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
SOCY60361 Social Network Analysis: concepts and measures Computer based assessment 2024-2025 DEADLINE: 26th Jan 2025, 2pm One assignment of 3000 words, +10% (i.e. 3300 words max). There is no lower limit for this assignment, but you must make sure your analysis is fully described and justified. Note: You must include an accurate word count on the front page of your essay. Failure to do so will lead to an automatic 2 mark deduction. Your word count should include all text in the essay (including any footnotes), but does not include tables, pictures and the bibliography. For this assignment you will be required to perform. analysis in Ucinet and to produce visualizations. Each performed task’s output and each visualization need to be added to a final document which represent your assignment (in a word/pdf file). All datasets are in Ucinet dataset files. The assignment is composed by 2 parts. Please answers all questions of all parts. The final mark is calculated as the average score of all the parts. PART 1. For this part, you will be using the dataset CAMP92, and the attribute file CAMPATTR These data were collected at the 1992 NSF Summer Institute on Research Methods in Cultural Anthropology. This was a 3 week course given to 14 carefully selected participants and 4 instructors (total 18 people in the network). Network data were collected at the end of each week. These data were collected at the end of the second week. The data were collected by placing each person's name on a card and asking each respondent to sort the cards in order of how much interaction they had with that person since the beginning of the course (known informally as "camp"). This results in rank order data in which a "1" indicates the most interaction while a "17" indicates the least interaction. The dataset CAMP92 contains network data for week 2 and week 3. The attribute file contains information about the gender of the participants (female=1/male=2) and their role (student =1/instructor =2). 1. Create a matrix which contains only the first 3 choices for each respondent in week 3 (include the matrix in your answer). Produce a network graph from your matrix. Colour the nodes according to gender, shape the nodes according to roles. 10/100 2. Are there any cohesive subgroups in the network? If so, how many? Explain and justify your answer, describing the method you have used to address this question and explaining why you chose that method. You can use more than one method. 30/100 3. Using any three measures identify the most central actors? Briefly explain the measures you have used and what they might tell us. 30/100 4. Is there any evidence of gender and/or role homophily in this network? Briefly explain the method you have used to answer this question. 30/100 PART 2. For this part, you will be using the dataset Krack-high-tech and its attribute file High-tech-attr. These are data collected from the managers of a high-tec company. The company manufactured high-tech equipment on the west coast of the United States and had just over 100 employees with 21 managers. Each manager was asked to whom do you go to for advice and who is your friend, to whom do you report was taken from company documents. In addition attribute information was collected. This consisted of the managers age (in years), length of service or tenure (in years), level in the corporate hierarchy (coded 1,2 and 3; 1=CEO, 2 = Vice President, 3 = manager) and department (coded 1,2,3,4 with the CEO in department 0 ie not in a department). This data is used by Wasserman and Faust in their network analysis book. 1. Produce one visualization with friendship ties, one with advice ties and one with report-to ties. Colour the nodes by level and size them by tenure. 30/100 2. Do ‘reporting’ and friendship ties help to explain who asks whom for advice? Justify and explain the method you have used to address the question, presenting all relevant outputs. Could you use a standard regression model to address this question? Explain your answer. 70/100
ECN 100B WQ 2025 Midterm 1 Practice Exam 1 Short answers Answer 2 out of 3. Please provide 2 to 3 sentences answering each question. 1.1 What is the optimal price cap for a government to impose on a monopoly? Why? 1.2 What is a potential problem that could arise when a govern-ment wants to regulate a monopoly with a price cap? 1.3 What three conditions must be met for a firm to profitably price discriminate? 2 Multi-part problems Answer 2 out of 3. Please answer all parts of the question. 2.1 Perfect competition question Imagine many small farms selling usb-c charging cables on a large online marketplace, in a setting of perfect competition. Each individual firm faces costs C(q) = 3q 2 . A. Derive a firm’s supply curve. Now assume there are 120 firms selling usb cables on the same large online marketplace. B. Derive the market supply curve. Suppose the market demand curve is QD(p) = 1400 − 50p. 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 surplus, producer surplus, and deadweight loss at the equilibrium? Now imagine a brand new usb-d port is introduced and the entire market shifts to pro-ducing usb-d cables. Assume the number of firms are the same, demand is the same, and costs are the same except for a new fixed cost of setting up new usb-d factories that each firm faces of F C = 50. F. What are the new equilibrium price and equilibrium quantity? 2.2 Monopoly question Imagine a firm called Bapple that is the monopoly in the market for smartwatches, with cost-function C(Q) = 99Q2 + 20000. Imagine the inverse demand function for smartwatches is p(Q) = 2000 − Q. A. What are equilibrium price and equilibrium quantity? B. What is the monopoly’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? Now imagine that the government decides to tax smartwatches using a specific tax of 200 per smartwatch produced and sold. F. What are consumer surplus, producer surplus, and deadweight loss at the post-tax equilibrium? How have these quantities changed from the no-tax case? 2.3 Monopsony question Imagine that UC Bavis is a monopoly employer of labor in the city of Bavis. Suppose the firm faces an inverse supply curve of labor of w(L) = 36 + 6L. A. What is the marginal expenditure curve for the Bavis? Now assume the monopsony has an inverse demand curve for labor of w(L) = 72 − 6L. 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 Bavis’s surplus, workers’ surplus, and deadweight loss at the equi-librium? E. Now assume the City of Bavis wants to set a minimum wage to ensure zero deadweight loss in the Bavis labor market. What should the City of Bavis set as the minimum wage? F. What are Bavis’s surplus, workers’ surplus, and deadweight loss at the post-minimum wage equilibrium?
P8483: Application of Epidemiologic Research Methods Spring 2025 Syllabus COURSE OBJECTIVES 1. Think logically! 2. Use SAS to walk through the steps of an epidemiologic analysis from data entry through regression analysis. 3. Operationalize conceptual epidemiologic and biostatistical concepts covered in other classes through application with real data sets. 4. Learn to summarize your research findings with succinct scientific writing. 5. Develop skills in “prompt engineering” to use generative AI to assist with writing computer code. The material builds on concepts introduced in Quantitative Foundations in Public Health and is intended to complement and serve as a bridge to the methods presented in more advanced epidemiology courses. WEEKLY STRUCTURE AND EXPECTATIONS This class is a hybrid. Recorded lecture material is supplemented by weekly in-person small group exercises. In-person attendance is expected. Most weeks following Week 1 will have the following structure. Tuesday 530-650 pm. Synchronous session. · First 15 minutes: Questions on asynchronous material from last week · Second 50 minutes: small group breakout sessions focusing on completing specific in-class assignments · Last 15 minutes: review of small group exercise as a class Tuesday following Synchronous session: · Asynchronous material for the following week is released o Slides with embedded recorded audio and video o Reading assignments o Homework assignment Wednesday am – Monday pm · Attend office hours as needed · Watch asynchronous material · Do readings · Work on homework All homework assignments will be due at 11:59 pm on the Monday prior to the synchronous session, with a no-penalty grace period until 7:59 am on Tuesday morning. No extensions will be provided. No exceptions. PREREQUISITES · Prior completion of the Core, P6400, or equivalent · Registered for the course on SAS On Demand OPTIONAL · This year I am exploring ways to integrate the R statistical program into this class using generative AI. There will be optional materials using R available. If interested, please download R and R Studio. SKILLS TO LEARN The primary objective of this course is to provide you with the tools necessary to import, clean, error-check, operationalize, analyze, and disseminate data from epidemiologic research studies. In this class we will be using the SAS statistical software package, but the logical processes this course develops will be useful across any statistical package. Generative AI tools such as ChatGPT are excellent resources at helping you to write statistical programming commands for epidemiologic analyses, and we will explore how best to use these tools in this class as well. By the end of the course, you should be able to: · Understand and implement the steps involved in data collection, management, data quality assurance, operationalization, descriptive analysis, and multivariable regression analyses using SAS o Read raw data from a variety of formats into SAS o Peruse, manipulate and clean data sets through printing, sorting, merging, and the use of conditional logical expressions o Apply simple statistical and graphical procedures for the descriptive analysis of normally distributed data o Conduct correlation, linear, and logistic regression in SAS and interpret SAS output for these analytical methods · Understand the concepts of statistical model building · Understand the difference between statistical model building and multivariable analysis for causal inference · Understand the purpose of indicator variables (“dummy” variables), how to create these, and how to interpret output for these variables · Conduct multivariable data analyses in SAS · Understand the concept of confounding and how to use standard methods to remove confounding · Develop skills in succinct summarization of findings from an epidemiological analysis through writing a scientific abstract. ASSESSMENT AND GRADING POLICY Assessment for this course is based on homework assignments, a mid-term exam, a final project, and weekly in-class laboratory assignments. The contribution of each grading assessment toward the final grade is as follows: Assignments: 45% In-class group exercises: 8% In class check-ins: 2% Midterm exam: 25% Final project: 20% Letter grades will be assigned by the instructor based on the following general rubric. No rounding up. A+ 99-100% Highly Exceptional Achievement A 94-98% Excellent. Outstanding Achievement A- 90-93% Excellent, close to outstanding B+ 88-89% Very good. Solid achievement expected of most graduate students B 84-87% Good. Acceptable achievement B- 80-83% Acceptable achievement, but below what is generally expected C+ 78-79% C 74-78% C- 70-74% Midterm Exam: The take-home midterm will take place during the approximate mid-point of the semester and will be similar in format to weekly homework assignments. More detail will be provided during the semester. Homework Assignments: There will be approximately 8 graded homework assignments. Assignments are to be completed and saved in SAS as enhanced editor files (.sas extension or .txt extension). Since most of you will not download SAS onto your computer, saving your SAS editor file as a .txt extension will allow you to actually view it prior to submission. Your name and Columbia email UNI must be included in all assignment submissions. All course assignments will be turned in electronically via CourseWorks. At the end of the semester, the top (n-1) grades will be used in compiling a student’s final grade. There will be no accepting late homework submissions. In-class check ins During weekly in-person classes, you will be given an in-person learning check at the beginning of each class. Grades will be based on completion. These will count toward 2% of your grade. To receive full credit you will need to be physically present in class for these. The two lowest scores on these will be excluded from your final grade. In-class group exercises The most important part of the Tuesday in-person sessions are the group exercises. You will work with your randomly assigned laboratory group on an assignment. These will count toward 8% of your grade. These will be due after the class and graded for reasonable effort. All lab group members are expected to participate in order to receive credit for the lab assignment. During submission, you will be asked to attest to which members were (1) present in person (2) present remotely or (3) not present. Credit will be given to all members present in person or remotely. Final Project: The objective of the final group project is to provide students with experience in analyzing data from a large scale data set. Specific details will be provided later on in the semester.
MPCS 55001 Algorithms Winter 2025 Homework 3 1 Whetting your Appetite: DP Smorgasbord (20 points) You are given an m × n array A. Each square A[i,j] contains a positive integer which represents the cost to visit that square. You are currently standing on the top left square of the array: A[1, 1]. You wish to find the total cost of the lowest cost path from this square to the bottom right square A[m,n]. You may only move one unit to the right or down at a time. Your total cost is the sum of the integers in all the squares you visit on your path (including A[1, 1] and A[m,n]). 1 1 2 5 1 3 1 8 5 3 4 1 5 3 8 2 1 4 2 1 Table 1: Example problem on a 5 × 4 grid. Total cost is 13 = 1+1+2+1+4+1+2+1. There might exist multiple lowest cost paths. The subproblem we will use to answer this question is: DP[i,j] = the minimum cost of a path from square (1, 1) to square (i,j). (a) (1 point) Given the subproblem above, what is the value of DP[1 , 1]; that is, what is the minimum cost of a path from square (1, 1) to square (1, 1)? (b) (1 point) Suppose you are standing at position (4 , 4) on some input grid A, and you know that DP[4, 3] = 6 and DP[3, 4] = 9. Furthermore, you know A[4, 4] = 1. What is the value of DP[4, 4]? (c) (2 points) Considering parts (a) and (b), write a recurrence which expresses the solution to each subproblem in terms of smaller subproblems. State any base case(s). Justify your recurrence and state the time complexity of your recurrence. Next we will explore modifications to the problem considered above. We will examine how these modifications impact our subproblems and recurrences. For variations (d) and (e) below, write a new recurrence which expresses the solution of each subproblem in terms of smaller subproblems. State any base case(s). Justify your recurrence and state the time complexity for a single entry. You should use the same subproblem we provided above. (d) Suppose now that you may move either one or two positions to the right or down at a time (you may not move diagonally). However, every time you move two positions you must pay an extra fixed cost c. • (2 points) Recurrence: (e) You may now move to any square that is further down or to the right (or both). However, for any move you need to pay an extra cost equal to the square of the distance you traveled. For example, moving from (x1 , y1 ) to (x2 , y2 ), where x1 ≤ x2 and y1 ≤ y2 , costs g = (x2 − x1 )2 + (y2 − y1 )2 . • (2 points) Recurrence: For variations (f), (g), and (h), you must: • Define a new subproblem that you will use to solve this problem precisely. Define any variables you introduce. What are the dimensions of your dynamic programming table? What is the space complexity? • Write a new recurrence which expresses the solution to each subproblem in terms of smaller subproblems. State any base case(s). Justify your recurrence and state the time complexity of your recurrence. (f) In addition to being able to move to any square that is further down or to the right (as defined in (e) above), you are given a single “coupon” which allows you to land on one square without paying its cost. • (2 points) Subproblem: • (2 points) Recurrence: (g) You are given k such coupons which allow you land on a square without paying its cost. • (2 points) Subproblem: • (2 points) Recurrence: (h) You may only move one position to the right or down at a time (as in the original problem). In addition, you may only move right k times in a row. For example, if k = 2, then if you move right twice, your next move must be down. • (2 points) Subproblem: • (2 points) Recurrence: 2 Largest Square of Contiguous 1’s (15 points) You are given an n × n bitmap, represented by an n × n matrix M[1..n,1..n] of 0s and 1s. An all 1’s block in M is a submatrix of the form M[i..i′ ,j..j′] in which all bits are equal to 1. An all 1’s block is square if it has the same number of rows and columns. Give a dynamic programming algorithm to find the maximum area of an all 1’s square block in M in O(n2 ) time. (You do not need to locate such a largest all-ones square, just determine its area.) Example input: 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 Example output: 9 In this example, the area of the largest all 1’s square block is 9. There are two 3 × 3 all 1’s square blocks. One is indicated below by bold; the other by underlines. 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 (a) (3 points) Define the subproblem that you will use to solve this problem precisely. Define any variables you introduce. (b) (4 points) Give a recurrence that expresses the solution of each subproblem in terms of the solutions of smaller subproblems. State any base case(s). (c) (3 points) Write pseudocode for a dynamic programming algorithm to solve this problem. Your algorithm should run in O(n2 ) time. Now we allow rectangular blocks. Give a dynamic programming algorithm to find the maximum area of an all 1’s rectangular block in M in O(n3 ) time. (Note: O(n2 ) is possible.) (d) (2 points) Define the subproblem that you will use to solve this problem precisely. (e) (3 points) Give a recurrence that expresses the solution of each subproblem in terms of the solutions of smaller subproblems. State any base case(s). 3 Card Game (16 points) A new card game is taking campus by storm! This game is played using a specialized deck, with number cards (which can represent any integer) and wild cards. Cards are placed face up in two rows of n cards each. You need to remove cards to make the two rows match while achieving the maximum score possible. You are only allowed to remove cards; you are otherwise not allowed to move the cards, i.e., the order of the remaining cards in each row must be preserved. Scoring works as follows, working from left to right: • A pair of matching number cards adds that number to your score. Of course, if the cards are negative, this would lower your score. • Wild cards can match with any number card. In this case, you multiply the current score by that number, instead of adding. • If you match two wild cards, you must choose whether to multiply the current score by 25 or −25. Suppose the two rows are as follows. * indicates a wild card. 8 -3 -10 -9 -7 -5 2 -10 8 -7 -9 * The best solution, for a total of 133 points, is to match the −10 cards, the −9 cards, and the wild card to the −7. -10 -9 -7 -10 -9 * Move Action Total points −10 matches −10 add −10 −10 −9 matches −9 add −9 −19 −7 matches * multiply −7 133 Table 2: Explanation of solution to example. The two rows of cards are given in arrays A[1 ... n] and B[1 ... n]. In this problem, you will develop a dynamic programming algorithm to solve this problem, and output the maximum possible score. Your algorithm must run in O(n2 ) time. First, though, consider a restricted version of the problem, where all number cards have positive value. Wild cards can still appear; if you match two wildcards, you multiply the current score by 25. (a) (4 points) Define the subproblem that you will use to solve the restricted problem precisely. Define any variables you introduce. (b) (4 points) Give a recurrence which expresses the solution to each subproblem in terms of the solutions of smaller subproblems. Specify any base case(s). (c) (4 points) Write pseudocode for an algorithm to solve this problem. Your algorithm must run in O(n2 ) time. Now consider generalizing your algorithm to the full version of the game, in which number cards can have negative values, and matching two wild cards lets you multiply the score by 25 or −25. (d) (4 points) Give a new recurrence which expresses the solution to each subproblem in terms of the solutions to smaller subproblems. Specify any base case(s). If necessary, you can also define new subproblems. 4 Programming: River Crossing (20 points) Follow this GitHub Classroom link to accept the assignment. Your code should be pushed to GitHub; you do not need to include it here. 5 Survey (1 point) (a) What was the most challenging concept or problem this week? (b) Which concept or problem did you enjoy the most this week? (c) Other comments?
CSCl251 Advanced Programming Assignment 3 Aim The objectives of this assignment includes: Learning about generic programming templates, operator overloading, STL (containers & algorithms) and writing io manipulators Apply the concepts learnt by developing a data processing program Background In this assignment,you are required to develop a program that reads in and process some 'messy'records from a file that contains data meant for different kinds of classes.These data are jumbled up and unsorted,and to make it worse,for any particular row of record,there may be multiple duplicates scattered over the entire file! You program should be called 'csci251_a3.app',and should posses the following capabilities: a)read in the records from a user-specified filename b)remove all duplicate rows of data c) filter and display the data according to user-specified sorting criteria d)store the records displayed in c),in a user-specified filename The next section provides information about the requirements for developing this program. Task Requirements A) Appendix A provides a sample input data from a file called 'messy.txt'It contains information meant to be stored in 4 classes:'Point2D','Point3D','Line2D'and 'Line3D'.Please refer to the table in Appendix A for a description of the format in which the input data for each of the classes is stored. B) Note1: You are to research and determine which kind of STL containers (e.g.Map, Vector,Set,Lists etc)you should use,to store all the various objects from the 4 classes. For this assignment you are not allowed to use array[]to store any of your data! C) Appendix B provides a description of the 4 classes:'Point2D','Point3D','Line2D' and 'Line3D',and the relationships between them.You are to study the diagrams and implement them accordingly. D) Appendix C provides the sample output format and a description of the format requirements,for each of the 4 classes.These format are to be applied whether the data from these classes are output to a file or terminal. E) Note2: To output data,you are required to create your own output manipulator(s) to display/store data in the format described in Appendix C.You are further required to overload the insertion operator ‘
Semester January 2025 Module Code FIL2201 Module Title Introduction to Film Criticism Coursework Structure Critical Film Analysis Assignment Weighting 40% Assignment Title Assignment 1 - SWAY/CANVA Presentation: Critical Film Analysis Coursework Submission Deadline Week 13 Assessment Criteria Learning Outcomes: Knowledge and Understanding tested in this assignment: List the Outcomes Mapped in Module Guide and Table of Specification • be able to demonstrate abroad knowledge and understanding of key aesthetic and cultural momentsin the study of the moving image • be able to articulate some of the ways in which the technology of the moving image contributes to meaning Learning Outcomes: Skills and Attributes tested in this assignment: List the Outcomes Mapped in Module Guide and Table of Specification • be able to demonstrate abroad critical engagement with at least three moving imagetextson an aesthetic, formal and symbolic level • be able to demonstrate abroad critical engagement with some of the basic technical vocabulary ofmoving image analysis • be able to demonstrate an ability to support their interpretative and evaluative analysis of the movingimage with basic theories and key concepts in the study of the moving image General Coursework Rules • Written Assignment must be submitted online through SafeAssign (or other plagiarism checker) via Blackboard for originality check. • Oral Presentation must be recorded and securely uploaded to YouTube (or other online video platform) for moderation purpose. The private link to video must be given to the lecturer during submission. • Assignment submitted after the deadline will be subject to a penalty. Please refer to the guidelines on Coursework Submission that can be found in the INTI-UH Student Guidebook. • Suspected academic misconduct will be handled according to the Policies and Procedures for Academic Dishonesty and Misconduct that can be found in the INTI-UH Student Guidebook. Assignment Brief Using Microsoft's SWAY application, or Canva this assignment requires students to research and present amedia-rich presentation on a film of their choice from across the module, analysing moments from the film from the perspective of at least one of the topics from topic 2-6 in the academic calendar of the semester. Your SWAY must be made up of maximum 14 slides (not including a TITLE OR A FINAL slide which includes your references and bibliography) that offers images, videos, written text or recorded audio narration that textually analyses chosen moments from your selected film. Students must also include a minimum of two relevant quotes from suitable academic readings and applythese to the chosen topic/or chosen film. These must be presented in HARVARD style. You will receive a workshop on how to use SWAY or Canva in the beginning of the semester of the module. This assignment is worth 40% of the overall module mark. Key Grading Criteria: • Students should provide a SWAY presentation with 14 slides containing images, videos, and textual analysis/descriptions of a chosen film from those set across the module. • Students should demonstrate a basic understanding of at least one of the film studies topics covered from Week 1-6 in their SWAY submission. • Students should offer close textual analysis of their chosen film, image(s)/video clips, topic of interest which includes textual description, interpretation and evaluation. • Students should make use of at least two academic references in their presentation, using Harvard referencing style. • Good communication and effective use of imagery, written text, audio/visual materials. For the content of SWAY or Canva, students may choose to write about many stylistic and aesthetic elements in the piece or concentrate on one or two. For example, you may discuss the arrangements of the shots, position and gestures of the performers, camera movement, setting, decor, costume, sound, music, or lighting. Do not merely point something out: writing that 'the film cuts' or 'the camera moves left' is not adequate. You must explain the significance of these features and the way they relate to each other. For example: the gestures of the performer will be shot from a certain perspective and distance, it may follow an important edit or something on the soundtrack; a different perspective or a different soundtrack will mean that the gesture expresses a different meaning. You may mention other areas of the film - indeed this maybe necessary for understanding the sequence - but do not dwell on these other areas. The techniques and skills needed for this study will be those developed in the lectures, so by the time this assessment takes place, you should have suitable experience. Films for selection (within week 2-6): 1. Carol (Todd Haynes, 2015) 2. No Country for Old Man (Ethan Coen & Joel Coen, 2007) 3. The Royal Tenenbaums (Anderson, 2001) 4. Carrie (Brian De Palma, 1976) 5. Babel (Alejandro González Iñárritu,2006) Here are some guidance to SWAY application: 1. Getting Started with SWAY: https://support.microsoft.com/en-us/office/getting-started-with-sway- 2076c468-63f4-4a89-ae5f-424796714a8a Other Specific Instructions for this Assignment NO changes are allowed to the SWAY or Canva presentation after the submission deadline! Assignment delivery: 1. UH cover page 2. A SWAY URL (in Word document with INTI Assignment Cover Page - compulsory) and 3. A PDF file of SWAY (you may edit Sway content to fit the PDF A4 page but must be easy to read) content of the assignment uploaded to Canvas via Turnitin. 4. Script. for video produced/audio recording in PDF format. [optional] Penalties for late submission (i) First-sit coursework submitted up to one week after the published deadline should be capped at the pass grade, and thereafter awarded a grade of zero; (ii) Deferred coursework submitted up to one week after the published deadline should also be capped at the pass grade, and thereafter awarded a grade of zero; (iii) Referred coursework submitted after the published deadline should be awarded a grade of zero unless an extension has been granted.
Course Outline Course Number MG-GY 8683 Economics & Strategies for Digital Platforms Spring 2025, 1/21/2025 – 5/6/2025 Course Scope and Mission The goal of this course is to equip students with the economic tools and strategic thinking necessary to understand how platform. markets function and how to carefully analyze, evaluate and develop strategies for digital platforms. Many companies are pursuing digital strategies, from a multitude of startups to major players including Google, Amazon and Meta. This course will cover topics that help inform. platform. strategy, such as two-sided markets, first mover advantage, network effects, the chicken-or-egg dilemma, monetization strategies, freemium models, intellectual property rights, startup strategy, crowdsourcing, platform. governance, regulation, societal aspects of platforms, ways in which platforms are changing competition, and reasons why platforms fail. We will apply economic and strategic thinking to the study of business cases of different platforms. Book (recommended) Geoffrey G. Parker, Marshall W. Van Alstyne, and Sangeet Paul Choudary. Platform. Revolution. 2016. W.W. Norton & Company, Inc. Evaluation and Grades Grades are a measure of the performance of a student in individual courses. Students will be evaluated on the basis of how well they command the course materials. i. Participation/Group Platform. Exercise 10% Ongoing ii. Case Questions Write-ups 20% Ongoing iii. Freemium Analysis (Individual) 35% March 10 iv. Group Platform. Exercise Presentation & Paper 35% May 5 (Pres. April 28) Grade Conversion A: 94 – 100 A-: 90 – 93 B+: 87 – 89 B: 84 – 86 B-: 80 – 83 C+: 77 – 79 C: 74 – 76 C-: 70 – 73 D+: 67 – 69 D: 65 – 66 F: Below 65 COURSE FORMAT AND EXPECTATIONS i. Class Participation/Group Platform. Exercise (10%) One of the primary goals of this course is to help you develop the ability both to clarify your own position on a strategic question related to digital platforms and to be able to articulate and defend it clearly. As this class is highly interactive, regular class attendance and class participation are a critical part of this course. Class contribution is based on attendance and participation in the weekly group platform. exercises. Each class, we will be doing a group exercise, where we apply the concepts learned in the lectures that week to the development of a platform. business model. At the start of the course, I will ask you to form. small groups (~5 students) and come up with an idea for a platform. Then, each class, we will apply the theoretical concepts we learn to your real-world platform. By the end of the course, you should have a well-developed platform. business plan. ii. Case Question Write-Ups (20%) For each class in which we will be discussing a case, I will provide an overview and background of the case, and pose some questions about the case that are relevant for the theme of that week’s topic. You are asked to form. small groups (~5 students) and work on the questions, writing up in sentence form. answers to each of the questions. I will ask each group to email me the write-ups (one write-up per group) and we will then reconvene as a class and have a group discussion about each case question. Case writeups will receive 1 or 0, based on completion. With cases, you should be able to identify the key issues, problems, and opportunities facing the platform, to articulate and evaluate alternative approaches to the problems, and to describe the course of action that you recommend and the reasons for your recommendations. iii. Freemium Analysis (35%) A take-home freemium analysis is due on March 10. This is an individual paper, as outlined below. Instructions: For this assignment, you are asked to choose a platform. that employs or has employed a freemium business model—note that platforms that offer free limited-time trials are not freemium—and analyze its strategy in a paper that does not exceed 1,000 words. Please do not choose any of the online storage companies (i.e. Dropbox, Google Drive, Apple iCloud, Box or Microsoft SkyDrive) for your assignment, as we are discussing those in class. Recommendations for platforms to choose: Spotify, YouTube. In your papers, answer the following questions. 1. What are the advantages and the costs of offering a free version of the product? 2. Could the platform. earn more by not offering a free version of the product? Explain the assumptions – including economic, competitive, and behavioral assumptions for consumers – to support your analysis, and provide information and quantitative evidence to justify those assumptions. iv. Group Platform. Exercise: Presentation & Paper (35%) Throughout the semester, you have been working weekly in groups to develop your own platforms. For this final group assignment, due on May 5, you are asked to write a paper of up to 1,500 words (due May 5) and give a presentation on April 28. This assignment consists of two parts. The first part is a 10 minute in-class “pitch deck”-style. presentation consisting of 10 slides (below) on April 28 (5%). This should be a concise presentation that provides an overview of your platform’s business plan. Your 10 slides should address the following: Pitch Deck – Key Components: 1. Introduction: Briefly introduce the platform, its name, and a one-liner that captures its essence (e.g., “A marketplace connecting freelancers with businesses.”) 2. Problem: Define the problem that exists in the market that your platform. is designed to solve. 3. Solution: Describe how your platform. solves this problem, including the key features and functionalities that enable users to connect, transact, or interact more efficiently. 4. Chicken or Egg Dilemma & Network Effects: How will your platform. solve the chicken or egg dilemma? How will it achieve positive network effects to create value? 5. Monetization Strategy: Describe how your platform. makes money. 6. Competitive Landscape: Discuss existing competitors (comparing, e.g., monetization strategy, number of users, etc.), and emphasize your unique value proposition and differentiation strategy. 7. Intellectual Property: How will you approach intellectual property? 8. Governance: How will you create and sustain good governance on your platform? 9. Regulation: What regulatory issues might your platform. raise, and how will you mitigate them? 10. Closing: End with a strong conclusion that reinforces the platform’s potential, the impact it could have, and your vision for the future. The second part is a paper, due May 5 (30%), that goes into more detail on the questions underlying the presentation slides.
[IE 6113] [Quality Control and Improvements] [Spring 2025] Course Pre-requisites. Students need to have good concepts of probability and statistics. Course Description This course provides students with a foundation in quality control and improvement. The course will cover various topics from quality management, such as cost of quality, quality assurance, and quality management. Emphasis is on the essential quality control tools such as control charts and their use, acceptance sampling. A term project is required at the end of this course. The project must include a detailed analysis of materials covered during the semester. Course Objectives The course intends to prepare students for understanding and applying quality control methods and improvements techniques for both service and manufacturing industries. At the end of the semester, the students should be able to: · Understanding the various philosophy and fundamentals of quality and being able to apply the concepts of total quality management, six sigma, and quality systems and standards. · Understanding the general principles underlying the various types of control charts and, why it works, how to interpret results and how to decide which method to use in any case. · Understand the sampling theory and the uses of sampling tables and define the right sampling plan for any area. · Understand the principle of Reliability and it is various application and implication during product design. · Understand the principles of design of experiments on improving product quality. Course Structure This course will be delivered via a series of lectures and discussions in quality control and improvements methods. The course focuses on both manufacturing and services industries. Students are responsible for reading the associated chapters and assigned cases and reviewing key concepts, terms, definitions, discussion questions, and topics. There will be a team project toward the end of the semester that focuses on the covered topics. · COURSE MGT Announcements, notes, resources, assignments, schedules, and due dates will be posted to NYU Brightspace. Readings The required textbook for the course is: 1. “Fundamentals of Quality Control and Improvement,” 5th editions 2021, Amitava Mitra), 13: 978-1-119-69233-1 Reference textbooks: (Should be found in School Library) 1. “Statistical Quality Control” 7th edition, E. Grant, R. Leavenworth ISBN: 0 – 07 – 043555 – 3 2. “Modern Methods for Quality Control and Improvement” 2nd edition, H. Wadsworth, K. Stephens, A. Godfrey), ISBN: 0 – 471 – 29973 – 1 3. “Introduction to Statistical Quality Control” 8th edition, Douglas C. Montgomery ISBN: 978-1-118-98915-9 (PBK), ISBN: 978-1-119-39911-7 (EVALC) 4. “Design and Analysis of Experiments” 8th Edition, Douglas C. Montgomery ISBN: 978 – 1 – 118 – 14692 – 7 Additional Reading Sources and software: (database available through library) American Society for Quality (ASQ) website Minitab Software IIE Transactions / Quality Journal “Lean Six Sigma Pocket” (Tool Book) By; Michael L. George, David Rowlands, Mark Price, John Maxey Course requirements Course requirements All course materials are posted on the Brightspace course web page. Students are expected to read lecture materials before class · Class attendance is mandatory · HW will be assigned and submitted electronically · HW should be submitted before the beginning of each class · HW will not be grades it is part of participation and will be discussed inside the class · Exams will consider all materials covered in lectures, which may not be in the textbook. · Students are responsible for quantitative problems to the extent those problems are covered in class or homework · Final Exam will be cumulative Policy All participants are expected to always handle themselves with professional conduct. Students are expected to adhere to all university policies and uphold academic integrity throughout the course. · If a student with a disability is requesting accommodations, please contact New York University’s Moses Center for Students with Disabilities at 212-998-4980 or [email protected].You must be registered with CSD to receive accommodations. Information about the Moses Center can be found at www.nyu.edu/csd. The Moses Center is located at 726 Broadway on the 2nd floor. · If you are experiencing an illness or any other situation that might affect your academic performance in a class, please email Deanna Rayment, Coordinator of Student Advocacy, Compliance and Student Affairs: [email protected]. Deanna can reach out to your instructors on your behalf when warranted. The NYU Tandon School values an inclusive and equitable environment for all our students. I hope to foster a sense of community in this class and consider it a place where individuals of all backgrounds, beliefs, ethnicities, national origins, gender identities, sexual orientations, religious and political affiliations, and abilities will be treated with respect. It is my intent that all students’ learning needs be addressed both in and out of class and that the diversity that students bring to this class be viewed as a resource, strength, and benefit. If this standard is not being upheld, please feel free to speak with me. The Department of Technology Management and Innovation does not permit remote attendance in any of its fully on-campus course sections. If you encounter a situation that will prevent you from attending your classes in person for more than one session, you should reach out to your Academic Advisor as soon as possible to discuss the available options (Term Withdraw, Leave of Absence, etc.). If you are sick and unable to attend a single session, you should contact your classmates for any notes or materials that you may have missed. If you require an excused absence to make up an assignment, please contact the Office of Student Advocacy to apply for one. Please note that if it comes to the attention of the department that you have not been attending your classes, but have been submitting work remotely, you will be subject to total withdrawal from these classes with potential full tuition and fee liability. Grading · Discussion, participation, [15%] · Attendance, [10%] · Term Projects [05/09/2025], [15%] · Midterm Exam [05/21/2025], [25%] · Final Exam [05/14/2025], [35%] Grade range: Total 50 65 70 75 80 85 90 95 Grade F C C+ B- B B+ A- A Part I: [Philosophies and Fundamentals] [01/22/2025] Session 1 “Introduction and Overview to Quality.” · to define quality as it relates to the manufacturing and service sector, · to introduce the terminology related to quality · to set up a framework for the design and implementation of quality · discuss total quality management, six sigma, and quality systems and standards · discuss the three functions: quality planning, quality assurance, and quality control and improvement · Reading Chapters 1 o pp. 2 to pp.45 Part II: [Statistical Foundations and Methods for Quality Improvement] [01/29/2025] Session 2 “Statistical concepts and techniques in quality control and Improvement.” · to review different statistical concepts and techniques · to learn how to use descriptive statistics based on collected data in quality. · to learn how to use inferential statistics to conclude a product or a process parameters performance through statistical analysis · to review some important probability distribution and their assumptions · be able to select an appropriate probability distribution for use in specific applications · use an approximation for some probability distributions · Reading Chapter 4 o pp. 153 – pp. 214 [02/05/2025] Session 3 “Data Analysis and Sampling.” · to expand on the various descriptive and inferential statistical procedures · learn how to analyze empirical data graphically since they provide comprehensive information and are a viable tool for analysis of product and process data · to test and identified a distributional assumption · to present a method for testing the validity of a distributional assumption · to discuss some transformations to achieve normality for variables that are nonnormal · Learn how to handle issues of determination of sample size is of paramount importance in quality · Identify Deming’s kp rule that minimizes average total cost of inspection is presented · Reading Chapter 5 o pp. 233 – pp. 244 o pp. 260 – pp. 268 o pp.270 – pp. 274 Part III: [Statistical Process Control] [02/12/2025] Session 4 “Statistical process control using control charts.” · To provides the necessary background for understanding statistical process control through control charts · to introduce the principles on which control charts are based. · what are the basic features of the control charts, along with the possible inferential errors and how they may be reduced, are presented · To understand the various types of out-of-control patterns · Reading Chapter 6 o pp. 287 – pp. 307 [02/19/2025] Session 5 “Control Charts for Variables.” · to introduce the principles on which variable control charts are based · to define the basic features of variable control charts, along with the possible inferential errors · to understand the statistical basis of variable control charts and design it · to learn how to set up variable control charts and interpret patterns · to define the different types of variable control charts · to learn how to set up and use control charts for individual measurements · to understand the rational subgroup concept for variables, control charts · Advantages and disadvantages of variable chats · Reading Chapter 7 o pp. 311 – pp. 341 [02/26/2025] Session 6 “Special Control Charts Topics.” · know how to set up and use the CUSUM control charts · design CUSUM control charts for the mean to monitor the process · know how to set up and use EWMA control charts · design EWMA control charts for the mean · understand the performance advantages of CUSUM and EWMA · set up and use control charts for a short production run · set up and use control charts for a short production run · Reading Chapter 7 o pp. 342 – pp. 357 [03/05/2025] Session 7 Mid Term Exam [03/12/2025] Session 8 “Control Charts for Attributes.” · to understand the statistical basis of attribute control charts and design it · to learn the different attribute control charts (p-chart, np-chart, c- charts, and u- charts) and set up the correct control chart for defects and nonconforming · to learn how to interpret patterns on attribute control charts · Advantages and disadvantages of attributes chats · Reading Chapter 8 o pp. 405 – pp. 448 [03/19/2025] Session 9 “Process Capability Analysis I.” · to present and learn how analyze whether a process or product or service meets the specifications required by the customer · to define measures that indicate the ability of the process to meet specifications; these are, in some sense, measures of process performance · to present some of the commonly used process capability measures, demonstrate procedures for their computation, interpret them, and discuss any associated assumptions. · to discuss methods for discrete variables satisfying the binomial or Poisson distribution, capability measures are also discussed · Reading Chapter 9 o pp. 469 – pp. 498 [03/26/2025] No Classes Spring Break [04/02/2025] Session 10 “Process Capability Analysis II.” · to learn methods to how to handle the measuring instrument, · to be able to set measures of precision of the instrument as well as the impact of various operators who use the instrument are also of interest, and appropriate measures are presented. · learn how to conduct Reproducibility and Repeatability analysis (Gage R&R) · Reading Chapter 9 o pp. 499 – pp. 510 [04/09/2025] Session 11 “Reliability.” · to expose reliability calculations of systems, with a variety of components, · understand the different systems configurations · to understand the concept of standby components and their impact on system reliability · to demonstrate the use of reliability and life testing plans and develop parameter estimates through sampling plans · Reading Chapter 10 o pp. 527– pp. 551 [04/16/2025] Session 12 “Quality Assurance Methods” · Handout [04/23/2025] Session 13 “DOE – ANOVA and Factorial Design.” · to understand how designed experiments can be used to improve product design and improve process performance · to be able to analyze and estimate the main effect and interactions of factors · to understand the factorial design concept and how to use ANOVA to analyze data from factorial designs · how DOE is used to reduce the cycle time required to develop new products and processes · to be able to construct and interpret contour plots and response surface plots. · Reading Chapter 11 o pp. 595 – pp. 622 [04/30/2025] Session 14 “Project Presentations and Course Review.” [05/14/2025] Session 15 “Final Exam.”
Module Code: CMT304 Module Title: Programming Paradigms Assessment Title: Logic Programming Assignment Consider the following situation: Patent requests are submitted to the patent office and are reviewed by members of the tech- nical board. To find a good match between patent requests and board members (referees), every member of the technical board declares their expertise for each submitted request that needs to be reviewed: EXPERT, KNOWLEDGEABLE, FAMILIAR or INEXPERT For example, declaring EXPERT for a given patent request, means “I am an expert on the topic of this request” . The goal is to write a program to automate this process. Using a list of bids, indicating the level of expertise for each patent request and board member, it should assign each submitted patent request to a specific number of n members of the technical board such that • the workloads of the technical board members are approximately equal, that is, do not differ by more than m; • no member of the technical board is required to review a submission that is placed in the INEXPERT category; • no member of the technical board is required to review more thank submissions from the FAMILIAR category; • the total number of cases when a submission is assigned to a member who placed it in the EXPERT category is as large as possible. The parameters n, mandk are arguments set when calling the program. Task 1: Write a logic program in ASP which finds all solutions to the problem, given n, m, k. Task 1: Write an ASP program (coursework.lp) that solves the problem for any instance. Your program will receive as input a set bid/3 of triples mem, req, exp, such that the member mem has declared to have expertise exp for request req. The output of your program is a set assign/2 of pairs mem and req such that the member mem has been assigned to review request req. Make sure you document your code so it is clear how it should be used and what the approach to solving the problem is. Document your code so the following is clear. 1. How it should be used. 2. What the approach to solving the problem is. In particular, you need to explain what each rule achieves and how the rule achieves it. Include your name and student id in the comments. Task 2: Write a short report on logic programming related to the problem: 1. Provide, in up to 300 words, an analysis of the design and functioning of your program in terms of the Guess-and-Test modeling methodology. The word limits are an upper limit, not a target length. Text longer than the word limit for each point will be ignored. Learning Outcomes Assessed • Explain the conceptual foundations, evaluate and apply various programming paradigms, such as logic, functional, scripting, filter-based programming, pattern matching and quantum computing, to solve practical problems. • Discuss and contrast the issues, features, design and concepts of a range of program- ming paradigms and languages to be able to select a suitable programming paradigm to solve a problem. Criteria for assessment Task 1: maximum 50 marks, assessed according to the following scale Fail 0 No code has been submitted. 1 − 14 Code does not run or does not produce valid output for any valid input; little to no relevant documentation. 15 − 24 Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). Even if the output is not a solution, a suitable attempt to solve the problem is visible. An attempt to document the code has been made. Pass 25 − 29 Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). A suitable attempt to solve the problem has been made, that will often find at least one solution (if there is any). The attempt has been reasonably documented, but no consideration has been given to optimise the program’s performance. Merit 30 − 34 Code is valid without syntax errors and creates a valid output for every valid input (or produces a suitable error message for valid cases it cannot process). A suitable attempt to solve the problem has been made, that will find all solutions (if there are any). The attempt has been well documented. Distinction 35 − 50 Code is valid without syntax errors and creates a valid output for every valid input. A suitable attempt to solve the problem has been made, that will find all solutions (if there are any) for all problems, with excellent performance. The attempt has been well documented and clearly shows an effort to op- timise the program’s performance, e.g. by using efficient algorithms and data repres1entations and also some heuristics. Task 2: maximum 50 marks, assessed according to the following scale Fail 0 No document has been submitted. 1 − 14 At most an incomplete attempt to analyse the design and functioning of the program has been made. 15 − 24 An attempt has been made to analyse the design and functioning of the program. Pass 25 − 29 A suitable attempt has been made to analyse the design and functioning of the program. Merit 30 − 34 The analysis of the design and functioning of the program is well-developed, showing a clear understanding of the Guess-and-Test methodology. Distinction 35 − 50 The analysis of the design and functioning of the program shows a clear understanding of the Guess-and-Test methodology and shows an under- standing of related performance issues.
EG501V Computational Fluid Dynamics SESSION 2016-17 00 December 2016 Problem 1 (a: 2 marks; b: 15 marks; c: 8 marks; total 25 marks) We use dimensionless quantities throughout this problem. Figure. Left: flow geometry and streamlines; right: discretization and numbering of unknowns. Consider the two-dimensional flow in a sharp 90o bend as sketched in the left panel of the figure. This flow can be described by means of a stream function φ(x, y) that obeys the following PDE: The right panel of the figure defines the flow geometry and boundary conditions: = 0 at the inlet (bottom); = 0 at the outlet (right) ; φ = 0 on the right and lower wall; φ = 1 on the left and upper wall. The figure also defines the discretization, with spacing Δ = 1 . We realize that the problem is symmetric with respect to the dashed line in the left panel. This implies that we only need to solve φ in the numbered points in the right panel of the figure. a. What type of PDE (parabolic, elliptic, hyperbolic) are we dealing with? b. From a discretization of the PDE, and from the boundary conditions determine the 9×9 matrix [A] and the 9-dimensional vector b such that the 9-dimensional vector φ containing φk , k = 1…9 satisfies [A]φ = b . Number the unknowns φk as indicated in the figure. c. The fluid velocity in x andy-direction ( ux and uy ) is related to the stream function φ according to ux = and uy = − . The solution to [ A b ]φ = b is φ = [0.6266, 0.4347, 0.3737, 0.3594, 0.9093, 0.8186, 0.7385, 0.7006, 0.6901]. Given this solution, determine ux and uy in points 1, 3, 4, and 5 based on central differences approximations. Problem 2 (a: 7 marks; b: 9 marks; c: 9 marks; total: 25 marks) Figure. Catalytic layer & discretization In steady state, the concentration c of a chemical species that is being consumed in a layer (thickness d) of solid catalytic material can be described by the following reaction-diffusion equation: with Γ the diffusion coefficient, and k the reaction rate constant. At the left side of the layer (at x=0) the concentration c is maintained at c0, at the right side (at x=d) at c=0. In dimensionless form the parameters of this problem are: d=4, Γ = 1 , k=1, and c0 = 1 . In order to solve for c as a function of x, c is discretized to ci , i = 1…3 , with a constant spacing Δx = 1 between the points, see the figure. a. First discretize the differential equation: write it as a linear algebraic equation in terms of ci . Then set up a linear system of equations in matrix-vector form [A] c(→) = b(→) with c(→) the vector containing the three unknown concentrations ci , [A]a 3x3 matrix, and b a three- dimensional vector. Determine [A] and b . The rest of this question is about solving [A] c(→) = b . If you do not have an answer under Question a., assume and (these [A] and b are not the correct answer for a.). b. Solve the system [A] c(→) = b by means of Gaussian elimination; show all the steps that lead to your solution. c. Perform. two (2) Gauss-Seidel iterations on the system [A] c = b. Take as the starting vector of the iteration process. Problem 3 (a: 5 marks; b: 5 marks; c: 15 marks; total: 25 marks) We are dealing with a turbulent flow in which the chemical reaction A + B → P takes place. The reaction is of second order which means that the number of moles of product P being produced per unit volume and per unit time (symbol rP, unit [mol/(m3.s)]) is rP = kPcAcB with cA and cB the concentration [mol/m3] of species A and B respectively, and kP the reaction rate constant [m3/(mol.s)]. We assume all species have the same diffusion coefficient Γ [m2/s]. a. For a non-reacting system, the transport equations for chemical species A and B read respectively. Argue that for the reacting system these equations become and b. What is the transport equation for the concentration cP [mol/m3] of chemical species P? c. Derive through a Reynolds decomposition of the equation an equation for the time-average concentration c . Assume a two dimensional situation. Identify the terms in the equation that need closure. Problem 4 (25 marks) We use dimensionless quantities throughout this problem. The discrete version of the pressure-correction equation reads: Given the 3x3 mesh of control volumes as in the figure, given the boundary conditions for pressure correction π which is ∂π∂n = 0 on all four boundaries, and the preliminary velocity values ux(*) and uy(*) as given in the figure, determine the matrix-vector system [A = b(→) that needs to be solved in order to in the same order as the pressure points numbered in the figure). Further given: hx = 1, hy = 0.5, ρ △t = 1 . Figure. Staggered mesh. Pressure defined in the centre of each control volume (dots); velocity at the vertices of each control volume (arrows). All values given are velocity values.
F24 ECE 551 HW06, Due 11PM Thu. Oct. 17 Pr. 1. Given an N × N matrix A and initial vector x0 ∈ F N , the power iteration uses the iterative recursion xk+1 = Axk/∥Axk∥2. If A is an N × N Hermitian matrix for which the eigenvalue with the largest magnitude exceed all others, i.e., |λn| < |λ1| , n = 2, . . . , N, then the sequence {xk} generated by the power iteration converges to e ıϕv1 as k → ∞, where v1 is the leading unit-norm eigenvector associated with the largest (in magnitude) eigenvalue λ1, and e ıϕ is an arbitrary phase factor. if v1 ′ x0 = [V ′x0]1 = 0. (Ch. 8 considers more generality.) (a) Let B denote an N × N Hermitian symmetric matrix with distinct (in magnitude) eigenvalues, ordered such that λN < λN−1 < . . . < λ2 < λ1. Suppose that λ1 is known. Describe how to use one run (where k → ∞) of the power iteration (possibly with a modified input matrix) to compute the eigenvector vN associated with the smallest eigenvalue of B, namely λN , assuming it is unique. Here we mean smallest value, not smallest magnitude. (Do not assume B is invertible.) Hint. What simple transformation of B maps its smallest eigenvalue to its largest (in magnitude)? Remember that eigenvalues can be negative so it is possible that |λ1| < |λN |. (b) Describe a simple way to compute λN from the vN result of part (a). The eigenvector vN is not unique because it could be scaled by e ıϕ. Does that “sign ambiguity” affect your calculation of λN ? (c) Describe how to modify the scheme to find vN if λ1 is unknown. (You may apply the power iteration more than once in this case, but do not invert B. Use as few applications of the power iteration as possible for full credit.) Pr. 2. This problem examines important properties of positive semidefinite and positive definite matrices. Recall from Ch. 3 that B′B ⪰ 0 for any matrix B. For each part, you may use results from previous parts if helpful. (a) (Optional) Show that B′B ≻ 0 if B has full column rank. (b) (Optional) Show that A ≻ 0 implies A is invertible. (c) (Optional) Show that A ⪰ 0 and B ⪰ 0 ⇒ A + B ⪰ 0. (d) Show that A ≻ 0 and B ⪰ 0 ⇒ A + B ≻ 0. (e) Show that A′A + B′B is invertible if B has full column rank. (This property is relevant to regularized LS problems.) (f) Show A′A + B′B is invertible if N (A) ∩ N (B) = {0} , i.e., if A and B have disjoint null spaces other than 0. (g) (Optional) Show that A ≻ 0, B ≻ 0 ⇒ BAB ≻ 0. Pr. 3. In many artificial neural network models used in machine learning, the final layer is often “dense” or “fully connected” and often is affine or linear. This problem focuses on the linear case. In a supervised learning setting, we are given training data (xn, yn), n = 1, . . . , N consisting of pairs of features xn ∈ RM and responses yn ∈ R. A linear artificial neuron makes a prediction simply by computing the inner product of an input feature x ∈ RM with a (learned) weight vector w ∈ RM, i.e., yˆn = w′xn. We want to train the weight vector w to minimize the average loss over the training data by solving the following optimization problem: Determine analytically the optimal weight vector wˆ in the case where the loss function is the squared error You may assume that the data matrix X = [x1 . . . xN] has full row rank. State any conditions needed on N for this assumption (and hence your answer) to be valid. Hint. You should be able to set this up as a linear least-squares problem and express your answer in terms of the training data feature correlation matrix Kx = N 1 P N n=1 xnx ′ n and the cross-correlation between the training data features and responses Kyx = N 1 P N n=1ynx ′ n . Pr. 4. (a) Consider the LLS problem arg minx ∥Ax − y∥ 2 2 . When A has full column rank, the solution is xˆ = (A′A) −1A′y, which involves inverting A′A. Express the condition number of A′A in terms of the singular values of A. (b) The Tikhonov regularized solution is arg minx ∥Ax − y∥ 2 2 + β ∥x∥ 2 2 = (A′A + βI) −1A′y. Here we invert a different matrix. Express the condition number of that matrix in terms of the singular values of A and β > 0. Verify that the regularized solution has a “better” condition number.
Synopsis & Storyboard for your Project Title: A Mother’s Journey Synopsis of the story The main character of the story is a female manager named Anna, who returns to work after having a baby. She was highly respected in the company before, but now she finds herself being marginalized. Anna was an important member in the company, and had outstanding performance and leadership. However, as her maternity leave ended and when she went back to work, she found that the colleague's attitude had changed. While she was on maternity leave, the company handed over the projectshe was working on to other colleagues without notifying her. Anna gradually realized that she was no longer the trusted manager. Her ideas are being listened to less and less. Her boss and colleagues seemed to imply that she was no longer able to work as hard as she once did as a mother. In addition to the indifference of her boss and colleagues, Anna also discovered that a young colleague Lily, was gradually replacing her position.. Lily took over Anna's work while she was on maternity leave and was highly praised by superiors for her excellent performance. What makes Anna unique is that she is not only an outstanding leader, but also a perseverance and intelligent woman. She has shown great resilience in balancing the challenges of career and family. However, facing exclusion in the workplace and the prejudice as a mother, Anna also had to face the reality that her career was being affected. After that, Anna decides to stop being silent, and actively participates in team meetings, seeks advice, and takes on small projects to show what she can do. She begins communicating with her boss about her passion for her work and her contribution to the team. At the same time, she also establishes a good relationship with Lily, sharing experience and seeking cooperation. Through persistent hard work, Anna gradually earned the respect of her colleagues and the trust of her superiors, regained her place in the team, and proved that motherhood did not hinder her career. Who: - Anna's supervisor: The change in her supervisor's attitude towards Anna reflects the company culture's implicit bias against female staff. - Colleagues Lily: A young and talented co-worker who takes over Anna's job while she is on maternity leave. Lily does not realize that she has inadvertently become Anna's competitor. She transforms into a supporter after the story. - Anna's Family: Anna's family was emotionally supportive during her career challenges and encouraged her to return to work and achieve her career goals. Their understanding and support provides Anna with greater confidence. - Other Colleagues: they may have negative attitudes toward Anna influenced by the company culture. What: Logline: A high-potential manager returns to the workplace after having a baby, but finds herself marginalized and ignored as her company implicitly excludes her. This forces her to face the harsh reality that becoming a mother could derail her career aspirations forever. Story include: - Discrimination and gender equality in the workplace - Female resilience and growth - Balancing family and career Where: The story is set in Toronto. Scenarios include: - Office - Conference Room - Lounge area - Character's home - Supervisor's office - Outside the office building When: The story takes place in 2023. In recent years, the issues of gender equality and motherhood protection have been emphasized, and the discussion of women's rights and interests in the workplace has become more and more widespread globally. Therefore, Anna's story can trigger deep thoughts on these topics. Why: Anna's experience exemplifies the prejudice that many recent mothers face when returning to the workplace,revealing the hidden discrimination that is prevalent in the workplace. This still exists in many companies, prompting a focus on how to create more inclusive work environments. Meanwhile Anna's character challenges society's stereotypes of mothers and demonstrates what mothers are capable of when balancing work and family. Her story encourages women to believe that they can still be successful in the workplace, even if they become a mother. How: A 120-minute film about the joy ofpregnancy to the confusion of the workplace, it centers on the growth and challenges of the main character, showing how she deals with her changing identity, the pressures of the workplace, and the balance of her family life. Target audience: - Women in the workplace: Many professional women who return to the workplace after giving birth will face many workplace challenges and discrimination. They may resonate with Anna's experience and look for inspiration and strategies to cope with their own workplace dilemmas. - HR professionals: Those responsible for company culture, recruitment and employee relations. They want to understand the impact of motherhood on women in the workplace and how to create a more inclusive work environment. - Management and business leaders: Holding managerial positions in companies. They want to learn how to better support the work needs and career development of their employees, especially women, during motherhood. - Gender equality and motherhood protection advocates: Organizations or individuals concerned about gender equality and women's rights. Hope to use the stories to spark discussion on the rights of mothers in the workplace and promote social change. - Mental Health Professionals: Psychologists and psychological counselors who are concerned about workplace stress and mental health. Research on the impact of the workplace environment on women's mental health, as well as strategies to provide support and advice. - Male partners: To inspire male partners to reflect on their own role in gender equality and supporting their partners through Anna's experience, and to stimulate their thoughts and actions. Storyboard
MATH2003J, OPTIMIZATION IN ECONOMICS, BDIC 2023/2024, SPRING Problem Sheet 12 Question 1: Determine whether each of the following is true or false. Justify your answers. (1) If S1 and S2 are two convex sets in R2, then their union S1 ∪ S2 = {x ∈ R 2 ∶ x ∈ S1 or x ∈ S2} must be a convex set in R2. (2) If f and g are two concave functions on R n , then the function f + g is concave on R n . Question 2: Sketch the following sets and decide which are convex. Justify your answers. (a) {(x, y) ∈ R2 ∣ x, y ≥ 0 and x + y < 1} (b) {(x, y) ∈ R2 ∣ 1 ≤ x2 + y2 ≤ 4} (c) {x ∈ R ∣ ∣x∣ > 1} Question 3: Consider the function C(x, y) = 100/1x2 − 10x + 300/1y3 − 9y for x, y ≥ 0. (a) Examine if C is concave, convex or neither of them. (b) Find the critical points of C and show that at these points C attains a minimum.
Computer Science CSC263H September 4, 2024 Homework Assignment #1 Due: September 11, 2024, by 11:00 am • You must submit your assignment through the Crowdmark system. You will receive by email an invitation through which you can submit your work. If you haven’t used Crowdmark before, give yourself plenty of time to figure it out! • You must submit a separate PDF document with for each question of the assignment. • To work with one or two partners, you and your partner(s) must form. a group on Crowdmark (one submission only per group). We allow groups of up to three students. Submissions by groups of more than three students will not be graded. • The PDF file that you submit for each question must be typeset (not handwritten) and clearly legible. To this end, we encourage you to learn and use the LATEX typesetting system, which is designed to produce high-quality documents that contain mathematical notation. You can use other typesetting systems if you prefer, but handwritten documents are not accepted. • If this assignment is submitted by a group of two or three students, for each assignment question the PDF file that you submit should contain: 1. The name(s) of the student(s) who wrote the solution to this question, and 2. The name(s) of the student(s) who read this solution to verify its clarity and correctness. • By virtue of submitting this assignment you (and your partners, if you have any) acknowledge that you are aware of the homework collaboration policy for this course, as stated here. • For any question, you may use data structures and algorithms previously described in class, or in prerequisites of this course, without describing them. You may also use any result that we covered in class (in lectures or tutorials) by referring to it. • Unless we explicitly state otherwise, you should justify your answers. Your paper will be marked based on the correctness and efficiency of your answers, and the clarity, precision, and conciseness of your presentation. • The total length of your pdf submission should be no more than 3 pages long in a 11pt font. Question 1. (20 marks) The following procedure has an input array A[1..n] with n ≥ 2 arbitrary integers. In the pseudo-code, “return” means immediately exit the procedure and then halt. Note that the indices of array A starts at 1. weirdo(A[1..n]) 1 n = A.size 2 for i = 1 to n // i = 1, 2, . . . , n 3 for j = 1 to n // j = 1, 2, . . . , n 4 if A[n − j + 1] ≠ j then return 5 if (A[i] ≠ n − i + 1) or (A[1] + A[2] = 2n − 1) then return 6 return Assume that each assignment, comparison, and arithmetic operation takes constant time. Let T(n) be the worst-case time complexity of calling weirdo(A[1..n]) on an array A of size n ≥ 2. Give a function f(n) such that T(n) is Θ(f(n)). Justify your answer by explaining why it is O(f(n)), and why it is Ω(f(n)). Any answer without a sound and clear justification may receive no credit. Question 2. (20 marks) We want to compute the median of every prefix of an input array A[1..n] of arbitrary integers. More precisely, design an algorithm that outputs another array M[1..n], so that M[i] is equal to the median of the integers in the subarray A[1..i]. Recall that when i is odd, the median of A[1..i] is the element of rank (i + 1)/2 in the subarray, and when i is even, the median is the average of the elements with ranks i/2 and i/2 + 1. Your algorithm should run in worst-case time O(n log n). Hint: Maintain two heaps for the subarray A[1..i]: one that contains ⌈i/2⌉ elements of this subarray, and one that contains ⌊i/2⌋ elements of this subarray. What elements of A[1..i] should each one of these heaps contain? What kind of heap each one them is? How do you use them to compute the median of A[1..i]? How do you maintain these heaps when you increase i to i + 1? a. Describe your algorithm in clear and concise English, and also provide the corresponding pseudocode. Argue that your algorithm is correct. b. Justify why your algorithm runs in time O(n log n) in the worst case. [The questions below will not be corrected/graded. They are given here as interesting problems that use material that you learned in class.] Question 3. (0 marks) Design an efficient algorithm for the following problem. The algorithm is given an integer m ≥ 1, and then a (possibly infinite) sequence of distinct integer keys are input to the algorithm, one at a time. A print operation input can also occur at any point between keys in the input sequence. When the algorithm gets a print operation input, it must print (in any order) the m smallest keys among all the keys that were input before this print. For example, suppose m = 3, and the keys and print operations are successively input to the algorithm in the following order: 18, 13, 29, 4, 11, 22, print, 8, 15, 7, 14, 3, 9, 12, print, 2, 5, . . . The first print should print 13, 4, 11 (in any order), and the second print should print 4, 7, 3 (in any order). Assume that: (1) m does not change during an execution of the algorithm, and (2) at least m keys are successively input to the algorithm before the algorithm gets its first print input. Describe a simple algorithm that solves the above problem with the following worst-case time complexity: • O(log m) to process each key input. • O(m) to perform. each print operation. Your algorithm must use a data structure that we learned in class. • State which data structure you are using and describe the items that it contains. • Explain how your algorithm processes a key input, and how it processes a print operation input. First describe this clearly and concisely in English, and then give the pseudo code. • Explain why your algorithm achieves the required worst-case time complexity described above. • Prove that your algorithm is correct (Hint: use induction. What is your induction hypothesis?) Question 4. (0 marks) Let A be an array containing n integers. Section 6.3 of our textbook (CLRS) describes a procedure, called Build-Max-Heap(A), that transforms array A into a max-heap in O(n) time. That procedure works “bottom-up”, using Max-Heapify repeatedly. Another way of transforming A into a max-heap is to insert the elements of A into the heap one at a time. Specifically, the algorithm is as follows: Build-by-Inserts(A) A.heapsize := 1 for i := 2..n do Max-Heap-Insert(A, A[i]) a. Give an example of an input array A for which the two procedures Build-Max-Heap and Build-by-Inserts produce different outputs. Keep your example as small as possible. b. Let T(n) be the worst-case time complexity of Build-by-Inserts for an input array A of size n. Prove that T(n) is Θ(n log n). (Recall that the worst-case time complexity of Build-Max-Heap is O(n), and therefore Build-Max-Heap is more efficient than Build-by-Inserts.)
Homework 1 Due on Friday, January 24th Instructions: • Install pdflatex, R, and RStudio on your computer. • Please edit the HW1 First Last .Rnw file in Rstudio and compile with knitr instead of Sweave. Go to the menu RStudio| Preferences . . . | Sweave choose the knitr option, i.e., Weave Rnw files using knitr? You may have to install knitr and other necessary pack- ages. • Replace ”First” and ”Last” in the file-name with your first and last names, respectively. Complete your assignment by modifying and/or adding necessary R-code in the text below. • You should submit both the data and the HW1 First Last.Rnw file in a zip-file in Canvas. The zip-file should be named ”HW1 First Last.zip” and it should contain all the necessary data files, the HW1 First Last .Rnw and HW1 First Last.pdf file, which was obtained from compiling HW1 First Last .Rnw with knitr and LATEX. NOTE: ”First” is your first name and ”Last” your last name. • The GSI grader will unzip your file and compile it with Rstudio and knitr. If the file fails to compile due to errors other than missing packages, there will be an automatic 10% deduction to your score. Then, the GSI will proceed with grading your submitted PDF. • Data. The zip-file should include also the ” .csv” file with the stock market data you down- loaded frin WRDS so that when everything is unzipped in one folder, the GSI is able to compile and reproduce your PDF. Problems: 1. (a) Read the tutorial on accessing and downloading data from WRDS available on this link. (b) Execute a query in Center for Research in Security Prices, LLC (CRSP) database to download the closing daily prices of the stocks with tickers TSLA and NVDA for the period Jan 1, 2022 through Dec 31, 2024. (c) Place the resulting csv file in a desired folder in your computer and modify the following code to produce plots of daily prices, returns, log-returns, and a scatter-plot of the log-returns of TSLA against those of NVDA. Identify the times of splits if any for the TSLA and NVDA stock in this period, if any. Uncomment, i.e., remove the ’%’, in the following lines when ready to compile. Remove also begin{verbatim} and end{verbatim} in the ”.Rnw” file. % = % dat = read.csv("data_file.csv",header=TRUE) % # Add code here to populate the necessary variables . % par(mfrow=c(2,2)) % plot(times$AAPL,stocks$AAPL,type="l") % plot(times$TSLA,stocks$TSLA,col="red") % # Add more code . . . % @ 2. Download the file ”sp500 full.csv” available in the Data folder of the Files section in Canvas. It provides the data on daily prices and returns (among other things) of the S&P 500 index. This is the same data set used in lectures. (a) Plot the time-series of daily returns and daily log-returns. You need to identify which variable gives the returns and also compute the log-returns from the daily closing values of the index. Comment on the extreme drops in daily returns/log-returns. Can they be associated with known market events? (b) Plot the auto-correlation functions of the 1-day (i.e., daily), 5-day, 10-day and 20-day log-returns and their squares. (c) Provide a table of the basic summary statistics for the 4 time series from part (b). That is, compute the minimum, 1st quartile, the median, the 3rd quartile and the maximum, for the k-day log-returns for k = 1; 5; 10; and 20. You can modify the code in the ”.Rnw” file that produces: returns = list("r1"=rnorm(100),"r5"=rnorm(50), "r10" = rnorm(20), "r20"=rnorm(10)) # The list is populated with random numbers, which you'd have to replace by the # corresponding returns. sum.stat = lapply(returns,summary) # What does this command do? x = matrix(0,nrow=4,ncol=6,dimnames=list(c("1-day","5-day","10-day","20-day"), names(sum.stat$r1))) x[1,]=sum.stat$r1 x[2,]=sum.stat$r5 x[3,]=sum.stat$r10 x[4,]=sum.stat$r20 kable(x) Min. Median 3rd Qu. 1-day -0.5695184 -0.0477111 2.110397 -1.622665 0.1826113 0.7654330 10-day -0.5967488 -0.1598409 1.703530 -2.057332 -0.3999786 0.7523935 3. (a) Using the same data set as in the previous problem, make a 2 × 2 array of normal quantile-quantile plots. You can uncomment and and modify the following code %= %par(mfrow=c(2,2)) %qqnorm(returns$r1) %qqline(returns$r1,col="red") %qqnorm(returns$r5) %qqline(returns$r5,col="red") %qqnorm(returns$r10) %qqline(returns$r10,col="red") %qqnorm(returns$r20) %qqline(returns$r20,col="red") %@ (b) What can you say about the tails of the returns? 4. (a) Goto the US Treasury web-site and lookup the annual yield to maturity of US government issued zero-coupon bonds of maturities 3 months, 5 years and 30 years, respectively. What are the names of these 3 types of securities? (b) Suppose that a bond with maturity T = 30 years, PAR $1000 and annual coupon payments C is selling precisely at its par value. Determine the value of the coupon payments C. You can assume that the yield to maturity is the one you found in part (a), corresponding to maturity T = 30. (c) Use the R-function uniroot to find the yield to maturity of a 30-year, par $1000 bond with annual coupon payments of $40, which is selling for $1200 now. Provide the R-code as well as the output. uniroot(function(x)(sin(x)-0.5), interval=c(0,pi/2))$root - pi/6 ## [1] -1.687498e-07 # Put your code above... Hint: Write an R-function that computes the price of a bond with yield to maturity r, annual coupon payments C, par value PAR and maturity T. You can borrow the function definition from the lectures. You can then use this function in your call to uniroot as I did in class, for example. 5. Suppose (although this is dangerously far from reality) that the daily log-returns of the S&P 500 are independent and identically distributed N (μ, σ2 ). (a) Using the data in file ”sp500 full.csv”, estimate μ and σ with the sample mean and standard deviation. (b) Using the independence and Normality assumptions, compute the value-at-risk at levels Q = 0.05 and Q = 0.01, i.e., VaR0.05 and VaR0.01 for the k-day log-returns, where k = 1, 5, 10 and 20. Hint: What is the distribution of the k-day log-returns, under the assumptions in the problem. (c) Provide a 2-row table of the proportion of times the k-day log-returns were lower than the -VaRQ values computed in part (b) for Q = 0.05 and Q = 0.01. That is, each entry in the table is the proportion of time the k-day log-losses were worse than the corresponding value-at-risk. p = matrix(0,nrow=2,ncol=4) colnames(p) = c("1-day","5-day","10-day","20-day") rownames(p) = c("0.05", "0.01") # Put your code here that populates p with the desired empirical proportions kable(p) 1-day 10-day 0.05 0 0 0 0 Comment on the results. What should the values of these empirical frequencies be for models that agree with the data? 6. In this problem we will first find a slightly more appropriate model for the log-returns of the SP500 index data set. The idea is to replace the increments of the normal random walk model in the previous problem with t-distribued increments. We will do so by trial and error and eyeballing QQ-plots. More sophisticated inference methods will come shortly. (a) As in Problem 2 above, load the SP500 data set from file sp500 full .csv. Select a consecutive period of 10 years. Standardize the log-returns in this period and produce a series of QQ-plots of the daily log-returns against simulated samples from the standardized t-distribution for varying degrees of freedom v = 2.1; 3; 4; . . .. Pick a value for the degrees of freedom v > 2 that result in the QQ-plot with the best fit. Produce a QQ-plot with this “best fit” value as well as with two other values of v – one smaller and the other larger. You can use some of the following code as a template and modify it as you see fit. Comment on why the value of v you chose is reasonable. %= %sp500 = read.csv("sp500_full.csv",header=TRUE) %t.sp = as.Date(x=as.character(dat$caldt),format="%Y%m%d") %idx = which(t.sp>as.Date("2000-01-01") & t.sp < as.Date("2010-01-01")) %rt = diff(log(sp500$spindx[idx])); %mu = mean(rt); %sig = sd(rt); %rt_standardized = (rt-mu)/sig; % %% The following function produces the desired QQ-plots . % %qqplot_against_std 2 and the volatility σ . Comment on how do the volatility and the weight of the tail (represented by the parameter v) afect the default probability. Note: Initially, use μ = 0.05/253 and σ = 0.23/√253 as in the text and vary v. Then you can fix a value of v and vary σ . Feel free to also produce heat-map images or 2-way tables of the default probability for a range of values of v and σ .
EG501V Computational Fluid Dynamics SESSION 2017-18 00 December 2017 Problem 1 [40 marks] We use dimensionless quantities throughout this problem. Figure. Left: solution domain and boundary conditions; right: discretization and numbering of unknowns. We want to numerically solve a steady convection-diffusion equation in the variable φ in a two- dimensional square domain with side length L=1. The equation reads ▽.(φu) = Γ▽2φ . The velocity vector u is constant in the entire domain and has components ux = 1, uy = 1 ; the diffusion coefficient Γ =1 . The boundary conditions are φ = 0 on the west boundary, φ = 1 on the south boundary, ∂φ∂x = 0 on the east boundary, ∂φ ∂y = 0 on the north boundary; see the left panel of the figure. The square domain is discretized according to the right panel of the figure. The dots are equally spaced. a. Give the discrete equations for points 1, 3, and 9 based on finite difference discretization with a central scheme for the convective term. [16 marks] b. Give the discrete equations for points 1, 3, and 9 based on finite volume discretization with an upwind scheme for the convective term and the volume centres coinciding with the numbered dots. [16 marks] A control volume based Peclet number can be defined as the spacing between points. c. Determine Pecv and decide if you want to apply the central or upwind scheme. [8 marks] Problem 2 [20 marks] We use dimensionless quantities throughout this problem. Figure: flow geometry, boundary conditions and discretization. Two-dimensional fluid flow can be described by means of a stream function φ(x, y) that obeys the following elliptic PDE: = 0 . Consider the two-dimensional geometry as shown in the figure. It defines the flow geometry and boundary conditions: = 0 at the inlet (left) and at the outlet (right); φ = 0 on the lower wall; φ = 1 on the entire upper wall. The figure also defines the discretization. a. From the discretization (with Δx = 1 and Δy = 0.5 ) of the PDE, and from the boundary conditions determine the 10×10 matrix [A] and the 10-dimensional vector b such that the 10-dimensional vector φ containing φk , k = 1…10 satisfies [A]φ = b . Number the unknowns φk as indicated in the figure. [12 marks] b. The fluid velocity in x andy-direction ( ux and uy ) is related to the stream function according to ux = and uy = − . The solution to [A] φ = b is φ = [0.3284 , 0.3200 , 0.2767 , 0.2641 , 0.6611 , 0.6487 , 0.5458 , 0.5219 , 0.7951 , 0.7678]. Given this solution, determine ux in points 1, 5 and 8, and determine uy in points 6 and 9 based on central differences approximations. Is the overall flow from left to right (in positive x-direction) or from right to left (in negative x-direction)? [8 marks] Problem 3 [20 marks] Water (density ρ = 1000 kg/m3 ; dynamic viscosity μ = 0.001 Pa.s) flows steadily through a horizontal, straight pipe with circular cross section of diameter D=0.2 m. The volumetric flow rate is φv = 0.01 m3/s. a. Argue that this is turbulent flow. [4 marks] Pressure drop in the pipe is due to friction. The pressure drop per unit length can be written as with U the average velocity in the pipe and f the friction factor. Given the pipe wall roughness f can be considered a constant: f = 0.015 . b. What is the average energy dissipation rate (symbol ε ) in the pipe? [4 marks] c. Argue − based on a dimensional analysis − that the expression for the Kolmogorov length scale (the micro scale of turbulence) reads l K = (ν 3ε)14 with ν = μρ the kinematic viscosity. Determine lK based on the average dissipation rate in the pipe. [6 marks] The shear stress at the inner pipe surface follows from a force balance in the streamwise direction over the liquid in the pipe: The wall shear velocity u* relates to the wall shear stress: We want to simulate the flow in the pipe with help of standard wall functions. For this the distance of the first grid point next to the inner pipe wall needs to satisfy the condition 30 < y+
GGR305 Biogeography Research Question Assignment Rubric Worth 5% of your final grade, this assignment is due Friday, Jan 31 by 11:59pm; Late submissions (after Jan 31) will occur 10% penalty per day (including weekends) for maximum five days. Assignments submitted five calendar days beyond the due date will be assigned a grade of zero. Basic Requirements: • Your assignment should be typed, and use 12pt Times font (or similar), double-spaced, submitted as a PDF file. • Make sure your name and student number are on your assignment. • You do not need a cover page. • Do not use direct quotes. Marks will be deducted if you use direct quotes to answer any of the questions listed under item number 3 below. Marking Scheme: Total point possible = 100 1. Research question (10 pts) Provide the research question you plan on addressing in your term paper. This research question is the foundation for your paper and must be sufficiently clear to ensure appropriate focus for your research paper. It can be more than one sentence. It should be phrased as a question. It should be related to biogeography either using one of the three suggested question approaches (on assignment guideline) or have a component that considers a taxon’s geographic distribution in some way (over time, in relation to limiting factors or humans, etc.) 10 pt- a clear and creative research question; grammatically correct. Appropriate for course. 9 pts- a clear but not creative question. (i.e. how has the geographic distribution of the X changed over time?). Appropriate for course. 7 pts- appropriate question but grammatically incorrect or not actually phrased as a question (but topic is appropriate in scope). 5 pts- grammatically incorrect and too broad and/or not appropriate for a course. 2 pts- so unclear/vague/poorly written you cannot figure out what the question is. 2. Reference list (10 pts) After using your key words/phrases to search scholarly article databases, provide the full reference for at least five articles relevant to your research question. Please follow APA style. These must be scholarly journal articles. Not websites/books/magazine articles. 2 pts- for each relevant article given in APA format, up to 5 articles. 1 pt- for each relevant article if not in APA format, up to 5 articles. 3. Choose one of the five articles you identified, answer the following questions. (80 pts) For one of the five articles you identify, please read it carefully and answer the following questions (make sure it is clear which article you have selected to answer the questions). You cannot use a review paper to answer these questions; make certain that the article is a primary source. In other words, it involves some type of data (e.g. field observations, samples of material, computer simulated data) that is analyzed and does not just provide a review of other scholarly papers. 1) What is the research question(s) that this paper is trying to answer? (10 pts) 10 pt- a clear statement (one or more sentences) of the research question in their article; grammatically correct. 7 pts- Some uncertainty what the research questions is/grammatical mistakes in writing. 5 pts- direct quoting (with or without quotes) from the article they read. 2 pts- so unclear/vague/poorly written you cannot figure out what the question is. 2) How is the research question addressed? In three to five sentences, please identify the type of data used (field observations, samples of material, computer simulated data, or something else) and how the data were analyzed. In other words, what methods were used in the paper. (15 pts) 15 pts- clearly stated description of data and analysis. No grammatical mistakes. Obvious student understands what the methods were. 12 pts- Methods stated. Either some uncertainty what the details could have been give and/ or grammatical errors. 7 pts- direct quotes of data used or methods. Or they used their own words, but did not include both parts (data and methods). Length of answer way off. 2 pts- so unclear/vague/poorly written you cannot figure out what the data/methods are. 3) In three to five sentences, please explain why you think this paper was published (addressing a basic gap in knowledge, testing a new hypothesis, applying an existing hypothesis or theory in a new situation, or something else). This information may be stated in the introduction of the paper and/or be your interpretation of the paper’s contribution. (15 pts) 15 pts- clearly stated explanation that is more than just repeating the specific research question. No grammatical mistakes. Obvious student understands what paper adds to knowledge. 12 pts- A reasonable reason given. Either some uncertainty about the details/weak argument and/or grammatical errors. 7 pts- direct quotes used. Or they used their own words, but do not provide a clear/convincing explanation. Length of answer way off. 2 pts- so unclear/vague/poorly written you cannot figure out what the reason is. 4) In one paragraph, describe the major findings or conclusions of the paper. (20 pts) 20 pts- clearly provides findings or conclusions that seems reasonable and are very well described. No grammatical mistakes. Obvious student understands. 17 pts- A reasonable set of findings is given. Either some uncertainty about the details (or lack of details) and/or grammatical errors. 10 pts- direct quotes used. Or they used their own words, but do not provide a clear/convincing set of findings. Length of answer way off. 5 pts- so unclear/vague/poorly written you cannot figure out what the reason is. 5) In one paragraph, explain how this paper is relevant to the question you are researching for your term paper. You must justify your choice/explanation by providing a logical rationale. (20 pts) 20 pts- clearly provides justification that is more than ‘on the same topic’. No grammatical mistakes. Obvious student understands article. 17 pts- A reasonable reason and justification. Either some superficiality to reasons and/or grammatical errors. 10 pts- direct quotes used. Or they used their own words, but do not provide a clear/convincing reason or justification. Length of answer way off. 5 pts- so unclear/vague/poorly written you cannot figure out what the reason is.
