What are the conditions for the steady-state distribution to exist? [4 marks] (c) Describe the M/M/1 queue and give a stochastic model for the number of customers present. Find the steady-state distribution for the number of ? ( (b) What does it mean for a PLC expression M to be in beta-normal form? [2 marks] (c) The long normal forms, L, and the neutral forms, N, are special kinds of PLC expression given by the following grammar: L ::= x :  (L) | (L) | N, N ::= x | N L | N . (i) Arguing by induction on the structure of L and N, or otherwise, show that all such expressions are in beta-normal form. [4 marks] (ii) Show that if N is a neutral form, then {} ` N :  is not provable in the PLC type system for any type  , where {} is the empty typing environment. (You may assume without proof that if  ` M :  is provable in the PLC type system, then the free variables of the expression M are contained in the domain of definition of the typing environment .) (iii) Hence prove that for any long normal form L, {} ` L :() is not provable in the PLC type system. 

Assume a denotational semantics is given for PCF: a mapping of PCF types to? domains [[ ]] together with a mapping of closed PCF terms of type , M : , to elements of the corresponding domain [[M]] [[ ]]. In the following you may refer to the notion of a PCF context without an explicit definition. (a) State clearly what properties the semantics must fulfil in order to be compositional. Give the fundamental property that a compositional semantics? enjoys with respect to arbitrary contexts. (b) Assume the standard typed evaluation operational semantics for PCF. Without referring to explicit evaluation rules or to the syntax of PCF, state clearly what properties the denotational semantics must fulfil in order to be: (i) sound; (ii) adequate. (c) Define: (i) the contextual preorder ctx for closed PCF terms;? (ii) contextual equivalence=ctx for closed PCF terms. (d) Prove that if a denotational semantics is compositional, sound and adequate then denotational equality implies contextual equivalence. (e) State the extensionality properties of the contextual preorder for both base types (bool and nat) and function types. (f ) Using extensionality, prove that the following terms are contextually equivalent: (i) (fn x : bool bool . 0)(fn x : bool . true) and 0; (ii) fn x : nat .

(fn y : nat nat . y(yx))(fn z : nat . succ(z)) and fn x : nat . succ(succ(x)).

(a) Summarise very briefly (one short paragraph each) the overall idea behind program analysis using (i) abstract interpretation;? (ii) set-constraint-based (CFA-like) analysis; (iii) rule-based analysis. [6 marks] (b) Consider the following language of integer expressions e and (integer) list? expressions E where n represents integer constants, x and X respectively range over integer and list variables, represents integer operations (e.g. +, etc.), and if and IF test their first argument for zero/non-zero as in C: e ::= x | n | e1 e2 | hd E | if(e0, e1, e2) E ::= X | [ ] | e :: E | tl E | IF(e, E1, E2) In escape analysis and optimisation, given a call to f such as g(x, y) = f(x :: x :: [ ], y :: [ ]) we want to know whether or not the result of f can include any of the cons-cells reachable from its arguments. A formal parameter of f that might be incorporated into its result is known as escaping. This is useful because if (say) formal parameter 1 to f cannot escape then cons-cells allocated for actual parameter 1 can be allocated (more cheaply) on the stack instead of in the heap. This problem may be formulated as an analysis that takes an expression, e or E, constituting the body of f. The parameters of f are the free variables, xi and Xi , of its body. Express this analysis using two of the techniques from part (a). In both cases state how to use the analysis result for e or E to test "parameter Xi definitely does not escape from E or e". [Hint: in some analyses it is easier to treat? the variables xi and Xi just as strings, and in others as variables ranging over {0, 1}.]

(a) When distributed systems are designed and engineered, certain fundamental properties have to be taken into account, including: 1. concurrent execution of components 2. independent failure modes 3. communication delay 4. no global time Give three examples of the implications of these properties (separately or in combination) on the engineering of large-scale, widely distributed systems. [9 marks] (b) (i) Define role-based access control (RBAC). (ii) Outline how RBAC could be used for a national healthcare system comprising many administration domains such as primary care practices, hospitals, specialist clinics, etc. Principals may, from time to time, work in domains other than their home domain, and must be authorised to do so. (iii) A national Electronic Health Record (EHR) service must be accessible from all domains. It is required by law that access control policy should be able to capture exclusion of principals and relationships between them. How could this requirement be met in an RBAC design?

(b) What is accomplished by the lateral signal flows within both plexiform layers of the mammalian retina, in terms of spatial and temporal image processing? and coding? [3 marks] (c) Give finite difference operators that could be applied to 1-dimensional discrete data (such as a row of pixels) in order to approximate the 1st and 2nd derivatives, d dx and d 2 dx2 . How would your finite difference operators actually be applied to the row of pixels? What is the benefit of using a 2nd finite difference (or derivative) instead of a 1st finite difference (or derivative) for edge detection? (d) Explain the formal mathematical similarity between the "eigenface" representation for face recognition, and an ordinary Fourier transform, in the following respects: (i) Why are they both called linear transforms, and what is the "inner product" operation in each case (ii) What is a projection coefficient and an expansion coefficient in each case? [1 mark] (iii) What is the orthogonal basis in each case, and what is meant by? orthogonality?

.Write program in C++ to print a welcome text in a separate line.

Write program in C++ to print the sum of two numbers Write program in C++ to display the operation of pre and post increment and decrement.

(a) Distinguish between the terms abstract class and interface. [3 marks] (b) Explain in detail what happens when class GPS below is instantiated noting, in particular, any assignments that are made. [17 marks] class GPS { public int[][] a = new int[4][4]; private int[] i = new int[1]; private int[] j = new int[1]; public GPS() { this.j[0] = this.gps(this.j, 4, new Pi(), new Fg()); } private int gps(int[] i, final int N, Pass z, Feval v) { i[0] = 0; while (i[0]

(a) Outline a method that could be used for modelling water and other fluids.

(b) (i) Show how to find the first intersection between a ray and a finite-length, open-ended cone, of unit slope, centred at the origin, aligned along the

PLC are calcium (Ca2+)- subordinate phosphodiesterases that hydrolyze phosphatidyl-inositol bisphosphate (PIP2) into 1,2-diacylglycerol (DAG) in addition to inositol trisphosphate (IP3) [1,2]. Once produced, IP3 rapidly diffuses in the cytoplasm and actuates IP3 receptors (IP3R) situated on the endoplasmic reticulum (ER) layer, bringing out a fast arrival of Ca2+ into the cytoplasm. PLC can likewise manage a few cell capacities through DAG creation, by means of initiation of protein kinase C [3] and through tweak of PIP2 levels [4]. Until now, a sum of 13 mammalian PLC isoforms have been recognized and ordered into 6 families: (1-4), (1-2), (1,3,4), , and (1-2) [5]. The PLC families have particular components of enactment. For instance, PLC isoforms are enacted by G and G/ subunits of heterotrimeric G proteins though PLC isoforms are initiated by tyrosine kinase receptors and PLC can be actuated by both [5]. PLC isoforms can likewise be recognized by their sub-atomic loads, Ca2+-responsiveness and subcellular restriction: together, these propose that each isoform could play a particular part in the balance of physiological reactions and this is additionally upheld by a few investigations utilizing knockout creature models [5-8]. For instance, PLC-invalid mice show unusual improvement of the aortic and aspiratory valves [9]. The shortfall of PLC2 articulation prompts diminished intracellular calcium delivery and superoxide creation in neutrophils [10]. These examinations reinforced the idea that each PLC isoform has a particular and corresponding job in physiology.

Downstream of PLC actuation, IP3R-subordinate Ca2+ discharge is a central member in endothelial capacity. For sure, these endothelial intracellular Ca2+ elements assume a significant part in the age of vasoregulatory signals [11-14]. Albeit exceptionally powerful, endothelial Ca2+ is finely tuned, true to form for a cycle with a critical utilitarian effect. A rising assortment of proof proposes that spatially limited Ca2+ signals are fundamental controllers of endothelial capacity. Of the endothelial neighborhood Ca2+ signals portrayed, Ca2+ pulsars are unconstrained IP3R-subordinate Ca2+ discharge occasions that happen inside the myoendothelial projection (MEP) [11]. Despite the fact that our ongoing information in regards to the guideline of spatially-restricted Ca2+ motioning in the endothelium is restricted, the inclusion of IP3/IP3Rs show a job for PLCs in the control of Ca2+ signals like pulsars. A superior comprehension of the articulation and subcellular restriction of PLCs in local ECs is important.

Cell-explicit articulation of individual PLCs is accepted to be associated with tweaking specific capacities. Jobs for PLC 3 [15], 1 [16] and [17] have been accounted for in ECs and the declaration of PLC isoforms was as of late analyzed in human umbilical vein endothelial cells (HUVECs) [18]. Notwithstanding, setting ECs in culture brings about phenotypic changes [19], including the deficiency of MEP and Ca2+ pulsars, proposing that the administrative pathways may be adjusted too. Consequently, the articulation profile of PLCs and the related flagging pathways might contrast among HUVECs and local ECs. Endothelium is a particular tissue whose capacities differ contingent upon the vascular bed, recommending that PLC articulation could likewise fluctuate from one vascular bed to the next [20-22]. Subsequently, it is vital to decide the articulation and subcellular circulation of PLC isoforms in local ECs from various vascular beds. In this review, we decided the declaration of PLC isoforms in murine ECs newly disconnected from mesenteric (MAECs), pneumonic (PAECs) and center cerebral corridors (MCAECs).