', `c', `d', `e'), and then we  save them to a file mydata   > a <- 1-10 > b <- letters[1-5] > save(a, b, file="./data/mydata.")   > a <- 1:10 > b <- letters[1:5] > save(a, b, file="./data/mydata")   > a <- 1...10 > b <- letters[1...5] > save(a, b, file="./data/mydata.Rdata")   > a <- 1:10 > b <- letters[1:5] > save(a, b, file="./data/mydata.Rdata")

Match the word/phrase in the first column to its definition/description in the second column. a. a quadratic that doesn't factor C.VReduced Row-Echelon Form b. the sum of terms of a sequence Irreducible Quadratci C. Gauss-Jordan elimination Matrix Multiplication d. described as row by column multiplication Arithmetric Sequence e. b. Series results in a common difference between consecutive terms

Use the critical path algorithm to create a priority list for the digraph below, then schedule the project with two processors. T1 (10) T4 (5) T7 (3) Т2 (5) T5 (11) T8 (8) End ТЗ (6) Т6 (6) T9 (3) Task 7 is done b Select an answer tarting at time Processor 1 Processor 2 Task 8 is done by SeIEtt al answer gstarting at time The finishing time for the schedule is

A.    Consider the line from (2,3) to (9,8). Use the Bresenham’s algorithm to  rasterize this line. Given the clipping window points x_min = 4, y_min = 4, x_max = 10, y_max = 8     Find the lines whether accepted or rejected line 1 : x1 = 5, y1 = 5, x2 = 7, y2 = 7, Line 2 : x1 = 7, y1 = 9, x2 = 11, y2 = 4,  Line 3 : x1 = 1, y1 = 5, x2 = 4, y2 = 1

Which of the following is not true about Kruskal's algorithm? Arrange the edges based on their weights Avoid loops Identify the edges and their weight The created edges is equal to the number of vertices