Question 4 - Your workbook should look like the Final Figures on the following pages. Save your changes, close the workbook, and then exit Excel. Submit your completed project via Assignment link on Brightspace.

(a) ZX is an information source, which produces symbols from the set {a, b, c, d, S} (i) If we assume X produces symbols with equal probability, what is the entropy of ZX? [11 mark] (ii) In fact, X produces symbols with non-equal probabilities. What do you know about the entropy of X compared to your previous answer? [1 mark] (iii) X produces symbols with probability distribution: p(a) = 0.4, p(b) = 0.2, p(c) = 0.2, p(d) = 0.1, p(S) = 0.1 Give an expression for the entropy of information source X. [2 marks] (b) The symbol sequence produced by X represents consecutive words of a language, where S indicates whitespace. (i) Describe and provide an equation for the entropy of the language produced by the symbol sequence. [2 marks] (ii) A student observes that when a word in the language contains c it is always followed by b. Explain how this redundancy helps communication over a channel that tends to swap b with d. [2 marks] (c) Define a noisy channel and describe how it could be interpreted with respect to human language communication. [6 marks] (d) Computational Linguists have hypothesised that natural languages have evolved to be both efficient and robust to noise. Do you agree? Justify your answer by referring to information theory and giving appropriate examples. [6 marks] 5 (TURN OVER) CST1+CST2.2019.7.6 5 Formal Models of Language This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English which aspects of language do the two tree types model? [2 marks] Explain how five independent dimensions of visual processing are multiplexed together into the three available spatial dimensions of neural tissue, by the structure of the cubic millimetre hypercolumns in the brain's visual cortex. [5 marks] (c) The retina is often regarded as an image capture device; but it has about 100 million input sensors (photoreceptors) yet only 1 million output fibres (optic nerve axons). What are some implications of this 100-to-1 ratio of input channels to output channels? [4 marks] Explain how the operation insert (a, c) into R can be correctly implemented in the {S 0 , R, T} database. [4 marks] (d) For an OLTP database, discuss the performance implications of this so-called optimisation. [4 marks] (e) This example illustrates a fundamental trade-off in the design and implementation of database applications. Discuss. [4 marks] 6 CST.2014.4.7 6 Databases (a) We are given a relational schema R(A, B, C, D, E) and told that the following table represents a legal instance of R. A B C D E tuple number 1 2 5 4 3 (#1) 1 4 5 4 4 (#2) 2 4 5 4 5 (#3) 2 5 5 4 3 (#4) Which of the following sets of functional dependencies may hold in R? If a set of dependencies cannot hold, then explain why. You can refer to tuple numbers in your explanation. (i) F1 is the set {A D}. [2 marks] FX and TX.In most of the Fast Ethernet applications, the individual devices are connected by twisted-pair copper wires i.e. 100BaseTX(maximum segment length is only 100 smeters) and the optical fibers are used for transmission over longer distances(as maximum segment length is 2000 meters of 100baseFX). So, 100baseTX to 100Base FX convertor ims requiared for sending the signal from the sender end over the optical fiber. Similarly, at the receiver end, 100baseFX to 100Base TX is required52.

A combinational logic circuit takes a 4-bit unsigned binary integer number at its inputs labelled D3 , D2 , D1 and D0 , where D3 is the most significant bit.