Suppose you are given two coordinates in n-dimensional space, p = (p1, p2, pn), and q = (q1, q2, qn). the golden distance d between p, and q is defined as d(p, q) = pn i=1(pi −qi) 4 . let pσ be formed by permuting the elements of p, and let qπ be formed by permuting the elements of q. for example, if p = (1, 2, 3) and q = (1, 3, 5), then one possible way to form the permutations could be pσ = (2, 1, 3) and qπ = (5, 3, 1). the golden distance, d(pσ , qπ ), of these two points would be (2 − 5)4 + (1 − 3)4 + (3 − 1)4 = 113. (a) design a greedy algorithm that chooses the permutations for pσ and qπ that maximizes their golden distance, d(pσ , qπ ). analyze the time complexity of your algorithm. (b) prove the correctness of your algorithm. (hint: you may use the following fact without proof (d − a) 4 + (c − b) 4 ≥ (b − a) 4 + (d − c) 4 for any numbers a, b, c, d such that a ≤ c

Consider a slotted aloha system, where the time slot equals the fixed duration of each packet. assume that there are 4 stations a,b,c,d sharing the medium. (a) stations a,b,c,d receive one packet each from higher layers at times 1.3, 1.5, 2.6,5.7 respectively. show which transmissions take place when, according to the slottedaloha protocol; describe all transmissions until all four packets have been successful.when needed, each station has access to the following sequence of random number, provided by a random number generator and drawn uniformly between 0 and 1: (1) station a draws numbers: 0.31, 0.27, 0.78, 0.9, 0.9, 0.11, 0. (2) station b draws numbers: 0.45, 0.28, 0.11, 0.83, 0.37, 0.22, 0. (3)station c draws numbers: 0.1, 0.2, 0.3, 0.4, 0. (4) station d draws numbers: 0.36, 0.77, 0.9, 0.1, 0.1, 0.1, 0.1, 0. (b) in slotted aloha, a station transmits in each time slot with a given probability. what probabilities would you assign to each of the four stations so as to: (i) maximize the efficiency of the protocol? (ii) maximize fairness among the four stations? (c) will the efficiency increase or decrease if we modify slotted aloha as follows: (i) get rid of slots and allow stations to transmit immediately? (ii) implement carrier sensing? (iii) implement collision detection? (iv) implement collision avoidance?

You are new to microsoft certification and want to start out by getting a certification geared around windows 8. what microsoft certification should you pursue?

The option enables you to modify a slide element in most presentation applications.