The total trip duration is the sum of travel times along its edges. We shall estimate the
Question:
The total trip duration is the sum of travel times along its edges. We shall estimate the dj using linear least squares estimation, i.e. solve arg min ky Xk 3 for a suitable matrix X and vectors and y. How might you expand the meaning of recursive identification to sets of processable capabilities? (read integer input from user) | e + e (addition) | e e (subtraction) | e e (multiplication) | (e, e) (pair) | fst e (first projection) | snd e (second projection) (a) (c.ii) Suppose that the following rules are proposed as possible optimizations to be implemented in your compiler. expression simplifies to expression (fst d, snd e) e fst (d1, d2) e1 snd (e1, e2) e2 Describe how you could implement these rules so that the simplifications are made only when the program's semantics is correctly preserved. [5 marks] inside the pleasant case [3 marks] Code a function flat such that flat(e) = flatten(e) for all e, justifying this claim. Show that flat's worst-case complexity is linear. [5 marks] 3 [TURN OVER CST.98.1.Four SECTION C 7 Discrete Mathematics State and prove the Chinese Remainder Theorem concerning the simultaneous answer of a pair of congruences to co-prime moduli and the individuality of that answer. [10 marks] An early form of public key encryption worked as follows. A man or woman, R, wishing to acquire mystery messages, selected two huge primes, p and q additionally co-high to p 1 and q 1, and posted their product, n = p q. Another individual, S, wishing to send a message m to R, encoded it as s = mn(mod n). Show how to calculate inverses a and b in order that ap 1(mod q 1) and bq 1(mod p 1). By considering s a (mod q) and s b (mod p) and recalling the Fermat-Euler theorem, display how R should recover the unique message, m. State simply some other consequences that you use. [10 marks] eight Discrete Mathematics What is a partial order on a fixed? What is a total order? Given two completely ordered units (A, 6A) and (B, 6B), define the Product Order and Lexicographic Order on A B and display that they're partial orders. Show that the Lexicographic Order is a complete order and that it includes the Product Order. [10 marks] Let S be the set of capabilities from N to zero, 1. Define a relation F on S by means of (f, g) F n N. F(n) 6 g(n). Show that F is a partial order. Define a relation G on S by using (f, g) G X nN f(n)10n 6 X nN g(n)10n . Show that G is a complete order and that it contains F. [10 marks] four CST.98.1.5 SECTION D 9 Programming in Java A whole Java application may use the equal call for several different methods or variables. Java has some of features that allow the user to prevent such re-use of names from causing chaos. Describe those underneath the headings: (a) scope regulations within character functions; [6 marks] (b) visibility of technique names within instructions, and the results of inheritance; [8 marks] (c) averting ambiguity when referring to the names of classes. [6 marks] 10 Programming in Java Write fragments of Java definitions, declarations or code to gain every of the following effects. You are not expected to expose the whole text of a application simply the parts at once crucial for the project described and you could describe in words in place of Java syntax any supporting definitions or context that you will want to rely on. Clarity of clarification can be regarded as at the least as crucial as syntactic accuracy within the marking scheme. It is likewise understood that names of methods from the usual Java class libraries are matters that programmers test in on-line documentation at the same time as writing code, so if you want to use any of those you do not want to get their names or exact argument-layout accurate supplied that (a) you describe without a doubt what you are doing and (b) your use is accurate at an overview stage. (a) Take an extended argument referred to as x and compute the long value received by way of writing the sixty four bits of x in the contrary order. [6 marks]
Statistics Principles And Methods
ISBN: 9780470904114
7th Edition
Authors: Richard A. Johnson, Gouri K. Bhattacharyya