Coursework Re-Assessment ANSWER ALL QUESTIONS Gender Identification Over-diversification of gender identities can lead to several challenges. Firstly, it may cause confusion and misunderstandings, both within the LGBTQ+ community and among the public. As the number of recognized identities grows, it becomes harder for people to understand and respect each distinct identity, potentially leading to miscommunication and inadvertent disrespect. Over-diversification can dilute the impact of advocacy efforts. When the focus is spread across avast number of identities, it becomes more challenging to address the specific needs and rights of each group effectively. This can result in a lack of coherent strategy and weaker political and social support for each identity. (a) Discuss in detail the above case study in the context of Kantian Theory principles (30 marks) Question 2 (a) Describe what is virtue ethics and explain a clear example to illustrate the theory being applied in real life. (10 marks) (b) A US major manufacturer, GA, has outsourced its 8,000-worker production plant to a lower cost country in order to boost profit margin and improve shareholders’ dividends. Many of the workers were made redundant as a result. Since the manufacturer no longer has a production facility in US, its suppliers who used to provide raw materials, machinery and other support services also suffered major losses and started retrenching their workers. The local government also collected fewer taxes since there were fewer employed workers and lowered business activities. Describe utilitarian theory and apply it to determine if GA’s decision to outsource its production is considered ethical or not. (20 marks) Question 3 (a) Identify and describe the corporate responsibility view that was advocated by Milton Friedman. (10 marks) (b) Entrepreneurs like Mark Zuckerberg of Facebook and Elon Musk of Space X have taken risks to build to their businesses and been successful at it. The fundamental premise for their success mostly hinges on the ownership of private property and free market forces. For billionaires like them who have made their wealth mostly based on their own effort and perseverance, would it be fair to impose high income tax on them to redistribute their wealth to help the poor? (20 marks) Question 4 (a) Describe the terms ‘sweatshop’ and ‘child labour’ . (15 marks) (b) Overfishing in countries like Japan has led to near distinction of some fishes due to the common believe that the supply of fishes is ‘free and unlimited’ . Identify and describe this incorrect assumption about nature and suggest a solution to overfishing. (15 marks) Question 5 (a) Distinguish between bribery and kickback with ONE example each to illustrate these unethical behaviours. (15 marks) (b) On average, female in US earn about 20% less than male in similar jobs requiring identical qualifications and experiences. Identity and describe the program that aims to close this gender pay gap. (15 marks)
Session 7 activities worksheet Due: February 14 Regrades until: March 20 Online listings: eigen_basis_class.cpp and diffeq_oscillations.cpp printouts. Now that we've got routines to solve differential equations, we're going to explore some interesting ones: nonlinear oscillators. Today we'll play with a program that solves for the time dependence of such an oscillator. Your goals for today (and ...): · If you didn't complete it, do the plot from Session 6 of relative error at t=1 vs. mesh size h. · Think about how to enhance the eigen_basis code with more C++ classes. · Run a code that solves the differential equation for a (driven) nonlinear oscillator and explore how the time dependence changes as various input parameters change. · Add friction (damping) to the code. A) More on C++ Classes: eigen_basis_class The code eigen_basis_class.cpp is a simple modification of eigen_basis.cpp to use the Hamiltonian class we introduced for eigen_tridiagonal_class.cpp. Here we'll take a few minutes to think about how to introduce additional classes. 1. Take a look at the eigen_basis_class.cpp printout and note how the Hamiltonian class is re-used without modification. (If you haven't done so yet, read the discussion of this class in the Session 7 notes.) The only tricky change is that matrix indices go from 1 to dimension rather than from 0 to dimension-1. What parts of the Hamiltonian class implementation do you not yet understand? 2. The potential is another good candidate for a class. We'd like to just evaluate the potential at r without having to use constructions like the switch statement in the Hij_integrand function with all the messy void parameters. (Think about how awkward and prone to error it is to add another potential.) What would you like the declaration statement (the one where the Potential object is declared in the main program) for the Potential class to look like? What method(s) would you like the class to have? 3. Give at least one example of an additional class that would be useful to define. B) Driven Nonlinear Oscillations The Session 7 notes describe the driven nonlinear oscillator that is coded in diffeq_oscillations.cpp. Note that the force depends on k and an exponent p, the external force has a magnitude f_ext, a frequency w_ext, and a phase phi_ext. The initial conditions in position and velocity are designated x0 and v0. You also have control over the time interval (increase t_end to see longer times), the step size h, and how often points are printed to the file (plot_skip). 1. Use make_diffeq_oscillations to create diffeq_oscillations. This code outputs to the file diffeq_oscillations.dat five columns of data: t, x(t), v(t), kinetic energy, and potential energy. There are four gnuplot plot files provided (diffeq_oscillations1.plt, etc.), each of which generates a different type of plot. Run diffeq_oscillations with the default values (enter "0" when it says "What do you want to change?") to calculate a data set. Start gnuplot and "load diffeq_oscillations1.plt" and then "load diffeq_oscillations2.plt". (Once you've given these commands once, you can use just use the arrows to go back and forth.) Briefly, what do each of these plots show? 2. Wouldn't it be convenient to generate all four plots at once in separate files? Load "diffeq_oscillations_all.plt"! (Check the warning in the file on what to do if you get an "unknown or ambiguous terminal type" error message!) 3. It's always a question whether or not you have coded a problem correctly, so you should always seek ways to check your results. One possibility is if we have a known solution. This works for p=2 (simple harmonic oscillator). What about other p? Another check is to identify a quantity that shouldn't change with time. Create a plot of such a quantity (you'll want to increase t_end) and observe the effect of changing the step size h to a larger value [e.g., try 10 and 100 times larger]. How do you decide on a reasonable h to use? (The "plot_skip" parameter indicates how often a point is written to the output file. So plot_skip=10 means that every 10 points is output.) 4. Verify that different amplitudes (e.g., different initial conditions determined by x0 and v0) lead to different periods for an anharmonic oscillator (p≠2). [Hint: You might find the "append" option useful.] Can you identify a qualitative rule? E.g., does larger amplitude mean shorter or longer period always? Try to explain the rule? Make sure you try different values of p, since they might lead to different rules! 5. Go back to the original parameters (quit the program and start it again), which has p=2. Now add a driving force f_ext=10 with w_ext=1 and look at the time dependence and phase-space plots. Then increase w_ext to 3.14 and then to w_ext=6.28. What are you observing? Now repeat with p=3 (starting with f=0). Can you find resonant behavior? C) Adding Damping Real-world systems have friction, which means the motion will be damped. The Session 7 notes have a list of three simple models for friction. We'll implement viscous damping: Ff = -b*v, where v(t) is the velocity. 1. Introduce the damping parameter "b" into the code: 1. add it to the force_parameters structure (with a comment!); 2. add it to the list of local force parameters in the main program; 3. give it an initial value; 4. add a menu item (e.g., [13]) and a case statement to get a new value. Try this part out before proceeding. Did it work? 2. Modify the "rhs" routine to include damping (you're on your own here!). What did you add? 3. Test your routine starting with p=2 and a small damping and look at both the time dependence and the phase-space plots. Then try some other p values. 4. Identify the three regimes described in the Session 7 notes: underdamped, critically damped, and overdamped. D) EXTRA: Looking for Chaos (Part I) Now we want to put it all together: a damped, driven, nonlinear oscillator. A different system with the same basic features is the realistic pendulum, which is described in the Session 7 notes. 1. In the notes there is a list of characteristic structures that can be found in phase space, with sample pictures. Can you find a combination of parameters for the non-linear oscillator that produce a pictures like the chaotic one in the notes? Provide the parameters you used and include a phase space plot. Make sure to set t_end to something large (e.g., 400), so that you are not only looking at transients. Also make sure to think about the necessary conditions for chaos when selecting your parameters and to turn on some damping (without that you will see transients forever). E) Reflection Write down which of the six learning goals on the syllabus this worksheet addressed for you and how:
[BUSINESS SCHOOL] ACADEMIC YEAR 2024/25 Assessment Brief Submission details Module title: Contemporary Issues in Banking and Finance Module code: UMEDFT-30-3 Assessment title: Task 5: Debate/Quiz Game Assessment type: Presentation Assessment weighting: 5% of total module mark Size or length of assessment: participation in one session Submission and feedback dates Submission deadline: depending on the debate-quiz game you are participating in, expect to submit your questions and participate as follows: - Debate-quiz game 1: Central bank policy o Questions due by email midnight Monday, January 27 o Debate-quiz game: Friday, January 31 - Debate-quiz game 2: Financial markets o Questions due by email midnight Monday, February 3 o Debate-quiz game: Friday, February 7 - Debate-quiz game 3: Financial crises o Questions due by email midnight Monday, February 10 o Debate-quiz game: Friday, February 14 This assessment is NOT eligible for 48 hour late submission window Submission format: Please submit word or PDF format. Marks and Feedback due on: 20 working days after your debate-quiz game (NB preliminary marks only until all presentations have been given) Marks and Feedback will be provided via: Email Module learning outcomes assessed by this task: 1. MO3 Apply critical thinking skills to develop informed arguments and propose evidence-based solutions in defined contexts. 2. MO4 Present in a professional manner Use of AI in assessment: You may not use AI to assist you in this assessment. Completing your assessment What am I required to do on this assessment? Assessed Individual Participation All marks for this assessment are individual. By midnight on the Monday before the debate-quiz game you must submit at least one question on the topic of your debate-quiz game, and you may submit no more than three questions on the topic. These questions should either be short answer or multiple choice questions, and you must also submit the correct answer for your question at the time that you submit your question. Keep in mind that this is individual work and that you can be penalized for collusion if you do not draft your questions on your own. Attendance on the day of the debate-quiz game to which you are assigned is mandatory. On that day you will be placed in a team with other participants. The teams will compete to earn the most points and answer the most questions. Active participation in answering questions will be an important factor in your mark, as will the quality of your responses. Where should I start? The topics align with the module content. Make sure you attend the lectures, the lectorials, the presentations and read the suggested material. Make notes as you go. If you miss a class, review the recorded lecture material and attempt the lectorial questions for yourself. Ask a friend if you can look at their notes. Come to office hours to check your understanding or if you have any questions. If there is something you don’t understand, bring it up in class, or come to office hours for a chat. You can also email for an appointment outside of office hours. What do I need to do to pass? The pass mark is 40%. How do I achieve high marks in this assessment? You mark will be determined as follows: 50% of the marks (50 of 100) will be awarded based on the quality of the highest scoring question that you submit. That is, submitting additional questions does not automatically improve your mark, but it allows you to have more chances at getting a higher mark. Marking of the questions is based on the following criteria: The question will be marked based on its critical engagement with the material covered in the module and/or engagement with the reading list and related research. Correct use of English and clarity of expression will also affect the mark. A basic factual question with an accurate answer (e.g. what is the name of the central bank in Malaysia) will receive a mark of 20. No questions submitted, a mark of 0. 50% of the marks (50 of 100) will be awarded based on your engagement with the quiz game itself, including making an attempt to answer questions. This mark will be determined by your participation, by your ability to answer questions and by the quality of your responses, and your demonstration of your critical thinking skills and your ability to present yourself professionally. What additional resources may help me complete this assessment? Further information about this assessment is available on the Blackboard site for this module and includes: The module handbook, reading list and debate folder. Make the most of the support offered by the university: https://www.uwe.ac.uk/study/study-support/study-skills What do I do if I am concerned about completing this assessment? It is recommended that you review all of the relevant materials on Blackboard. You can also speak to your module leader for advice and guidance. UWE Bristol offer a range of Assessment Support Options that you can explore through this link, and both Academic Support and Wellbeing Support are available. For further information, please see the Student study essentials.
Economics 120B Econometrics, Winter 2025 Description: This course prepares students for empirical analysis in an academic or business setting. It covers the fundamentals of regression, including estimation and hypothesis testing in a univariate and multivariate framework. It presents ideas using the “potential outcomes” framework and makes the important distinction between prediction and causality. The course discusses reasons why estimators may be biased or inconsistent, and how both randomized experiments and natural experiments can be used to obtain causal estimates. The material can be difficult and the workload substantial, particularly for those who find math courses challenging. However, your payoff for all this work is a set of skills, analytical tools, and ways of thinking about data that are extremely useful and in high demand in the marketplace. Important Dates and Times: Class: Tuesdays and Thursdays, 9:30 – 10:50 am (location: MOS 0113) Midterm: Tuesday, February 11 in class Final: Saturday, March 15, 3:00 – 6:00 pm Class: Tuesdays and Thursdays, 11:00 – 12:20 pm (location: PODEM 1A20) Midterm: Tuesday, February 11 in class Final: Saturday, March 15, 3:00 – 6:00 pm Class will be held in person and attendance is strongly encouraged. Class lectures will not be recorded; if you miss a class, the best option is to find a classmate who can share notes and fill you in on what you missed and/or to visit a TA during office hours for extra help. We will also have some in-class “bonus” quizzes which can only be completed by attending class. Instructor: Gordon Dahl Office hours: Tuesdays, 12:30 – 1:30 pm Location: Atkinson Hall 6320 email: [email protected] (please do not use the email built into canvas, as I do not monitor it) Feel free to stop by in person so that I can get to know you. As these are large classes, I will prioritize speaking with students about things which the TAs cannot help with, such as strategies to do better in the course, unusual circumstances, graduate school options, etc. In other words, while I am happy to talk about homework, if there are any students needing to talk about other things, then they will jump to the front of the queue. Graduate Teaching Assistants: Maddison Erbabian, Kurtis Gilliat, Alec Hoover, Haoyu Wei Undergraduate Instructional Assistants: Varun Naik, Ryan Zhao The graduate TAs are a valuable resource, and I encourage you to take advantage of their help during their office hours. This is an excellent resource for help in understanding course content, homework assignments, and the Stata programming package. If you have a general question about the class, rather than a specific question about content, homework, or Stata (which you should ask about during TA office hours), please use the class email [email protected]. A graduate TA will monitor this email, and forward anything which they cannot answer to me. Please do not use the email built into canvas, as it will not be monitored. The undergraduate assistants are also a great resource. They will also be holding office hours and I encourage you to take advantage of their help. They have recently taken the class, and so have a first-hand perspective about the types of questions you might have and are well-prepared to answer homework and class questions. Details on the office hours of the TAs and UIAs will be announced in Canvas. The current plan is to have at least some, and perhaps all, office hours via zoom. TA and UIA office hours will start on week two of the quarter unless otherwise noted. Review Sessions: There will be review sessions each week which will be conducted by a graduate TA. The weekly review sessions will normally focus on helping students get started on the homework, but will also occasionally review topics covered in class and help prepare for exams. You are welcome to attend any of the review sessions, regardless of which one you are registered for. Further details on review sessions will be provided during the first week of class and announced on Canvas. Class Web Site: canvas.ucsd.edu The class web site contains the syllabus, lecture notes, homework assignments, and class announcements. You should check it regularly as you are responsible for any information posted there in addition to any announcements made in class. Text and Online Videos: For this course we will be using both a textbook and online videos. The two are not always substitutes for each other. For some class topics the videos are the better resource, while for others the textbook is better. I will make sure to point students to the most appropriate resource during class lectures. Text: The textbook is the Pearson eBook Introduction to Econometrics, 4th Edition by Stock and Watson. The eBook access for the course is being delivered through Follett’s BryteWave RedShelf as a link on Canvas. The UCSD Bookstore has not provided information this year on specific details on how to opt out of purchasing this ebook. If you have any questions about billing, etc., you can try contacting [email protected]. EVH Videos: We will also be using the Econometrics Video Handbook (EVH), a series of videos developed and maintained by by Professors Brendan Beare, Eli Berman, Graham Elliot, Gordon Dahl, Yixiao Sun, Kaspar Wuthrich, Joel Watson, and Melissa Famulari of the University of California San Diego, in conjunction with IT Services Educational Technology at UC San Diego and funded by an Innovative Learning Technology Initiative grant from the Office of the President of the University of California (Melissa Famulari and Joel Watson, Co-Principal Investigators). You can access the EVH as a module on the class web page. There is no charge to access these videos as part of this course. Some of these videos are useful to review concepts you learned in ECON 120A, and some are useful for the material in ECON 120B. Software: Part of the course involves learning to use a software package called Stata. Stata is essential for problem sets, so you need to be able to access Stata. UCSD maintains a site license so that students can download and install Stata on their own computer for free. We will provide details on how to do this as a separate announcement on Canvas as soon as possible. You can also lease a copy of Stata to install on your own computer for a small fee (but there is no particular reason to do this since UCSD has a free site license): https://www.stata.com/order/new/edu/profplus/student-pricing/ If you would like a book to help you learn Stata, a good suggestion is A Gentle Introduction to Stata, Revised Sixth Edition, by Acock. However, this book is not required for the course. There are also many online sites devoted to helping individuals learn Stata. For a list, see: https://www.stata.com/links/resources-for-learning-stata/ Homework: Homework is an integral part of this course, because the best way to learn econometrics is to do it. I will periodically assign problem sets throughout the quarter. These assignments will be posted on the web, and it is your responsibility to check the class web page regularly. Homework assignments will generally be due about 6 days later. Your homework needs to be turned in on Canvas before midnight (i.e., by 11:59 pm) on the due date. Neither late nor emailed homework will not be accepted. You must scan your answers into a single pdf file and upload the file to Canvas. You are allowed to miss one homework without penalty, as I will drop the lowest score before calculating the homework portion of your grade. The tradeoff for this benefit is that I will be strict about not accepting late homework. Homework will be graded on a two-point scale. A score of 1 will be given to homework which has made substantial progress, but is incomplete. A score of 2 will be given to homework which attempts to answer all of the assigned problems, including any Stata questions. Students can work together on problem sets, although solutions must be written up and handed in separately (including any Stata output, which should part of the pdf file you upload onto Canvas when turning in your homework). It is a good idea to attempt the problems on your own before meeting with a group. While you can collaborate with others, any homework you turn in must represent your own work. Solution keys to the homework will be posted on the class web page. It is a good idea to check your answers versus the solution key so that you can figure out which questions you need to understand better. Tests: There will be a midterm and a final exam. You must take both the midterm and the final exam at the scheduled time for the class you are registered for (see dates and times listed earlier in the syllabus). There will be no make-up exams, and any conflicts or emergencies should be approved by me in advance of the exams. In case of illness or accident at the time of the midterm – with proper documentation from, for example, a doctor – the final will be weighted 90%. Details on the administration of the exams will be discussed in class. Bonus Quizzes: There will be between 5 to 7 “bonus” quizzes spread throughout the quarter. The dates of these quizzes will not be announced in advance. These are short quizzes, where you will get full credit for taking the quiz, even if you do not get the answer correct. You will need to bring your phone to class to complete the quiz, and you must be physically present in the class you are registered for to take the quiz. There are no make-up bonus quizzes. The way these bonus quizzes work is that for every bonus quiz you complete, your final exam will count for 1% less, and instead you will get a full 1% towards your course grade. Grades: The following weights will be used to determine your course grade: Homework: 15% Midterm exam: 40% Final exam: 38 to 45% (depending on how many bonus quizzes are completed) Bonus quizzes: 0 to 7% (depending on how many bonus quizzes are completed) Grading Policy: If you think a mistake was made in grading your exam, you may ask for a regrade. You should submit your regrade request via Canvas within 7 days after exam scores are posted. Note that unless your answer is fully correct, the assignment of partial credit is a matter of judgment, and we are unlikely to change your grade since we want to treat all class members fairly. From past experience, most regrade requests do not result in a grade change.
Econ 571 Homework 1 Spring 2025 Due Date: February 11, 2025 12:00pm (before class time) 1. Short Answer Question a. Explain the six important economic features associated with digital platforms and explain how they shape the market competition landscape in the digital spaces. b. Explain the current state of antitrust regulation concerning digital platforms, with a focus on recent developments in the EU, UK, US and China. c. (Preparation for the Final Project) Identify one recent antitrust case that involves platforms’ self-preferencing behavior. Apply the economic analysis we learned in class to investigate the antitrust matter and explain your thoughts. Hint: Lecture Notes on Blackboard provide few candidate cases. You may use academic literature, news article and court documents to support your argument. d. (Preparation for the Final Project) Identify one recent antitrust case that involves platforms’ envelopment strategy. Apply the economic analysis we learned in class to investigate the antitrust matter and explain your thoughts. Hint: Lecture Notes on Blackboard provide few candidate cases. You may use academic literature, news article and court documents to support your argument. 2. Platform. Self Preferencing Strategy The market consists of two upstream firms A and B, and one downstream firm R. Both firms produce products A and B at the marginal cost of 20 (i.e., MCA=20, MCB=20) and sell products at a wholesale price of 30 (i.e., WPA=30, WPB=30) to downstream firm R. The downstream firm R purchases both products from upstream firms at wholesale prices and sells them to end consumers at prices of PA and PB respectively. The market demand for both products A and B are given by QA=90-2PA+PB and QB=90+PA-2PB a. When Firm A and B are both independent from Firm R, solve Firm R’s profit maximization decision to get the market equilibrium. In particular, calculate PA, PB, QA, QB, πA, πB and πR . b. When Firm A and B are independent, does Firm R have any incentive to decrease PA (i.e., elimination of double marginalization incentive) or increase PB (i.e., raising rival’s cost incentive). Show how both incentives change after Firm A and R become vertically integrated. c. When Firm A and R are vertically integrated, solve Firm R’s profit maximization decision to get the new market equilibrium. In particular, calculate P’A, P’B, Q’A, Q’B, π’B and π’R. d. Compare the market equilibrium from a) and c) above. In particular, compare PB, QA, QB, πB and πR when Firm A and R are independent versus when Firm A and R are vertically integrated. Based on your comparison, can you explain Firm R’s self-preferencing behavior? 3. Platform Envelopment Strategy Platform. A and T are monopolists in two different markets. Consumers’ utilities of consuming platform. A and platform. T are uniformity distributed between zero and VA and VT respectively. a. Before the platform. envelopment strategy, each platform. chooses the optimal price of platform. A and platform. T at VA/2 and VT/2 respectively. Use graph to show how consumers make their purchase decisions among 1) consuming A only, 2) consuming both A and T, 3) consuming T only, 4) consuming non-A and non-T. b. Now platform. A (i.e., the attacker) want to enter platform. T’s market by inventing a similar platform. T’ and bundle A and T’ together. The attacker offers the bundle AT’ to consumers at the sum of two optimal monopolists’ prices, i.e. (VT′ +VA )/2. Use graph to show how such platform envelopment strategy can diminish the incumbent platform. T’s market share in the attacking market. c. Assuming the attacker now offers the AT’ bundle with a discount, i.e. (VT′ +VA )/2 – d. Use graph to show how offering a discounted bundle price can diminish the incumbent platform. T’s market share even more in the attacking market. 4. Horizontal Merger - Duopoly Model The market consists of two firms before the merger. Each firm’s marginal cost of production is mc1 = 10 and mc2 = 10. The market demand is P = 80 − 5Q. Two of the firm decides to merge together. After merger, the market has only one merged firm, with the marginal cost of production unchanged atmcm = 10. a. Characterize the market equilibrium before the merger. In particular, characterize the equilibrium price and quantity, each firm’s supply and profit. b. Characterize the market equilibrium after the merger. In particular, characterize the equilibrium price, quantity, and profit of the merged firm. c. Compare the pre- and post-merger market outcomes. Explain how such merger can impact the market outcomes and whether it is considered as a pro- or anti- competitive merger. After merger, the merged firm generates cost efficiency gains. Its marginal cost of production decreases tomcm = 5. d. Recharacterize the market equilibrium after the merger. In particular, characterize the equilibrium price, quantity, and profit of the merged firm. e. Compare the pre- and post-merger market outcomes. Explain how such cost efficiency gains can impact the market outcomes and whether it is considered as a pro- or anti-competitive merger.
LIN205 (WS25) Assignment 1 • This assignment is individual work. Please follow the Community Respect policy when you are working on this assignment. I am trusting you to do honest work, without any form of unauthorized aid. Unauthorized aid includes (but is not limited to) coaching from external “tutors” . Please also note that sharing the course content (including this document) with those who are not enrolled in the class is a big form of disrespect towards me. • As a reminder, generative AI tools such as ChatGPT may not be used in any capacity for submitted graded material in this class. Not respecting this policy goes against our Community Respect rules. • This assignment is not a “research” assignment, but rather a “problem set” assignment. That is, you should not consult resources outside of what has been given to you in the course so far. You can consult your notes, readings that have been assigned so far in class, and materials used during lectures/tutorials — but you are not allowed to, for example, search on the internet for additional resources. What you have learned in class and the information you have been given on this assignment are sufficient for answering all questions. • I will show my respect for your need for clarity by explaining to you how (your TAs and) I grade assignments. I will also show my respect for your need for honesty and fairness by providing sensible justifications for the grade that you receive. • There is no “rubric”, but Iwill explain during the 2/4 lecture what each part is assessing you on, and what strong answers are generally like on a linguistics assignment. • Please submit your work on Crowdmark. 1 Basic syntactic structure (60%) For each of the following sentences, draw brackets (i.e., [ ]) around the kind of clause(s) specified in the parentheses after the sentence. There could be one or multiple clauses you have to identify. If there is more than one clause to bracket, please put a subscript on the brackets so that the grader can tell where each clause begins and ends (e.g., [1 [2 ]2 ]1 ). 1. The professor expected for the students to acknowledge that they eventually make mistakes. (Bracket all finite clauses) 2. Sarah thinks that her sisters want for her parents to spend more time together. (Bracket the want clause) 3. I heard that my colleagues said Reading Week will provide relaxation. (Bracket the provide clause) 4. My friend hoped that his girlfriend wanted her parents to go to the concert. (Bracket all non-finite clauses) 5. Meredith wants for her granddaughter to ask her boss for a raise in her salary. (Bracket all embedded clauses) Q6. Using X,-theory, provide a tree diagram for the italicized sentence. Clearly label each node with the appropriate category (e.g., XP, X, , X). Please rewrite the sentence at the bottom of your paper/screen, and draw the tree on top of the sentence, as we have been doing in class. The message to the very large department expected for each professor to cook for their colleagues annually (Meaning: ‘The message to the very large department expected this: for each professor to cook for their colleagues annually’) 2 Meaning predicts structure and structure predicts meaning (15%) Consider the following dataset and the following trees: Dataset 1: (1) This one has shocked the community Intended meaning: ‘This/the arrest of the popular blogger has shocked the community’ (2) * It of the popular blogger has shocked the community Intended meaning: ‘The arrest of the popular blogger has shocked the community’ (3) * The one of the popular blogger has shocked the community Intended meaning: ‘The arrest of the popular blogger has shocked the community’ (4) It has shocked the community Intended meaning: ‘The arrest of the popular blogger has shocked the community’ Tree A: Tree B: Q1. Based on Dataset 1, which tree is the correct structure for the sentence The arrest of the popular blogger has shocked the community? Please choose one: Tree A or Tree B Q2. For the tree you did NOT choose in Q1, use Modus Tollens to explain why the tree you did not choose is an impossible tree for the given sentence. Make sure you set up your logical argument clearly like we did in class, and mention the specific substitution datapoint (from Dataset 1) that serves as the evidence in your argument. Not all datapoints from Dataset 1 will be relevant for this question. Q3. Now consider the following datapoint. (5) The arrest this month of the popular blogger has shocked the community Considering that this month is an adjunct that tells you when the arrest took place, it would make sense for it to form a constituent with arrest. We can hypothesize a structure like this (a triangle in a tree is an abbreviation that means ‘there’s more structure under here’): Tree C: Uh-oh, this tree is a problem. We are kind of forced into proposing this structure based on our reasoning so far, but it’s probably not the right structure for this sentence based on what we know about X,-theory from class. Here is your question. What problem does this additional datapoint (and its supposed structure in Tree C) pose for what we have been assuming about X,-theory in class? Please make reference to the concept of compositionality as it specifically relates to X,-theory in your explanation. (Hint: Substitution data is not super relevant for this question. Also, this question is NOT asking what the“correct” structure for the sentence would look like.) 3 Thinking more about compositionality (25%) Consider the following Dataset. Dataset 2 (6) I can finish this project by midnight Meaning ‘I can finish this project by midnight’ (7) I can’t finish this project by midnight Meaning: ‘I cannot finish this project by midnight’ (8) I will see if I can finish this project by midnight Meaning: ‘I will see if I can finish this project by midnight’ (9) I will see if I can’t finish this project by midnight Meaning: ‘I will see if I can finish this project by midnight’ In some varieties of English, (9) reportedly means ‘I will see if I can finish this project by midnight’, even though there is the negation not (contracted as n't) present in the sentence. Please answer the following questions. Q1. Why might Dataset 2 pose a problem for the principle of compositionality in language? Please provide a brief discussion. Q2. If we still assume compositionality to apply in all sentences (we have pretty good reasons to think so!), how might we be able to explain why the sentence in (9) does not contain the meaning of negation? Please provide a brief discussion. Note: If you do not know the answer to either or both of the questions, I hereby give you the option of putting “I’m not sure” as your answer. If you do this, you will receive partial credit for the question, as a token of appreciation for your honesty and respect for the grader’s time. If you actually try to answer but your answer is completely wrong or irrelevant, you will not receive any partial credit. This assignment is designed so that if you get a zero in this part but get all other questions in the other two parts right, you get a 75% (a B) on the assignment overall.
„Numerische Methoden II“ Wintersemester 2024/2025 Aufgabe 3 - PDE Für das erfolgreiche Bestehen von Aufgabe 3 müssen lauffähige Programme, sowie ein kurzer Report zu den Aufgaben abgegeben werden. Partielle Differentialgleichungen (PDE) Bei einem Chemieunfall in Bad Cannstatt wurde der Neckar mit einem hochkonzentrierten Stoffgemisch auf Alkoholbasis verunreinigt. Um ein großes Fischsterben zu verhindern, muss die Kontamination entfernt werden. Dazu ist es nötig die örtliche Ausbreitung der Stoffe im Neckar abzuschätzen. Betrachtet wird der Neckar. Es wird angenommen, dass der Transport der Schadstoffe im Neckar nur in x-Richtung stattfindet. D.h., dass sich die Konzentration der Schadstoffe über die Breite und die Tiefe im Flussbett nicht ändert. Das hierdurch vereinfachte Transportmodell ist in Abbildung b) dargestellt und kann durch die folgende eindimensionale Konvektions-Diffusions-Gleichung mit folgender Orts- und Zeitdimension beschrieben werden: Hierin beschreibt uj(x,t) die Konzentration des Schadstoffes j, abhängig vom Ort x und der Zeit t. Es handelt sich somit um eine Partielle Differentialgleichung (PDE). 1. Teil: Im ersten Teil dieser Aufgabe sind die effektiven Diffusionskoeffizienten Dj der Stoffe j und die Geschwindigkeit v über die Länge konstant und haben folgende Werte: v = 0.2, D1 = 0.01, D2 = 0.005, D3 = 0.0005. Am Start- und Endpunkt des Neckarabschnitts soll für die Zeitdauer der Berechnung ein zeitlich konstanter Konzentrationswert vorliegen, was einer Dirichlet-Randbedingung entspricht: uj(x = 0,t) = 0, uk(x = 1,t) = 0. 1. Um das Konzentrationsprofil des Stoffs j über x und t zu berechnen, muss die Transportgleichung diskretisiert werden. Leiten Sie hierfür die semidiskretisierte Form. im Ort mit dem Finite Volumen Verfahren (zentral Differenzen Schema und Upwind-Schema) für die Konvektions-Diffusions-Gleichung her. 2. Zum Zeitpunkt t = 0 findet der Chemieunfall statt, daher liegt als Anfangsbedingung der folgende Konzentrationsverlauf vor: Erstellen Sie ein Programm, mit dem die semidiskretisierte PDE gelöst wird. Programmieren sie hierzu für die Diskretisierung der PDE das Finite Volumen Verfahren mit Zentraldifferenzen und das Upwind Verfahren. Für die örtliche Disktretisierung wird Δx = 0.02 und für die Integrationsschritteweite Δt = 0.01 angenommen. Verwenden Sie zur Lösung des ODE-Systems das Semi-implizite Euler Verfahren. Berechnen Sie in Ihrem Programm die numerische Péclet-Zahl. 3. Um die Genauigkeit der numerischen Lösung abschätzen zu können, wird ein Vergleich mit der analytischen Lösung für einen Konzentrationspuls in Form. eines Dirac-Pulses angestellt. Die Analytische Lösung der Konvektions-Diffusionsgleichung lautet für diesen speziellen Fall: Vergleichen Sie die numerische Lösung der verschiedenen Diskretisierungsverfahren mit der analytischen Lösung, plotten Sie dafür die Konzentrationsprofile für t = { 0.5, 1.0} getrennt für den jeweiligen Stoff. Erklären Sie die Abweichung zur analytischen Lösung für beide Verfahren (und die Gründe dafür), und formulieren Sie eine Empfehlung, wie der Fehler verringert werden kann. Nehmen Sie eine Integrationsschrittweite von Δt = 0.01 an. Für die örtliche Diskretisierung betrachten Sie Δx = {0.02, 0.01, 0.005}. Bestimmen Sie die numerische Péclet-Zahl. Wie verhält sich die numerische Péclet-Zahl sowie die Abweichung zur analytischen Lösung mit feinerer Diskretisierung? 2. Teil: Im zweiten Teil dieser Aufgabe sind die effektiven Diffusionskoeffizienten Dj der Stoffe j konzentrationsabhängig und verändern sich damit auch über die Ortskoordinate. Für die Diffusionskoeffizienten gilt: Es liegt wieder am Startpunkt des betrachteten Neckarabschnitts für die Zeitdauer der Berechnung ein zeitlich konstanter Konzentrationswert vor, was einer Dirichlet-Randbedingung entspricht: uj(x = 0,t) = 0, Am Ende des Abschnitts liegt nun ein konstanter Gradient der Konzentration vor, sog. Neumann-Randbedingung. 1. Leiten Sie hierfür unter Berücksichtigung der konzentrationsabhängigen Diffusionskoeffizienten die semidiskretisierte Form. der Konvektions-Diffusions-Gleichung her, und implementieren Sie sie in Ihrem Programm. Hinweis: Als Bestandteil des Flussterms hängen die Diffusionskoeffizienten von den Zuständen auf den Rändern der Finite-Volumen-Zellen ab 2. Nach erfolgreicher Validierung des Modells sollen Sie nun abschätzen, zu welchem Zeitpunkt und Ortspunkt die maximale Konzentration des giftigen Stoffs C3 unter u3 ≤ 1 sinkt? Zum Zeitpunkt t = 0 findet der Chemieunfall statt, daher liegt als Anfangsbedingung der folgende Konzentrationsverlauf vor: Hinweis: Plot max(uj) = f(t)
Data Science and Machine Learning in Finance (ACCFIN 5246) Practice Quiz This practice quiz provides a guidance, in terms of structure and contents, surrounding the formal quiz on 4 Feb which will run via the course Moodle page under section indicated as In-Course Exam (ACCFIN52461C) General Instruction — Answer all questions. — This is an individual assessment. — The quiz comprises 12 multiple choice questions. — Select only one option. Each part carries an equal weight. There is no negative mark. — The computational questions are designed so that a calculator is generally not required, however, you can use a calculator to carry out computations. — The composition of questions, relating to statistical computations, qualitative questions based on the reading list and empirical facts, etc. may vary in terms of the number of questions appearing in the actual quiz. Multiple Choice Questions Question 1 Consider two investment assets X and Y. The observed asset returns generated by X exhibit low volatility and observed to be either +1% and -1%, whereas observed returns generated by Y have been outperforming but with a higher volatility and equal to +2% and +5%. Furthermore, the following table provides pairwise information for the aforementioned asset returns: Table 1: Each tabulated value associated with X and Y are financial returns in percentage points. Assume the table characterises the population. The standard deviation of each asset return associated with X and Y , respectively, are (rounded to two decimal points): (a) 1.50 and 0.87 [x] (b) 1.50 and 1.00 (c) 1.73 and 0.87 (d) 1.73 and 1.00 Question 2 With reference to Table (1) in Question (1), what is the conditional probability P(X = +5|Y = -1)? (a) 0 (b) 3/1 [x] (c) 2/1 (d) 4/3 (e) 1 Question 3 With reference to Table (1) in Question (1), the median returns associated with assets X and Y , respectively, are: (a) 2 and -1 (b) 2 and +1 (c) 3.5 and -1 [x] (d) 3.5 and +1 Question 4 A specification model is described as yi = β0 + β1 exp(zi)/xi + ϵi. Specify the model either as linear or nonlinear, and further as identified or not identified: (a) Linear, identified [x] (b) Linear, not identified (c) Nonlinear, identified (d) Nonlinear, not identified Question 5 Consider a firm-level dataset providing three characteristics: EBITDA, cash holding and the total assets, described across columns by a 3 × 3 matrix x (each row corresponds to firms 1, 2, 3): Determine the column rank of the dataset summarised by matrix X: (a) 0 (b) 1 (c) 2 [x] (d) 3 (e) 4 Question 6 Suppose the number of outstanding shares of company A held by three investors are summarised by vector q = (45, 55, 65)′ , where each element corresponds to investors 1, 2, 3, respectively. Each investor purchased their shares at a different point in time according to the prevailing prices summarised by p = (£100, £110, £105)′ . What is the firm’s shareholder value formulated by the following inner product q′ .p if each element in p also corresponds respectively to investors 1, 2, 3? (a) £15,125 (b) £17,375 [x] (c) £20,225 (d) £25,500 Question 7 Returns generated by company RA are tabulated alongside treasury returns RG . The Sharpe ratio is formulated as where σ(x) is the standard deviation of the argument value x. What is the Sharpe ratio of returns described for company A according to the table above (assume the table represents the population information): (a) 2.35 (b) 2.45 [x] (c) 2.55 (d) 2.65 (e) 2.75 Question 8 What is the correlation coefficient summarising the co-movement between companies A and B asset returns when the table below represents the population data: (a) −1 (b) −2/1 [x] (c) 0 (d) +2/1 (e) +1 Question 9 A comprehensive financial dataset including 200,000 observations covering the UK companies is split into two groups G1 and G2 each including 5,000, 195,000 firms, respectively and according to an ascending cash to total assets ratio benchmark (G1 : low cash to total assets and G2 : high cash to total assets). It is desired to learn if firms with lower cash to total assets ratios underperform, in terms of their average interest coverage ratios (ICR, where higher ICR corresponds to better performance), relative to the remaining firms. Propose how you formulate this argument in terms of a testable null hypothesis (H0 ) versus an alternative hypothesis (Ha ), as- suming that the performance associated with high cash to total assets group ICR2 is representative of the population information. (a) H0 : ICR1 = ICR2 vs. Ha : ICR1 ≠ ICR2 (b) H0 : ICR1 ≥ ICR2 vs. Ha : ICR1 < ICR2 [x] (c) H0 : ICR1 ≠ ICR2 vs. Ha : ICR1 = ICR2 (d) H0 : ICR1 ≤ ICR2 vs. Ha : ICR1 > ICR2 Question 10 According to “’Financial Constraints, Investment, and the Value of Cash Holding’ by Dennis and Sibilkov (2009), what are the four approaches to quantify the level of financial constraints? (a) Annual payout ratio, Firm size, Debt rating, Paper rating [x] (b) Annual payout ratio, Firm location, Debt overhang, Paper rating (c) Annual payout ratio, Firm industry, Debt rating, liquid assets (d) Annual dividend policy, year, Debt rating, Paper rating Questions 11-12 Similar computational or qualitative questions from the reading list.
Assignment 1 (M365) Problem 1. Suppose Ω is an infinite set and Ω ∩ N = ∅, where N = {1, 2, . . .}. Prove that Ω ∪ N has the same cardinality as Ω. Problem 2. Having the following definition for a fixed non-empty set X ⊂ R ” inf{x : x ∈ X} = a if [∀x ∈ X x ≥ a] and [∀y > a ∃x ∈ X : x < y] ”, formulate the formal statement that a ≠ inf{x : x ∈ X} using only the words ”and”, ”or”, and mathematical symbols like ∀, ∃, ∈, . . .. Problem 3. (i) Give an example of two fields F1 and F2 over the same universal set Ω such that F1 ∪ F2 is not a field. (ii) Let Ω = {1, 2, 3} and construct the minimal field containing the subset {1, 2}. Is this field also a σ-field? Justify your answer. Problem 4. (i) Prove that if F is a σ-field (as defined on the lectures) and A1, A2, . . . ∈ F, then An ∈ F. (ii) Prove that any σ-field is a monotone class. By submitting solutions to this assessment you affirm that you have read and understood the Academic Integrity Policy detailed in Appendix L of the Code of Practice on Assessment and have successfully passed the Academic Integrity Tutorial and Quiz in the course of your studies. You also affirm that • the work you are submitting is your own and you have not commissioned production of the work from a third party or used artificial intelligence software in an unacceptable manner to generate the work*, • you have not copied material from another person or source, nor com-mitted plagiarism, nor fabricated, falsified or embellished data when com-pleting the attached piece of work. • you have not colluded with any other student in the preparation and/ or production of this work. Marks achieved on this assessment remain provisional until they are ratified by the Board of Examiners in June 2024. Please note that your submission will be analysed by Turnitin for plagiarism and an Artificial Intelligence detection tool. *software applications include, but are not limited to, ChatGPT, Bing Chat, DALL.E, Bard.
CHEM 191 MODULE 5 CHEMICAL REACTIONS: PRECIPITATION and OXIDATION - REDUCTION Learning Objectives. By the end of this module you should be able to: • Classify chemical reactions as decomposition, combination, displacement or exchange • Recognise spectator ions in a chemical reaction and write ionic equations • Use solubility rules to identify the products of precipitation reactions • Describe the dissolving process and account for solubility in terms of solute and solvent interactions • Recognise oxidation-reduction reactions by identifying electron transfer between reactants • Write balanced half-equations and use these to write balanced equations for redox reactions • Identify oxidants and reductants in redox reactions • Determine and use oxidation numbers to identify redox processes Reference: ESA Chapters 5, 21, 4 CLASSIFYING CHEMICAL REACTIONS Chemical reactions can be classified in two ways; according to the way the reactant particles behave in relation to each other or according to changes that occur to the reacting particles. If we focus on the number and nature of the reactants and products and on the type of transformation needed to convert the reactant(s) into the product(s), reactions can be classified as: • Combination (Synthesis) - elements or less complex compounds come together to form a single more complex compound • Decomposition - a compound breaks apart into either elements or less complex compounds • Displacement - a single element replaces another one in a compound • Exchange – ions from one compound switch places with ions from another compound to form two new compounds Examples of different types of reactions Decomposition • This is the simplest type of reaction. • A single compound is broken down into several different compounds. Example 1: When green crystals of copper(II) carbonate are heated, a gas (which can be identified as carbon dioxide) is released and black copper(II) oxide is left as a residue. i.e. CuCO3(s) → CuO(s) + CO2(g) Since one reactant has visibly become two products, decomposition must have occurred. Combination • This is the opposite of decomposition • It involves the joining of two or more elements or compounds to form a single compound. Example: Hydrogen and chlorine react to produce hydrogen chloride H2(g) + Cl2(g) → 2HCl(g) In a combination reaction, there will be several reactants but only one product. Displacement Reactions • In a displacement reaction, one element is displaced from a compound by another element in its elemental form. • The equation describing the reaction must have an element and a compound as reactants and a different element and compound as products. Example: If zinc metal is placed in a solution of copper(II) sulfate, the blue solution is decolourised. Colourless zinc sulfate is formed and copper metal forms a brown deposit. Zn(s) + CuSO4(aq) → Cu(s) + ZnSO4 (aq) Exchange Reactions • An exchange reaction is one in which atoms or groups of atoms are interchanged between two compounds. • For ionic compounds, an exchange reaction can be identified when two reactants give two products by a change ofpartners between the anions and cations. Example: When solutions of barium chloride and sodium sulfate are mixed, a precipitate of barium sulfate is formed and sodium chloride is left in solution. BaCl2(aq) + Na2SO4(aq) → BaSO4(s) + 2NaCl(aq) Written as an ionic equation: Ba2+(aq) + SO42-(aq) → BaSO4(s) Activity 5.1 Types of reactions Classification of Reaction Example: Using Symbols Example Reactions Combination A + B → AB 2H2(g) + O2(g) → 2H2O(l) Decomposition XY → X + Y 2H2O(l) → 2H2(g) + O2(g) Displacement A + BC → AC + B 2Al(s) + 3Cu(NO3)2(aq) → 2Al(NO3)3(aq) + 3Cu(s) Exchange AC + DE → AE + DC Pb(NO3)2(aq) + 2KI(aq) → PbI2(s) + 2KNO3(aq) Questions 1. List the number of reactants and the number of products found in the combination reaction (as shown in the table) and link this to the definition of a combination reaction. 2. List the number of reactants and the number of products found in the decomposition reaction (as shown in the table) and link this to the definition of a combination reaction 3. Explain how you would compare a displacement reaction to an exchange reaction. Exercise 5.1 Identify the type of reaction shown in each of the following chemical equations. Justify your answers. (a) 2KClO3(s) → 2KCl(s) + 3O2(g) (b) AgNO3(aq) + KCl(aq) → AgCl(s) + KNO3(aq) (c) 2H2(g) + O2(g) → 2 H2O(g) (d) 2AgNO3(aq) + Cu(s) → Cu(NO3)2(aq) + 2Ag(s) (e) CaCO3(s) → CaO(s) + CO2(g) (f) 2NaI(aq) + Cl2(g) → 2NaCl(aq) + I2(s) Ionic Equations and Spectator Ions When ionic compounds are dissolved in water, the anions and cations dissociate and so essentially exist independently. For example, when solid sodium chloride, NaCl(s), is dissolved in water we can write: This implies that the ions have separated and dispersed through the solution so they will be surrounded by water molecules. A solution of sodium chloride is usually written as NaCl(aq) which is misleading as it does not show the separated ions. However, recognising the dissociation of ions can simplify the way equations for some reactions are written. For example: For the reaction of sodium chloride and silver nitrate solutions NaCl(aq) + AgNO3(aq) → AgCl(s) + NaNO3(aq) We can consider the dissociation of the salts in solution and write the equation as: Na+(aq) + Cl-(aq) + Ag+(aq) + NO3-(aq) → AgCl(s) + Na+(aq) + NO3-(aq) Since nothing has happened to the Na+ and NO3- ions during the reaction they are known as spectator ions so they can be eliminated from the equation as follows: Ag+(aq) + Cl-(aq) → AgCl(s) This is known as a net ionic equation, or more often, an ionic equation. (Note that the formation of solid AgCl implies a new compound as the ions have “changed partners” from those in the original solutions and the formation of the solid removes the ions from the solution). Activity 5.2 – ionic equations This activity is designed to help you understand ionic equations Questions 1. Consider the reactions modelled in the beakers drawn in the box (a) (i) Which beakers contain solid, insoluble substances? Give reasons for your answers. (ii) Which beakers contain solutions of ionic substances? Give reasons for your answers. (iii) Which of the reactions produces a gas? How do you know this? (b) Indicate which of the equations (i) to (iii) corresponds to the reactions 1, 2 or 3 above. (i). Zn (s) + 2HCl (aq) → ZnCl2 (aq) + H2 (g) (ii). Zn (s) + Cu(NO3)2 (aq) → Zn(NO3)2 (aq) + Cu (s) (iii) Zn(NO3)2 (aq) + Na2CO3 (aq) → ZnCO3 (s) + 2NaNO3 (aq) (c) In each of the reactions 1 to 3, there are ions present in the solutions that do not participate in the chemical reaction. In other words, they exist in the same form. both before and after the reaction. These substances are called spectator ions. Use the equations (i) to (iii) to identify the spectator ions for each reaction. 2. In the table below, the equation for one of the previous reactions is written in three different ways. Molecular Equation Zn(s) + Cu(NO3)2(aq) → Zn(NO3)2(aq) + Cu(s) Ionic Equation Zn(s) + Cu2+ (aq) + 2NO3 −(aq) → Zn2+ (aq) + 2NO3 −(aq) + Cu(s) Net Ionic Equation Zn(s) + Cu2+ (aq) → Zn2+ (aq) + Cu(s) (a) (i) Which equation represents the ionic substances as bonded together in the solution? (ii) Which equation represents the ionic substances as separate ions in solution? (iii) Which equations is a better representation of how the species take part in the reaction? (iv) Compare the net ionic equation to the other two equations. a. What chemical species is missing in the net ionic equation? b. Explain why it is valid to remove this species from the equation. (b) Write ionic and net ionic equations for the remaining reactions in 1: Zn(s) + 2HCl (aq) → ZnCl2 (aq) + H2 (g) Zn(NO3)2 (aq) + Na2CO3 (aq) → ZnCO3 (s) + 2NaNO3 (aq) Exercise 5.2 (a) Write the following equations as balanced net ionic equations. (i) BaCl2(aq) + Na2SO4(aq) ⎯→ BaSO4(s) + 2NaCl(aq) (ii) Zn(s) + H2SO4(aq) ⎯→ zinc sulfate (aq) + hydrogen (g) (iii) HNO3(aq) + Ba(OH)2(s) ⎯→ Ba(NO3)2(aq) + H2O(ℓ) (b) Balance the following ionic equations (the spectator ions have been eliminated). Some of these maybe quite difficult but they would be worse if the spectator ions had been included. (i) Ca2+(aq) + PO43-(aq) → Ca3(PO4)2(s) (ii) Cu2+(aq) + NH3(aq) → Cu(NH3)42+(aq) (iii) MnO4-(aq) + H+(aq) + Fe2+(aq) → Mn2+(aq) + H2O(ℓ) + Fe3+(aq) (iv) S2O32-(aq) + I2(aq) → S4O62-(aq) + I-(aq) (v) Cr2O72-(aq) + Fe2+(aq) + H+(aq) → Cr3+(aq) + Fe3+(aq) + H2O(ℓ) DISSOLVING Dissolving a solute in a solvent to make a solution is a physical process. A solution is a mixture and the properties of the components are retained. For example, when salt is added to water the solution tastes salty in the same way as do the salt crystals. Since many chemical reactions occur in aqueous solutions, it is useful to understand the interactions between the particles in a solution. • For aqueous solutions, the activity of the water solvent is related to the nature of the water molecules. • The water molecule, H2O, is bent with the H-O-H angle being about 105o. The O-H bond is polar because the oxygen atom is more electronegative than the hydrogen atom and attracts the electron density in the bond towards itself. • As a result, the water molecule has a negative “end” at the oxygen atom, and positive “ends” at the hydrogen atoms. (In the diagram the δ symbol means ‘slightly’ – showing that the ends are only slightly positive and slightly negative). The shape of the water molecule is important in determining its solvent properties. • Substances dissolve in one another because the solution they form together is more stable than if the two substances exist separately. • This implies that the attractive forces between the solvent molecules and the solute particles (which can be molecules or ions) are greater than the attractive forces within the solute structure and the attractive forces between the solvent molecules. • Ionic solids normally have strong attractive forces between their oppositely charged ions so for water to dissolve an ionic substance the water molecules must have some way of overcoming these attractive forces within the solid. • The polar nature of the water molecule enables it to reduce the attraction between the charged ions because the negatively charged oxygen atoms in the water molecule interact with the positive ions in the ionic solid and the positively charged hydrogen atoms in the water molecule interact with the negative ions. Fig 5.1 Dissolving sodium chloride in water. Note the orientation of the water molecules around the ions • Solvents that are composed of polar molecules are able to dissolve both ionic and polar substances but those with non-polar molecules cannot do so because they cannot overcome the attractive forces between the ions. In contrast non-polar solvents are more able to dissolve non-polar solutes. • Non-polar solutes generally have weak intermolecular interactions in the solid or liquid and they interact weakly with the solvent. If their interactions with solvent molecules is similar to or stronger than their interactions with each other in the solid state, then the solute molecules maybe soluble. • Thus a general rule emerges - like dissolves like. That is, polar solvents are more likely to dissolve ionic and polar solutes, and non-polar solvents are more likely to dissolve non-polar solutes. Focussing Questions 1: 1. How would you know that a chemical reaction has taken place? 2. What do the terms “solute” and “solvent” refer to? 3. Explain, in terms of energy, why some substances dissolve in water. 4. What needs to happen for an ionic solid to dissolve in water? 5. To what does the rule “like dissolves like” refer? 6. Why are two layers observed when oil and water are mixed? PRECIPITATION REACTIONS Recall that when ionic solids dissolve in water they completely dissociate (see fig.5. 1) – that is the ions remain separated from each other in solution. NaCl(aq) → Na+(aq) + Cl-(aq) So an aqueous solution of sodium chloride, NaCl(aq), contains the ions Na+ and Cl– surrounded by water molecules. Not all ionic solids (salts) are soluble in water, but even insoluble salts will dissolve to a very small extent. Solubility rules can be used to determine whether a salt will dissolve or not. (In this context insoluble means that very little will dissolve and soluble means that a reasonable amount will dissolve). The rules are based on observations of salts of common cations and anions. Solubility Rules 1. All salts of the Group 1 metals and of the ammonium ion, NH4 + are soluble. 2. All nitrates, chlorates and ethanoates are soluble. 3. All chlorides, bromides and iodides are soluble except those of Ag+ , Hg2 2+, Cu+ and Pb2+ . 4. All sulfates are soluble except those of Ca2+, Ba2+ and Pb2+ . 5. All hydroxides, carbonates and sulfides are insoluble (except when Rule 1 applies). Mixing two ionic solution sometimes results in the formation of a solid known as a precipitate. The solubility rules can be used to help identify a precipitate. For example: A mixture of silver nitrate solution, AgNO3(aq),,and sodium chloride solution, NaCl(aq), results in a precipitate. • The ions present on mixing will be Ag+, Na+, NO3- and Cl- . • The two new combinations of ions in the mixture are AgCl and NaNO3. • Using the solubility rules, we can see that the only combination that will give an insoluble salt is AgCl. • Rule 1 says that all salts of group 1 metals are soluble so NaNO3 is a soluble salt. Rule 3 lists the chlorides of Ag+ as being insoluble. The equation for the reaction: NaCl(aq) + AgNO3(aq) → AgCl(s) + NaNO3(aq) This can be written as an ionic equation: Ag+(aq) + Cl-(aq) → AgCl(s) Activity 5.3 Precipitation Reactions Answer the questions below using the equations in the box and the solubility rules given above. EQUATIONS 1 A. AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq) B. 2HNO3(aq) + Mg(OH)2(aq) → Mg(NO3)2(aq) + 2H2O(ℓ) C. Na2CO3(aq) + CaCl2(aq) → CaCO3(s) + 2NaCl(aq) D. Ba(NO3)2(aq) + Na2SO4(aq) → BaSO4(s) + 2NaNO3(aq) E. FeBr2(aq) + K2SO4(aq) → FeSO4(aq) + 2KBr(aq) Questions: 1. Use the equations to predict which of the reactions A to E would result in a precipitate. Give a reason for your answer. 2. Precipitation reactions are sometimes called “double replacement reactions” because the ionic solids dissolved in water are said to ‘switch partners ’. Use equation A to illustrate the idea of double displacement. 3. In equation A, only one of the products of the reaction will form a precipitate. Identify the solubility rules that apply to the reaction products. 4. Predict the precipitate that forms in the following reactions and write a balanced equation for the reaction. (a) FeCl3(aq) + NaOH(aq) → (b) KI(aq) + Pb(NO3)2 → Exercise 5.3 (a) (i) Solid iodine is composed of the molecules I2. Explain why iodine is more likely to be soluble in the non-polar solvent, carbon tetrachloride, CCl4, than in water. (ii) Explain why it is possible for ionic solids to dissolve in water in spite of the strong forces of attraction between the ions. (b) Determine whether a precipitate will form. when the aqueous solutions of the following salts are mixed. Write a balanced equation for each reaction where a precipitate is observed. (i) Calcium chloride and potassium sulfate (ii) Lead nitrate and calcium chloride (iii) Ammonium sulfate and sodium nitrate (iv) Copper(II) sulfate and potassium hydroxide (v) Sodium carbonate and barium nitrate (c) Write a balanced net ionic equation for the following reactions. (i) Calcium chloride and potassium sulfate (ii) Lead nitrate and calcium chloride (iii) Copper(II) sulfate and potassium hydroxide (iv) Sodium carbonate and barium nitrate OXIDATION AND REDUCTION REACTIONS Antioxidants The term antioxidant will be a familiar term for you from the advertising of such things as ‘superfoods’ and anti-wrinkle creams. Antioxidants in biological systems are substances which may prevent some types of cell damage. Oxidation reactions in cells produce free radicals (molecules with an unpaired electron) that can damage or kill cells. Antioxidants stop oxidation reactions from occurring. Some commonly recognised antioxidants in biological systems include the Vitamins A, C and E. Oxidation - reduction reactions, commonly known as redox reactions, are classified according to the changes that take place in the reacting particles. They can be described at particle level as electron transfer reactions – one species loses electrons which are gained by another species. Examples of redox reactions include the rusting of iron (iron metal (Fe) is oxidised to form. rust, a compound containing Fe3+ ions), the burning of coal or wood (carbon,or carbon containing compounds are converted to CO2) or the action of a household bleach. In biological systems, respiration and photosynthesis are processes that involve oxidation-reduction reactions. Definitions If, in a chemical reaction, a species (atom, ion or molecule) loses electrons, it is said to be oxidised. This term originally meant ‘reacted with oxygen’ as atoms of all elements (except fluorine) lose electrons when they react with the very electronegative oxygen atom. The electrons cannot be lost completely, they have to go somewhere, and the species that gains the electrons is said to be reduced. Oxidation of one species cannot happen without the corresponding reduction of another species. To help you remember you can use one of the following mnemonics: • Oxidation Is Loss of electrons Reduction Is Gain of electrons (OIL RIG) • Loss of Electrons is Oxidation Gain of Electrons is Reduction (LEO GER) In the reaction, the species that is oxidised (loses electrons) causes another species to be reduced (by providing it with electrons). Hence the oxidised species is known as a reducing agent or reductant. Similarly, the reduced species removes electrons from another species causing it to be oxidised. Hence the reduced species is known as an oxidising agent or oxidant. Representing Oxidation-Reduction Reactions Consider the reaction of magnesium with oxygen. 2Mg(s) + O2(g) → 2MgO(s) The product, magnesium oxide, is an ionic compound made up of Mg2+ and O2- ions. We can consider each reactant separately: Mg atoms lose electrons to become Mg2+ ions: Mg → Mg2+ + 2e– O atoms gain electrons to become O2- ions: O2 + 4e- → 2O2– During the reaction, electrons are transferred from Mg atoms to O atoms. When considered separately these steps are known as half reactions represented by half equations. The half reaction equations explicitly show the number of electrons involved in the process. When the same number of electrons are involved in each half reaction then the sum of the two half-reactions (above) gives the overall reaction. 2Mg + O2 + 4e- → 2Mg2+ + 2O2- + 4e- Cancelling the electrons on both sides of the equation and combining the ions as MgO(s) gives the equation, 2Mg(s) + O2(g) → 2MgO(s) In this reaction, magnesium is oxidised (loses electrons) and is a reducing agent or reductant because it causes the oxygen to be reduced. Oxygen is reduced (gains electrons), and is an oxidising agent or oxidant because it causes the magnesium to be oxidised. Example: When zinc metal is added to hydrochloric acid, bubbles of hydrogen gas are produced and the zinc metal eventually all disappears. Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g) In this reaction the zinc is oxidised (its atoms lose electrons) to Zn2+(aq) and the H+(aq) of the acid is reduced (the ions accept electrons) and it becomes molecular hydrogen. Zinc is thereductant, and H+ is the oxidant, To identify the redox processes (as shown in the half equations) it is helpful to first, consider the species present in the reactants and products: Since we have ZnCl2(aq) and HCl(aq) we can write: Zn(s) + 2H+(aq) + 2Cl-(aq) → Zn2+(aq) + 2Cl-(aq) + H2(g) The chloride ion, remains unchanged - it is a spectator ion and can therefore be omitted from the equation: Zn(s) + 2H+(aq) → Zn2+(aq) + H2(g) So the half reactions can be identified as: Oxidation: Zn → Zn2+ + 2e- Reduction: 2H+ + 2e- → H2 Adding these half equations and cancelling out the electrons gives: Zn(s) + 2H+(aq) → Zn2+(aq) + H2(g)
Data Science and Machine Learning in Finance (ACCFIN 5246) Problem Set 1 – Spring 2025 Question 1 Consider two investment assets X and Y . The observed asset returns generated by X have been historically low but always non-negative and equal to 0%, +1% and +2%, whereas observed returns generated by Y have been more volatile and equal to −5%, +2% and +8%. Furthermore, the following table provides further information about their joint investment perfor-mances with a summary that informs the likelihoods associated with each observed return outcomes across each other: Table 1: Each value within the table is a probability and values across the top row and left column are returns in percentage points. Each entry shows the probability of the corresponding X and Y values occurring jointly. For example: P(Y = 5, X = 1) = 0.2, (1.1) Compute the marginal distributions for X and Y . In other words, compute the unconditional probabilities for each value of X: P(X = 0), P(X = 1), P(X = 2), and do the same for Y : With these in hand, compute E[X] and E[Y ]. (1.2) Compute the conditional distribution of Y given X, that is, P(Y = y|X = x) for all possible values of X and Y . Recall that: (1.3) Compute the conditional expectation of E(Y|X = x) for all three values of X. (1.4) Compute E[E[Y|X]] and compare with E[Y]. Question 2 (2.1) “Failure to reject H0 means the null hypothesis is true”, true or false? If true, explain why? If false, explain why. (2.2) Is the statement, “A matrix is a projection matrix iff it is an idempotent matrix”, true? If so, explain why? If not, explain when this can be true. (2.3) “An idempotent matrix is always invertible”, true or false? (2.4) “A projection matrix is always invertible”, true or false? (2.5) In March 1994, Michigan voters approved a sales tax increase from 4% to 6%. In political advertisements, supporters of the measure referred to this as a two percentage point increase, or an increase of two cents on the dollar. Opponents of the tax increase called it a 50% increase in the sales tax rate. Explain which way of measuring the increase in the sales tax is more accurate. Question 3 Let yi represent the share price of a stock in the S&P, and xi be a dummy variable equal to 1 if stock i is classified in the financial sector and 0 otherwise. Suppose we see N stocks total, and Nx of these stocks are in the financial sector (which of course means that N − Nx are in other sectors). (3.1) Write (the average of xi) in terms of Nx and N. (3.2) Suppose we run an OLS regression of yi on a constant and xi : yi = β0 + β1xi + νi (2) Show that is quantitatively equal to the difference in means between the two sectors: Question 4 Categorical variables d1 and d2, and 1n each is a vector of size n × 1, and that d2 = 1n − d1 with n = n1 + n2 (n1: number of men and n2: number of women) such that: suppose: (4.1) Show that (4.2) Compare and from two OLS regressions: Question 5 Consider the regression model (y and u each is N × 1, X is N × k and β is k × 1): y = Xβ + u and that we additionally wish to examine Rβ = r where R is q × k and r is q × 1. Let RSSU and RSSR denote the unrestricted and restricted sum of squared residuals, respectively. (5.1) Write a formal expression for the null and alternative hypotheses. (5.2) Write the problem in terms of a constrained problem (Lagrange problem). (5.3) Derive the first order conditions and solve. (5.4) What the value of Lagrange multiplier? Interpret the Lagrange multiplier. What is the sign? (5.5) What are the equations for RSSU and RSSR? (5.6) Derive an expression in terms of regression residuals for, RSSR − RSSU . (5.7) Interpret the term RSSR − RSSU . What is the sign and why? Question 6 Consider the model yi = α + exp(xiβ) + ui . Derive the NLS estimators for α and β.
Division of Biostatistics Qualifying Exam, PhD in Biostatistics Comprehensive Exam, MS in Biostatistics June 17, 2024 9:00am – 3:00pm The dataset Osteoporosis.csv will be used for problems 1 and 2. These data come from a study of the demographic, lifestyle, and dietary factors with bone mineral density (BMD) and osteoporosis (Chaudhari et al., 2019, PMCID: PMC6556264). The study included 169 participants aged at least 50 years old, seen in hospitals of Kathmandu, Nepal. The participants were administered questionnaires, and had their bone density measured via dual-energy X-ray absorptiometry (DEXA scans) in three locations: lumbosacral spine, right femur, and left femur. The variables in the dataset are: age age in years sex participants’ sex (male, female) occupation participants’ occupation ethnicity participants’ ethnicity (Brahmin chhetri, Janjati, Newar, other) bmi body mass index (BMI), in kg/m2 bmd bone mineral density (BMD) T-score, in standard deviations, compared to healthy 25-35 year olds of same sex and ethnicity. Computed as the lowest T-score from the three DEXA scan locations (lumbosacral spine, right femur, left femur) diagnosis osteoporosis (BMD ≤ −2.5), osteopenia (-2.5 < BMD ≤ −1), or normal (BMD > −1) op osteoporosis indicator (1 if BMD ≤ −2.5, 0 otherwise) smoking smoking status (yes, no) alcohol alcohol consumption (yes, no) exercise daily exercise (yes, no) tea tea consumption (yes, no) calcium estimated dietary daily calcium intake, in mg vitamind estimated dietary daily vitamin D intake, in IU l.femur BMD T-score measured in the left femur r.femur BMD T-score measured in the right femur lumbosacral BMD T-score measured in the lumbosacral region of the spine Please use appropriate plots, statistics and explanations in your answers below. 1. Problem 1: Osteoporosis Consider the relationship between the response bone mineral density (BMD) and the predictor BMI. (a) Describe the linear association between BMD and BMI quantitatively in a simple sentence. However, show that model diagnostics suggest that the association may not be linear throughout the BMI range. (b) A BMI ≥ 25 defines overweight. A careful analysis suggests that in this range, the benefit of BMI is greatly diminished. Fit a linear spline (broken-stick) model with a knot at BMI = 25. Is there statistical evidence for different BMI slopes when BMI < 25 and when BMI ≥ 25? (c) Fit the model BMD ∼ sex + age + sex × age. On a single plot show the relationship between BMD and age, separately for men and women. Use different colors for men and women in the plot. (d) What is the age slope for men? Include a 95% CI and p-value. Does BMD decline with age for men? (e) What is the age slope for women? Include a 95% CI and p-value. Does BMD decline with age for women? The BMD variable was computed as the minimum T-score of the DEXA scans at three locations for each individual (lumbosacral spine, left femur, right femur). The BMD from the individual locations are available in the dataset. (f) Are there any systematic differences in mean BMD between the three DEXA scan locations? Produce an appropriate graph. Demonstrate the pairwise differences statistically, if there are any. (g) Is a correction for multiple comparison appropriate in the context of this analysis comparing the BMD at the three DEXA scan locations? If so, does this affect your results? (h) Instead of calculating BMD as the minimum of the three DEXA measurements (analysis A), another approach is using the first principal component without centering (analysis B), while a third approach is using the average of the three measurements (analysis C). Compare these three BMD definitions graphically and quantitatively in terms of their values, the weights applied to the three individual scan locations, and interpretability. Do all three BMD definitions have the same units of measure? 2. Problem 2: Osteoporosis (Continued) Please be sure you answer the questions which ask you to ’summarize’ or ’interpret’ or ’discuss briefly’- please demonstrate your ability to communicate what you have done and what it means!! Credit will be given for all reasonable answers, even if not exactly as intended. :) We use the data from the Osteoporosis study to conduct a brief study of the association of alcohol use with a diagnosis of osteoporosis. We consider the biological variables age, sex and BMI, because they are well-known to be strongly associated with osteoporosis (younger age has lower risk of osteoporosis, low BMI has higher risk of osteoporosis because of associated hormonal changes). We also consider the dietary factors calcium intake and vitamin D intake (low is bad) and the modifiable health behaviors alcohol consumption (presumably bad), exercise (presumably good), and smoking (presumably bad). The varables are listed below for your convenience. (a) First, we investigate the association of alcohol use with osteoporosis, without adjusting for any other variables. Write a short paragraph that summarizes the number of alcohol drinkers and non-alcohol drinkers in the study; the prevalence of osteoporosis among the drinkers and the non-drinkers; and gives the difference in risk of osteoporosis between alcohol drinkers and non-drinkers. Include confidence intervals where appropriate. Does this difference in risk demonstrate that alcohol consumption leads to a reduction in the risk of osteoporosis? (b) Next, we investigate multivariate models which study the joint effects of predictors on the risk of osteoporosis. Create appropriate factors as defined below, and set the reference level for all predictors to the presumed or known low-risk category. Please use categorical versions of the variables for all of Question 2. • Age60, an indicator for age 60 years or older • LowBMI, an indicator of BMI < 25 (i.e. not overweight) • LowCalc, an indicator of dietary calcium < 500 mg • LowD, an indicator of vitamin D intake < 600 iu Fit a model with only the known biological predictors of age (categorical version), sex, and BMI (cate-gorical version). (Main effects only- let’s keep it simple! :) ). Do these variables appear to be strongly associated with a diagnosis of osteoporosis, as expected? Explain briefly. (c) Now we investigate the association of alcohol use with osteoporosis, adjusting for potential confounding factors. We consider the known risk factors age, sex, and BMI, and the potential confounders of dietary calcium, dietary vitamin d, smoking, and exercise. Before you begin your analysis, describe your model selection strategy (Main effects only- keeping it simple! :) ). Tell me why you don’t recommend allowing alcohol to be considered for inclusion/exclusion as part of any variable selection algorithm. (d) Now, carry out your model selection strategy above. Call the result Model 1. Present Model 1 as a table of estimated coefficients on the odds ratio scale, with confidence intervals and p-values. Briefly summarize your results in a short paragraph. Be sure to report your main conclusion regarding alcohol use and risk of osteoporosis. (To keep the exam simple, do **NOT** present model diagnostics! In fact, the model fits pretty well.) (e) Next we explore whether Model 1 has enough information to usefully distinguish between high risk and low risk subjects, using the easily observed variables which are included in the model (age, sex, BMI, smoking, etc.). Use Model 1 to compute the estimated risk of osteoporosis, with appropriate confidence interval, for an hypothetical extremely high risk subject (e.g. an older woman smoker, non-drinker, with low BMI and low calcium) and for an hypothetical extremely low risk subject. Then compute the range and the quartiles of estimated risks for subjects actually observed in the data. Why do the hypothetical and the observed ranges differ? Do you think this model could potentially be useful in identifying people at high risk and at low risk of osteoporosis, for a similar population of patients ? Discuss briefly. (f) The association of alcohol use with lower osteoporosis risk may be surprising. However, in many obser-vational studies of health outcomes, moderate alcohol use is associated with better outcomes. On the one hand, in some settings (eg red wine and heart disease) some people argue that there is a real causal effect, and on the other hand we know that there are often systematic differences between drinkers and non-drinkers. This motivates us to conduct further analysis. Recalling a result from Problem 1, add the interaction of age and sex to Model 1, and call the result Model 2. Compare Model 1 and Model2. Does this analyses increase your confidence that the apparent protective effect of alcohol use is real? Why might this be considered an exploratory analysis, rather than the primary analysis in your study? Explain in a few sentences. (g) Briefly summarize your analysis, and discuss the extent to which these data provide evidence for a protective effect of drinking alcohol for osteoporosis prevention. Be clear, professional, and quantitative in your answer. Figure 1: Mean composite driving score over time, for each treatment arm (and 95% confidence intervals). 3. Problem 3: Driving Miss Mary Jane The file Driving.csv includes data from a double-blind, placebo-controlled parallel randomized clinical trial conducted at the UCSD Center for Medicinal Cannabis Research, aiming to determine effect of cannabis on driving performance. A total of N = 190 cannabis users were asked to smoke at least 4 puffs from a cigarette containing either placebo, low dose THC, or high dose THC, according to the randomly assigned treatment arm. The participants completed computer-based driving simulations pre-smoking (baseline, 0 minutes) and at 4 timepoints after smoking: 0.5 hours (h), 1.5h, 3.5h, and 4.5h. The outcome is composite driving score (CDS), measuring the driver’s overall performance, with higher values indicating worse performance. CDS is a standardized score with no units of measure. A score of 0 reflects average driving ability. The given dataset is in the long format. The variables in the dataset are: • pid: participant ID • treatment (3 levels): placebo, low THC, or high THC • THC : indicator of THC-containing treatment, 0 if placebo, 1 if low or high THC dose • time_min: time since smoking in minutes (0 is pre-smoking) • CDS: composite drive score • frequent_user : 0 if current cannabis use < 4 times/week, 1 if ≥ 4 times/week • age: participant’s age in years • education: participants’s years of education • gender : Male or Female • miles_past_year : estimated self-reported number of miles participant drove in past year (a) Add two additional time-related variables: occasion, a categorical version of the time variable; and an index variable that indexes the measurement time points in increasing order, from 1 (baseline), 2 (30 minutes), . . . , to 5 (270 minutes post-smoking). Produce a boxplot of CDS as a function of occasion. Is the response distribution approximately normal? Is there a data transformation that is obviously necessary? (b) Consider modeling the CDS as a function of time using a longitudinal general linear model. What is a good choice of covariance structure for this general linear model? Use the chosen covariance structure in subsequent modeling. (c) Choose an appropriate mean model for this randomized clinical trial: consider a response profile model (RPM), and parametric time models with either linear, quadratic, or cubic time effects. Discuss whether there is any advantage in this case in using a parametric model for time, instead of a response profile model. (d) Based on the RPM, test whether overall there are any differences in the response profiles of the three study arms. (e) The test at the previous question confirms what Figure 1 suggests: overall, there are significant differ-ences in the trajectories of the three groups. Follow-up this analysis by testing for pairwise differences in the CDS trajectories between the three treatment arms. Are the results consistent again with what Figure 1 suggests? For each comparison state the null hypothesis in terms of the vector of mean coefficients β. (f) Interestingly, in Figure 1 the low THC group has apparently worse driving scores than the high THC group. One hypothetical explanation is that the participants in the high THC group can feel the strong THC and do not smoke the entire cigarette. In any case, the previous analysis shows no significant difference in driving scores between the two THC groups. This suggests combining the two THC groups into a single group (see the variable THC in the dataset). Fit an appropriate response profile model for the trajectories of the two groups over time: THC and placebo, and show that these trajectories differ. (g) Following up on the previous question, estimate the causal effect of smoking THC on driving at each time point. Include 95% confidence intervals and p-values. (h) Are the effects of smoking THC on driving large? To put this in perspective, in a cross-sectional study a Cohen’s d effect size d = 0.5 is considered moderate, and d = 0.8 is considered large. Finally, summarize in a few sentences the study findings regarding the effects of smoking cannabis on driving abilities.
BEM3088 Advanced Strategic Management Assignment Brief 2024-25 Assessment component #1: Business Article Review Assessment & feedback Assessment is an essential part of learning. It’show we benchmark your understanding, measure the development of your key skills and recognise achievement. However, assessment is about much more than just a grade. The key reason we mark work is to provide you with feedback to support ongoing learning. Feedback is an essential part of this process and Iam committed to providing you with as much honest, open and constructive feedback as I can. This feedback can take a number of formats; it maybe verbal or written feedback from me as your course tutor, it maybe highlighting how you have performed against the relevant marking criteria or it maybe feedback from your peers. Feedback, in whatever form, is provided to help you understand what you have done well and highlight areas where you might improve. It is always given with the aim of supporting your learning journey. If this feedback is ever unclear or you do not understand what you need to do to improve, you should ask me. Iam always here to help and will be happy to discuss this with you one-to-one. Similarly, feedback should never be just one way! If you have ideas or would like to make suggestions, please do not hesitate to contact me. I welcome any ideas that might help me to improve the support I offer to students. Module ILOs As part of our commitment to ensuring that each Module is clearly outlined and identifies the key skills you will develop during the course, we define ‘Intended Learning Outcomes’ or ILOs. These are split into 3 areas: Module-specific skills, discipline specific skills and personal aims. For this module, the ILOs have been defined as: Module-specific 1. Critically discuss organisational design principles, and the different types of organizational structures that support effective strategy design and execution. 2. Evaluate models that drive innovation and facilitate strategic adaptation and sustained long-term firm performance. 3. Evaluate the significance of managing organisational networks, and how network dynamics impact successful strategy implementation. Discipline specific 4. Synthesize theory and organisational data in order to think strategically about organisational design, networks, and innovation. 5. Demonstrate awareness of emerging trends, tools, and practises in strategic management. Personal & Key aims 6. Analyse and critically evaluate real-life company situations and business cases. It’s important to review and understand these, as not only do they highlight what you will learn during this course and how this will support your future personal and profession aims, but it also highlights what you will be assessed on. Assessment Overview Assessment 1 Assessment 2 Deadline February 27, 2025 March 28, 2025 Formative/Summative Summative Summative Type Individual Individual Title Business Article Review Case Study Analysis Value 40% 60% Word Count 1’500 max 2’500 max Skill assessed ILO 2,3, 4 ILO 1,5,6 N.B. All submission dates are provisional, approval pending Assessment Advice and Information Word count • Submissions must not exceed the stated word count (+10%). Any additional text beyond this limit will not be considered in the marking process, thereby limiting your opportunity to score well on this module. • If you choose to write less than the recommended word count, you may do so but will be limiting your chances to score well on this submission. • The header page,index, appendix and reference list are not included in the word count. • In-text references and headings are included in the word count • Text in tables and charts is not included in your word count. However, please note that tables and charts are usually visually or data-focused and rarely include extensive text. Always consider the legibility and effectiveness of your charts as a means of communication. If text is not legible (recommended no smaller than 9 point font) it cannot be considered in the marking criteria and similarly, if your chart is not an effective means of communication, you may be marked down in the ‘Structure and style’ section of the marking criteria. Referencing • Please use APA 7th Edition style referencing for your in-text citations and reference list. • A detailed A to Z guidance on referencing is available on ELE: https://ele.exeter.ac.uk/course/view.php?id=6748§ion=3 • In addition, you can use your University login to access Cite Them Right, which contains a range of useful referencing informationhttps://www- citethemrightonline-com.uoelibrary.idm.oclc.org/Home Style. & Presentation • Minimum 12-point font for text, 9 points in tables and charts. • You are encouraged to include relevant figures/tables/images in your essay, referenced below the figure itself. Further details on referencing charts and figures can be found in the Business School guidance (link above) How to submit your work • Please submit your work as a PDF. All submissions must be readable files. Written text, unless this is within a chart or graphic, should NOT be pasted as an imagefile. • The submission link will be made available on the ELE page of this module. • Failure to submit on time may incura penalty and could be capped at the pass mark. Please see Business School Guidance on late submissions for further information.
Algorithms and Data Structures I Project 1: ReallyLongInt Background Note: All starter files will be shared in a link at the end of this document. In this project, we will use what we’ve reviewed about object-oriented programming in Java in combination with the Bag ADT from lecture to create and use a 2D array-based data structure. Your Task: Design and implement a generic class (ArrayDS) that will act as a data structure for accessing sequences of Java Objects. Your ArrayDS class will primarily implement SequenceInterface. The details of this interface is explained in SequenceInterface.java . Readthis over very carefully before implementing your ArrayDS class. ArrayDS For the details on the functionality of your ArrayDS class, carefully read over the files SequenceInterface.java and Project1.java. You must use these files as specified and cannot remove/alter any of the code that is already written in them. There are different ways of implementing the SequenceInterface interface methods, some of which are more efficient than others. Try to think of the best way of implementing these methods in this assignment, but the most important thing at this point is getting them to work correctly. A lot of pencil and paper work is recommended before actually starting to write your code. Later we will discuss the relative merits of different implementations. Important Note: The primary data within your ArrayDS class must be a two-dimensional array. You may not use any predefined Java collection class (e.g., ArrayList) for your ArrayDS data fields. You may not declare and/or use any one-dimensional arrays except in the toArray() and hasSub sequence() methods. Any methods besides these three will only be eligible for 50% credit if they are found to use one-dimensional arrays. This will be applied after the project is due! You must use the following instance variables inside the ArrayDS class: private final BagInterface[] [] array; //the underlying 2-D array private int size ; //the number of items in the sequence private T [] alphabet ; //the possible item values (e .g ., the decimal digits) private T firstItem; //the first item in the sequence private T lastItem; //the last item in the sequence You should add other variables and named constants to follow the secure programming practices we mentioned in class. To illustrate how to store a sequence of objects as a two-dimensional array, let's have an example. Let's take the sequence 9875732732 as an example. This is a sequence of decimal digits. The sequence alphabet is the set of possible values from which the sequence items are drawn. So, in this example the alphabet is the set of decimal digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. This sequence can be visualized like this: Each of the ten digits of the alphabet is represented by a circle. Every pair of consecutive digits in the sequence results in an arrow in the diagram, and the arrow's label includes the position of the second digit in the pair. For example, because 9 is followed by 8 in the sequence, there is an arrow from 9 to 8 in the diagram. Because the position of 8 in the sequence is 1, the arrow from 9 to 8 has 1 in its label. Because 3 is followed by 2 twice in the sequence, the arrow from 3 to 2 is labeled by 6 and 9, the positions of 2 in the sequence in both occurrences of 32 in the sequence. To construct the sequence from the diagram, we follow the arrows starting from the firstItem (9), then 8 then 7. With each step, we keep track of our position in the sequence. At 7, we are at position 2 and we have to decide whether to go to 3 or to 5. We go to 5 because of the label {3} of the arrow from 7 to 5, indicating that 5 is at the next position (3). We keep following the arrows until we reach the last item. The circles that we will go through represent the sequence. Here are some properties of the sequence in the example above. Please match these with the methods in SequenceInterface.java: size() == 10 first() == 9 last() == 2 predecessor(8, 7) == true predecessor(9, 2) == false getFrequencyOf(3) == 2 itemAt(3) == 5 firstOccurenceOf(7) == 2 indexInAlphabet(3) == 3 nextIndex(7, 2) == 5 nextIndex(7, 7) == 3 prevIndex(2, 6) == 3 prevIndex(2, 9) == 3 hasSub sequence(732) == true hasSub sequence( 983 ) == false The diagram above (which, by the way, is called a graph) is represented as an NxN two-dimensional array, where N is the size of the alphabet, which is 10 in the example. The array representation of the diagram above is: Each cell at row i and column j in the array contains the label of the arrow going from item i in the alphabet to item j in the alphabet. If there is no arrow between i and j, the cell is empty (null). Each cell is a BagInterface of Integers. The sequence after append(7) will look like this: Its array representation is: After prefix(0): You will also need to override the following method. You might find it helpful to implement this first so you can use it while debugging your other methods: public String toString() ; This method will return a String that is the concatenation of all of the items in the Sequence implemented by the ArrayDS object appended together without spaces. For example, if an ArrayDS object contains the numbers 1, 2, 3, 4, 5, 6, toString() should output 123456. To check your implementation of ArrayDS, the Project1.java file should compile, run, and give output identical to P1Out.txt. Please note that this statement doesn't suggest that you delay testing until you are done with all the methods of ArrayDS. Instead, you should use stubs (comment out what you haven’t implemented yet) and incrementally test your code using Project1.java as you complete each of the methods. Starter Code All starter code (including the shell of ArrayDS.java) and example output is available for download from this folder: https://drive.google.com/drive/folders/1_Z85TGqy_noblGr3jhQBhR2gEnd12B7z?usp=sharing Deliverables You are responsible for submitting ONLY ArrayDS .java. All other files will be automatically supplied to Gradescope. I would suggest avoiding making code changes to any of the other files (besides stubbing out Project1.java to test parts of your implementations at a time as you work). If you use Eclipse or any other Java IDEs to work on this project, remember to test on a command line before submitting. Sometimes editors add package lines to the top of .java files that will break the autograder. Hints - See file P1Out.txt to see how your output for task A should look. As noted, your output when running Project1.java should be identical to this. - In order for the Project1.java output to show correctly, you must override the toString() method in the ArrayDS class. - Think carefully about the order in which you implement ArrayDS methods as some methods can make others considerably easier to implement!
COMMRC 0300: Communication & Society (Individual) Case Study Assignments DUE DATES Submit the electronic copy to Canvas as a Microsoft Word document by the deadlines listed below: • Case Study 1: Monday, February 17 by 11:59 PM • Case Study 2: Thursday, March 20 by 11:59 PM COMPONENTS 1. What are we talking about? Provide a brief introduction to the company and product being discussed. 2. What happened? Provide any background information that is helpful to understand about the company, stakeholders, the advertisement itself, and the advertisement’s reception. 3. What is the problem? What is a key issue in the advertisement that could be changed for future versions of this ad campaign? • These might be problems in ad design or related to cultural sensitivity, audience, etc. • You may wish to cite information from the advertisement or its reception — external research is optional but can be helpful in strengthening your case. 4. What’s the fix and why? What is a potential solution that addresses the key issue you have identified, and why would it be effective? • Pick one solution as a final set of recommendations and consider why your solution would be effective. Include a single sentence on space for further research. • This should be the most detailedportion ofyour case analysis. 5. How does this relate to class? You are to apply 3 concepts from the course in your case study and put the name of the concepts in bold. • How might you apply the concepts mentioned in lecture to the advertisement you are to analyze? • This can be done at various stages of the case study, as course concepts may influence how you view problems or help you think through potential solutions. OTHER REQUIREMENTS Formatting: The paper should have an original title and must be stapled so please do not use report covers or other binding materials. The document itself must be single-spaced andformatted using size 12-point Times New Roman font with 1-inch margins. Also, be sure to include all the required information at the top of the document: course number and name, recitation instructor’s name, the name ofthe assignment, andyour name. For your convenience, I have created a Microsoft Word .docx template and uploaded to Canvas to help facilitate proper formatting.
„Numerische Methoden II“ Wintersemester 2024/2025 Aufgabe 4 – Lineare Gleichungssysteme und iterative Solver Für das erfolgreiche Bestehen von Assignment 4 müssen lauffähige Programme, sowie ein kurzer Report zu den Aufgaben abgegeben werden. Es sollen verschiedene Verfahren zur Lösung von linearen Gleichungssystemen untersucht werden. Die Lösungsroutinen aus der Eigen-Bibliothek werden hierbei an einem Wärmeleitproblem angewendet und in C++ programmiert. Aufgabenstellung In dieser Aufgabe wird eine quadratische Metallplatte mit der Länge L = 1 betrachtet, die mithilfe einer Induktionsspule homogen beheizt wird. Aufgrund der geringen Dicke der Platte kann die Berechnung zweidimensional erfolgen. Die Temperatur am Rand der Metallplatte kann als konstant angenommen werden. Abbildung 1: Zweidimensionale Modellierung einer induktiv beheizten Metallplatte Das Problem wird stationär betrachtet, sodass es mit der Poisson-Gleichung beschrieben werden kann: Wobei u die Temperatur und f der flächenspezifische Wärmeeintrag ist. Am Rand der Platte wird eine konstante Temperatur angenommen, sodass Dirichlet-Randbedingungen definiert werden können: Zur Diskretisierung kann das finite Differenzenverfahren verwendet werden, mit einer konstanten Schrittweite h = 1/n, wobei n die Anzahl der Schritte in x- und y-Richtung angibt. Das diskrete Problem für die Poisson-Gleichung ist ein lineares Gleichungssystem welches ohne Randpunkte folgende Anordnung besitzt: Es gilt hierbei: dabei ist T ∈ R{n−1×n−1} und I die (n − 1) × (n − 1) Einheitsmatrix. Für den Rand werden Dirichlet-Randbedingungen verwenden, sodass für die rechte Seite gilt: Wobei 2 ≤ j ≤ n − 2 gilt. Für die Nummerierung der Gitterpunkte wurde dabei eine Standardanordnung verwendet (siehe Einführungsveranstaltung). Hinweis: • Für diese Aufgabe werden Funktionen aus der Eigen-Bibliothek verwendet (siehe Einführungsveranstaltung) Aufgabe 2.1. Folgendes lineares Gleichungssystem (LGS) A x = b ist gegeben. Zur Lösung eines solchen LGS kann die Matrix als dense oder als sparse Matrix-Typ betrachtet werden. Um dünnbesetzte Matrizen als sparse Matrix-Typ abzuspeichern kann das Compressed Row Storage (CRS) Verfahren verwendet werden. Hierbei werden nur die von Null unterschiedlichen Einträge der Matrix abgespeichert. Dies geschieht in Form. eines Arrays val, wobei die Informationen der abgespeicherten Werte in zwei weiteren Arrays ir und ic abgespeichert werden (siehe Einführungsveranstaltung). 1. Führen Sie das CRS-Verfahren für die Matrix A händisch durch. 2. Erstellen Sie ein Programm zur Lösung von LGS, bei der das direkte LU-Verfahren mit einer dense/sparse Matrix verwendet wird. Das Programm soll folgende Funktionen beinhalten: a. Einlesen der Daten aus einer Datei b. Auswahl und Abfrage des Matrix-Types (dense/sparse) c. Lösung des LGS mit LU (aus der Eigen-Bibliothek) d. Fehlerbehandlung e. Ausgabe der Ergebnisse Hinweis: • Die Dokumentation für den LU-Solver von sparse Matrix-Typen befindet sich auf folgender Website (https://eigen.tuxfamily.org/dox/classEigen_1_1SparseLU.html ) Aufgabe 2.2. 1. Modifizieren Sie ihr Programm aus Aufgabe 2.1. so, dass Sie neben dem Testsystem ebenfalls die Matrix A und b zur Lösung des Wärmeleitproblems aufrufen können. a. Erstellung der Poisson-Matrix A in Abhängigkeit der Anzahl der Schritte zwischen der Gitterpunkten n, des Wärmeeintrags f und der Werte am Rand g. ➔ n, f und g sollen aus einer Datei oder über die Konsole vorgegeben werden b. Speicherung von Matrix A soll als sparse Matrix c. Auswahl zwischen direkten Solver (LU) und iterativen Solver (konjugierte Gradienten) d. Lösung des LGS mit ausgewählten Solver e. Ausgabe der Ergebnisse 2. Vergleichen Sie die zur Lösung benötigten CPU-Zeiten und Iterationen des direkten und des iterativen Lösungsverfahrens für sparse besetzte Poisson-Matrizen mit der Schrittanzahl n =10, 25, 40, 60 miteinander. Stellen Sie hierfür die genannten Größen über die Schrittanzahl beider Solver dar. Welche Unterschiede fallen auf und welche Gründe gibt es dafür? Hinweise: • Erstellen Sie zunächst die Blöcke T und I und belegen Sie damit die Matrix A • Für die weiteren Aufgaben gilt f = 1 und g = 0 • Die Dokumentation für den konjugierte Gradienten-Solver von sparse Matrix-Typen befindet sich auf folgender Website (https://eigen.tuxfamily.org/dox/classEigen_1_1ConjugateGradient.html ) Auswertung: • Stellen Sie die Temperatur im Gebiet Ω in einem 3D-Plot dar. Verwenden Sie hierfür die Unterfunktion gnuplot_splot()
BA – Film & Television MEDA 37028. Post-Production Supervisor Series Schedule Brief Using Excel, generate a series post-production schedule with the provided deliverable information. Deadline Due end of Week 5 February 7th, 2025 by 11:59pm - Save Excel as: Last name_Series_Schedule - Submit onto Slate: Assessments – Assignments – Series Schedule Components - Read the series information/deliverables / guide - Generate a realistic post-production schedule (from offline to delivery) in Excel - Include Freeze Panes (so you can read the headings as your scroll) - Format the schedule (font style, font size, alignment, colour) - Include a title and headings to the schedule - Spell-check the document - Colour Code the phases, assistant editors & editors - Include accurate dates & block off holidays/weekends - Add buffer time (1-2 days) between phases - Deliver before Network Delivery due date - Post-Production Supervisor can only be in one place at a time - Be aware of stat holidays or office closures and when the footage is released (or shot) Objectives Think through a Post-Production schedule Budget the appropriate time for each phase Apply previous & new knowledge to Excel Follow the instructions Evaluation: The assignment is worth 15% of your final grade: This assignment is due on the above date during your section. Late submissions will result in a penalty of 10% per day. If delivered after 7 calendar days (1 week late), it will result in a zero. All components must be completed individually.
SAMPLE MIDTERM EXAM ECON 120B ECONOMETRICS Table: Standard Normal Distribution Table Large-sample critical values for the t-statistic from the Standard Normal Distribution Significance Level 10% 5% 1% 2-sided test (=) 1.64 1.96 2.58 1-sided test (>) 1.28 1.64 2.33 1-sided test (
