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Assumption Maximization (EM) (25 focuses) In this question you will carry out the EM calculation for Gaussian Mixture Models. A decent perused on gaussian combination EM can be found at this connection. An example dataset for this issue can be downloaded in material records. For this issue: n is the quantity of preparing focuses f is the quantity of highlights k is the quantity of gaussians X is a n f lattice of preparing information w is a n k grid of participation loads. w(i, j) is the likelihood that xi was created by gaussian j is a k 1 vector of combination loads (gaussian earlier probabilities). i is the earlier likelihood that any point has a place with group I is a k f lattice containing the method for each gaussian is a f f k tensor of covariance lattices. (:, :, I) is the covariance of gaussian I (a) Expectation: Complete the capacity [w] = Expectation(X, k, , , ). This capacity takes in a set of boundaries of a gaussian blend model, and results the participation loads of every data of interest (b) Maximization of Means: Complete the capacity [] = MaximizeMean(X, k,w). This capacity takes in the preparation information alongside the participation loads, and works out the new greatest probability mean for each gaussian. (c) Maximization of Covariances: Complete the capacity [] = MaximizeCovariance(X, k,w, ). This capacity takes in the preparation information alongside enrollment loads and means for each gaussian, what's more, works out the new most extreme probability covariance for each gaussian (d) Maximization of Mixture Weights : Complete the capacity [] = MaximizeMixtures(k,w). This capacity takes in the enrollment loads, and works out the new most extreme probability combination weight for each gaussian. (e) EM: Put everything together and carry out the capacity [, , ] = EM(X, k, 0, 0,0, nIter). This capacity runs the EM calculation for nIter steps and returns the boundaries of the basic GMM. Note: Since this code will call your different capacities, ensure that they are right first. A decent method for testing your EM work disconnected is to actually look at that the log probability, lis expanding for every cycle of EM.

Describe the kinds of properties that can be expressed using Sugar Extended Regular Expressions (SEREs), Foundation Language (FL) formulae and Optional Branching Extension (OBE) formulae of the Sugar 2.0 property language. [4 marks] (e) Consider the property: "whenever a, b and c occur on successive cycles, then on the cycle that c occurs, d must occur also, followed on the next cycle by e" (where a, b, c, d and e are boolean expressions). Use this property to illustrate how SEREs can sometimes help specify properties more compactly than pure LTL.

Describe the initial plan used as a starting point by the partial-order planning algorithm. [5 marks] (d) Outline the way in which the partial-order planning algorithm constructs a plan beginning with the initial plan. Include in your answer a description of a threat along with an explanation of how the algorithm can attempt to remove threats by promotion or demotion. [5 marks] 9 Database Theory (a) Describe the key features of the ODMG object model. [6 marks] (b) Describe the key features of the semi-structured data model. [6 marks] (c) Consider the following DTD. (i) Detail how XML data satisfying such a DTD could be stored in a traditional (non-complex value) relational DBMS. Comment on the efficiency of your strategy. [5 marks] (ii) Detail how XML data satisfying such a DTD could be stored in an ODMG-compliant DBMS.

8 CST.2003.8.9 10 Information Theory and Coding (a) An alphabet has six symbols with the following probabilities of occurrence: a b c d e f 0.31 0.18 0.21 0.08 0.17 0.05 (i) Construct an optimal prefix code (an Huffman code) for this alphabet. (ii) What is the average number of bits per symbol in your code? Is this greater than, less than, or equal to the entropy of the alphabet? [3 marks] (b) Jane's Furniture Store sells 2-, 3- and 4-seater sofas in two styles: classic and modern. At the end of May, Jane tallies the number of each type that has been sold in each style during May. Type (no. of seats) Style 2 3 4 Classic 8 24 4 Modern 8 8 12 (i) Let X be the type of sofa (2-, 3-, or 4-seats) and Y be the style (classic or modern). Calculate the values of H(X), H(Y ), H(X, Y ), H(X|Y ), H(Y |X), and I(X; Y ). [9 marks] (ii) In part (b)(i), you should have found that I(X; Y ) 6= 0. For the month of June, Jane wants to have I(X; Y ) = 0 while still selling the same number of sofas of each type as in May. Change the numbers in the table so that the same number of sofas of each type are sold (i.e. the column totals remain unchanged) but so that I(X; Y ) = 0. What is H(X, Y ) in this revised table?

The data sheet for a new workstation CPU tells you simply that it has a 8KB L1 data cache and 512KB L2 cache. As an inquisitive computer scientist, you wish to learn more about the system's memory hierarchy. (a) Devise a method for determining the cache line size. You may assume that the L1 and L2 caches use the same line size, and that the operating system provides a microsecond accurate time function. Provide high-level language pseudo code of any test programs you would use, and describe how you would interpret their output. [6 marks] (b) Describe how you produce an accurate estimate for the load latency incurred by accesses to the two caches and main memory. [6 marks] (c) Outline a method you could use to determine the associativity of the caches. [8 marks] 2 CST.2003.8.3 2 VLSI Design The designer of a CMOS standard cell library has proposed the following circuit for an XOR gate: Vdd A B Q Gnd Explain how the circuit operates. [2 marks] Although the circuit appears digitally correct, it operates slowly. Moreover, when two of the XOR gates are cascaded to calculate the XOR of three signals, the results are unreliable. Suggest explanations for these two problems. [4 marks] Propose a modification to the circuit which retains the general design but introduces two pairs of additional inverters to address the problems. [4 marks] Another designer cascades two of the revised gates as part of a full adder, and observes that the resulting circuit is large and slow. Extend the design to provide the XOR of three inputs directly. Compare its size and speed with the cascaded version. [5 marks] Yet another designer is working on an asynchronous design and needs a two-input XOR gate for dual-rail logic. Sketch a design which ensures that all the input signals become valid before any output does so, and that all the inputs become clear before any outputs do so. [5 marks] 3 [TURN OVER CST.2003.8.4 3 Digital Communication II Two hosts are connected to two separate 100 Mbps local area networks. One is a user's machine with a web browser, the other is a web server. The networks are connected via a pair of routers and a long haul, point-to-point link with the following characteristics: 640 kbps, 50 ms delay, and a Maximum Packet Size of 1 k bytes. The routers have 8 kbytes of packet buffer memory. (a) Assuming standard TCP behaviour (slow start, congestion control, and fast retransmit/recovery), approximately how long does it take to download a file of 8 Kbytes of data? You may assume that packet headers and store-and-forward times are insignificant. You may find it easier to illustrate your answer with a time-sequence diagram of the packet exchanges. [5 marks] (b) How long, approximately, does it take to download a file of 8 Mbytes from one computer to the other using TCP? [5 marks] (c) Illustrate your answer to the previous section with a diagram showing TCP's behaviour over time, indicating the two important stages and transitions between them. [5 marks] (d) What would happen qualitatively if the routers had only 4 Kbytes of packet buffer memory?

(a) Explain the terms Work Conservation and max-min fairness, in the context of packet switching. [8 marks] (b) Outline the operation of two work-conserving queueing schemes that provide max-min fairness, and two (simpler) ones that do not. [8 marks] (c) Give at least two main implementation costs associated with implementations of fairness in packet switched routers. [4 marks] 3 Security (a) Describe the Bell-LaPadula security policy. [6 marks] (b) Describe the Chinese Wall security policy. [6 marks] (c) To what extent is the Chinese Wall policy an extension of Bell-LaPadula? [6 marks] (d) Are either of these policies relevant to digital rights management? [2 marks] 2 CST.2003.7.3 4 Advanced Graphics (a) We want to find the first intersection point between an arbitrary ray and a sphere of arbitrary radius at an arbitrary position in space. (i) List and define all of the parameters required to specify the geometry of the ray and the sphere. [2 marks] (ii) Give an algorithm which returns the desired intersection point (if it exists) and the appropriate normal vector at the intersection point. [5 marks] (b) Describe a method which converts an arbitrary sphere to a triangle mesh at a desired resolution. The desired resolution is specified as a desired number of triangles, D. Your method should produce a number of triangles, N, which is within an order of magnitude of D: D/10 < N < 10D. [4 marks]

Define access control lists and capabilities, and discuss their relative strengths and weaknesses. [5 marks] Describe how the access control list mechanisms work in Unix. [5 marks] You have been asked to build a funds transfer system in which a payment is authorised only once it has been approved by both a manager and an accountant at a bank branch. How would you implement this system using Unix security mechanisms as the foundation? [10 marks] 6 Data Structures and Algorithms Describe Larsen's method of dynamic hashing that enables a record to be located on a disk given its key using just one disk transfer and only a modest amount of information held in main memory. [10 marks] In Larsen's method each key has associated pseudo-random sequences of probe and signature values. Discuss what properties these sequences should have. Outline an algorithm that could be used to compute the n th probe-signature pair for a given key. You may assume that the key is a character string. [6 marks] Briefly discuss why Larsen's method is not used in most current filing systems.

. Write program to calculate simple interest rate. User should supply principal amount, interest rate and time 7. Write program that checks whether an integer number is prime or not.