ST2195 Coursework Project Instructions to candidates This project contains two questions. Answer BOTH questions. All questions will be given equal weight (50%). Part 1 In this part, you are asked to work with the Markov Chain Monte Carlo algorithm, in particular the Metropolis-Hastings algorithm. The aim is to simulate random numbers for the distribution with probability density function given below where x takes values in the real line and jxj denotes the absolute value of x. More specifically, you are asked to generate x0 ; x1 ; : : : ; xN values and store them using the following version of the Metropolis-Hastings algorithm (also known as random walk Metropolis) that consists of the steps below: Random walk Metropolis Step 1 Set up an initial value x0 as well as apositive integer N anda positive real numbers. Step 2 Repeat the following procedure for i = 1; : : : ; N: • Simulate a random number x* from the Normal distribution with mean xi—1 and standard deviations. • Compute the ratio • Generate a random number u from the uniform. distribution between 0 and 1. • If u < r (x*; xi—1), set xi = x*, else set xi = xi—1 . (a) Apply the random walk Metropolis algorithm using N = 10000 and s = 1. Use the generated samples (x1 ; : : : xN ) to construct a histogram and a kernel density plot in the same figure. Note that these provide estimates off (x).Overlay a graph off (x) on this figure to visualise the quality of these estimates. Also, report the sample mean and standard deviation of the generated samples (Note: these are also known as the Monte Carlo estimates of the mean and standard deviation respectively). Practical tip: To avoid numerical errors, it is better to use the equivalent criterion log u < log r (x*; xi — 1 ) = log f (x*) - log f (xi — 1 ) instead of u < r (x*; xi — 1 ). (b) The operations in part 1(a) are based on the assumption that the algorithm has converged. One of the most widely used convergence diagnostics is the so-called R value. In order to obtain a valued of this diagnostic, you need to apply the procedure below: • Generate more than one sequence of x0 , . . . , xN, potentially using different initial values x0 . Denote each of these sequences, also known as chains, by (x0(j), x1(j), . . . , xN(j)) for j = 1, 2, . . . , J. • Define and compute Mj as the sample mean of chain j as and Vj as the within sample variance of chain j as • Define and compute the overall within sample variance W as • Define and compute the overall sample mean M as and the between sample variance B as • Compute the R value as In general, values of R close to 1 indicate convergence, and it is usually desired for R to be lower than 1.05. Calculate the R for the random walk Metropolis algorithm with N = 2000, s = 0.001 and J = 4. Keeping N and J fixed, provide a plot of the values of R over a grid of s values in the interval between 0.001 and 1. Part 2 The 2009 ASA Statistical Computing and Graphics Data Expo consisted of flight arrival and departure details for all commercial flightson major carriers within the USA from Oc- tober 1987 to April 2008. This is a large dataset; there are nearly 120 million records in total, and it takes up 1.6 gigabytes of space when compressed and 12 gigabytes when un- compressed. The complete dataset, along with supplementary information and variable descriptions, can be downloaded from the Harvard Dataverse at https://doi.org/10.7910/DVN/HG7NV7 Choose any subset of ten consecutive years and any of the supplementary information provided by the Harvard Dataverse to answer the following questions using the principles and tools you have learned in this course: (a) What are the best times and days of the week to minimise delays each year? (b) Evaluate whether older planes suffer more delays on a year-to-year basis. (c) For each year, fita logistic regression model for the probability of diverted US flights using as many features as possible from attributes of the departure date, the sched- uled departure and arrival times, the coordinates and distance between departure and planned arrival airports, and the carrier. Visualize the coefficients across years. General Instructions • All questions should be answered using R and Python for all tasks. • Your answers should be provided in a separate structured report of no more than 1 page for part 1 and 6 pages for part 2. The page limit excludes title, references and table of contents but includes graphics and tables. The report should be in PDF format and also contain adequate explanations for readers not familiar with programming. In addition to the report, you will also be asked to provide your R and Python code in RMarkdown and Jupyter notebooks, respectively. All the relevant files must be submitted in the designated Atrio or VLE submission portal. • For part 2, each report should detail all steps you took starting from raw data up to the answer for each question. Any databases you setup, data wrangling/cleaning operations you carryout, and any modelling decisions you make should be clearly described in each structured report. Each report should also include any relevant graphics and tables as part of the answer. • If you are using elements (e.g. code, databases, graphics, etc) from your answer to a previous question to answer the current one, you will need to refer to those elements. • You should also supply the code you used to answer each question, in a way that can be used by someone else to replicate your analyses. You can do this either as separate scripts or separate RMarkdown/Jupyter notebooks per question, clearly indicating (both with comments and in the filename) which question each script. refers to.
Module: Artificial Intelligence Assignment: Solution of n-Tile Problems Learning outcomes · Improve your understanding of basic and advanced search methods learnt in the course after applying and implementing them to solve search problems for the given n-tile puzzle. · Enhance your Python programming and problem-solving skills for Artificial Intelligence application. Specification Overview The aim of this coursework is to develop solutions for a classical AI search problem, to contrast the efficiency of the techniques implemented, and suggest how the techniques can be adapted to the solution of a variant of the problem. Description In this coursework you are asked to implement two state space search algorithms: Iterative Deepening Depth First Search (IDDFS) and Iterative Deepening A* (IDA*) for the solution of the n-tile problem. You are also asked to suggest how a variation of the problem could be solved efficiently. See Parts 1 and 2 for detail. Part 1. Solution of n-tile problems (programming in Python) Using the state representation seen in lectures, a state corresponding to the configuration of the 8-tile puzzle in the figure below can be described as [2, 2, [[1, 2, 3], [4, 5, 6], [7, 8, 0]]] You are asked to solve the following 8-puzzle instances, each with a corresponding goal state, in the smallest number of moves. Case Initial state Goal state 1 [0, 0, [[0, 7, 1], [4, 3, 2], [8, 6, 5]]] [0, 2, [[3, 2, 0], [6, 1, 8], [4, 7, 5]]] 2 [0, 2, [[5, 6, 0], [1, 3, 8], [4, 7, 2]]] 3 [2, 0, [[3, 5, 6], [1, 2, 7], [0, 8, 4]]] 4 [1, 1, [[7, 3, 5], [4, 0, 2], [8, 1, 6]]] 5 [2, 0, [[6, 4, 8], [7, 1, 3], [0, 2, 5]]] 6 [0, 0, [[0, 1, 8], [3, 6, 7], [5, 4, 2]]] [2, 2, [[1, 2, 3], [4, 5, 6], [7, 8, 0]]] 7 [2, 0, [[6, 4, 1], [7, 3, 2], [0, 5, 8]]] 8 [0, 0, [[0, 7, 1], [5, 4, 8], [6, 2, 3]]] 9 [0, 2, [[5, 4, 0], [2, 3, 1], [8, 7, 6]]] 10 [2, 1, [[8, 6, 7], [2, 5, 4], [3, 0, 1]]] You have to create Python code to solve the instances with the Iterative Deepening Depth First Search (IDDFS) and Iterative Deepening A* (IDA*). For each instance, both codes you have implemented for the IDDFS and IDA* should output to the console with the following information and results: (1) Case number. (2) The number of moves to solve the case (i.e. the number of states – 1 in the shortest path from the initial state to the goal). (3) The number of nodes opened, that is, the number of yield made by the move method during the search for a solution. (4) The computing time the search took. For the IDDFS, you are allowed to reuse/adapt the move method provided in our lecture notes. You can also reuse the DFS code provided. As seen in the lab exercises, note that you may have to deal with the fact that Python lists are passed by reference. Hence, you may consider implementing a deep copy approach. For the IDA*, you should rely on an h function made of the sum of evaluation functions of the numbered tiles (not including tile “0”), where the evaluation of a tile is the Manhattan distance between its position in the current state and its position in the goal state. This indicates the minimum number of moves that tile has to make to get into its final position. Your code should also work for different n-tile designs; for example, 15-tile puzzle. Part 2. Problem representation (problem-solving) The objective of this part is not to provide code, but to explain how a variation of the n-tile problem (here called new problem) could be solved, assuming that you are addressing a programmer who has read your code for Part 1 and is sufficiently experienced on the topic. First, in the new problem columns in the grid wrap around, i.e. the last row of the grid is a neighbour of the first row. For example, in the following configuration the blank tile can be exchanged with tile number 3 to produce: Question 2.1. What would be the changes to make to your IDA* code for Part 1 to consider this change into the n-tile problem specification? In fact, the new problem also allows an extra type of move that consists in shifting all the rows circularly down or up by one position. For example, from the state a down shift would produce while an up shift would produce Also, in this problem the cost of such shift moves is zero. Question 2.2. Explain how you would modify your IDA* code for part 1 to solve this problem efficiently? Question 2.3. What physical design of an n-tile-like puzzle would correspond to this problem? If you are not aware of any, how could you design one? Explain how it would work. Relationship to formative assessment Lecture slides and lab exercises provide the baseline to design solutions for the n-tile problem. Extension of work on search methods seen in labs. Deliverables You are required to produce two independent Python programs to solve the n-tile problem using: 1. Iterative Deepening Depth First Search (program should be named “IDDFS.py”) 2. Iterative Deepening A* (program should be named “IDAstar.py”) Your programs must contain a function named solve_puzzle with two parameters (start_state and goal_state) and will return the output data described in Part 1. The aim of the function is to provide an entry point to test your work. Failure to define the solve_puzzle function may result in marks penalty. def solve_puzzle(start_state, goal_state): # Your code. You can make calls the methods you create. return (moves, yields, time, path) You must provide a comment at the start of each program that contains the results you were asked to output, that is the output of the solution method used in the program for each of the provided instances in the order they are listed in this specification. Note that solve_puzzle function returns the path (sequence of moves) to solve a test case from the initial to the goal state. It is not necessary to include the path in the comment at the start of each program along with the output results. The code provided in the lectures and labs uses Python’s generators to create of new states. Your code must also rely on generators. Failure to implement generators may result in marks penalty. Your Python code must be well structured, tidy, and well documented (i.e. adding comments to describe functions, generators, and lines that you consider very important). In addition, you must answer Questions 1 and 2 of Part 2. The answers should be provided in a Word document named “Part2.docx”. Use the Part2.docx file provided on BB as a template (not a Word template). The answer to this part must not exceed one page. The submission must strictly follow the specification of the provided template, i.e. fonts, font sizes, line spacing and header/footer/margin sizes should not be changed. Any change or one-page exceed would result in a rejection of the document and a zero mark for Part 2 will be given. Submission Submit your two Python source files and your Word document as separate files to the designated point on the blackboard by the deadline. You must not zip your three files into one compressed zip file. Resources · Lecture notes. · Labsheet solution on search. · Python tutorial: https://docs.python.org/3.7/tutorial/index.html · Best practices for high-standard coding https://peps.python.org/pep-0008 Marking scheme The Iterative Deepening Depth First Search program is worth 20 marks: 10 marks for the correctness on the test cases, 5 marks for code efficiency and robustness, and 5 marks for readability and code quality. The Iterative Deepening A* program worth 50 marks: 20 marks for correctness on test cases; 25 marks for efficiency and robustness, and 5 marks for readability and code quality. The answers to Part 2 are worth 30 marks: 20 marks for Q 2.1, 5 marks for Q 2.2 and 5 marks for Q 2.3. Although readability of programs only counts for 5 marks at each program, students may be further penalised; for example, if they do not provide sufficient comments, or submit incomprehensible code and the correctness of which cannot be ascertained by the marker in reasonable time. Total 100 marks.
ASSIGNMENT 2 FIN246 Spring 2025 DUE: Monday, March 3th at the beginning of class (3:25pm EST) 1. Using the last 4 digits of your student number, look up Bitcoin block 820000 + last 4 digits of your id (Example, if the last 4 digits are 1234, look up block 761234) at the following site: https://www.blockchain.com/explorer Once you have the details of the block loaded, answer the following: (a) How many leading 0s are in the final hash? (b) Click on the hash for the block to see the transaction detail: (i) What is the nonce? (ii) How many possible nonce calculations are there? (c) Looking at the transaction detail, what details are publicly available on the blockchain? What do you not see? (d) Why is the first transaction in this block different from the rest in terms of input/output matching? What is going on here? 2. Go to https://bestwallettoken.com/en Evaluate the BestWalletToken ($BEST) initial coin offering based on details you can find: (a) Who are the executives, directors and major owners of the company and were is it located? Is the company owned through holding $BEST? Explain based on what you can learn. (b) How is the coin/token mined (proof of work, proof of stake, etc.)? Explain. (c) How does the staking rewards work? Does the buyer of the $BEST token profit from the business operations? Explain. (d) Is this token a security under the Howey test? Apply the test in detail and consider arguments for and against the test applying. 3. Find the address pair (n,e) that matches the last 4 digits of your student number in FIN246 Blockchain-RSA(Spring 2025).xlsx (posted with the assignment). These are addresses from a simulated Bitcoin-type blockchain based on RSA public key cryptography. Each address pair (n,e) applies to transactions in the blockchain (which can be messages or amounts of coins). (a ) Your friend, Bob, who believes their communications are being monitored sends you a 10 alphanumeric password using RSA public-key encryption. He sent 10 separate numbers (one for each letter/number) to the public address (n,e) associated with the last 4 digits of your student number. Each number is given in the FIN246 Blockchain - RSA file. After you decrypt this password, you can then communicate with Bob through shared files/social media and/or other places where knowing the password allows access. (i) Break the RSA address (n,e) by finding p, q, (p-1), (q-1), d. (Note: you will have to use process below to break the RSA pair (n,e) and find d). (ii) Use d to unencrypt each of the 10 numbers (Note: you will need https://www.dcode.fr/modular-exponentiation:) (iii) Each resulting number is in ASCII form, which you should convert to alphanumeric using the =char() function in Excel (iv) Write out the password (which is case sensitive) (b) Choose a pair (n*,e*) from the Unassigned tab in the spreadsheet where n* contains at least 4 different digits from your student number and transfer coins equal to the last four digits of your student number from the given address (n,e,) to this new address (n*,e*). (i ) Find the d* that goes with the new address (n*, e*) (ii ) Calculate the transaction message using https://www.dcode.fr/modular-exponentiation: m (n + tokens + n*) mod n (iii ) Then calculate the digital signature, c, again using the online calculator: digital signature: c md mod n (iv) Write out the transaction details: n, tokens, n*, c (v) Verify the transaction by calculating m ce mod n This should be the same m as calculated above using m (n + tokens + n*) mod n Details of FIN246 Blockchain & RSA: Each block address is a number pair [n, e] where n = p x q and e is the public key (which is actually an exponent variable). The factors p and q are not known publicly, but can be determined by factoring n. (Hint: the prime numbers used in this assignment are all chosen from the primes listed in a tab in the spreadsheet) A valid transaction on this blockchain requires a digital signature, c, to prove that the sender has the private key, d, to the address. This digital signature is of the message, m, is created by taking the transfer block address n and adding to it the message (number of tokens and the new owner’s block address n* (example: 582918502 + 5361 + 624530918 = 1207454781). “Breaking” RSA public key cryptography requires: For each block address, you are given n, e. If you can factor n into p x q, then you can follow the steps in the RSA algorithm (see the Wiki page for additional help): (i) Find (p-1)(q-1) (ii) Find the least common multiple (lcm) of (i): in excel use =lcm((p-1),(q-1)) (iii) Find Use the totient function to find d: d= (lcm((p-1) , (q-1)) + 1) / e [Note: this can be a tricky step, so I have carefully chosen all pairs, n, e, so that d is an integer result] (iv) Verify your solution by using https://www.dcode.fr/modular-exponentiation to prove with modular arithmetic that 1 d x e mod lcm
[pdf-embedder url="https://assignmentchef.com/wp-content/uploads/2025/03/assignemt-notice.pdf"] CVEN 3303 Steel Structures Term 1, 2025 Assignment 1 – Design of members subjected to axial loads Figure 1: Sketch of steel support structure to be designed Figure 1 illustrates a sketch of a proposed pin-jointed triangulated steel truss structure of dimensions L1 and L2 to support a given load P and Q. You are required to design members, M1 (length = L1 ); and M2 (length = ) Assume: • All joints are pin-jointed • All nodes are assumed to be fixed from movement out-of-plane • All members have a mid-point restraint for buckling out-of-plane • Member M1 has a net area in tension of 0.85 Ag Note: • Choose any steel sections allowable in AS4100 • State any further assumptions • You do not need to design the connections, merely sketch them based on your chosen section Design Parameters: Your student number is of the form. zABCDXYZ and the parameters for your design are given in Table 1. For example, if your student number is z5412345, then the parameters for your design are given by your last student number Z as 5. L1 = 4.Y m = 4.4 m L2 = 4.X m = 4.3 m P = 700 kN Q = 750 kN Table 1: Design Parameters Last student number Z L1 (m) L2 (m) Dead load P (kN) Live Load Q (kN) 1 4.Y 4.X 500 950 2 5.Y 3.X 550 900 3 6.Y 2.X 600 850 4 7.Y 3.X 650 800 5 4.Y 4.X 700 750 6 5.Y 3.X 750 700 7 6.Y 2.X 800 650 8 7.Y 3.X 850 600 9 4.Y 4.X 900 550 0 5.Y 3.X 950 500 Marking Scheme The following table provides the overall marking criteria for Assignment 1 1. Calculate the member forces using principles of statics 2. Determine the reactions using the principles of statics 3. Design member, M1 using AS4100 4. Determine the elongation of member M1 using mechanics of materials principles 5. Design member, M2 using AS4100 6. Provide sketches and drawings of the members and connections and how this would be constructed. Please provide comments. You do not need to design the connections, however provide sketches showing the sections and scale of the members and connections. Provide comments on the design and optimisation. Item Total Marks 1.Calculate member forces for M1 and M2 /15 2.Determine the reactions at thesupports /15 3.Designmember, M1 /15 4.Determine the elongation of member, M1 /15 5.Designmember, M2 /15 6.Sketches/drawings of member andconnections/comments /25 Overall /100
SCM3202 Topic 6 Assignment A Chinese company wants to set up a manufacturing plant in Germany that purchases raw material from a supplier in Berlin and deliver finished goods to customers in five markets including Hamburg, Bremen, Hanover, Leipzig, and Dresden. The freight rates, weight of raw material and finished goods to be transported, and latitude and longitude of the source and markets are shown in the following table. Note: The tonne is a metric unit of mass equal to 1,000 kilograms. It is also referred to as a metric ton. Use the Center-of-Gravity (COG) method to determine the least-cost location for the plant location. Round the answer of latitude and longitude of COG to 2 decimal places. You can apply the following formula and templates to perform the calculation. Rate Latitude Weight €/tonne-km y-coordinate Tonnes Source r d s rs rds S1 Total Rate Latitude Weight €/tonne-km y-coordinate Tonnes Market R D M RM RDM M1 M2 M3 M4 M5 Latitude of COG = Total Rate Longitude Weight €/tonne-km x-coordinate Tonnes Source r d s rs rds S1 Total Rate Longitude Weight €/tonne-km x-coordinate Tonnes Market R D M RM RDM M1 M2 M3 M4 M5 Total · Longitude of COG =
ENGG1340 Programming Technologies / COMP2113 Computer Programming IIAssignment 1Deadline: 1 March (Saturday), 2025 23:59General InstructionsSubmit your assignment via VPL on Moodle. Ensure that your program can execute, and generate the required outputs inVPL. Work incompatible with the VPL may not be marked.For shell scripts (Problem 1 and 2), they must starts with the header #!/bin/bash, and will be executed using the Bashshell on our standard environment.As a developer, ensure that your code works flawlessly in the intended environment, not just your own. While you maydevelop your work in your own environment, always test your program in our standard environment before submission.EvaluationFor tasks requiring user input, utilize the standard input. Likewise, your program should output/print through thestandard output. Strict adherence to the sample output format is required, or your answer may be marked incorrect.Your code will be automatically graded for technical correctness. Essentially, we use test cases to evaluate yoursolution, failure to pass any of the test cases may result in zero marks. Partial credits are generally not given forincomplete solutions as it may be challenging to objectively assess incomplete program logic. However, your work maystill be considered on a case-by-case basis during the rebuttal stage.Additional test case will be used during grading. Scoring full marks on VPL does not ensure full marks in the assignment.Sample test cases may or may not encompass all boundary cases. Designing proper test cases to verify your program’saccuracy is part of the assessment.Academic dishonestyYour code will be cross-checked with other submissions and online sources for logical duplication. Note that providingyour work to others, aiding others in copying, or copying from others will be considered plagiarism, and will be dealt withas per departmental policy. Please refer to the course information notes for more details.Use of generative AI tools, like ChatGPT, is not permitted for all assignment.Getting helpYou are not alone! If you are stuck, post your query on the course forum. This assignment should be educational andrewarding, not frustrating. We are here to help, but we can only do so if you reach out.Please avoid spoilers on the discussion forum. Do not post any code directly related to the assignments. You are,however, encouraged to discuss general concepts on the forums.SubmissionDeadlines are strictly enforced. Resubmission beyond the submission period will not be accepted.Late Policy:If you submit within 2 days after the deadline, 30% deduction.If you submit within 3-5 days after the deadline, 50% deduction.After that, no mark.Problem 1: Count Substring MatchesWrite a shell script that takes two command line arguments substring and file. It will count the words that containssubstring in file and produce the result.Input:The shell script does not read input from user. However, it expects two command line arguments substring andfile.Output:The script should list all words found, with the number of occurrences of that word in file. Refer to the sampleoutputs for the exact format.The words should be listed in descending order of the number of occurrences. For words with the same number ofoccurrences, they should be listed in ascending order of their ASCII values.The script should output nothing when there are fewer than two command line arguments specified or when thefile does not exist.Assumptions:The command line argument substring contains alphabets only. There will be no digits, symbols, or whitespacecharacters in substring.file, if exists, is a plain text file and is readable by all user.The locale settings of the shell can affect the result of sorting. The shell script will be executed using Locale “C”. Ifyou are testing in your own Linux environment, please execute command export LC_ALL=C.UTF-8 to change thelocale settings accordingly.Requirements:For this question, a word is bounded by spaces or symbols, or by line boundaries (i.e., start of a line or end of aline). For example, the string Gutenberg(TM)'s should be treated as three words Gutenberg, TM, and s.Substring matching should be case insensitive. E.g., searching for tale should find TALE and tale.On the other hand, when counting the number of occurrences of a word, it should be done in a case-sensitivemanner. E.g., TALE and tale should be counted separately.Notes:A file ebook.txt is provided for testing. A different file may be used when grading your work.Study the man page of grep and sort to learn about possible options to use for this task.There is no need to follow the exact amount of leading spaces shown in the sample outputs. Leading spaces willbe ignored in evaluation. If you are testing in your own environment, you can use flag -Bw of command diff forcomparison.Sample Test Cases1_1Command: ./1.sh tale ebook.txtOutput:3 TALE2 Tale1_2Command: ./1.sh time ebook.txtOutput:30 time10 times3 Sometimes1 lifetime1 oftentimes1 sentiment1 sometimes1_3Command: ./1.sh jerry ebook.txtOutput:14 Jerry1_4Command: ./1.sh pokemon ebook.txtOutput: (it’s empty)Problem 2: Credit card number validationWrite a Shell Script for validating credit card numbers using the Luhn algorithm.The steps to validate a credit number using the Luhn algorithm are as follows:1. Starting from the rightmost digit (that is the check digit), double the value of every second digit.2. If the doubled value is a two-digit number, sum the digits of that number together to form a single digit.3. Add all the 16 digits together.4. If the final sum is divisible by 10, then the credit card is valid. If it is not divisible by 10, the number is invalid or fake.For example, consider the credit card number 4512 3456 7890 1234. Applying the Luhn algorithm:Double every second digit, starting from the right: 4, 6, 2, 2, 0, 18, 8, 14, 6, 10, 4, 6, 2, 2, 5, 8.Sum all the resulting digits: 4 + 6 + 2 + 2 + 0 + 9 + 8 + 5 + 6 + 1 + 4 + 6 + 2 + 2 + 5 + 8 = 70.Since 70 is divisible by 10, the credit card number is valid.Input:The shell script reads one credit card number from user.Output:The script should output a message reporting the validity of the credit card number. Refer to the sample outputsfor the exact format.Assumptions:You can assume that the input is always a 16-digit number, and each digit is in the range [0, 9]. There is no need toconsider invalid inputs.Sample Test Cases (Inputs are shown in blue)2_1Enter the number for checking:4512345678901234The number 4512345678901234 is valid.2_2Enter the number for checking:4512345678901235The number 4512345678901235 is invalid.2_3Enter the number for checking:1234567890123456The number 1234567890123456 is invalid.2_4Enter the number for checking:1234567890123452The number 1234567890123452 is valid.
Assignment MISCADA Computer Vision moduleAcademic year 2024/2025 Academic in charge and contact informationProfessor Paolo Remagnino, Department of Computer ScienceIntroductionThis assignment is split in two parts, with separate deadlines; details follow.Description (15%)A thorough description of the used libraries and methods and the results is expected. Please refer to the marking scheme table for more detail.Part 1 (30%)A computed tomography (CT) scan is a non-invasive imaging procedure that uses X-rays to create detailed pictures of the inside of the body. CT scans are used to diagnose and treat a variety of conditions, such as tumours, pneumonia and internal bleeding.A CT scan is composed of a large and variable number of slices, each one of them is a greyscale image, examples of CT slices are provided in figure 1. figure 1 examples of CT scan slices: top row contains raw data, bottom row annotated data: both leg bones and calcium concentration are labelled.For this part, you will have to search for areas that might indicate the presence of calcium deposit. In CT scans, calcium and bones are visible as brighter areas, while other organs usually have low intensity values. The provided data (see later in the document for details) represent portions of CT scans of the lower limbs. In simpler terms, those slices represent cross sections of both patient’s legs. Presence of calcium might indicate serious indication of blockages in the arteries. So, the larger is the amount of deposit, the higher the risk is for a patient.For this part, you will have to develop code in Python, using Jupyter Notebook to provide solutions to the following two tasks:Task 1 (15%): creating masks on a slice basisYou are asked to create greyscale masks for each slice of the given CT scans. Each CT slice will need to be normalised to represent a probability density map. Segmentation must then be applied to each map to highlight those pixels that might indicate the presence of calcium concentration.Task 2 (15%): estimating volumes of calcium depositCalcium deposit is a three-dimensional object, as an artery is a 3D object, while each CT slice is merely a 2D representation of the deposit at a given position in the CT scan. You are asked to make use of the probability density maps created for the previous task, to develop code to estimate the volume of calcium deposit across CT scan slices. Do assume the thickness of each slice is 0.5mm, assume pixels are squares of 1mmx1mm size. Part 2 (55%)You must develop code to analyse video clips taken from the last Olympic games (Paris 2024). To start with, you are asked to download the video clips from Blackboard. They have been prepared for you, instructions where data can be found are provided later.For this part, you have additional tasks to solve; please read the following instructions for details:Task 3 (15%): Target detection - for this part, you are asked to exploit one of the taught algorithms to extract bounding boxes that identify the targets in the scene. Targets are represented by either objects or people moving in the video clips.Expected Output: Bounding rectangles should be used to show the target, as well as an ID and/or a different colour per target. Task 4 (20%): Target tracking - for this part, you are asked to use one of the taught techniques to track the targets. Tracking does mean using a filter to estimate and predict the dynamics of the moving target, not simply detecting targets in each frame.Expected Output: For this task you should provide short video clips using the processed image frames, the current position of the targets in the scene and their trajectories. Targets should be highlighted with a bounding rectangle in colour or a polygonal shape and their trajectories with a polyline in red (do see the examples in figure 2). Ideally, you could have prediction and new measurement highlighted using two bounding rectangles of different colour per target. figure 2 example of tracked targets: bounding rectangles and trajectories.Task 5 (20%): Optical flow – for this task, you are asked to use one of the algorithms taught in class to estimate and visualise the optical flow of the analysed scene.Expected output: Once you have run the algorithm of your choice you can use any of methods used in the workshop or any method you find one the Internet to visualise the optical flow. A video clip must be generated, with optical flow overlapped to the original clip. Figure 3 shows two different ways to visualise optical flow. figure 3 visualising optical flow using vectors (left), and dynamics direction using colour.DatasetDataset of CT scans and Olympic clips are available in our Assignment folder on Blackboard. Marking schemeTask comment %Descriptions A general introduction to your solutions must be provided (5%), as well as a detailed description of how you solve each of the following tasks (10%). 15Task 1 Hint: CT scan slices are greyscale images, segmentation can be implemented using one of the taught methods/algorithms. For the normalisation and generation of probability maps needs to enforce each map to sum up to one. Marking: 10% will be assigned to a fully working method, 5% only if the method partially works. 15Task 2 Hint: one can think of aligning CT slices and related segmented maps. Combining adjacent slices means checking the likelihood of calcium deposit and building an estimate of the volume. Marking: the implementation must clearly demonstrate volume estimates are correctly built. Full 15% to a complete solution, if the solution works in part, then 10%. 15Task 3 Hint: For this part I am expecting you to exploit the latest YOLO and SAM versions to detect the targets. You are also welcome to use any traditional method of your choice. Marking: the implementation exploits existing deep architectures, so validation and testing will be essential to get full marks. Ideally, the result will have to show “tight” bounding rectangles or closed polylines for the extracted targets, with an error measure such as the intersection over union (IoU) as a viable metric. Comparison of existing architectures/methods applied to the problem attracts 10%, the other 5% is for the most suitable metric to assess the result. 15Task 4 Hint: For this task, you can use the dynamic filters you have been taught to track targets in the scene. You can feel free to use any deep learning method as well you have read during the four weeks.Marking: the accuracy of the tracking will be a determining factor to obtain full marks, you are recommended to use the metrics you used to solve Task 3. Full marks if any spatial-temporal filter is implemented and manages to track the targets in the scene. A comparison of at least two filters attracts 8%. The other 5% is for the generation of a video clip as qualitative output and 7% for quantitative results. 20Task 5 Hint: For this task, you can use any of the algorithms taught to use for the detection and visualisation of optical flow. Again, you can feel free to use any deep learning method as well you have read during the four weeks.Marking: 10% for the detection of the optical flow, trying to disambiguate between moving camera and targets and 10% for the visualisation. The latter must be integrated in a video clip, with flow overlapped over the video clip frames. 20Total 100Submission instructionsFor each part, you are asked to create a Jupyter Notebook, where you will provide the textual description of your solutions and the implemented code. Your notebook should be structured in sections. An introduction should describe in detail the libraries you used, where to find them and how you solved the tasks. Then you should include one section for each task solution, where again you describe your solution. The code must be executed, so that the solutions are visualised, in terms of graphics, images and results; it is strongly recommended you also include snippets of the formulae implemented by the used algorithms and the graphics of the employed architecture. Your code should be implemented in Python, using OpenCV as the main set of computer vision libraries. PyTorch or TensorFlow can be used to use the deep learning methods you have chosen. Please do make sure your code runs and it is executed. Notebooks will have to be uploaded on Gradescope, while all the videos to Panopto.Submission and feedback deadlinesPlease refer to the following table for details on the submissions:Part Release date Submission date Submission method Feedback date1 17 Jan 2025 20 Feb 2025 Gradescope 20 Mar 20252 3 Feb 2025 17 Mar 2025 Gradescope and Panopto 14 Apr 2025Extension policy and related documentsIf you require an extension for a piece(s) of summative coursework/assignment you MUST complete the form via the Extension Requests App.On this form you must specify the reason for the request and the extra time required. Please also ensure that supporting documentation is provided to support your extension request. Your extension request will not be considered until supporting documentation has been received.If the extension is granted the new deadline is at the discretion of the Programme Director.Once the completed form has been received by the Learning and Teaching Coordinator it will be distributed to your Programme Director who will decide on the outcome. You will normally be notified by email within two working days of the outcome of your request.Please note that, until you have received confirmation that your extension request has been approved, you MUST assume that the original deadline still stands.Further information on the University's extension policy and academic support can be found here.Where circumstances are extreme and an extension request is not enough a Serious Adverse Circumstances form (SAC) should be considered.PLAGIARISM and COLLUSIONStudents suspected of plagiarism, either of published work or work from unpublished sources, including the work of other students, or of collusion will be dealt with according to Computer Science and University guidelines. Please see:https://durhamuniversity.sharepoint.com/teams/LTH/SitePages/6.2.4.aspxhttps://durhamuniversity.sharepoint.com/teams/LTH/SitePages/6.2.4.1.aspxPLAGIARISM with chatGPT or/and similar AI toolExamples of plagiarism include (but are not limited to) presentation of another person's thoughts or writings as one's own, including:- cutting and pasting text, code or pictures from generative AI services (e.g. ChatGPT).What is acceptable?If you want to include any text or code produced using generative AI in a submission, that text or code must be clearly marked as being AI generated, and the generative AI that has produced the text or code must be clearly cited as the source.The University has provided a guide on generative AI, with the following page on whether it can be used in assessment:
Technology Management and Innovation Department Industrial and Manufacturing Engineering Program Course Outline: IE-GY 6213 A “Facility Planning and Design” Spring 2024 Course Description: A practical approach to facility planning and design with an emphasis on real world issues rather than solely theory and detailed analysis. The course is reasonably general to encompass a broad range of facilities including offices, hospitals, schools, industrial facilities etc, while leaning towards industrial facilities and master industrial site planning. See course objectives and lecture descriptions below. Course Objectives: 1. Gain an understanding of the phasing of facility design work and its importance in the engineering and construction field today 2. Learn how to layout an industrial plant from a practical point of view. 3. Understand the various engineering entities involved in planning and design, and the complexity of their interactions. 4. Understand how planning and design techniques involved in an industrial plant apply to other facilities such as offices, hospitals, schools, etc. 5. Gain an understanding of the role that the legal component plays in the planning, design and permitting process. 6. Understand how to develop a budget estimate for the capital investment required for the design and construction of facilities and how different techniques apply to different design phases. 7. Gain an introductory understanding of project management and how it impacts the planning and design process. Course Structure: Lectures, class discussion, assignments and some assignment presentations, Term Project and presentation, mid-term and final exams. Exams will be on-line via Brightspace but will be taken in-class at normal class time on the dates scheduled. Text: “Facilities Planning and Design” Alberto Garcia-Diaz and J. MacGregor Smith Note: It is not necessary to purchase this textbook Course Requirements: Reading of specific handouts, class participation, homework assignments (some with brief class presentations), mid-term exam, term project (working in teams with 15 - 20 min in-class presentation) and final exam. Reading of class lecture slides prior to the class is optional. Lecture slides are supplemented by and expanded upon by oral presentation by the professor each week. Simply reading and memorizing slides is not adequate preparation for exams….understanding of the material presented is required. Course grades will be calculated per the weighting below: Assignments: Minimum of five (5) assignments 15% of final grade #1 Phases of Design (5 min class presentation required) #2 Building Codes and FAR Calculation #3 Reverse Cumulative Yield Calculation #4 Footprint Calculation #5 Material Handling Equipment Systems (5 min class presentation required – work can be done with same team as assigned for Term Project or individually) Assignments are due the following week unless advised otherwise. All assignments are to be done without collaboration unless Prof Posner advises otherwise. Mid-term Exam: 30% of final grade Term Project (working in teams assigned by Prof): 20% of final grade Term project is a Preliminary Phase Design of an industrial facility. In-class 20 min presentation required. Final Exam (based on entire semester): 35% of final grade Total 100% Notes: 1. Course grades will be calculated as above. There are no opportunities for extra credit at any time unless included in the exam itself. Nor are there opportunities for grade changes once grades for the course have been posted on Albert. Students are advised to please not ask for such a change. 2. AI – Students should not use AI tools in this course unless specifically noted as allowed in the description of a specific assignment or exam/quiz
LUE1002 Assessment 2 Task Sheet (Writing) Take-Home Argumentative Essay Comprises 25% of your final course grade Your final written assignment due for this course is an Argumentative Essay of 900 – 1,100 words. This is an individual task. Your work will be graded for its preliminary planning, paraphrasing, content, organisation & cohesion, citation & referencing, and task achievement. For more details about grading, see the marking scheme on pages 5-7. Details of the assessment areas follows: The Scenario To encourage critical thinking about issues of global concern and the development of excellent skills of oral and written expression among students, the Office of Student Affairs is organising an essay contest with linked mini-presentation and viva. As a Lingnan University student, you want to bean entrant in the contest to express your views on the given topic. Essay Topic The topic for the essay contest is social media. You need to explore the topic from an academic and interdisciplinary perspective, and present your thoughts in the form of an argumentative essay that addresses a debateable question about social media. This genre of writing requires you to develop a specific/novel/interesting question related to the topic; investigate the issue; collect, generate, and evaluate evidence; and establish a position on the topic in writing of a formal academic style. Here are some questions that may help you brainstorm possible issues related to the topic: • Has the role of social media had a positive or negative impact on one area of life or society in which you’re interested? • In what way(s) has social media changed the way we see the world and/or communicate with others? • Are social media making our lives (as individuals or as societies) better or worse? Please note that these are only some of the possible questions you may explore in relation to social media. If you have other ideas, you are free to explore them – as long as the question remains argumentative and ‘debatable’. Remember that your GENERAL ideas need to be narrowed down into a more manageable, specific, original and debatable question for your essay. For example, you may choose to focus on one specific type of social media and explore its impact on the lives (e.g. learning, politics, health, business) of aparticular group of people (e.g. elderly people in Hong Kong). Students are reminded that ‘originality’ is rewarded in the ‘content’ marking criteria (30% of criteria). You will lose marks if you use a debatable question presented in other LUE1002 course materials or assessments without changing the focus somehow or adding a ‘twist’ to the question (focussing on a more specific question or issue). The most original essays which add a unique contribution are likely to be best received (and achieve higher grades). Essay Requirements You need to: • write an essay of between five and six paragraphs (you should NOT use section headings) • show your awareness of different arguments on the issue. • express your stance with a clear thesis statement highlighting all the supporting arguments • explain your ‘pro-arguments’ with support from both your own logical explanations and reference to the literature (sources). • include at least one counterargument and refutation. • cite at least 3 English written sources which should come from at least 2 different disciplines (for example, education + history). o You may use any sources in the sources found through Lingnan library portal searches or any other sources that are appropriate for the genre. o If your chosen article has an interdisciplinary focus, treat it as ONE discipline and choose your second article from a different discipline or a different combination of disciplines. o Your in-text citations and reference list should be in APA style. o You should put your reference list (name it “References”) on anew page. o You should type in the discipline for each source you have used in bracketed italics, e.g. (Psychology) at the end of each reference entry. For examples, see the Research Readings list on Moodle. o You should mainly use paraphrases/summaries from the literature (with citation) to support your arguments. Where appropriate, you may also use quotations (but you are discouraged from excessive use of quotations which do not count towards the word count and must not exceed 10% of the overall essay). Students must read and reference the original literature, not summaries generated by AI (no citations to Gen AI should be made). The research and writing process You should keepa folder of your preparation work, known as the “Work in progress folder”. This should include screenshots of interactions with GenAI, drafts, plans and anything you do in preparation for the assessment. You will submit all of this as a zip file alongside the final submission of your essay. This will not be assessed and there is no penalty for non-assessment. However, if there is a question over the authorship of your essay this folder can be considered. There are three stages of submission of this essay assignment: 1. Plan (question, thesis and outline) You must write and submit a plan that includes: your chosen essay question, your thesis statement and an outline of your essay organisation. 2. Paraphrase table You will submit a ‘Paraphrase Table’ that showshow you plan to paraphrase, cite and reference some of the sources for your essay. 3. Final Submission You will submit a final version of your argumentative essay in two parts: 1) the full essay and 2) a zipped file of your“Work in progress folder”. Suggested process of researching and writing the essay Think about the Social Media topics that interest you and conduct some general reading around the topic to understand the key terms and issues. Check that there are academic readings and sources of information related to the topic. Identify a topic for the essay and aska classmate to give you feedback on your title and thesis. Search for more academic source materials to support your argument. Revise your essay question (if necessary), write a thesis statement and outline Use any feedback from your peers and tutor to make sure your counterarguments and any refutations are aligned to your thesis. Take notes from sources and begin paraphrasing some pro-arguments and counterarguments from the sources. Complete the paraphrase table and submit to Moodle. Complete your first draft. Make sure you have convincing refutations for your counterarguments. Conduct a self-review, peer review and edit your final draft. Submit your final essay (along with your ‘Work in progress folder’ through Turnitin on Moodle.
Complex Networks (MTH6142) Formative Assignment 4 • 1. Degree distribution of random graphs A random graph ensemble G(N, p) with has a binomial degree distribution that in the limit of N >> 1 can be approximated by a Poisson distribution PP (k) given by (a) Calculate the generating function for the binomial degree distribution PB(k) given by Eq. (1). (b) Using the properties of the generating functions, evaluate the first moment h ki and the second moment of the degree distribution PB(k) given by Eq. (1). (c) Calculate the generating function for the Poisson degree distribution PP (k) given by Eq. (2). (d) Using the properties of the generating functions, evaluate the first moment h ki and the second moment h k(k − 1)i of the degree distribution PP (k) given by Eq. (2). (e) Show that the first h ki and second moment of the binomial distribution PB(k) obtained in (b) are the same as the first h ki and second moments of the Poisson distribution PP (k) obtained in (d), as long as with c constant and N → ∞. • 2. A given random network Consider a random network in the ensemble G(N, p) with N = 4 × 106 nodes and a linking probability p = 10−4 . (a) Calculate the average degree h ki of this network. (b) Calculate the standard deviation σP using the approximated degree distribution given by Eq. (2). (c) Assume that you observe a node with degree 2 × 103 . How many standard deviations is this observation from the mean? Is this an expected observation or is this an unexpected observation?
ITMD 534: Human Computer Interaction, HW2, Spring 2025 Due March 3rd, 2025, Midnight Please submit a PDF copy of your homework to Black Board Below are a list of products/interfaces. Each student could pick a device from this list or any other interface of their choice. You will use your selected device or interface to decide on a goal to attain through it for Contextual Inquiry. The task for attaining the goal needs to be fairly complex to at least have about 5 steps. You will then select 2 users and get them to perform. the task that you planned – one at a time. Choose 1 user familiar with the product, 1 user unfamiliar with the product. Describe the task and ask the user to accomplish the goal. Do not help the user. Record every aspect of the user’s actions and mannerisms in your documentation. This documentation needs to be recorded in a dialogue format as shown in the example in class. Ask the user to be verbal about what they are doing in every step. Prepare a report with a brief description of the product/interface, provide the initial interview questions and the specific instructions for accomplishing the goal. Describe the performance of each user including the troubles they faced – what they did wrong and what they did right. Record also a brief persona of each user you have chosen. The persona needs to cover significant details of the user. When you ask the users to perform. the task – describe only the goal and not the steps. Let the user figure out the steps while you note their actions. Draw out a flow diagram (Flow Model as discussed in class) of the interaction, as part of your report. Your report needs to include: 1. A clear description of the product and the interface you are evaluating. 2. Initial queries to the user. 3. Test script. that you shared with the user. 4. Interview transcript. in a dialog format – remember to include line numbers. 5. Analysis including diagrams and problems identified. 6. Persona of the two users (like explained in class). For the suggested items below – choose only the ones where you may find some kind of digital control interface preferably with display. 1. Any desktop or web interface that has at least 30 controls, not counting web links. For web pages, it should have at least 10 pages (including product description pages). For desktop applications, it should have at least 5 different screens or dialog boxes. 2. Desk phone with speed dial 3. Answering machine with selective playing, deleting of recorded calls 4. Copy machine with 2-sided copying 5. Cell phone for placing calls using an address book 6. Cell phone for doing SMS using an address book 7. Cell phone address book management (add, remove, update addresses) 8. VCR or DVD/R: basic setup (which channels, clock, input source, record speed, etc.) 9. VCR or DVD/R: setting timed recordings (record in the future) 10. Cable TV or DishNetwork configuration and control interfaces 11. Data Projector configuration user interface (pick source, brightness, keystoning, etc.) 12. Conventional television with contrast, brightness, channels, input sources 13. High definition television with various wide-screen modes 14. Digital camera including taking pictures, specifying different resolutions, turning on and off the flash, etc. 15. Digital Picture Frame 16. Camcorder 17. Digital Watch 18. Microwave with cooking, defrost, set current time, timed cooking, etc. 19. Wall Oven, with bake, broil, self-clean, timer for timed cooking, etc. 20. Washing machine, with parameters for water temperature, different cycles, etc. 21. Dryer with parameters for different cycles, heat, cool down, etc. 22. Programmable Coffee maker 23. Digital refrigerator (?) 24. Robotic vacuum cleaner (speed, obstacle avoidance) 25. Conventional vacuum with digital controls 26. Digital video recorder (schedule recordings) (e.g., TIVO) 27. Digital music player (e.g., iPod) 28. Digital FM radio with presets 29. Universal remote control (programmable) 30. PC Music player with play-lists (e.g., Windows Media Player) 31. Augmented calculator (e.g., ability to see past computations, etc.) 32. Complex Alarm clock (set time, set alarm, multiple alarms, snooze) 33. Audiobook player (select book, navigate chapters) 34. Programmable Massage chair 35. Programmable light (brightness, weekly on/off schedule) 36. Programming lawn watering system, with timers and sensors 37. Voice recorder (play, delete, record, rewind) 38. Printer configuration (orientation, sides, color, scale) 39. Multi-function printer (print/fax/copy) 40. Wireless network chooser (select, security settings, on/off) 41. Movie schedule mobile web application (by movie, by location) 42. Stand-alone air purifier 43. Home heating and air conditioning (HVAC) controls (programmable) 44. Automobile heating and air conditioning (HVAC) controls 45. Automobile HD Radio 46. Stand-alone HD Radio 47. Automobile Satellite radio 48. Stand-alone Satellite radio 49. Automobile navigation system 50. Hand-held navigation system 51. Any digital medical device 52. ATM 53. Airport Ticket kiosk 54. Play/Movie Ticket kiosk 55. Photo printing kiosks 56. Vending machine for movies (like outside the Giant Eagle in Squirrel Hill) 57. Self-checkout system for supermarket (like at Target) 58. Programmable exercise equipment 59. PA lottery touch screen machine 60. Wireless Network Router setup (set up security, etc.)
UWP 22 Paper 2 – Open Letter Timeline Week 7 Tu: Introduce P2 Week 8 Tu: P2 Outline Week 8 Th: P2 Peer Review Week 9 Tu: P2 Rough Draft (I will read papers up to 3x per student) Week 10 Tu: Conferences Week 10 Th: P2 Final as part of your portfolio Course Outcomes to Meet ü Identify and apply writing strategies o a) analyze a writing task to determine necessary knowledge and skills understanding not just the topic, but also the purpose/genre of a writing assignment o b) self-evaluate writing according to assignment expectations o c) organize ideas and structure writing according to conventions of genre o d) translate feedback from peers and instructor into conscious action (revising using others' feedback and comments) ü Use evidence to achieve purpose o a) use source for specific purpose (to inform, explain, support) o b) understand and apply knowledge of the underlying values and practices of one citation system (attributing sources correctly and consistently) ü Use language to achieve purpose o b) develop sentences that show awareness of purposeful moves in line with conventions of a genre o d) write with detail and specificity Prompt: In 850-950 words: Write a formal open-letter to UC Davis faculty, informing them about 1) the experience of multilingual freshmen, and 2) what professors are already doing well and/or what professors can do to better help freshmen. If you want to tailor the prompt to your interests, talk to me. In 850-950 words: Write a formal open-letter to UC Davis faculty, informing them about 1) the experience of multilingual freshmen, and 2) what professors are already doing well and/or what professors can do to better help freshmen. If you want to tailor the prompt to your interests, talk to me. Sources You are required to use at least two of our readings (P1R1, P1R2, P1R3, P2R1, P2R2, or P2R3). Grading This paper will be included in your portfolio, which is worth 30% total. You will get an advisory grade on your rough draft. Extra Credit opportunity: If you submit your open letter to the California Aggie and it gets published, you will get 5 extra points added to your portfolio grade. [email protected]
COMP 3022: Algorithm Engineering Lab 5. Generating Random Data 2025 Generation of a random double Generate a random double number in [0, 1) 1 double rand_d () { 2 return rand () / ( RAND_MAX + 1.0); 3 } Generate a nonnegative inteer strictly smaller than bound. 1 int rand_range (int min , int max ) { 2 return rand () % ( max - min + 1) + min ; 3 } 4 int rand_bound (int bound ) { 5 return rand_range (0 , bound ); 6 } Generation of a random permutation All permutations of [1..n] have the same probability to be generated. The algorithm runs in O(n) time. 1 void random_perm (int perm [] , int n ) { 2 for ( i = 0; i < n ; i ++) 3 perm [ i ] = i +1; /* initialization */ 4 for ( i = n - 1; i > 0; i - -) { 5 j = rand_bound ( i ); /* random index 6 int tmp = perm [ i ]; 7 perm [ i ] = perm [ j ]; 8 perm [ j ] = tmp ; 9 } 10 } rand_d ()) 2 generate ( A ); 3 else 4 generate ( B ); Bernoulli process () Events occur independently. The outcome of each event: A (with probability p) and B (with probability 1−p) Example: coin toss; Erdős–Rényi graphs () 1 X = - ln ( rand_d ()) / lambda ; Poisson process () Events occur independently and at a constant average rate: λ events per s/m/h Example: MTR arriving at a stop; packets arriving at a router To generate the waiting time X for the next event: Tasks Download random.c. Test the random_perm function and record the result. Finish function sample_d. Add code in the main function to test sample and sample_d. Optional tasks Conduct experiments for n > 5. I used a simple trick in the main function, which cannot work for n = 6. You need to . Conduct experiments on generating ordered real numbers.
Complex Networks (MTH6142) Formative Assignment 5 • 1. Random networks in the G(N, p) ensemble Assume that p = a/Nz , where a > 0 and z ≥ 0, and a, z independent on N. (a) Determine the average degree 〈k〉 in the limit N → ∞ for the following values of the parameters (i) a = 0.5, z = 1; (ii) a = 2, z = 1; (iii) a > 0, z = 2; (iv) a > 0, z = 0.5. (b) In which of the above cases does the random network contain a giant component in the limit N → ∞?. (c) Given p = a/Nz with generic values of a > 0, z ≥ 0 determine the average degree 〈k〉 in the large network limit N → ∞. (d) Determine the conditions on a and z for these random networks to be subcritical, i.e. with a fraction S of nodes in the giant component given by S = 0 in the N → ∞ limit. (e) Determine the conditions on a and z for these random networks to be supercritical, i.e. with a non vanishing fraction S of nodes in the giant component (S > 0) in the N → ∞ limit. (f) Determine the conditions on a and z for which these random networks are critical, in the large network limit, i.e. in the limit N → ∞.2 • 2. Random networks in the G(N, p) ensemble with p = c/(N − 1) where c > 0. (a) Calculate the average number of triangles in the network, by evaluating first the number of ways to select 3 nodes out of N nodes, and secondly the probability that the selected nodes are all connected to each other. (b) Show that in the limit N → ∞ the average number of triangles in the network is This means that the number of triangles is constant, neither growing or vanishing, in the limit of large N.
Department of Electrical and Electronic Engineering EIE2105 Digital and Computer Systems Tutorial 3: Combinational Logic II Q1. The truth table of a logic circuit is given as follows. a. Implement the circuit with 8-to-1 multiplexers. b. Implement the circuit with a 3-to-8 decoder and, if necessary, some additional OR gates. Q2. The truth table of a priority encoder has been given as follows. a. What is the implied priority order of inputs D0, D1, D2 and D3 in this encoder? b. Modify the truth table such that the priority order becomes D2 > D3 > D1 > D0. c. Based on the modification result obtained in (b), write down the Boolean functions for outputs A1, A0 and V. You should simplify the functions with K-map in your answer (show the steps in details). d. Draw the circuit diagram of the modified encoder by using simple logic gates (i.e., 2-input AND, 2-input OR, and NOT gates). e. Can you reduce the number of logic gates by gate sharing? Give the number of used logic gates and draw the corresponding circuit. f. What is the literal cost and the gate input cost of your circuit at the end?
ELEC222 and ELEC273 Lesson 5: Sustainable Development and Ethics Session aim In this session, we will: • Discuss ideas for the content of your Sustainable Development and Ethics assignment • Analyse examples of each section for content, organisation and useful language • Plan paragraphs for each section The assignment structure The structure and guidance for the assignment can be found in the Sustainable Development and Ethics – Assignment PDF in the EE-Year 2 Canvas. 1. Look at the guidance and discuss the questions below. • What are the sections of the SDE assignment? How much is each worth? • How many pages is this assignment in total? (Yes, including references.) • What does it say about writing in the ‘third person’ on page 3? • Which page has the Chief Executive’s concerns to consider? Familiarisation with the Regulations You will need to consider the sustainable development and ethical implications of your project in detail with your group. For this lesson we will brainstorm some ideas. 1. Consider your project and the regulations that may apply to it. • How it's made, what it's made of, how it's used, or how it's thrown away. • Look at the websites below (from the assignment instructions) and try to find anything that is relevant to your project. • If they don’t apply, consider other possible areas of regulations that might. UK laws: • https://www.gov.uk/guidance/rohs-compliance-and-guidance • https://www.gov.uk/government/organisations/office-for-product-safety-and-standards • https://www.gov.uk/electricalwaste-producer-supplier-responsibilities • http://www.hse.gov.uk/waste/waste-electrical.htm Sustainable development goals (UN and UoL, from the lecture slides): • Take Action for the Sustainable Development Goals - United Nations Sustainable Development • Sustainability - The University of Liverpool Section 1 Regulatory considerations 1. Read the guidance from the Assignment Instructions document again. What does Section 1 need to include? Above: Screenshot of the Section 1 guidance from the Assignment Instructions document. 2. Read the example Section 1 text below and answer the following questions. a) Which regulations are relevant to the project, and what do they cover? b) What project-specific details do the writers include? Consider materials, components, disposal, documentation, and compliance. c) How is the section structured? What does each paragraph focus on? d) Identify useful language related to: regulations and compliance, hazards and risks, effective academic sentence structures. Example Section 1 text Regulatory considerations The Waste Electrical and Electronic Equipment (WEEE) Directive regulates the disposal and recycling of electronic products [1]. The robotic arm includes electronic components, such as the Arduino microcontroller, wiring, and camera, which must be recycled through certified e-waste facilities to prevent landfill waste. WEEE compliance requires a clear disposal plan for these components, ensuring they do not contribute to environmental harm [1]. The Restriction of Hazardous Substances (RoHS) Directive limits the use of toxic materials like lead, mercury, and cadmium in electronic products [2]. Since the robotic arm’s circuit components were sourced from CE-marked suppliers, they are expected to comply with RoHS standards [2]. The 3D-printed plastic structure is not covered under RoHS or WEEE regulations, as it is not an electrical component. However, certain plastic additives or coatings could fall under RoHS restrictions if they contain hazardous substances. While common filaments such as PLA, ABS, and PETG are generally RoHS-compliant, checking supplier documentation for material composition would be good practice. RoHS compliance requires supplier documentation, such as a Declaration of Conformity (DoC), verifying that components meet regulatory requirements [2]. Manufacturers may also obtain a Certificate of Compliance (CoC) from suppliers to confirm that parts are free from restricted substances [2]. WEEE compliance necessitates a clear end-of-life disposal plan for electronic components to ensure proper recycling and waste reduction [1]. 3. Consider your own project. Make notes about the following: 1. Which regulations could apply to your project? • Look at the websites listed in the assignment brief. Which laws apply to your project? • Does it involve restricted materials, product safety, or disposal regulations? (RoHS, WEEE) • Does it involve data protection, cybersecurity, or privacy concerns? (GDPR may apply to software-based projects) 2. Which parts of your project are affected by regulations? Physical products: • Are any materials restricted under RoHS? • How will end-of-life disposal and recycling be managed (WEEE)? • Are there safety concerns during manufacturing or use? Software products: • Does your project store or process personal data? • Would it need to comply with laws on data security or ethical AI use? 3. How would you ensure compliance? • What evidence or documentation would be needed (e.g., supplier certifications, product testing)? • Would your project need design modifications to meet legal requirements? 4. What useful language from the model text could you adapt? Section 2 Implications of large-scale manufacture For this section, you will need to imagine that your project is going to be massproduced or used by many people. 1. Read the guidance for Section 2 in the Assignment Instructions and consider the following. a) What are the five areas it asks you to cover in your answer? b) Which are most relevant to your project if the company started to massproduce it on a larger scale? c) For software projects: What does the guidance say about software? Consider if your software was sold to lots of customers and used around the world. Above: Screenshot of the Section 2 guidance from the Assignment Instructions document. 2. Read the example Section 2 below and answer the following questions. a) Which of the five assessment points are covered, and how? b) How is the section organised? c) What useful language is included? (Look for words related to sustainability, ethics, regulations, and risks.) Example Section 2 text The robotic arm is not inherently a sustainability product, but its manufacturing process can be optimised for environmental impact. A key concern is 3D printing waste, as excess plastic is often trimmed during production. The sustainability of the 3D-printed parts depends on filament choice. PLA is biodegradable but hard to recycle, while ABS and PETG are recyclable under certain conditions. However, if mass-produced, the arm may use injection moulding or other techniques, which could change material selection and sustainability impact. Choosing a durable and recyclable material would improve the product's long-term footprint. Despite these challenges, 3D printing improves resource efficiency by using precise material amounts and reducing waste. On-demand production also limits excess inventory and may reduce energy and transport needs. The robotic arm provides a broader sustainability benefit by reducing human exposure to hazardous waste. By enabling safe remote operation, it minimises health and environmental risks, making it valuable for waste management and industrial applications. Given the product’s intended use for hazardous waste removal, and the potential risks to human safety and the environment, the company should provide safety certification or training to prevent misuse and accidents. Sales restrictions may be needed to ensure the product is sold only to industries where hazardous material removal is required. As a remotely controlled device, the arm must be protected from unauthorised access. While not internet-connected, safeguards should prevent signal interference, ensuring safe handling of hazardous materials. To improve sustainability and security, there are three measures the company needs to consider. First, select durable, recyclable materials for large-scale production. Second, implement a take-back scheme under the WEEE Directive to ensure responsible electronics disposal. This is a legal requirement. Third, ensure security safeguards to prevent unauthorised access to the arm control system. 3. Consider your own project. Make notes about the following: Sustainability in manufacturing: • Hardware projects: What materials or processes will be used in large-scale production? • Software projects: How much energy does your software require to run? Does it create unnecessary processing load? • Could your project be made using more sustainable materials or methods? • Would mass production change how sustainable it is? Wider sustainability impact (health, safety, security): • Could your project help protect people or the environment? • Does it reduce waste, pollution, or energy use? • Are there any health or safety risks that need to be considered? Ethical sales & responsible use: • Who should be allowed to buy and use your project? • Are there risks if it is sold to the wrong users or industries? • Should customers need training or certification before using it? Misuse & security risks: • Could your project be misused, hacked, or cause harm? • Does it need built-in security measures? • Are there risks if people use it incorrectly? Design improvements for sustainability & security: • Could your project be made more sustainable (e.g., reusable materials, recycling options)? • Would it need a take-back or disposal scheme at end-of-life? • What safety or security improvements would be needed? Section 3 Implications of follow-on products/markets For this section, you will need to imagine that your project can be expanded, adapted or used for other projects. 1. Read the guidance for Section 3 in the Assignment Instructions and consider the following. a) What is your role in the company and what are the two purposes you have for writing this section of the report? b) What do you need to consider in terms of expanding the project? c) What does the guidance say about the ‘green market’? d) What is the final point to consider about SDE issues? Above: Screenshots of the Section 3 guidance from the Assignment Instructions document (there is a page break in the guidance document). 2. Read the example Section 2 below and answer the following questions. a) Identify where the text discusses new products or markets, sustainability implications, ethical concerns, and growth-related risks. b) How is the section structured? What does each paragraph focus on? c) What useful language is included? Consider how new opportunities, risks, and improvements are introduced and justified Expanding the capabilities of the Arduino Bot presents opportunities for new products and applications. The robotic arm could be adapted for delicate precision tasks in medical robotics, such as assisting in minimally invasive procedures. Alternatively, it could be integrated into automated recycling facilities, using cameras and sensors to sort waste efficiently. These developments would require enhancements such as higher-resolution imaging, more advanced motion control, and improved durability, opening the project to new industries. From a sustainability perspective, these adaptations introduce both benefits and challenges. If used in automated recycling, the arm could contribute to waste reduction by improving sorting accuracy. However, higher energy demands from advanced motors and sensors could increase its environmental footprint. Material selection would also become more critical—while 3D printing was suitable for prototyping, a durable and recyclable material like aluminium or reinforced bioplastics would be more appropriate for long-term use. Ethical concerns must also be addressed as the technology evolves. If the arm becomes wireless or integrates with external networks, the risk of hacking increases, potentially leading to unauthorized use or system failures in critical environments. Implementing secure encryption protocols, restricted user access, and fail-safe mechanisms would be essential. Additionally, ensuring that only trained operators use the robotic arm—through licensing or mandatory safety certification—could mitigate risks in sensitive applications. While expansion offers commercial and industrial advantages, it also raises sustainability and security concerns. Increased production could lead to higher electricity consumption and electronic waste, particularly if follow-on products rely on non-recyclable components or complex electronic systems. To address this, improvements such as modular design for easier repairs, energy-efficient motors, and adherence to WEEE disposal requirements should be integrated into future developments. 3. Consider your own project. Make notes about the following: Follow-on products and market opportunities • How could your project be adapted, upgraded, or expanded into a new product? • Could it be used in a different industry or application? Sustainability considerations • If the project expands, would sustainability challenges change? • Would new materials, energy use, or waste management become important factors? Ethical concerns in new products or markets • What ethical issues could arise if the product is developed further? • Would additional safety, security, or accessibility measures be needed? Challenges of growth and profitability • Could expanding the project introduce new sustainability or ethical risks? • Would scaling up require different regulations, security measures, or responsible business practices?
Manufacturing Process Improvement 6040MAA Improving the Manufactring process at Arrow Industries Assignment Task Arrow Industries is a manufacturing company of tractor components for OEMs. Over the last two years Arrow industries have lost two of their major orders to overseas competitors. In an attempt to improve the manufacturing performance to be able to continue in a competitive environment, the company has employed you, as an expert in Lean principles, to turn around their manufacturing performance. Production Processes An initial analysis of the production data identified that the Tubular manufacturing area is one of the more profitable areas of the company, in particular the product family that contains the two parts, TB115 and TB116 which are high value, high volume, and runner products. Arrow industries is currently producing to mass production principles. The machines have a functional layout (Figure 1) and produce parts in large batches. All moves within the same section are done manually, using trolleys. The key manufacturing processes include sawing, turning (lathe work: lathe 1 and lathe 2), milling, painting through to assembly and packing. The painting process is perform. in a separate building in batches of 500. Figure 1. Current facility layout plan Customer Requirements · 12,500 tubes per month o 5,700 TB115 o 6,800 TB116 · Products are delivered every day to the customer by lorry. Work Time · 20 working days in a month · Operating a 3 shift system in all production operations · 6am-2pm, 2pm-10pm, 10pm-6am · 30 mins lunch and two 15 min breaks per shift Production Control information Supplier Brooks ltd provides the metal raw material on weekly bases. Every Wednesday morning, MRP system at Arrow industries sent a notification to Brooks ltd for the requirements of raw material from the approaching week. Brooks ltd deliver straight to Arrow industries on Friday. Weekly schedule are generate by the MRP system and each department receives a weekly instruction by email. Daily shipment is required by customer. PROCESS INFORMATION The processes to produce the tubes TB115 and TB116 occur in the following order: Processes Cycle Time (secs) Change Over time (mins) Process Availability Quality Pass rate Saw (shared resource ) EPE 2 weeks 55 1.5 97% 99% Lathe 1 150 11 84% 94% Lathe 2 130 2 95% 85% Mill 82 1.1 90% 95% Painting (in a separate building) 1200 (20 mins) 15 95% 95% Assy Carrier & Inner 68 None 100% 95% Final Assembly 175 None 95% 83% Packing 75 None 100% 98% WIP (Inventory) · The raw material before the first process ( Saw) it is estimated to stay 5 days (waiting ) before passing to their respective processes. · The observed WIP inventory after each process are: Processes WIP Saw 1,500 TB115 1,100 TB116 Lathe 1 600 TB115 750 TB11 Lathe 2 400 TB115 850 TB116 Mill 1200 TB115 1350 TB116 Painting (in a separate building) 790 TB115 640 TB116 Assy Carrier & Inner 360 TB115 370 TB116 Final Assembly 590 TB115 450 TB116 Packing 820 TB115 630 TB116 · Due to the transportation required before and after the painting process there are two extra WIP inventories: One before the painting process and another one before the Assembly of the carrier and inner as follows: o Before Painting: 900 TB115 1,200 TB116 o Before Assembly Carrier and Inner : 940 TB115 750 TB116 Despatch Department The observed inventory of finish goods observed ready to be sent to customers is: 4,200 TB115 3,800 TB116. Assignment tasks and marks distribution: 1. Using the data provided develop the current state map for manufacturing facility. (15 marks) 2. Calculate the timeline, lead times, Takt time and VA ratio. (30 marks) 3. Using the information provided and lean tools knowledge, critically appraise the current state of Arrow Industries, this should include Future state map with new recommendations. (45 marks) 4. Report structure, presentation style. and neatness. (10 marks) · Design and optimize the current production process that meets customer requirements. · Appraise the manufacturability of the component based on both technical & process compliance assisted by virtual tools. The report to include and identified individual student contribution (2000 – 2500 words). Submission Instructions: You will submit the assignment on or before the due date. The submission must be in Microsoft Word, other file types will not be marked, please submit on link on turn it in. If you are graded as a pass on any of your submission attempts you will have completed the Core assessment part of this module. Development of Skills and Attributes: · Act with integrity o Have awareness of how to act in a professional environment o Take pride in my work and my achievements, leading by example · Adapt my approach o am resilient with the ability to self-reflect and react positively to change, challenging situations, or areas of uncertainty · Think Creatively o want to continue learning, recognising that personal development is ongoing and life-long. · Communicate effectively o Collaborate and work with other well o Have awareness and appreciation and respect for diversity of background culture and thought
Economics 1 — Semester 2 — Tutorial Sheet 6 — Week 7 Labour Required reading: - Recent lecture notes - Frank & Cartwright, Microeconomics and Behaviour, Chapter 15 Homework: - To earn full credit for tutorial homework you must upload your attempt at tutorial homework to Learn by 5pm on the Sunday before the tutorials occur. - The attempt should be equivalent to at least two sides of handwritten A4 and should be clear enough to read. - Your homework does not need to be complete, and indeed it does not even need to be correct. You just need to show that you have made an honest attempt. As long as you have shown an honest attempt, you will get credit, and as long as you do this for 14 of the 18 tutorials during the year, you will get full credit. Recordings: - Questions marked with an asterisk* have video solutions recorded by Sean, which will be released after the Sunday 5pm submission deadline. Because the asterisk questions are covered in video, they will mostly not be covered within the tutorials themselves. Tutorial Questions Q1. Eurostat estimates the following data on the average hourly labour costs across the European Union. Comment on anything that strikes you in the graph. What do you think explains such large differences? * Q2. The economy of Japan is widely considered to have had a “lost decade” starting in about 1991. GDP per capita had increased rapidly in the 1980s, but much more slowly in the 1990s (see the solid blue line in the graph below). But when we look at GDP per hour worked, we see a different picture – roughly the same pattern as GDP per capita before 1991, but a much less pronounced slowdown afterwards. Why do you think the series diverged? (Hint: why is this question being asked in a tutorial sheet about labour?) * Q3. Suppose that there are two firms, one of which is in a competitive industry, and one of which is in an imperfectly competitive industry. What is different between these two firms in the way they value (and are willing to pay) a marginal (additional) worker? * Q4. If a would-be monopolist acquired most of the firms in a formerly competitive industry, worked to construct barriers to entry against new firms, and gradually accumulated more and more market power, how would the quantity of labour employed be affected? * Q5. What does economic theory suggest about the prevalence of unfair discrimination in perfectly vs. imperfectly competitive industries (or in public sector employment)? * Q6. Members of two groups, the blues and the greens, each have productivity values that range from £10 to £30/hr. Even though the ranges are the same, however, the averages are different: the productivity of the blues is £12/hr and the corresponding average for the greens is £24/hr. It is easy for anyone to see whether an individual is blue or green, and it is common knowledge that the group average productivities are £12/hr and £24/hr, but it is not easy to see how productive any individual is. A new productivity test has been devised though, and 1/3rd of the time it is able to give a correct measurement of an individual’s productivity, but the other 2/3rds of the time it gives random productivity value drawn from the relevant colour-group distribution. a) Assuming labour markets are competitive, how much will a blue with a test value of 18 be paid? b) How much will a green with the same test value be paid? c) Is it correct to say that statistical discrimination accounts for why the greens, as a group, are paid more than the blues? Q7. Given the information about the number of workers (L) compared to their marginal products (MP) in the following table, fill in the value of the marginal product of labour (VMP) for price P = 4. Find the perfectly competitive firm’s optimal labour demand for a wage w = €4/hr. MPVMP Q8. In his current job, Smith can work as many hours per day as he chooses, and he will be paid €1/hr for the first 8 hours he works, €2.50/hr for each hour over 8. Faced with this payment schedule, Smith chooses to work 12 hr/day. If Smith is offered a new job that pays €1.50/hr for as many hours as he chooses to work, will he take it? Explain. Q9. Consider the following two antipoverty programs: (1) A payment of €10/day is to be given this year to each person who was classified as poor last year; and (2) each person classified as poor will be given a benefit equal to 20% of the wage income they earn each day this year. a) Assuming that poor persons have the option of working at €4/hr, show how each program would affect the daily budget constraint of a representative poor worker during the current year. b) Which programme would be most likely to reduce the number of hours worked? * Q10. Suppose vacation time comes in one-week intervals, and that the total willingness to pay for total vacation time by younger and older workers in a competitive industry is as given in the following table: Total Willingness to Pay Total Younger Older vacation workers workers time, weeks 1 1000 2000 2 1900 3000 3 2700 3700 4 3400 4200 5 4000 4500 6 4400 4700 a) Suppose VMP = 750/wk for younger workers, 900/wk for older workers, and that existing firms give all their workers, young and old, five weeks per year of vacation time. Can these firms be maximizing their profits? If so, explain why. If not, say what changes they should make, and how much extra profit will result. b) Suppose that the government now taxes 1/3 of everyone’s wages and uses the money mostly on transfers (pensions, benefits etc.) and public goods (roads, defence, the national broadcaster, etc.), and that these accrue to the public regardless of how much they work or how much tax they pay. Workers are still willing to pay the same amount per week of holiday (they don’t feel meaningfully any poorer because roughly the same amount of money is still spent on them), but now they only get at most 2/3 of their VMP in wages. What happens to the optimal amount of holiday time? * Q11. Based on the discussion in the textbook, what do you think might be some reasons why unemployment has on average been so much higher in Europe in the 21st century than it was in the late 1960s and early 1970s? Note particularly the comparison of three continental countries (Sweden, France and Italy – bold lines in green/blue) with the USA and UK (thin lines in orange/red). * Q12. Goto Marginal Revolution University’s website and watch the 4-minute video3 “The Missing Men” by Tyler Cowen. (a) What was the main finding about participation rates discussed in the video? (b) Which factors were given as related to the change in male participation rates? (c) Which factors were dismissed as explanations for the change? * Q13. In contrast to America’s ‘missing men,’ Japan has made great strides in increasing female labour force participation in recent years. As recently as the year 2000, Japanese female labour force participation was about 10 percentage points lower than the US rate. Now, though, the Japanese rate is significantly higher (see graph below). For an explanation of why the Japanese female participation rate has risen, please read the article “Japanese women are working more, but few are getting ahead” (from the Economist on 18/11/2017 – reproduced along with this tutorial sheet). a) What are some of the factors given in the Economist article to explain the increased female participation rate? b) What are some non-explanations for the fact that Japanese women are more likely to be in the labour force than American women? (I.e. things you might have thought would explain it, but which don’t actually explain it.) c) Given your answers to parts (a) and (b), can you understand why these issues might not be discussed in the textbook? Discuss. * Q14. A monopsonist’s demand curve for labour is given by w = 12 − 2L, where w is the hourly wage rate and L isthe number of person-hours hired. a) If the monopsonist’s supply (AFC) curve is given by w = 2L, which gives rise to a marginal factor cost curve of MFC = 4L, how many units of labour will they employ and what wage will they pay? b) How would your answers to part (a) be different if the monopsonist were confronted with a minimum wage bill requiring them to pay at least €7/hr? c) How would your answers to parts (a) and (b) be different if the employer in question were not amonopsonist but a perfect competitor in the market for labour? * Q15. Please read the Economist article “What harm do minimum wages do?” to answer the questions below. a) On the question: “What harm do minimum wages do?”, how (and why) has the consensus among economists changed since the early 1990s? b) Are there any structural reasons why the real effect of the minimum wage on employment might have changed overtime? Q16. A monopolist can hire any quantity of labour for €10/hr. If their marginal product of labour is currently 2, and their current product price is €5/unit, should they increase or decrease the amount of labour hired? Q17. Acme is the sole supplier of security systems in the product market and the sole employer of locksmiths in the labour market. The demand curve for security systems is given by P = 100 − Q, where Q is the number of systems installed per week. The short-run production function for security systems is given by Q = 4L, where L isthe number of full - time locksmiths employed per week. The supply curve for locksmiths is given by W = 40 + 2L, where W is the weekly wage for each locksmith. How many locksmiths will Acme hire, and what wage will it pay? Q18. The Ajax Coal Company is the only employer in its area. Its only variable input is labour, which has a constant marginal product equal to 5. Because it is the only employer in the area, the firm faces a supply curve for labour given by w = 10 + L, where W is the wage rate and L isthe number of person-hours employed. This supply curve yields the marginal factor cost curve MFC = 10 + 2L. Suppose the firm can sell all it wishes at a constant price of 8. a) How much labour does the firm employ, how much output does it produce, and what is the wage? b) Suppose now the firm sells a special kind of coal such that it faces a downward-sloping demand curve for its output. In particular, assume that Ajax faces the demand curve given by P = 102 − 1. 96Q. How much labour does the firm employ, how much output does it produce, what price does it set for the output, and what is the wage? c) Assume that Ajax still faces the demand curve P = 102 − 1. 96Q, but now further assume that Ajax has five labourers under contract to produce coal at a wage of 15. If Ajax has the option of hiring additional labourers at a higher wage without increasing the wage to the five labourers already under hire, will Ajax increase its labour force? Explain. Q19. A firm produces output according to the production function Q = K2/1 L2/1 . If it sells its output in a perfectly competitive market at a price of 10, and ifK is fixed at 4 units, what is this firm’s short-run demand curve for labour? Q20. How would your answer to the preceding problem be different if the employer in questionsold his product according to the demand schedule P = 20 − Q? Q21. A and B face the choice of working in a safe mine at €200/wk or an unsafe mine at €300/wk. Output is the same at each location, and the wage differential between the two mines reflects the €100/wk costs of the safety equipment in the safe mine. The adverse consequence of working in the unsafe mine is that life expectancy is shortened by 10 years (assume there is no other adverse effect) . A and B have utility functions of the form ui [xi,si, R(xi)] = xi + si + R(xi) for i = A, B, where xi is i’s income per week in euros, si is 200 if the mine is safe and 0 otherwise, and R(xi) = 200 if xi > xj, 0 if xi = xj and −250 if xi < xj. a) What does it mean for workers to have preferences like the ones characterised by the R(xi) function just described? Why might workers have such a preference? b) If the two workers choose independently, which mine will they work in? Explain. (Hint: Use the utility function to construct a game theory payoff matrix like the one described in the text.) c) If they can negotiate binding agreements with one another at relatively low cost (e.g. by forming a union), will their choice be the same as in part (a)? Explain.
