describe what each of the three coordinates represents [2 marks… describe what each of the three coordinates represents [2 marks each](b)

describe what each of the three coordinates represents [2 marks… describe what each of the three coordinates represents [2 marks each](b) describe why the coordinate system is a useful representation of colour?[2 marks each]Draw either the first eight one-dimensional Haar basis functions or the first eightone-dimensional Walsh-Hadamard basis functions. [4 marks]Calculate the coefficients of your chosen eight basis functions for the followingone-dimensional image data:12 16 20 24 24 16 8 8 [4 marks]?Explain why, in general, the Haar or Walsh-Hadamard encoded version of an imageis preferable to the original image for storage or transmission. [4 marks]?2CST.97.6.3SECTION B5 Programming in C and C++declaration of a C++ class that might be used to implement a binary treewith each node able to hold an integer. Your implementation (i.e. the class itselfand those bodies which conveniently fit within it) should make it impossible forcasual programmers to access the pointer fields that link parts of the tree togetherexcept through cleanly specified access functions. Show how you would overloadthe “+” operator in C++ to provide a neat notation for adding a new item intosuch a tree. [20 marks]6 Compiler ConstructionInvestigate whether the following grammar for regular expressions is SLR(1) byattempting to construct its Action and Goto matrices.S -> R eofR -> F | R + FF -> P | F PP -> x | ( R ) | P *Find all the conflicts, if any, in the two matrices. [20 marks]7 Prolog for Artificial IntelligenceA binary tree is constructed from binary compound terms n(a, b) called nodes, wherecomponents a and b are either nodes or integers. Suppose integer components arerestricted to the values 0 and 1.Prolog program to return a list of all the 0’s and a list of all the 1’s in agiven tree. For example, the goal enum(n(n(0,1),1),X,Y) should instantiate X to[0] and Y to [1,1]. The program is required to use difference lists. [20 marks]3 [TURN OVERCST.97.6.4 8 DatabasesWhat particular strengths of the relational model have led to the pre-eminentposition that it holds today as a vehicle for database management? [8 marks]Identify any weaknesses in the model, illustrating your answer by examples.[6 marks]How might these weaknesses be remedied while retaining the advantages of themodel? [6 marks][information I(X; Y ) for this error-prone replication process? [4 marks] (b) Financial markets generate daily asset valuations like the time-series f(t) in the left panel, reflecting the dynamics of greed and fear. But underlying such fluctuating indices there may exist meaningful trends, such as a business cycle (right panel).  auto-correlation integral that can extract the coherent quasi-periodic signal on the right from noisy valuations f(t), and explain how computing the Fourier transform F(?) of f(t) makes it efficient. [5 marks] 0 0 Figure a sine wave in noise and b autocorrelation (c) Brain tissue contains about 105 neurones per mm3 , and each neurone has a? single output axon whose length r (in dimensionless units) before terminating at synapses to other neurones has probability density distribution p(r) = e ?r . 0 1 2 3 r 0 1 p(r ) = e ?r Note: Z ? 0 e ?r dr = 1 (i) Define differential entropy h for continuous random variables in terms of general probability density distribution p(x), and then calculate the value of h in bits for this axonal length distribution p(r) = e ?r . [5 marks] (ii) If the axon’s branching terminals make altogether about 1,000 synapses (connections) with different neurones within the axonal tree’s 1 mm3 volume, uniformly distributed, roughly how many bits of entropy describe the uncertainty of whether a neurone gets such a? connection? [2 marks] 10 CST2.2021.9.11 10 Machine Learning and Bayesian Inference Consider the following Bayesian Network: A B C D E All random variables (RVs) are Boolean. For an RV R we denote R = T by r and R = F by r. We have Pr(a) = 0.1, Pr(b) = 0.2, Pr(d|b) = 0.7 and Pr(d|b) = 0.4. For the remaining RVs we have A B Pr(c|A, B) F F 0.2 F T 0.2 T F 0.5 T T 0.6 C B D Pr(e|C, B, D) F F F 0.3 F F T 0.5 F T F 0.6 F T T 0.3 T F F 0.1 T F T 0.2 T T F 0.1 T T T 0.9 In this question you must? use the Variable Elimination algorithm to compute Pr(A|e). You should begin with the factorisation Pr(A|e) = Pr(A) X B Pr(B) X C Pr(C|A, B) X D Pr(D|B) Pr(e|B, C, D). You should express factors as tables of integers, leaving any necessary normalisation until the final step in Part (d). (a) Define conditional independence of two RVs X and Y with respect to a third RV Z. [2 marks] (b) Deduce the factor FE,D(B, C) corresponding to the summation over D. [8 marks] (c) Deduce the factor FE,D,C (A, B) corresponding to the summation over C. [6 marks] (d) Complete the computation to find the distribution Pr(A|e). [4 marks] 11 CST2.2021.9.12 11 Mobile and Sensor Systems (a) Contrast the measurement of biosignals from conventional medical devices with those from smartphone and wearable device sensors. [5 marks] (b) A researcher wishes to screen users for the hand tremor symptom via a smartphone app. They recruit a cohort of people with diagnosed tremor and a control cohort about which nothing is known. The researcher has a smartphone that collects data from its sensors. They give it to each participant and ask them to hold it as still as they can while sitting. The researcher then uses the data captured to develop a tremor classifier that has sensitivity 0.97 and specificity 0.99. (i) Why is getting a high specificity a particular priority for a smartphonebased screening app? [4 marks] (ii) Explain why the prevalence of the disease must also be taken into account in deciding whether to deploy this app, illustrating your answer by considering tremor prevalences of 0.1% and 5%. [3 marks] (iii) The smartphone app is deployed. It asks users to test their tremor monthly at home, when sitting and trying to hold their phone still. Why might the screening be less effective than expected from the collected data? [3 marks] (iv) The researcher changes the app to do background tremor screening. The app now constantly monitors for the user holding the phone appropriately. When it observes this it captures sensor data and applies the tremor classifier. Discuss the advantages and disadvantages of this approach compared to the previous approach. [5 marks] 12 CST2.2021.9.13 12 Optimising Compilers The following excerpt from a program in C-style code is optimised with a compiler using code-motion transformations. The function read() returns a signed integer from the user. l0: a = read(); l1: b = read(); l2: p = &a; l3: q = &b; l4: r = &p; l5: if (read() > 0) { l6: a = b + 5; l7: } else { l8: i = 0; l9: while (i < 10) { l10: c = b + 5; l11: **r += *q; l12: i += 1; l13: } l14: a += c; l15: } l16: print(a); (a) Describe loop-invariant code motion (LICM) and which expresion(s) in the loop above it should move. [2 marks] (b) Describe a simple data-flow analysis and a way of using it to identify loopinvariant expressions. Use this to analyse the code above. [5 marks] (c) Explain whether all expressions described in Part (a) are found through the analysis in Part (b). [2 marks] (d) Describe an analysis that can aid in making LICM more precise in this example. [3 marks] (e) Apply the analysis from Part (d) to the code above and redo the analysis from Part (b) to show which expressions described in Part (a) are now found. [4 marks] (f ) Describe another code motion transformation that could be applied to the code after LICM and show the final code after its application. [4 marks] 13 CST2.2021.9.14 13 Principles of Communications (a) Multicast routing provides IP packet delivery from a source to a set of receivers. One clear use case for this is for large scale content distribution (e.g. software updates). In such a case, we would expect the end-to-end protocol to provide flow and congestion control. How might such a reliable multicast transport protocol be designed? [10 marks] (b) Mobile systems move. In cellular networks, this is can be handled by the radio access network, and measuring signal strength to determine to which cell a handset is best assigned. In the Internet, the IP layer typically hides this information. How might we combine information across layers to make mobile IP routing more efficient? In your discussion, pay attention to problems of software layering, and also of managing the dynamics (e.g. route flapping) in such systems. [10 marks] 14 CST2.2021.9.15 14 Quantum Computing (a) Find the eigenvectors, eigenvalues and spectral decomposition of the observable A = 0 1 1 0 and give the outcome of measuring the expectation of the observable on the states: (i) |0i (ii) ? 1 2 (|0i ? |1i) (iii) 1 2 |0i + ? 3 2 |1i [8 marks] (b) A quantum mechanical system has Hamiltonian H = H1 + 2H2 It is desired to use a quantum computer to approximately simulate the operator e ?iHt for some t. It is possible to build quantum circuits U1 and U2 to perform the operations U1 = e ?iH1t U2 = e ?iH2t Give a circuit, U, consisting of one of more instances of U1 and U2 that approximates e ?iHt such that e ?iHt ? U = O(t 3 ). Show your calculations to verify that the circuit does indeed achieve this. [8 marks] (c) Quantum Phase Estimation can be used to estimate the ground state energy of quantum mechanical systems. The Inverse Quantum Fourier Transform is a key component of Quantum Phase Estimation. Give the circuit for the 2-qubit Inverse Quantum Fourier Transform using only gates from the set {H, CT, Image transcription textQUESTION 19 Which of the followingstatements is correct? O A-Floating-point arithmetic ... Show more... Show moreImage transcription textQuestion 41 In Scheme. a let special form can be used todefine a recursive function. True False 1 points Question42 In Scheme. arithmetic operators are writte... Show more... 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