For assignment questions we will give you a sample executable — this is our solution to the problem which you will be tested against. You should use this assignment question to check what the expected output is. If you ever have a question “What should our program do when XYZ” the answer is what does the sample executable do? With the notable exception of invalid input. Breaking the rules of what the program expects is considered invalid input and wouldn’t be a valid test case unless we explicitly told you what your program should do to handle such a problem. noindentNote: These sample executables are compiled on the student environment — that means they are only guaranteed to work on that environment. They will likely not work on your local machine, and will only work on Linux environments that are similar to the student environment. Most of the questions of this assignment are steps to building a larger script which will help you throughout this course with testing your own assignment code. We suggest you start early so that getting stuck on an early question does not mean you won’t be able to finish later questions. Introductory Information: Most of this assignment is about writing a script in bash that will help you test your own programs to come. When testing your programs you’ll want to have many varied test cases. Running many tests manually can be a pain, so instead you’d like to automate it. So we will use a simple system.We will have a text file which will contain the names of all our test cases. This test file we’ll call our “test set file”. The contents of this file is, sort of, the names of each of our test cases separated by whitespace. For example sample set.txt might look like: funTest intTest floatTest Then, within your current working directory you would need the files required for each testcase test1, test2, and test3. For our purposes each test will be made up of four files, an input file (.in), a command line arguments file (.args), an expected output file (.out), and a description file (.desc).Each of the files of a test case are used to define what that test case is. The test case is meant to test one particular run of a program. The .desc file contains a description of the test case, and perhaps its purpose. The .in file contains everything, that if running that test manually, we would type into standard input when the program asks us for input. The .args files contains any command line arguments we’d like to pass to the program. Finally, the .out file is the expected output our program should generate when we run this test case — this is the file we’ll use to check if our program passes the test case. All 4 of these files are written by you, the programmer who istesting their own program. We’ll give you some samples in this assignment however. We’ll call the names of our test cases, which are in our test set files, file stems. That is because the names of our tests are everything that is going to come before our file extensions .in, .args, .out, and .desc. That means, for example, given the test named funTest shown above we would have the files funTest.in, funTest.args, funTest.out, and funTest.desc in our current working directory when we run our testing script. However, the stems don’t have to be only local paths — they can also be any filepath to a file stem we see fit, this is demonstrated in the first question.1. This question is about writing a bash script — you should not write any C code for this question. In this question you are writing a bash script named testDescribe which expects one command line argument which is a filepath. The filepath testDescribe receives should be to a test set file. Here is an example of the contents of a test set file named set1.txt: test1 /home/rob/foo/test2 ./test3 test4 The strings inside the test set file we’ll call file stems. These strings are meant to represent every part of a filepath except for the file extension. You’ll notice that the contents can be absolute or relative paths — this should not affect how you write your script. Your script must iterate through the contents of the test set file and for each file stem it should perform the process described below. Note that in each place the process says stem it means each of the strings contained within the test set file. (a) If no command line argument is given for the test set file print a usage message to stderr (b) If the file stem.desc does not exist print out the message stem: No test description (c) If the file stem.desc does exist print out the contents of the file stem.desc (d) Make sure steps (b) and (c) are repeated for every stem in the test set file For example consider your current working directory contains the file test1.desc with the following contents: This test uses negative inputs And your current working directory contains the file test3.desc with the following contents: This test using zero as an input And your file system contains the file /home/rob/foo/test2.desc with the following contents: This test uses positive inputs Then the output of executing your script as follow $ ./testDescribe set1.txt would be This test uses negative inputs This test uses positive inputs This test using zero as an input test4: No test description Hint: You may need some conditions we didn’t talk about in class for your if statements in bash. Here’s a useful website with lots of bash tips https://devhints.io/bash. Deliverables: For this question include in your final submission zip your bash script file named testDescribe 2. This question is about writing a bash script — you should not write any C code for this question. In this question you will be writing a bash script runInTests which expects two command line arguments, the first command line argument is a command to run, and the second command line argument is a test set file (as described in question 1). Below is an example run of your script: ./runInTests wc wc_set.txt Consider the file wc set.txt contains the following: wcTest1 wcTest2 Your script runInTests will iterate through the file stems in the test set file and perform the following set of steps for each file stem. Note in all output shown you are not meant to be printing literally stem, but rather the current file stem you are considering. (a) Run the command given to your script while redirecting input from the file stem.in (b) Compare the output from that execution of the command to the contents of the file stem.out (c) If the output does not differ, then output Test stem passed (d) If the output does differ, then output Test stem failed, followed on the next line by Expected output:, followed on the next line by the contents of stem.out, followed on the next line by Actual output:, followed on the next line by the output produced by running the given command with the given input file. Try out sample executable with the sample command above with the provided files to see a sample output. Note: If your program creates any files they must be temporary files. They must also be deleted once you are finished with them. Hint 1: Consider using the diff command to help you solve this problem. Remember you can read the exit status of the previous command you executed with $? — read the man pages of the diff command to see if the exit status could help you. Hint 2: If you want to run a command, but don’t want the output produced by that command to print, you can redirect that commands output to /dev/null. Deliverables For this question include in your final submission zip your bash script file named runInTests 3. This question is about writing a bash script — you should not write any C code for this question. In this question you will be updating your script runInTests from question 2, your new updated script should be named runTests. The changes you will need to make to your previous question will be quite small if you wrote your solution well. Our sample solution only needed a change to one line. Update your previous solution so that when it runs each test case not only does it redirect input from stem.in but it also passes command line arguments to the command which are the contents of the file stem.args. For example, if one of your command was wc and one of the stems was wcTest1 and the contents of the file wcTest1.args were as follows: -l -w Then ultimately, for that test case, you’d run the command wc -l -w < wcTest1.in Of course, this needs to be done for each test case. You are not literally writing -l -w in the command, as the arguments to pass are the contents of the .args file. Hint: You’ll need to place the contents of each args file directly in a command — what have you seen in class that could help solve this problem? Deliverables For this question include in your final submission zip your bash script file named runTests 4. For this question you will be writing a C program. In this question you will be writing a simple C program divisors.c Your program should: Read one integer from standard input. Print every divisor of the read in integer, from smallest to largest, with a space inbetween every divisor. You must not print any additional spaces, including before the first divisor or after the last divisor. Your program should print a newline after the last divisor. For example, if your program was executed with the input 256 it would print: 1 2 4 8 16 32 64 128 256 You should test your program with your runTests script from the previous question. Deliverables For this question include in your final submission zip your c file named divisors.c 5. Extra exercise: This question is not for any marks — it is additional steps you can take to make your runTests program more helpful and user friendly. Some programs only read input, some only use command line args, some will use both. Our runTests looks for an .in and .args file for every single stem — we may not want that. Update your script so it only provides input or args to the command when the corresponding files exist. We may have forgotten to create a given output file for our test set, right now runTests assumes that every .out file exists. Update your script so that it prints a meaningful error message when a .out doesn’t exist. Consider your first program testDescribe, those descriptions could be handy to view for each test case. Consider updating your runTests script so that when printing out if a test failed or passed it also prints out description of that test. In the real world you’ll have to create your expected outputs yourself since you won’t have an already compiled executable of the code you’re trying to write. In this class you will be given sample executables for the programs you need to write, so take advantage of this! Create a new version of your runTests script that takes a third argument, the sample executable, and instead of using .out files this version compares the output of the two executables provided for each test case. How to submit: Create a zip file a1.zip, make sure that zip file contains your three bash scripts testDescribe, runInTests, runTest, and your C file divisors.c. Assuming all four of these files are in your current working directory you can create your zip file with the command $ zip a1.zip testDescribe runInTests runTests divisors.c Upload your file a1.zip to the a1 submission link on eClass.
EECS 551 Midterm Exam, 10/12/2022, 6 – 8 pm 1. If A, B, C, D are matrices such that the product ABCD is defined (conformable), then (ABCD)′ = D′ C′B′A′ . (2 pts) True False 2. If P is an orthogonal projection matrix, then ‖(I − P)x ‖2 ≤ ‖x ‖2 (2 pts) True False 3. If Y and Z are both unitary matrices and B = YAZ, then B and A have the same singular values, assuming the matrix sizes match. (2 pts) True False 4. If x ∈ ℝ3 andy ∈ ℝ4 are nonzero vectors, then the nullity of xy′=2 (2 pts) True False 5. Let b1, … , bN be an orthonormal set of vectors in FM and define matrix B = [b1, … , bN ]. Then ‖Bx‖2 = ‖x ‖2 for any x ∈ FN . (2 pts) True False 6. For A = [3 −4], ‖Ax‖2 is maximized for unit norm x when (2 pts) True False 7. If B is an orthogonal projection matrix and B is also an orthogonal matrix, then B = I. (2 pts) True False 8. If A+ = A′ then A has orthonormal columns. (2 pts) True False 9. If A is invertible, then AA+ = I (2 pts) True False 10. Let A be a Hermitian symmetric matrix and Q be a unitary matrix. If x is a unit-norm eigenvector of A, then Q)1x is a unit-norm eigenvector of B = Q′AQ. (2 pts) True False 11. If x andy are two non-zero vectors in ℂN, then ‖x + y‖2 = ‖x ‖2 + ‖y‖2 , if y = αx for any non-zero α ∈ ℝ . (2 pts) True False 12. Let b1, … , bN be a set of non-zero vectors in ℝN that are all pairwise perpendicular to each other. Then the matrix B = [b1, … , bN ] is an orthogonal matrix. (2 pts) True False 13. If A is an M × N matrix with rank N, where M ≥ N, then A+A = I. (2 pts) True False 14. If A is an M × N matrix, then R(A′) = R(A′A). (2 pts) True False 15. If A is an M × N matrix, then R(A) = R(AA+ ). (2 pts) True False 16. The matrix for which P2 = I, has all non-zero eigenvalues. (2 pts) True False 17. Define the matrix A ∈ R2N×2N such that for any x ∈ RN andy ∈ RN : Then the matrix A is idempotent. (2 pts) True False 18. If B is a normal matrix and z is any unit-norm eigenvector of B, then there is an SVD of B where z is one of the left singular vectors. (2 pts) True False 19. If A is an M × N matrix with rank N, where M ≥ N, then minx ⅡAx — yⅡ2 = 0. (2 pts) True False 20. If C = [A B] then minx ⅡCx — yⅡ2 > minz ⅡAz — yⅡ2, assuming dimensions match appropriately. (2 pts) True False 21. If B is a 200 × 400 matrix with rank 100, then: (2 pts) a. dim]R(B)^ = 100 b. dim]R (B)^ = 100 c. dim]N(B)^ = 100 d. dim]N (B)^ = 100 e. The number of distinct singular values is at least 2 22. When the unit-norm vector x that maximizes ‖Ax‖2 is: (2 pts) a. [1 2]'/√5 b. [6 4 2]'/√14 c. [2 4 6]'/√14 d. [2 1]'/√5 e. [3 2 1]'/√14 f. None of the above 23. The value displayed by the JULIA code A=ones(2,8); norm(A,2) is (2 pts) a. 2 b. 4 c. 8 d. 16 e. 32 24. Let u and v be two orthogonal vectors in F' . The number of non-zero eigenvalues of the matrix uv′ is (2 pts) a. 0 b. 1 c. N-1 d. N e. None of the above 25. For an M × N matrix with rank r, the number of singular values is (2 pts) a. r b. M c. N d. M + N e. MN f. min(N, M) g. None of the above 26. Let V ∈ F'×' denote a unitary matrix. For y ∈ F', the most computationally efficient JULIA code for solving argmin+∈F! ‖Vx − y‖! is: (2 pts) a. pinv (V) * y b. V y c. V * y d. V’ * y e. Inv(V) * y 27. Let α and β denote the spectral norms of matrices A and B, respectively. The spectral norm of the matrix is (2 pts) a. αβ b. α + β c. √α2 + β2 d. min (α, β) e. max (α, β) f. None of the above 28. Let A be an M × N matrix with non-zero rank. The orthogonal complement of the null space of A+ is. (2 pts) a. R(A) b. R(A9) c. N(A) d. N(A9) e. R (A) f. R (A′) g. N (A) h. N (A′) 29. Let A be a tall matrix having rank r with SVD given by Define Pr = I − urur ′ and P0( ) = I − u0 u0 ′ and B = P0( )Pr . Then: (2 pts) a. B is a unitary matrix. b. B is not a unitary matrix. c. Need more information to assess 30. If B is an N × N idempotent matrix with trace{B} = K, then rank(B) is (2 pts) a. 0 or 1 b. K c. N − K d. N e. None of the above 31. The vectors {b1, b2, b3 } form. an orthonormal basis for a subspace S of ℝN, for N ≥ 5. Complete the following JULIA function so that given input vector x ∈ ℝN, it returns the nearest vector in S. For full credit, your code must use as few floating-point calculations as possible. (4 pts) function neareast (x, b1, b2, b3) return end 32. Determine the spectral norm of for b ∈ ℝ . (4 pts) 33. A simple linear system takes as input n (possibly complex) scalar values and returns as output the sum of those values. Thinking of the input as an n-dimensional vector, what unit norm input vector produces an output value with the largest possible magnitude? (4 pts) 34. Determine what will be displayed as output by the following JULIA code: (4 pts) B = [3 0 0 -4]; pinv(B) 35. Complete the following JULIA function so that it returns the nullity of a matrix argument. (4 pts) function nullity ( A ) (M,N)=size(A) return end 36. Determine the output value displayed by the following JULIA code. (4 pts) A = 7 * ones(5,3); (U, s, V) = svd(A); B = U[:,1] * s[1] * V[:,1]’; Vecnorm ( A – B ) 37. Complete the following JULIA function so that it returns an orthonormal basis (as a matrix) for the span of the four input vectors a, b, c, d (assumed to be of the same length). (4 pts) function spanbasis (a, b, c, d) end 38. Let U and V denote unitary N × N matrices. Complete the following JULIA function so that given input vector y ∈ ℂN, it returns the linear least-squares solution argminx ‖UVx − y‖2(2). For full credit, your code must use as few floating-point calculations as possible. (4 pts) function best (y, U, V) return end 39. Determine a simple expression for the solution to the following regularized least-squares cost function for δ > 0. x = argminxf(x) where f(x) = 2/1 ‖Ax − y‖2(2) + 2/1 δ 2 ‖Cx‖2(2), where C has full column rank. Your final expression should not have any pseudo-inverse in it and should be in terms of the original problem variables: A, C, y, δ . (8 pts)
553.420/620/421 Intro. to Probability Assignment #09 Due Friday, April 19 11:59PM as a PDF upload to Canvas Gradescope. 9.1. Suppose that X|Y = y ∼ Poisson(y) and Y ∼ exp(1). (a) From the information given, write down the joint probability distribution. Notice here we have a mixture of different types of rvs. (b) Derive the marginal distribution of X. Show that it has a geometric( 1 2 ) distribution. (c) Identify the conditional pdf of Y given X = x if you can. Remark: What changes in this problem had Y ∼ exp(a) instead for some fixed constant a > 0? 9.2. Fred and Greg are each rolling a fair 6-sided die repeatedly. They each stop rolling the moment they get a 6. If the total number of rolls it takes between them for this to happen is 14, what’s the probability it took Fred at least twice as many rolls as Greg to see his first 6? 9.3. The delayed unit exponential is the (continuous) distribution of a random variable with pdf e −(x−y) for x > y. The value y > 0 in this pdf is the “delay”. Suppose X is a delayed unit exponential but whose delay is random, say, the delay Y is Gamma(α, 1). (a) Derive the (unconditional) pdf of X. Did you get an interesting answer? (b) Now find the conditional pdf of Y given X = x. (c) Assume α = 3. Compute P(Y < 2 1 |X = 1). 9.4. Suppose X1, X2, X3, . . . , Xn represent the lifetimes of n components each of which independently has exp(λ) distribution. If Yi (for i = 1, 2, . . . , n) represent the order statistics. Determine the distribution of the lifetime of the first component to die (i.e., Y1 = min{X1, . . . , Xn}). 9.5 Consider the situation in problem 9.5 above except instead of X1, x2, . . . , Xn being iid, they are just independent; that is, assume X1, X2, . . . , Xn are independent, where, for each i = 1, 2, . . . , n, Xn ∼ Exp(λi) (and we allow the λi ’s to be any positive numbers not necessarily all the same value). Show that Y1 = min{X1, X2, . . . , Xn} follows another exponential distribution and identify its parameter. Remark. Moral of the story: the minimum of independent exponentials is exponential. 9.6. Suppose X1, X2, X3 ∼ iid Exp(1). (a) Write down the joint pdf of Y1, Y2, Y3. (b) In class we showed that Yj has the pdf (n j−1, 1,n−j) (F(y))j−1f(y)(1 − F(y))n−j , where F(y) is the cdf of the underlying X-distribution. Write down the marginal pdf of Y2 in our situation of n = 3 and exp(1) distribution. (c) Re-derive the pdf of Y2 from this joint pdf in part (a) by appropriately integrating out the variables y1 and y3 once a value of 0 < y2 < ∞ is fixed. 9.7. (continued from problem 9.6) We still have n = 3 iid Exp(1) rvs. and their order statistics Y1, Y2, Y3. (a) Construct the joint pdf of the spacings: W1 = Y1, W2 = Y2 − Y1, W3 = Y3 − Y2 using the method of Jacobians. Be sure to get the domain of this pdf correct. Do you notice anything interesting about what this pdf says about the collection W1, W2, W3? (b)∗ Y1 < Y2 < Y3 splits up the nonnegative real line into 3 finite pieces (and one infinitely long piece from Y3 to ∞). In this way, we think of W1 as the first piece, W2 as the second piece, and W3 as the third piece. We (temporarily) ignore the infinitely long piece. Find the distribution of the shortest piece. Do you recognize this distribution? If so, what is it? (c) Compute the mean length of the shortest piece. ∗Hint: the shortest piece W = min{W1, W2, W3}, use the CDF method P(W ≤ w) = 1 − P(W > x). 9.8. Let X1, X2, X3 be independent unif(0,1) and let Y1, Y2, Y3 denote their order statistics. (a) Find P(X3 > X2 > X1) and P(Y3 > Y2 > Y1). (b) Write down the joint pdf of Y1, Y2, Y3, then from this joint pdf compute the (bivariate) marginal of Y1, Y3. (c) Use the bivariate marginal in part (b) to compute P(Y3 > 2Y1). (d) The sample range in this case is the rv R = Y3 − Y1. Compute E(R). 9.9. Suppose that Y1, Y2, . . . , Yn are the ordered statistics of X1, X2, . . . , Xn ∼ iid uniform(0, 1). Suppose 0 < a < b < 1. Find simple formulas for each of the following: (a) P(Y1 > a, Yn < b) (b) P(Y1 > a, Yn > b) (c) P(Y1 < a, Yn < b) (d) P(Y1 < a, Yn > b) (e) P(Yk < a, Yk+1 > b) for 1 ≤ k ≤ n − 1 (f) P(Yk < a, Yk+2 > b) for 1 ≤ k ≤ n − 2. Hint: For parts (a,b,c,d), it might be helpful to let A = (Y1 > a) and B = (Yn < b) and use Venn diagrams. Of course, the event A means all the Xi ’s are greater than a, the event B means all the Xi ’s are less than b, and you can easily compute their probabilities by independence.
MODULE TITLE: VISUAL COMMUNICATION MODULE CODE: COM62204 / COM61004 AUGUST 2023 SEMESTER Module Name: VISUAL COMMUNICATION Module Code: COM62204 / COM61004 Synopsis: This module emphasizes the basic understanding of visual literacy and communication within the current media industries through the comprehension of design elements and principles. It also focuses on the practical application and ethical considerations of the visual aspect in screen and print based visual communication design. The learning and teaching approach for the module will be computer-lab based, by having students to learn and engage in practical tasks in a computer lab environment. As a result, the lecturer is able to have a good view at students’ learning progress during class so that it aligns with the learning outcomes. Prior to every assignment’s submission, two progression checks are carried out to ensure students are on the right track, this serves as a constant review of their works. This module is supported by a combination of classroom practical learning and online learning. The assignments are designed to enable students to gain the knowledge of visual literacy and communication as well as the practical skills needed to achieve the end product. Name(s) of academic staff teaching the module, module leader and staff email: Staff teaching the module: Module Leader – Tee Meng Wah ([email protected]) Tutor – Tee Meng Wah (fignon.tee @taylors.edu.my) Year-level: 1 Semester Offered: March (Long) / August (Long) Credit Value: 4 Pre-requisite: Co-requisite: Nil Anti-requisite: Nil School offering the module: School of Media and Communication, Faculty of Social Media and Leisure Management Module offered as: Common Core / Primary Major / Minor / Free Elective Programme Name: Bachelor of Mass Communication (Hons) Domain Name (for free electives only): N/A LEARNING OUTCOMES: Upon completion of the module you should be able to: Module Learning Outcome Programme Learning Outcomes Assessment/s 1 Identify core fundamentals of visual design namely design elements and principles pertaining to visual communication design. 2 3 2 Implement visual design concepts (e.g. colour harmony, principles of typography) in the creation of communication design documents 3 1 3 Demonstrate the theoretical considerations and discussions of visual communication 5 3 4 Apply visual design techniques and conceptualization skills into visual production through the use of industry standard software (i.e. Adobe Illustrator, Adobe Photoshop and Adobe InDesign). 3 2 Transferable Skills: Skills learned in this module of study which can utilize in other settings. These transferable skills include: MLO1, MLO2, and MLO3 TEACHING, LEARNING AND ASSESSMENT Description of assessment components: Assessment Task Weight Module Learning Outcomes Assessed Programme Learning Outcome Due Date Assessment 1 – Poster design 30% 2 Implement visual design concepts (e.g. colour harmony, principles of typography) in the creation of communication design documents 3 Wk 7 Assessment 2 – Packaging label design 30% 4 Apply visual design techniques and conceptualization skills into visual production through the use of industry standard software (i.e. Adobe Illustrator, Adobe Photoshop and Adobe InDesign). 3 Wk 14 Assessment 3 – Lab Tests 20% 1 Identify core fundamentals of visual design namely design elements and principles pertaining to visual communication design. 4 Wk 7, 10 20% 3 Demonstrate the theoretical considerations and discussions of visual communication 5 TAYLOR’S GRADUATE CAPABILITIES The teaching and learning approach at Taylor’s University is focused on developing the Taylor’s Graduate Capabilities (TGC) in its students; capabilities that encompass the knowledge, cognitive capabilities and soft skills of our graduates. The TGC gives students the edge to start and stay ahead. The TGC ensure that a Taylor’s graduate has proven ability and is capable in the following areas: 1.0 Discipline Specific Knowledge Ability to demonstrate professional competence, articulate and adapt discipline specific knowledge to novel situations, and be able to contribute from their discipline to interdisciplinary solutions to problems. 2.0 Critical Thinking and Problem Solving Skills Ability to rationally and critically analyse, synthesize and evaluate evidence to arrive at solutions. 3.0 Lifelong Learning Ability to adopt flexible and resilient learning methods to continuously learn, unlearn and relearn in a self-regulated manner. 4.0 Communication Skills Ability to create and deliver messages effectively and sensitively in appropriate contexts and communication styles. 5.0 Personal Competencies Ability be self-aware and to self-regulate through skilful management of one’s personal goals, intentions, responses and behaviour. 6.0 Social Competencies Ability to understand the feelings of others, interact positively with them and foster a stable and harmonious relationships. 7.0 Entrepreneurialism Ability to influence change by being proactive, resourceful and prudent in assuming risk. 8.0 Global Perspective Ability to see the world as interconnected, seek to understand an individual’s, a society’s, or a culture’s place in it and practice humility.
ARCH 523bl - Fall 2024 Homework 3 Problem 1 (30 points) A single-span steel beam with simple supports is uniformly loaded as shown in Figure 1. A) Determine if the Wide Flange W18x76 is adequate for bending (due to DL+LL) and deflections (due to LL and DL+LL). B) Determine if the HSS20x12x1/2 is adequate for bending (due to DL+LL) and deflections (due to LL and DL+LL). Figure 1- Beam Diagram Given: • Distributed dead load, qDL= 400 lbf/ft • Distributed live load, qLL= 800 lbf/ft • Yield stress, Fy= 50 ksi • Allowable bending stress, Fb= 30 ksi • Modulus of Elasticity (Young’s modulus), E= 29,000 ksi • Deflection limits: o DL + LL: L/240 o LL: L/360 • Assume the section profile is compact and the beam is adequately braced. Figure 2- Wide Flange profile Parameters: • L= 50 ft (span) Hint: Use Tabulated Moments and Deflections for Beams provided in the lecture notes 3. Figure 3- HSS Profile Problem 2 (20 points) A single-span timber joist supports one concentrated load as shown in Figure 4. A) Determine if the 4x16 wood joist is adequate for bending and deflections (LL and DL+LL). Figure 4- Beam Diagram Given: • Point dead load, PDL= 600 lbs • Point dead load, PLL= 1100 lbs • Allowable bending stress, Fb= 1725 psi • Modulus of Elasticity (Young’s modulus), E= 1,900 ksi • Deflection limits: o DL+LL: L/240 o LL: L/360 • Assume the section profile is compact and the joist is adequately braced. Figure 5- Joist Profile Parameters: • L= 20 ft (span) • a= 3.5 in (design width) • b= 13.25 in (design depth) Hint: • A= a*b • I= a*b3/12 • S= a*b2/6 Problem 3 (20 points) A single-span steel beam with simple supports is uniformly loaded as shown in Figure 1. Three options are provided in Table 1 for the beam section profile. A) Select the lightest profile among the three that satisfies the bending strength and deflection requirements. Figure 6- Beam Diagram Given: • Distributed dead load, qDL= 400 lbf/ft • Distributed live load, qLL= 800 lbf/ft • Yield stress, Fy= 50 ksi • Allowable bending stress, Fb= 30 ksi • Modulus of Elasticity (Young’s modulus), E= 29,000 ksi • Deflection limits: o DL + LL: L/240 o LL: L/360 • Assume the section profile is compact and the beam is adequately braced. Parameters: • L= 55 ft (span) Table 1- Section Profile Options Hint: 1- Calculate the required plastic modulus (Z) from the design bending moment and allowable stress (Required Z= M/Fb). 2- calculate the required moment of inertia (I) from the distributed loads and the allowable deflection (Figure 7). The required I value should be determined for 1) DL+LL, and 2) LL, as the deflection criterion is different for each. 3- Use the maximum of the two I values to determine the required I. 4- Enter Table 1 with the required Z and I and select the section whose Z and I are greater than the required values. Figure 7- Required I values Problem 4 (20 points) A 50 ft long cable, made of stainless steel, is attached to the ceiling and is used as a hanger. Determine the thermal expansion and contraction for the following conditions: A) The temperature increases 60 degrees Fahrenheit. B) The temperature decreases 80 degrees Fahrenheit. C) If we switch the material to mild steel, without doing any calculation, determine whether it will expand more or less than the steel cable. Given: • Coefficient of thermal expansion: o Stainless steel: a= 8.9*x10-6 1/Deg. F o Mild Steel: a= 6.0*x10-6 1/Deg. F Problem 5 (10 points) For the building materials listed below, determine the allowable stresses: A) A36 Steel: Fy= 36ksi and Fu= 58 ksi B) A500 grade C Steel: Fy= 50 ksi and Fu= 65 ksi Hint: The allowable stress equations are provided in Lecture Notes 3.
Tutorial EG501V Computational Fluid Dynamics (AY 2023/24) Tutorial 1. Convection-diffusion equation Convection and diffusion are two mechanisms for transporting a scalar (which can be thought of as a concentration of a chemical agent, or temperature). In this Tutorial we will consider the scalar to be a concentration c (unit kg/m3). Convective transport means that the scalar goes with the flow; diffusive transport is the process of evening out concentration gradients (transport from areas with high to areas with low concentration). In mathematical terms: Convective transport : Diffusive transport: The symbol stands for the scalar flux. It is the amount of scalar passing through a unit surface per unit time: kg/(m2·s); it is a vector since it has direction. The vector u is the velocity of the flow, the coefficient Γ is the diffusion coefficient (unit m2/s). In this example we assume that the scalar does not react, i.e. c does not change as a result of a chemical reaction, it only changes as a result of transport. Your assignment Based on a mass balance of the scalar over a small two-dimensional volume dx×dy×W (similar to what was shown in LN01, Figure 1.2), derive that the concentration c satisfies the following equation This is known as the convection-diffusion equation. Take inspiration from the section Mass Balance that starts on page 2 of LN01.
MATH2003J, OPTIMIZATION IN ECONOMICS, BDIC 2023/2024, SPRING Problem Sheet 13 Question 1: For which a ∈ R is the function f ∶ R 3 ! R, f(x, y, z) = x 2 + xz + ayz + z 2 convex? Question 2: Show that the function f ∶ R 4 ! R, with f(x, y, z, w) = x 2 + y 2 + z 2 + w 2 − 2xw − 4yz is neither convex nor concave on R 4 . Also, give an example of a function g ∶ R 4 ! R which is both convex and concave. Question 3: Show that the function f defined for K, L > 0 by f(K, L) = A[δK−ρ + (1 − δ)L −ρ ] −1/ρ, where A > 0, ρ ≠ 0, 0 ≤ δ ≤ 1, is concave for ρ ≥ −1 and convex for ρ ≤ −1.
Musical Cultures modules Formative Research Project Plan About the Research Project The Research Project brings together the ideas about researching music and musical cultures that you’ve looked at over the course of the module, and gives you the opportunity to explore those themes in detail within a specific area. You’ll examine a topic of your own choice and can carry out and present your research in any appropriate form. agreed with the module tutor: we encourage you to think creatively about the best and most appropriate way to present your research. For practical or applied projects, you’ll also submit a short accompanying report that explains and contextualises the research aspect of your work. The Research Project is worth 50% of your marks for the module: - Year 2 students: equivalent to 2,500 words, which may include a contextual report of up to 300 words - Final Year students: equivalent to 3,000 words, which may include a contextual report of up to 400 words Suggested lengths/word-count equivalents are approximate, depending on the complexity of your project, whether you are a Year 2 or Final Year student, and/or if you are combining multiple formats or approaches. Check with your tutor or module leader if you are unsure, but a rough guide would be: · Composition: 4-6 minutes of original music · Seminar presentation (delivered live, or submitted as slides with narration): 13-15 minutes, including examples · Lecture recital: 13-15 minutes, including examples · Performance: c. 10-12 minutes of music · Podcast: 12-14 minutes, including examples · Video essay: 8-10 minutes, including examples (see here for an example of an excellent video essay) Use the information and questions below as a template to structure your proposal. There is no set word count for this formative assignment, but the more detail you can give, the more helpful tutors can be with feedback on your ideas. Your classes will also include more information about relevant approaches to music research, and suitable methodologies and formats. You’ll have lots of opportunities to ask questions and discuss ideas. Tutors will provide feedback on your proposal in a number of ways, which might vary by option. Some tutors will provide written feedback, others will invite you to sign up for a tutorial slot to discuss your ideas. Make sure you take advantage of this feedback: it will help to make sure your project is feasible within the time available, and is of the appropriate length, format, and complexity. You should also check the assignment rubric on Brightspace. This shows how your work will be assessed. Choosing a topic and format Think about some of the topics you’ve studied so far on the module – or that are coming up in term 2. You might choose to extend some of the work you’ve done already on these musical traditions or communities, or to apply some of the methodological approaches studied to a new area related to your own interests. Once you have a broad area of interest, start to narrow it down by thinking about the way in which you’d like to carry out your research; the particular issues that interest you the most; and the practicalities of formulating a project that fits within the time and resources you have available. You’re encouraged to be creative about how you carry out your research. Options include an illustrated seminar presentation; or composition, performance, or recording work (audio and/or video) focused around your own participation in or observation of a musical community or activity. You can also write a traditional essay, or produce a podcast or video essay. You can draw on more than one of these approaches if it’s appropriate for your topic. No format is better or worst than another: think about what you want to communicate, and what format will work best for that. Think about what you want to find out: this will help you define your central research question(s), and these will help you stay on track during the project. All projects need to demonstrate an informed, research-led approach. For creative projects, you’ll explain your research questions, approach, and conclusion(s) in the short accompanying report. For presentations, podcasts, and video essays, some or all of this material may be covered in the research project itself. Reports Reports should be a maximum of 300 words for Year 2 and 400 words for Final Year students. They should contain information to help explain and contextualise your project, rather than replicating the content/structure of a traditional essay. If the context and research elements/approach are straightforward and clear from the nature of the research project itself, then the report can be similarly straightforward and concise, or may not be needed at all. Ask your tutor if you are unsure. Your report should include the following: · Explain your research question(s) and any relevant background or context for the research project (you are strongly encouraged to reference appropriately here: show your familiarity with relevant sources). · Outline briefly what you did in order to investigate those issues, and how you presented your findings. · Outline your conclusions: what did you find out; could you answer your research question(s)? · Anything else relevant we should know in order to understand your project. · Bibliography (not counted in the word count). Submitting your project You can submit multiple files to Turnitin. Please make sure file names are clear so we can understand what each file contains. · Include any ethics clearance/participant consent forms where relevant. · If you did a seminar presentation or live performance, then please upload something that is indicative of the live content (e.g. slides, scores, chord charts, or a script/notes – just one of these is fine). · It is your responsibility to make sure your markers can access your work in order to assess it. Remember that Turnitin accepts a maximum file size of 100MB, so if you have a large file (DAW composition or presentation slides for example) then allow yourself time to deal with this before the deadline. We can accept pdfs of slides, for example, or a fully unlocked/shareable OneDrive link for large sound or video files. You can also direct us to weblinks or Vimeo/YouTube video. Student name: Musical Cultures option: Research Project proposal What area or topic do you wish to research? (Give as much detail as possible, and try to come up with one or two main research questions that summarise the key things you want to find out.) What approach or format will you use to carry out and/or present the research? (This will vary for different kinds of topic – think about the kinds of sources you’ve been looking at in class to give you some ideas: e.g. a written essay; a composition in a particular style; a concert or performance(s); a video diary; a podcast; recordings; an illustrated seminar presentation…) Does your project involve other participants (e.g. as interviewees, other performers, a group you will observe etc.)? (If so, you are likely to need to complete the ethics review process and will be given more information on how to do this at the start of term 2 – don’t worry, it is straightforward!) What will be the key milestones for your project? How will you stay on track to submit on time? (e.g. data collection stage; creative processes; editing; scheduling performances; recruiting participants etc. – what stages do you need to carry out to fulfil your ideas?) Who else has researched this area? What are some of the key sources for background research or contextual information? (List at least 5-10 sources of reliable information relevant to your research question(s).)
AMATH 481/581 Autumn Quarter 2024 Homework 2: Quantum Harmonic Oscillator DUE: Friday, October 18 at midnight The probability density evolution in a one-dimensional harmonic trapping potential is governed by the partial differential equation: where is the probability density and V(x) = kz2 /2 is the harmonic confining potential. A typical solution technique for this problem is to assume a solution of the form. which is called an eigenfunction expansion solution (o=eigenfunction, E,=eigenvalue). Plugging in this solution ansatz to Eq. (1) gives the boundary value problem: where we expect the solution (z)→0 as z→±oo and e, is the quantum energy. Note here that K=km/h2and en=E,m/h2. In what follows, take K=1 and always normalize so that nl2dr=1. (a) Calculate the first five normalized eigenfunctions (фn) and eigenvalues (en) using a shooting scheme. For this calculation, use -L, L] with L4 and choose zspan-L: 0.1: L. Save the absolute value of the eigenfunctions in a 5-column matrix (column 1 is 1, column 2 is o2 etc.) and the eigenvalues in a 1x5 vector.
FN3142 ZA Quantitative Finance Question 1 (a) What is the“efficient markets hypothesis”? [30 marks] (b) Suppose we are at time t, and we are interested in the efficiency of the market of a given stock. Let Ωt(w) denote the weak-form. efficient markets information set at time t, Ωt(ss) denote the semi strong-form. efficient markets information set at time t, and Ωt(s) denote the strong-form. efficient markets information set at time t. To which information set, if any, do the following variables belong? Explain. [70 marks] 1. The stock price today. 2. The 3-month US Treasury bill rate today. 3. The inflation rate last year. 4. Next year’s expenditures just approved by the company’s board of directors (and not announced yet). 5. The value today of a put option on the stock that has a six-month maturity. 6. The value of the stock at time t + 3. 7. The number of shares AQR Capital Management (a hedge fund) purchased today of the stock. Question 2 (a) Show that a stationary GARCH(1,1) model can be re-written as a function of the unconditional variance and the deviations of the lagged conditional variance and lagged squared residual from the unconditional variance. [20 marks] Hint: a GARCH (1,1) model can be written in the form. σt(2)+1 = W + βσt(2) + Qεt(2) ; where W, Q, and β are constants, and εt is zero-mean white noise with conditional variance σt(2) . (b) Derive the two-step ahead predicted variance for a GARCH(1,1), denoted by σt(2)+2.t and defined as Et [εt(2)+2], as a function of the parameters of the model and the one-step ahead forecast. [40 marks] (c) Derive the three-step ahead predicted variance for a GARCH(1,1) and con-jecture the general expression for a h-step ahead forecast. Give an example of a financial application that may require using ah-step ahead forecast. [40 marks] Question 3 (a) Define the concept of “trade duration” in financial markets and explain brieflywhy this concept is economically useful. What features do trade durations typically exhibit and how can we model these features? [25 marks] (b) Describe the Engle and Russell (1998) autoregressive conditional duration (ACD) model. [25 marks] (c) Compare the conditions for covariance stationarity, identification and positiv-ity of the duration series for the ACD(1,1) to those for the GARCH(1,1). [25 marks] (d) Illustrate the relationship between the log-likelihood of the ACD(1,1) model and the estimation of a GARCH(1,1) model using the normal likelihood function. [25 marks] Question 4 Consider two stochastic processes: (i) Xt , about which we do not know anything for now, and (ii) vt , which is a zero-mean white noise with Moreover, we know that v and X are uncorrelated at all leads and lags, that is, E[Xtvt-j ] = 0 for all j integers. Let an observed series Zt bedefined as Zt = Xt + vt. (a) What does covariance stationarity mean? [15 marks] (b) Prove that the process Zt is covariance stationary if and only if Xt is covariance stationary. [20 marks] Now assume that Xt is an MA(1) process: Xt = ut + δut-1 , where ut is zero-mean white noise with (c) Calculate the autocovariances of the process Xt and show that it is covariance stationary. [20 marks] (d) Calculate the autocovariances of Zt and show that they are zero beyond one lag. [20 marks] (e) Is it possible to represent the process Zt as an MA(1) process? In particular, assume that we write Zt = εt + θεt-1 , (1) where εt isa zero-mean white noise with variance σε(2) . What would be the required restrictions on θ and σε(2) so that Ztis an MA(1) process? [25 marks] Hint: based on the assumption (1), derive the autocovariances of Z as a function of θ and σε(2), and compare them to your results in (d) .
Tutorial EG501V Computational Fluid Dynamics (AY 2023/24) Tutorial 2. Incompressible Navier-Stokes equations In Lecture Notes 1 the Navier-Stokes equations (momentum balance) for incompressible flow were derived. They were eventually written in the following form. In this equation, the viscosity μ and the density ρ are constants. We now consider two simple flow configurations. Config. 1. The steady state flow of a liquid in the space between two very large static parallel plates at distance H of each other in the presence of a constant pressure gradient in the x-direction Gravity is pointing in the negative y-direction. Config. 2. The start-up of the flow of liquid between two very large parallel plates at distance H of each other. There is no pressure gradient. Before time t=0 everything is standing still. At t=0, the upper plate starts moving with a constant velocity U. In this configuration we do not consider gravity. Your assignments For Configuration 1: a. Begin with the full, two-dimensional Navier-Stokes equations and determine which of the terms are zero and which are not. b. Derive an expression for the velocity ux as a function of y by applying the simplified NS equations (as found under Item a.) and by applying the no-slip condition at the two plates. For Configuration 2: c. Begin with the full, two-dimensional Navier-Stokes equations and determine which of the terms are zero and which are not. d. Make sure that when steady state has been reached ( t → ∞ ), the simplified form of theNS equations as found under Item c. leads to a linear velocity profile between the plates.
ECN 100B Problem set 1 DUE MONDAY, JANUARY 27TH, NOON CA TIME ON GRADESCOPE See syllabus for additional details Question 1 Imagine many small farms selling strawberries at the Davis Farmers Market, in a setting of perfect competition. Each individual firm faces costs C(q) = 100q 2 . A. Derive a firm’s supply curve. Now assume there are 200 firms selling strawberries at the Davis Farmers Market. B. Derive the market supply curve. Suppose the market demand curve is QD(p) = 1000 − 8p. C. What are equilibrium price and equilibrium quantity? D. Graph the inverse demand and inverse supply curves for the market and indicate the equilibrium price and quantity. E. What are consumer and producer surplus? Question 2 Imagine a CEO retreat in the desert in which CEOs spend hours in a sauna each day and cannot leave the desert between sauna sessions. The folks running the retreat (our firm) sell lemonade after each sauna session. They are a monopoly in the market of refreshments for this CEO camp in the desert. Imagine CEOs at the retreat have the inverse demand function p(Q) = 3600 − 600Q for lemonade after using the sauna. Furthermore, the folks running the retreat have the cost-function C(Q) = 300Q2 + 800 for lemonade. A. What are equilibrium price and equilibrium quantity? B. What is the folks running the retreat’s profit at the equilibrium? C. Prove that this profit level is a global maximum. D. Show the equilibrium price and equilibrium quantity graphically. Include the inverse demand curve, firm’s marginal revenue curve, and firm’s marginal cost curve. E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? Question 3 Now imagine that the government (of Mexico in this case, as it turns out) decides to tax lemonade using a specific tax of 1800 per unit of lemonade produced and sold. A. What are the new post-tax equilibrium price and equilibrium quantity? B. What is the folks running the retreat’s new profit at the equilibrium? C. Prove that this new profit level is a global maximum. D. Show the new equilibrium price and equilibrium quantity graphically. Include the inverse demand curve, firm’s marginal revenue curve, and firm’s pre- and post-tax marginal cost curves. E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How have these quantities changed from the no-tax case in Question 2? Question 4 The government of Mexico has decided it would rather ensure that there is no deadweight loss in this market for after-sauna lemonade at the CEO retreat by removing the tax and instead setting a price cap. A. At what price should the government cap lemonade sales? B. What are the new post-price cap equilibrium price and equilibrium quantity? C. What is the folks running the retreat’s new profit at the equilibrium? D. Prove that this new profit level is a global maximum. E. Show the new equilibrium price and equilibrium quantity graphically. Include the original and regulated inverse demand curves, firm’s marginal revenue curve, and firm’s marginal cost curve. F. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How have these quantities changed from the no-tax case in Question 2? Question 5 Now imagine that the CEO retreat is a monopsony employer for laborers (to make lemonade) in the geographic market surrounding the retreat. Suppose the firm faces an inverse supply curve of labor of w(L) = 4000 + 1000L. A. What is the marginal expenditure curve for the CEO retreat? Now assume the monopsony has an inverse demand curve for labor of w(L) = 13000−1000L. B. What are the equilibrium wage and labor quantity? C. Show the equilibrium wage and equilibrium labor quantity graphically. In-clude the inverse demand curve and the firm’s supply and marginal expenditure curves. D. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium?
ARCH 523bl - Fall 2024 Homework 4 Problem 1 A reinforced concrete beam has a rectangular cross-section as shown in Figure 1. a) Calculate the steel reinforcement area. b) Calculate the steel reinforcement ratio. Given: • Compressive strength, f’c= 4,000 psi • Rebar yield strength, fy= 60 ksi • Rebars: 4 No. 9 Parameters: • b= 12 in • d= 17 in • clear cover, cc= 2 in Figure 1- Beam Cross Section Problem 2 For the beam cross-section in Problem 1, determine: a) The minimum steel reinforcement area required by the ACI 318 code. b) The minimum steel reinforcement ratio required by the ACI 318 code. c) Does the provided reinforcement meet the code requirements? Problem3 For the beam cross-section in Problem 1, determine: a) Whether the section is tension-controlled, or compression controlled. b) Strength reduction factor for bending. Problem 4 A single-span reinforced concrete beam is uniformly loaded as shown in Figure 2. The beam cross section is provided in Problem 1. Verify if the beam bending strength is adequate for the applied loads. Given: • Distributed superimposed dead load, qSDL= 400 lbf/ft • Distributed live load, PLL= 8 kip • Weight of concrete, sw= 150 lbs/ft3 (normal weight) Parameters: • L= 40 ft (span) Figure 2- Simply Supported Beam Hint: 1. Calculate the self-weight of the beam (lbs/ft) and add to super superimposed dead load to obtain the DL distributed load. 2. Use Tabulated Moments and Deflections for Beams provided in the lecture notes 3. Problem 5 A concrete hanger and a concrete beam are shown in Figure 3. Which one of these members must be designed with tension reinforcement? Please explain your answer. Figure 3- Concrete Members Problem 6 A retaining concrete wall is supported at the top and base and is resisting soil pressure as shown in Figure 4. a) Does the wall need tension reinforcement? Please explain your answer. b) If reinforcement is required, show where the replacement needs to be placed, close to side A or B? (provide a sketch) Figure 4- Concrete Wall
CHI212H5S-LEC0101 & PRA0101 Chinese for Academic Purposes II Winter 2025 COURSE DESCRIPTION This course, designed for native or near-native speakers of Mandarin Chinese, continues the study of rhetorical knowledge and critical thinking skills for effective academic reading and writing. It also prepares students for upper level courses which demand in-depth reading, writing, as well as professional presentation skills. [24L/12P] Prerequisites CHI211H5 or appropriate language level as indicated by the Chinese Language Assessment Questionnaire ( https://www.utm.utoronto.ca/language-studies/language-course-assessment- questionnaires) or interview. Exclusions CHI200Y5 or CHI201Y5 or CHI202H5 or EAS200Y1 or EAS201H1 or LGGB60H3 or LGGB61H3 or LG GB62H3 or LGGB63H3 or LGGB64H3 or LGGB65H3 Learning Outcomes This course aims to provide students with knowledge and skills in writing a research paper in Chinese. Upon successful completion of this course, students will be able to: 1. become familiar with the process of writing a research paper; 2. identify connections in reading and writing research papers; 3. evaluate and analyze the language and writing techniques used in academic papers; 4. compose well-structured research proposals and papers by using the learned language and writing techniques; 5. cite the sources of research papers properly; 6. conduct presentations in a professional manner; 7. enhance study habits through reflection and effective time management; 8. prepare, engage, and contribute positively to class dynamics by actively participating in discussions and respecting diverse perspectives. Textbooks and Other Materials Textbooks are not required. The instructor will provide handouts with reference to the following books: 1. 、 ，《 ： 》〈 ： ，2010 〉。 2. ，《 ： 》（ ）〈 ： ，2014 〉。 3. ，《 ： 》〈 ： ， 2010 〉。 Turniin Normally, students will be required to submit their course essays to the University’s plagiarism detection tool for a review of textual similarity and detection of possible plagiarism. In doing so, students will allow their essays to be included as source documents in the tool’s reference database, where they will be used solely for the purpose of detecting plagiarism. The terms that apply to the University’s use of this tool are described on the Centre for Teaching Support & Innovation web site ( https://uoft.me/pdt-faq). If you wish to opt out of using this tool, please notify the instructor regarding the decision via email by January 19, 2025. Your materials can be submitted via email and you will meet with the instructor during her office hours when required. IMPORTANT COURSE INFORMATION Lectures begin the week of January 6, 2025. The first practical will take place on January 6, 2025. Official information regarding campus closures is posted on the UTM Campus Status page. Tri-campus information is available on the UofT Campus Status webpage. Expectations Read the materials and write down your thoughts. You are encouraged to read and think about the works we are going to discuss before class. Keep active thinking during the class and write down your thoughts and inspirations right away. Cumulative learning. Decide the topic of your presentation and essay as early as possible. Keep the topic in mind and extend your thinking to any possible connected knowledge. Cumulative learning will help you to fulfill your studying goals smoothly and efficiently. Please do not hesitate to contact the instructor for any questions concerning the project and essay. Email Policy Please do not hesitate to contact me via email: j[email protected]. Please always include “CHI212-SEC0101” in the email subject, along with the topic in question, for example, ‘CHI212- SEC0101: Inquiry on Assignment 1’ . I will reply to you within 48 weekday hours of the regular work week! Please use only your @mail.utoronto.ca email to reach me. Office Hour Policy Please book your appointment at least 48 hours in advance to secure a spot during office hours. Notify the instructor by email with the subject line: “CHI212–SEC0101: Office Hour Request.” Enrollment Conflict Students who enroll in courses with conflicting lectures, tutorials, lab, or practicals (scheduled at the same or overlapping time slot) may NOT receive accommodations for conflicting tests, quizzes, assignments, lecture material, in-class participation and attendance. Source: Academic Calendar Copyright for Instructional Materials Please be advised that the intellectual property rights in the material referred to on this syllabus [and posted on the course site] may belong to the course instructor or other persons. You are not authorized to reproduce or distribute such material, in any form or medium, without the prior consent of the intellectual property owner. Violation of intellectual property rights may be a violation of the law and University of Toronto policies and may entail significant repercussions for the person found to have engaged in such act. If you have any questions regarding your right to use the material in a manner other than as set forth in the syllabus, please speak to your instructor.
BIO2101 Comprehensive Biology Laboratory Exercise #3b PBS vs Water PBS (Phosphate Buffered Saline) For washing and dilution of cell culture Contains sodium chloride, sodium phosphate and potassium phosphate; pH = 7.4 Osmotic pressure (isotonic) Lysis buffer (Triton X-100) Triton X-100 is widely used to lyse cells to extract protein or organelles, or to permeabilize the membranes of living cells. It is a nonionic surfactant that has a hydrophilic polyethylene oxide chain and an aromatic hydrocarbon hydrophobic group, which disrupt the hydrophobic-hydrophilic interactions of membrane component. Protein assay – Bradford reagent (contains phosphoric acid, avoid contact with the mouth and skin) Standard curve Construction of protein standard plot Prepare 1:1 serial dilutions of bovine serum albumin (BSA) standard (0.6 mg/mL) provided to construct a range of standard solutions between 0 and 0.6 mg/mL (e.g. 0, 0.0375, 0.075, 0.15, 0.3 and 0.6 mg/mL). This can be accomplished as follows: To start serial dilution, pipette 50 µL of 0.6 mg/mL BSA standard from tube 6 into tube 5. Then pipette 50 µL from tube 5 into tube 4 until you have reached 0.0375 mg/mL conc. (tube 2). Do not dilute into tube 1 so that it can serve as a “Blank” for the assay. Protein standard curve Protein Standard plot 1. Linear Regression Straight line equation Y=aX+b a is the slope, b is the y-intercept. 2. The coefficient of determination is such that 0 < r 2 < 1, and denotes the strength of the linear association between x and y. The coefficient of determination represents the percent of the data that is the closest to the line of best fit. 3. Coefficient of determination (R2 ) should be 0.9 or above Protein Assay Lab report for Exercise 3 Introduction Procedure (Materials and Methods) Results (used the data of cell numbers to 1. plot the curves of cell concentration; and the data of protein concentration to 2. plot a growth curve of the protein amount per cell) Discussion Lab report #3 requirement (result) Part A: Cell counting with the hemocytometer ◦ Data shown by table and graph for 4% and 20% FBS cell culturing conditions ◦ Table should contain data of i) raw cell count, ii) dilution factor (if any), iii) standard deviation and iv) average number of cells ◦ Formulae for calculating ‘Av. no. of cells’ from ‘Raw cell count’ and ‘dilution factor’ obtained from Part A Lab report #3 requirement (results cont.) ◦ Graph: growth curves of cell concentration ◦ Data (Conc. of cells)
FN3142 QUANTITAIVE FINANCE PRELIMINARY EXAM 2019 Question 1 Consider a forecast of a variable, Yt. You have 100 observations of and Yt and you run the following regression: The following results are obtained: Estimate std error t-statistic β0 -0.085 0.0052 -16.34 β1 2.6135 2.0398 1.28 a) What, if anything, can we infer from this output? 60 marks b) The picture in the Figure 1 is based on daily returns on General Electric over the period 1990-1999. What does this picture reveal about the conditional variance of General Electric returns? What volatility model do you suggest for this asset? 40 marks Figure 1: Figure for question 1b x-axis represents return on day t; y-axis represents the squared return on day t+1. Question 2 a) Define the Efficient Market Hypothesis (EMH) and distinguish between its weak- form, semi-strong and strong form. 15 marks b) Discuss Fisher Black's interpretation of the EMH and explain why it maybe difficult to test empirically. 10 marks c) What is the role of forecasting models and search technologies in refining the information set? Define market efficiency according to Granger and Timmerman (2003) 25 marks d) After extensive empirical research, someone finds evidence of predictability in stock returns that cannot be possibly explained as compensation for risk bearing. Is it necessarily a violation of the EMH? 25 marks e) Briefly state the random walk model for asset prices and discuss whether the EMH implies the random walk model. 25 marks Question 3 Consider using a historical simulation method (HS) and a GARCH method for forecasting volatility. After building the so called hit variables: the following regressions are run, with standard errors in parenthesis corresponding to the parameter estimates: Hitt(H)s = 0.0814 + μt (0.0132) Hitt(GA)RCH = 0.0207 + μt (0.0123) a) Describe how the above regression output can be used to test the accuracy of the VaR forecasts from these two models and decide whether the VaR forecasts are accurate or not? 40 marks b) Describe how you can determine the best convex combination of the two forecasts in the sense of mean squared error minimisation. 60 marks Question 4 a) Show that a stationary GARCH(1,1) model can be re-written as a function of the unconditional variance and the deviations of the lagged conditional variance and lagged squared residual from the unconditional variance 20 marks b) Derive the two-step ahead predicted variance for a GARCH(1,1) as a function of the parameters of the model and the one-step forecast. 40 marks c) Derive the three-step ahead predicted variance for a GARCH(1,1) and infer the general expression for a h-step ahead forecast. Give an example of a financial application that may require using a h-step ahead forecast? 40 marks
TRA2001 Introduction to Computer-aided Translation (CRN1004) Assignment 1 Deadline: 11 February 2025 (Tue) at 17:00 Background: You will be required to translate a corporate finance document of connected transaction of a listed company as your next assignment. You have decided to use Termsoup to complete the translation. Before that, you need to prepare a Translation Memory and a Termbase for use with the CAT tool. Fortunately, certain data files (in source language only) are available already. You are required to complete the following three tasks: (1) Create a Translation Memory of 100 translation units (TUs). ATU should include one source language segment and one target language segment (i.e. one language pair). The direction is from English to Chinese. The TM should be prepared in MS Excel format. [Hint#1: try to identify similar sentences among the data files. Pick similar sentences for inclusion to the TM as they are more likely to be useful data for future assignment. Hint#2: content in summary boxes may contain such similar sentences] (2) Create a Termbase of 50 bilingual items. The direction is from English to Chinese and the items are listed in alphabetical order. The Termbase should be prepared in MS Excel format. [Hint#3: priority should be given to jargons in the TM you have created] (3) Create a log file containing screenshots of successful import of your TM and TB. The log file should be prepared in MS Word format.
Video Games CMN 176v Instruction for Game Design Paper In this individual activity, students will familiarize themselves with game design handbooks and then will apply design principles in a 7-page written proposal (12-font, 1-inch margins, Times New Roman font, APA 7th format). The proposal will either (1) sketch out recommendations to intensify and enhance a given outcome (e.g., player identification, enjoyment, guilt) or (2) outline an original game idea. Option 1: Improving on an existing video game 1- Read the Game Design Essentials (Mitchell, 2012) and Art of Game Design chapters (Schell, 2008). 2- Identify a game that was personally influential. Choose a game that had a strong impact on you. Why was this game influential to you? Tie your experience to motivations for playing, identification, moral engagement, cognitive effects, or any other relevant class concept. Select two class concepts to discuss. 3- List the name, gameplay style, and ESRB rating of the game. 4- Briefly define each of the four basic elements of your selected game (Story/lore, Aesthetics, Mechanics, and Technology). 5- Create a flowchart summarizing the game’s starting point, story, and main events. Keep it simple. If the game features complex branching stories that depend on character choice, then attempt to outline the game based on the classic three act structure (Act 1 - Setup: Exposition, inciting incident; Act 2 - Confrontation: Rising action, midpoint; Act 3 - Resolution: Pre climax, climax, story outcome). If the game has complex branching stories or is an open-world game then create a flowchart for a specific quest within the larger narrative. You may also select Flowchart tools 6-Using the game design readings, propose a new or improved (a) story/lore, (b) characters, (c) mechanics, and (d) technology for your game of choice. 7- Define the term theme and then summarize the theme of your chosen game. In addition, discuss a concrete step that you would take to increase the resonance of the game’s theme. 8- Explain how your proposed game design elements may increase motivation for playing, identification, moral engagement, cognitive effects, or any other relevant class concept. Option 2: Propose a new game 1- Read the Game Design Essentials (Mitchell, 2012) and Art of Game Design chapters (Schell, 2008). 2- List the name, gameplay style, and ESRB rating of the game proposal. 3- Briefly define each of the four basic elements of your game proposal (Story/lore, Aesthetics, Mechanics, and Technology). 4- Create a flowchart summarizing the new game’s starting point, story, and main events. Keep it simple. If the proposed game features complex branching stories that depend on character choice, then attempt to outline the game based on the classic three act structure (Act 1 - Setup: Exposition, inciting incident; Act 2 - Confrontation: Rising action, midpoint; Act 3 - Resolution: Pre climax, climax, story outcome). 5-Using the game design readings, propose a (a) story/lore, (b) characters, (c) mechanics, and (d) technology for your game proposal. 6- Define the term theme and then summarize the theme of your new game proposal. In addition, discuss a concrete step that you would take to increase the resonance of your game’s theme. 7- Explain how the game design elements of your new game proposal may increase motivation for playing, identification, moral engagement, cognitive effects, or any other relevant class concept.
