BA457 Final Exam Practice Questions: (Note: On the final exam, as on prior exams, a question could include multiple issues.) Question 1: {trademark} Lladro Exportadora, a Spanish corporation, registered the Lladro trademark for its porcelain in Spain. Several years later, Weil Ceramics & Glass, Lladro’s wholly-owned subsidiary in the United States, purchased from Lladro the right to use Lladro’s trademark for porcelain sold in the United States. Weil registered the Lladro trademark in the U.S. and became the exclusive distributor of Lladro porcelain in the United States. Later, Weil discovered that Jalyn Corporation was importing and selling Lladro porcelain in the United States under the Lladro trademark. Issue: If Weil protests these sales, will the U.S. Customs Service prohibit the imports? Rule(s): Outcome: Rationale: [Hint: See Chapter 13, “gray market” imports Study note: notice the relationship in this hypothetical between Weil and Lladro. How may that affect the analysis?] Question 2: {patent} [Note: I initially considered this question in case we also got to antitrust, which we did not. So please ignore such issues about exclusivity, integration, and pricing discrimination (ch.14/Sherman Act/Clayton Act/Robinson-Patman Act) and focus on chapter 13 patent principles as stated in the issue.] Barnes patented a line of virtual reality headsets which it offered for sale only through independent retail dealers at physical locations in various U.S. cities. This permitted Barnes to maintain a dual pricing system with high prices in the Northeastern and Western states and much lower prices in the Midwest and South. Barnes’ contracts with the dealers in the Midwest and South include strict maximum resale pricing requirements, territorial restrictions and prohibit all internet sales. After the headsets’ popularity began to grow, Barnes’ dealers in the Eastern and Western states complained that they were being undercut by online sales. Barnes then discovered that Applegate, an Ohio corporation unaffiliated with Barnes, had been purchasing lower-priced headsets from Midwest dealers and reselling them online throughout the country. Barnes sued Applegate for patent infringement. Issue: Will Barnes win its patent infringement lawsuit? [Hint: you could phrase this another way, such as--can Barnes prohibit Applegate from re-selling the headsets?] Rule(s): Outcome: Rationale: [Hint: See chapter 13 on patent] Bonus: while this patent issue does not address extraterritorial enforcement, Question 3: {copyright} Indiana University regularly sells a line of sweatshirts that prominently display the “IU” logo. The university owns the copyright on clothing that displays the IU logo. University officials recently discovered that counterfeit IU sweatshirts were being sold at a kiosk in one of the corridors of a local shopping mall. Despite warning both the mall owner—Maplewood—and the kiosk operator of its copyright claims, the sales of the counterfeit sweatshirts persisted. Although the mall lease gave Maplewood the right to inspect merchandise sold by its tenants and the right to evict tenants who violated its rules, Maplewood refused to evict the kiosk operator. Issue: Are the kiosk operator or Maplewood Mall likely to be liable to the university? Rule(s): Outcomes: Rationale: “Bonus” issue on copyrights: After paying a fee, subscribers can access sexually explicit photographs on a computer bulletin board service operated by Warren. Subscribers can earn credits for further access by uploading images onto the service. It was later discovered that numerous photographs uploaded onto the service were photographs owned by Playboy magazine. Will Warren be liable for copyright infringement? Question 4: {trade secret} Matthews Corporation, a company doing business in the United States, developed a secret process that enabled it to produce widgets at a higher quality and for a lower cost than its competitors. Accordingly, the company produced its widgets in a closed facility protected by a fence and tight security measures. Despite the security measures, Cornwell was able to sneak into the factory one evening and take photographs of the secret process. Issue: If Matthews sues Cornwell for misappropriation of its trade secret in a U.S. court, would it likely be successful? [Note: for such a question you should define when a company enjoys trade secret protection.] Rule(s): Outcome: Rationale: Question 5: A report funded by the U.S. Department of Labor’s International Development Fund and developed by the Payson Center for International Development at Tulane University finds that upwards of half of lithium-mining operations in Africa and Asia employ “the worst forms of child labor.” Lithium is a critical component of batteries used in cell phones, such as those manufactured by Pineapple, Inc. Pineapple, Inc. is a large consumer electronics multinational corporation, which prides itself on its plain, yellow packaging of its phone products. Charles wants to sue Pineapple for not publishing on its packages that “the worst forms of child labor exist in Pineapple’s supply chains.” Charles (as a class action representative) bring a suit in federal court in California (in the Ninth Circuit) under California’s consumer protection statutes such as the Unfair Competition Law and False Advertising Law. Issue: Will Charles’s lawsuit likely succeed to enjoin Pineapple to print such labels on their packaging? Rule(s): Outcome: Rationale:
PHAY0032 – Preformulation Problem-based learning workshop In the module so far, we have looked at a range of physicochemical concepts and discussed how they relate to the formulation of a drug. In this workshop, we will look at some exercises to see how these properties will impact formulation decisions. In advance of the workshop: Please have a look through the questions below and the material covered to date, and make a list of things you are unsure of – we can discuss these before we start the exercises. In the workshop we will work through the exercises below together. Exercises 1. A company is looking to develop a fast dissolving formulation of a drug D. The structure of D is given below. a) Consider the structure of D. Do you expect it to have high solubility in water? What about its permeability? b) Experiments are performed to determine the partition coefficient for D. Explain what is meant by the term partition coefficient, and explain why it is useful to determine its value. c) 43.7 mg of D is dissolved in 170 mL of octanol, and 330 mL of water is added. After shaking, the final amount of D in the aqueous phase is 1.72 mg. Determine log P for D. Show your working in full in your answer. d) During preformulation studies, it is found that D exists as two polymorphs, form. I and form. II. What is meant by the term polymorphism? What differences will there be between form. I and form. II? e) Form. I and form. II of D have melting points of 67.2 and 123 °C respectively, and ΔfusH values of 34.5 and 89.3 kJ mol-1. Calculate the ideal solubility of both polymorphs at 25 °C. What assumptions are made in ideal solubility? f) Which form. is the most stable one? g) When the solubility in water is measured, the x2 values for forms I and II are found to be 1.34 x 10-6 and 3.45 x 10-8 respectively. Compare and contrast these to the values you calculated in part e. h) The company attempt to formulate the metastable form. of D into a tablet. They perform. a dissolution test for 24h, and obtain the data below. Explain these findings. i) Comment on the feasibility of making i) an immediate release and ii) an extended release formulation of D. j) How might the physical form. of D be altered to improve the solubility? 2. Ultimately, the company abandon their work on D, and start to explore a new drug, D’. a) The structure of D’ is given below. How does this relate to the original active ingredient D? Explain the rationale for the company’s shift to this new active. b) The company want to formulate D’ as an immediate release formulation. Comment on the likelihood of this. c) The solubility of D’ is measured at a number of different pH values, and the results are given in the table below. Use these data to calculate its intrinsic solubility. The pKa of D’ is 3.22. pH Solubility (μg / mL) 1 0.571 2 0.602 4 3.99 d) The partitioning of D’ is studied at pH 1 and pH 4. 10 μg of drug is dissolved into 100 mL of an aqueous buffer for each experiment, and this is then shaken with 100 mL of octanol. At pH 1, the amount of drug in the water layer after this is found to be 0.237 μg, while at pH 4 1.45 μg of drug remains in the aqueous phase. Calculate log Po,w and log Do,w at both pH values. e) Although the company find that D’ performs better than D, they are still not happy with its performance. Thus, they consider forming a salt. Suggest some suitable salt formers to use with D’. f) In dissolution tests of some salts of D’, it is found that the rate of dissolution at pH 2 (representative of the stomach) is very similar to that at pH 6.8 (representing the lower parts of the gastrointestinal tract). Explain why these observations are seen. g) The dissolution rate is found to be too slow for practical applications of the D’ salts. How might the company solve this problem? 3. a) Pseudopolymorphs such as co-crystals can be used to give active pharmaceutical ingredients improved properties. Explain what is meant by the terms pseudopolymorph and co-crystal, and explain how a co-crystal differs from a solvate. b) What benefits can co-crystals have in pharmaceutical formulation? Give examples of co-crystal systems for each benefit you give. c) A company prepares co-crystals of a new drug E and suberic acid. The structures of each are given below, together with some dissolution data. Rationalise the observations seen in the dissolution experiment. d) E is intended to be taken alongside another drug, F. The structure of F is shown below. In in vivo experiments on rats, kidney problems are observed to arise after approximately two weeks of taking both active ingredients simultaneously. Explain why this occurs. e) How are co-crystals usually produced in industry? Why can this method be problematic?
Math 132A Assignment 1 Due: Wednesday, January 15th at midnight. Submit on Gradescope. 1. Consider the following table indicating the nutritional value of diferent food types. You need to decide how many servings of each food to buy each day so that you minimize the total cost of buying your food while satisfying the following daily nutritional requirements: • caolories must be at least 2000, • fat must be at least 50g, • protein must be at least 100g, • carbohydrates must be at least 250g. Write a linear program (LP) that will decide how many servings of each of the aforementioned foods we need to meet all nutritional requirements, while minimizing the total cost of the food. (you may buy fractional numbers of servings). Use an LP solver to actually find an optimal point and optimal value. Most spreadsheet programs like Excel have an LP solver included. These days you could ask chatGPT to solve it but be careful that it ’s output makes sense! I recommend trying to learn how to do these in Matlab, Mathematica or Maple, or for heavy duty LP problems, CPLEX. 2. The director of a startup needs to decide what salaries to ofer to its employees for the fiscal year 2024. In order to keep the employees satisfied, she needs to make sure of the following. • Tom wants at least $20, 000 or he will quit. • Peter, Nina and Samir want each to be paid at least $5000 more than Tom. • Gary wants his salary to be at least as high as the combined salaries of Tom and Peter. • Linda wants to make $200 more than Gary. • The combined salaries of Nina and Samir should be at least twice the combined salary of Tom and Peter. • Bob’s salary is at least as high as that of Peter’s and at least as high as Samir’s. • The combined salaries of Bob and Peter should be at least $60, 000. • Linda should make less money than the combined salaries of Bob and Tom. (a) Write an LP that will determine the salaries for the employees such that the above constraints are satisfied but the total salary of everyone is minimized. (b) Write an LP that will determine the salaries for the employees such that the above constraints are satisfied but the salary of the highest paid employee is minimized. Hint: Define a new variable. 3. (A Transportation Problem). A company makes a product at factories 1, 2, . . . , p and sells it to stores 1, 2 . . . , q. Factory i produces si units per month and store j orders tj units per month. Assume that every unit made is shipped to a store, and every store receives exactly the number of units ordered. The cost of shipping one unit of the product from factory i to store j is cij dollars. (a) Model the problem of finding the cheapest way to ship the product from the factories to the stores as an LP. To start, set xij be the number of units shipped from factory i to store j. (b) Prove that the feasible region is nonempty if and only if (Hint: For the hard direction, try showing there is a solution with x11 = min(s1, t1 ) . Can you find a transportation problem with fewer factories or stores such that feasible solutions of the smaller program extend to feasible solutions of the original with this value for x11 ?? ) 4. Let t be a real number and consider the following LP maximize − 2x1 + x2 subject to x1 − x2 ≤ −1 −x1 + tx2 ≤ 0 x1 , x2 ≥ 0. (a) Let T be the values of t for which the problem has a feasible solution. Use geometry to guess T. (b) Give an algebraic proof that the LP is feasible if and only if t ∈ T. (c) Let S be the set of values of t for which the LP is unbounded. Use geometry to guess S. (d) Give an algebraic proof that the LP is unbounded if and only if t ∈ S.
ELE000172M BEng/MEng Degree Examinations 2024-5 Department: School of Physics, Engineering and Technology Title of Exam: Research Methods Theory & Data Analysis Question: [40 marks] Write a consultancy report for GreenBuild Materials investigating factors influencing employee productivity. Your report should include the following sections: A. Introduction (200 to 250 Words): [6 marks] This section should explain the report's purpose and value to the Executive Board. • It should clearly outline your specific hypotheses relevant to the research question. [3 marks] • You need to identify relevant variables from your hypotheses and provide reasons for your chosen research direction. [3 marks] B. Methodology (200 to 250 Words): [11 marks] • You need to explain the methods / tests you used to conduct the research process - including data cleaning procedures. [5 marks] • You need to provide reasons for each of your choices. [6 marks] C. Results (250 words): [10 marks] • Present the findings using charts or tables created in SPSS, Excel, Python, or another statistical software. [5 marks] • Use diagrams, graphs, or charts to present the data clearly and visually illustrate productivity scores across shifts, noise levels, and other variables. You should provide a complete picture of the empirical analysis and not pick-and-choose findings based on their significance. [5 marks] D. Discussion and Reflection (100 words to 150 words): [10 marks] • Interpret the statistical findings to address the research questions, highlighting factors that significantly affect productivity. E. Conclusion (50 words to 100 words): [3 marks] • Provide actionable recommendations for GreenBuild to improve scheduling, work environments, or employee engagement based on the findings. Supplementary Evidence Requirement You must include supplementary evidence, such as graphical data or tables generated in SPSS or another statistical software, to enhance clarity and support your findings. Evidence may include histograms, bar charts, box plots, correlation matrices, or ANOVA output tables. Note: The instructions are outlined as follows: Case: GreenBuild Materials - Manufacturing Efficiency Consultancy Report for GreenBuild Materials: Investigating the Effect of Workplace Factors on Employee Productivity GreenBuild Materials is a leading company in sustainable construction, operating multiple manufacturing facilities across the region. Recently, the Board of Directors has raised concerns about variable productivity levels among employees across different shifts and environmental conditions. They believe that factors such as shift type, noise exposure, workplace temperature, employee satisfaction, and salary may significantly impact productivity, affecting overall efficiency. To gain a clearer understanding of these factors, GreenBuild conducted a survey among their manufacturing workforce. The data collected will help the company identify the most influential factors on productivity, enabling the Board to implement targeted changes to optimize employee performance and satisfaction. Some key questions they are interested in exploring include: • How do different shift types (morning, afternoon, night) impact productivity? • Is there a relationship between noise level exposure and employee productivity? • Does workplace temperature affect productivity levels? • What is the correlation between employee satisfaction and productivity? • How does annual salary relate to productivity scores? You may be able to think of other important questions the company should be asking that can be answered by this data set. Marks will be awarded for deeper insights and additional exploration of the dataset. Dataset overview: The dataset comprises responses from 120 employees across GreenBuild’s facilities, with data collected on the following key variables: • Employee ID: Unique identifier for each participant. • Age: Age of the employee. • Gender: Gender of the employee. • Shift Type: Type of shift (Morning, Afternoon, Night) worked by the employee. • Noise Level Exposure: Noise exposure level in the workplace (Low, Medium, High). • Workplace Temperature (°C): Average temperature in the employee’s work area. • Employee Satisfaction: Satisfaction level on a scale of 1 to 5, with 5 indicating “highly/Very satisfied.” • Productivity Score: Productivity score based on performance evaluations on a scale of 1 to 10, where 10 is the highest productivity score. • Years at Company: Duration of employment at GreenBuild. • Training Hours Last Year: Training hours completed in the past year. • Workload Intensity: Perceived job intensity (Low, Moderate, High). • Annual Salary (£): Annual salary of the employee in British pounds (£). Instructions for Candidates: Your task is firstly to explore which variables relating to salary are the most important, then statistically analyse the dataset gathered by the Board of Directors and use the findings from your analysis to write a report for the Executive Board. Your statistical analysis should follow these steps: Instruction: Step 1: Formulate Appropriate Hypotheses: • To answer the research question, you will need to select relevant hypotheses - there is a strong recommendation to propose three hypotheses in total. This step will be important in shaping your statistical analysis and guiding the investigative journey. Step 2: Identify relevant variables from your hypotheses: • You need to identify what the relevant variables are for your selected hypotheses. These variables will play a crucial role in shaping the study's focus and analytical framework. Step 3: Complete Data Cleaning: • Before the analysis phase, rigorous data cleaning procedures are essential to ensure the dataset is accurate, reliable, and ready for scrutiny. This preparatory step should fix any dataset discrepancies or anomalies that might affect the validity of the findings. Step 4: Identifying and applying statistical tests for analysis: • The core of the research process involves systematically conducting statistical tests and analysis to assess the validity of the formulated hypotheses. This step is central to uncovering empirical evidence and gaining a better understanding of the research question. Step 5: Interpret the results: • The insights derived from the analysis, whether significant or not, will require effective interpretation. Use diagrams, graphs, or charts to clarify / visualise the findings. Step 6: Write your Report. • The report must be between 800 to 1000 words. This word count ensures a concise yet thorough presentation of the research process, findings, and implications. Note: Graphical evidence such as graphs and tables are excluded from the word count. Additional information: ● No references are required. ● You must add supplementary evidence such as graphical data from SPSS or any statistical tools you used for this data analysis. ● Cover page, contents list, figures, appendices, and references are excluded from the total word count.
Homework 1 AMATH 482, Winter 2025 Assigned Jan 10, 2025. Checkpoint Due on Jan 20, 2025. Report and Code Due on Jan 26, 2025 at midnight. Directions, Reminders and Policies Read these instructions carefully: There are two stages for submitting the assignment. 1. You will be submitting a Checkpoint approximately one week after the assignment was published (see due date above). The checkpoint includes submission of your Report and Code in progress (at least 1/3) (2 points) and taking the checkpoint quiz (3 possible points). 2. You will be uploading a Report (PDF) to Canvas along with a zip of your Code (15 possible points). The grade will be based on how completely you addressed the problem as well as neatness and important things like: have you labeled your graphs and included figure captions (7 points will be given for the overall layout, correctness, and neatness of the report, and 8 additional points will be given for specific things that the TA will look for in the report and the code. • The report should be a maximum of 6 pages long with references included. Minimum font size 10pts and margins of at least 1inch on A4 or standard letter size paper. • Do not include your code in the report. Simply create a zip file of your main scripts and functions, without figures or data sets included, and upload the zip file to Canvas. • Your report should be formatted as follows: – Title/author/abstract: Title, author/address lines, and short (100 words or less) abstract. This is not meant to be a separate title page. – Sec. 1. Introduction and Overview – Sec. 2. Theoretical Background – Sec. 3. Algorithm Implementation and Development – Sec. 4. Computational Results – Sec. 5. Summary and Conclusions – Acknowledgments ( no more than four or five lines, also see the point below on collaborations) – References • LATEX(Overleaf is a great option) is recommended to prepare your reports. A template is provided on Canvas in Homework/Files. You are also welcome to use Microsoft Word or any other software that correctly typesets mathematical equations and properly allows you to include figures. • Collaborations are encouraged; however, everything that is handed in (both your report and your code) should be your work. You are welcome to discuss your assignments with your peers and seek their advice but these should be clearly stated in the acknowledgments section of your reports. This also includes any significant help or suggestions from the TAs or any other faculty in the university. You don’t need to give all the details of the help you received, just a sentence or two. A similar guideline applies to the use of Large Language Models (LLM). These are permitted for the study of topics and code presented in class and a better grasp of the problem and its solution. However, everything that is handed in (both your report and your code) should be your work and cannot be based on LLM content (modified or direct). Any use of external help should be specified in the acknowledgments section of the report. • Late reports are subject to a 2 points/day penalty up to five days. They will be no longer accepted afterwards. For example, if your report is three days late and you managed to get 16/20, your final grade will be 16 − 6 = 10, so be careful with late submission. Problem Description: Finding Submarines Your goal in this homework is to locate a submarine that is moving in the Puget Sound. We do not know much about this submarine as it is a new technology that emits an unknown acoustic frequency that you need to detect. Broad spectrum recording of acoustics pressure data obtained over 24 hours in half-hour increments is available to you. You can download the data using the Google drive links on Canvas; either of the data files subdata.npy for Python users, subdata.mat for MATLAB users or subdata .csv in text format if the previous two formats are insufficient. The data file contains a matrix with 49 columns of data corresponding to the measurements of acoustic pressure taken over 24 hours. These measurements are noisy (which is typically the case). The measurements themselves are 3D and taken on a uniform grid of size 64 × 64 × 64. The provided (hwhelper) notebook will visualize this data for you and define the physical scales of the problem. If the 3D plots are slow and you cannot see the dynamic behavior of the data consider downloading the GIF file subdata.gif on Canvas. Some comments and hints Here are some useful comments and facts to guide you along the way. 1. First, observe that you are provided three-dimensional dynamic data, that is acoustic pressure measure- ments in 3D and as a function of time. This makes visualization difficult as the data set is effectively four-dimensional (3D+time). If you would like to see temporal variations then I suggest looking at slices of the data (eg isosurface command) as a function of time. 2. In class we only saw/ will see 1D and 2D Fourier transforms but here you may need a higher dimensional Fourier transform. Not much changes in the N-D setting except that you need to use the fftn function. fftshift remains valid and is still needed. 3. Recall Code Samples (FFT examples) and the discussion of the Gaussian function. We saw a useful fact about noise and Fourier transform that will help you in this assignment and in many applications: It is known that adding mean zero white noise to a signal (Gaussian noise) is equivalent to adding mean zero white noise (Gaussian noise) to its Fourier series coefficients. This fact enables one to devise a simple and effective “preliminary" noise filtering technique in situations where multiple measurements are available that are subject to the same noise. This is the case in imaging or acoustics applications like our submarine problem. Since the noise is random and mean zero it should average to zero over many samples. Thus, averaging the measurements in the Fourier domain is expected to reduce the noise. The reduction will improve with an increasing number of aligned measurements, but in the case of our submarine, we only have a few measurements so you would still need to do additional filtering. Tasks Below is a list of tasks to complete in this homework and discuss in your report. 1. Through averaging of the Fourier transform determine the dominant frequency (center frequency) generated by the submarine. Verify your results through visualization. 2. Design and implement a Filter to extract this center frequency in order to denoise the data and determine a more robust path of the submarine. Visualize the denoised measurement the 3D path of the submarine and inspect the validity and effectiveness of the denoising. 3. Determine and plot the ∞,y coordinates of the submarine path during the 24 hour period. This information can be used to deploy a sub-tracking aircraft to keep an eye on your submarine in the future.
Principles of Banking - N1577 Seminar 9 Banking crises Question 1. Why is financial liberalisation often blamed for banking crises? Discuss. Support your discussion with some examples. Question 2. Critically discuss the effectiveness of deposit insurance in preventing banking crises. Question 3. Referring to the article “Financial crises explanations, types, and implications” identify and discuss the main causes of banking crises.
ECON6012 / ECON2125: Semester Two, 2024 Tutorial 1 Questions A Note on Sources These questions do not originate with me. They have either been influenced by, or directly drawn from, other sources. Key Concepts Methods of Proof, Proof by Deduction, Proof by Induction, Proof by Con-tradiction, Proof by Contraposition, Disproof by Counterexample, Binary Relations, Potential Properties of Binary Relations, Weak Completeness, Re-flexivity, Irreflexivity, Symmetry, Antisymmetry, Transitivity, Strong Com-pleteness, Rationality, Equivalence Relations, Partitions, Partially Ordered Sets, Ordered Sets (or Totally Ordered Sets), Well Ordered Sets, Weak Pref-erence Relations, Indifference Relations, Strict Preference Relations. Tutorial Questions Tutorial Question 1 Tutorial Question 2 Show that √ 3 ∈/ Q, where Q := {b/a : a ∈ Z, b ∈ N} is the set of rational numbers, Z := {· · · , −3, −2, −1, 0, 1, 2, 3, · · · } is the set of integers, and N := {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, · · · } is the set of natural numbers. Tutorial Question 3 Either show that following claim is true or provide a counter-example that establishes that it is false. Claim: The strict preference relation is antisymmetric if and only if the weak preference relation is strongly complete. Tutorial Question 4 Consider the set A = {1, 2, 3}. Show that the set equality relation is an equivalence relation on the power set of A. • Some background facts. – Weak Subset: Let X and Y be two sets. X ⊆ Y if and only if every element of X is also an element of Y . – Proper Subset: Let X and Y be two sets. X ⊂ Y if and only if both X ⊆ Y and Y 6⊆ X. – Set Equality: Let X and Y be two sets. X = Y if and only if both X ⊆ Y and Y ⊆ X. – Power Set: Let X be a set. The power set of X, which is often denoted by 2X, is the set of all subsets of X. Additional Practice Questions Additional Practice Question 1 Suppose that X is the consumption set for some consumer and % is a rational weak preference relation that is defined on X (or, more accurately, X × X). (Recall that a weak preference relation is rational if it either (i) weakly complete, reflexive, and transitive, or, equivalently, (ii) strongly complete and transitive.) 1. Show that the indifference relation, ∼, on X is reflexive, symmetric and transitive, but not strongly complete. 2. Use your answer to part one of this question to conclude that the indifference relation on X is an equivalence relation. 3. Suppose that x ∈ X. Define the indifference set for x as I (x) = {y ∈ X : y ∼ x} . Show that, for all (x, y) ∈ X × X, either I (x) = I (y) or I (x)∩I (y) = ∅. 4. Show that for every x ∈ X, we have I (x) = ∅. 5. Use your answers to part two and part three of this question to argue that the set of all indifference sets, {I(x) : x ∈ X}, partitions the ele-ments of X into a set of non-overlapping subsets of X without leaving out any elements of X.
ECON6012 / 2125: Semester Two, 2024 Tutorial 2 Tutorial Assignment 1 This assignment involves submitting answers for each of the tutorial ques-tions, but not for the additional practice questions, that are contained on the tutorial 2 questions sheet (this document). You should submit your answers on the Turnitin submissions link for Tutorial Assignment 1 that is available on the Wattle site for this course (under the “In-Semester Assess-ment Items” block) by no later than 08:00:00 am on Monday 5 August 2024. If you have trouble accessing the Wattle site for this course or the Turnitin submission link, please submit your assignment to the course email address (which is [email protected] if you are a postgraduate student, and [email protected] if you are an undergraduate student). One of the tutorial questions will be selected for grading and your mark for this tuto-rial assignment will be based on the quality and accuracy of your answer to that question. The identity of the question that is selected for grading will not be revealed to students until some point in time after the due date and time for submission of this assignment. A Note on Sources These questions and answers do not originate with me. They have either been influenced by, or directly drawn from, other sources. Key Concepts Binary Relations, Potential Properties of Binary Relations, Weak Pref-erence Relations, Indifference Relations, Strict Preference Relations, Al-gebraic Structures, Metric Spaces, Properties of Distance Metrics, Open Sets, Closed Sets, Clopen Sets, Sets that are Neither Open Nor Closed, Continuity. Tutorial Questions Tutorial Question 1 1. Show that (Q, +) is a group when addition of two rational numbers is defined by b/a + d/c = bd/ad + bc. 2. Show that (Q {0} , ×) is a group when multiplication of two rational numbers is defined by b/a × d/c = bd/ac. Tutorial Question 2 1. Show that the discrete metric is a valid distance metric for any set X. 2. Show that the Euclidean metric is a valid distance metric for Rn, where n ∈ N. 3. Show that the sum-of-absolute-differences metric is a valid distance metric for R n , where n ∈ N. Tutorial Question 3 Let (A, d) be a metric space and suppose that a, b ∈ A with a = b. Prove by contradiction that B∈(a) ∩ B∈(b) = ∅ for any ∈ < d(a,b 2 ) . (Hint: You will need to use the triangle inequality.) (Note that B∈(x) is the “open epsilon-neighbourhood”, or “open epsilon-ball”, centred on the point x ∈ A and with a “radius” of ∈ > 0.) Tutorial Question 4 Let (A, d) be a metric space and suppose that x ∈ A and s > 0. Given any a ∈ Bs(x), show that there exists some r > 0 such that Br(a) ⊂ Bs(x). Tutorial Question 5 Prove that both (−∞, x] and [x, ∞) are closed subsets of R for all x ∈ R. Additional Practice Questions Additional Practice Question 1 Lexicographic Preferences on R 2 +: Suppose that a consumer has lex-icographic preferences over bundles of non-negative amounts of each of two commodities. The consumer’s consumption set is R 2 +. The consumer weakly prefers bundle a = (a1, a2) over bundle b = (b1, b2) if either (i) a1 > b1, or (ii) both a1 = b1 and a2 > b2. In any other circumstance, the consumer does not weakly prefer bundle a to bundle b. (Note that these preferences are not continuous. Furthermore, they cannot be represented by a utility function.) 1. Under what circumstances will bundle c = (c1, c2) be strictly pre-ferred to bundle d = (d1, d2)? 2. Under what circumstances will bundle c = (c1, c2) be indifferent to bundle d = (d1, d2)? 3. Are these preferences weakly complete? Explain why. 4. Are these preferences reflexive? Explain why. 5. Are these preferences strongly complete? Explain why. 6. Are these preferences transitive? Explain why. 7. Are these preferences rational? Explain why. 8. Show that these preferences are not continuous. Additional Practice Question 2 Show that {(x, y) ∈ R2 : y > x} is open in R2. Additional Practice Question 3 Let (A, d) be a metric space in which d is the discrete metric. 1. Show that every subset of A is clopen in this case. 2. Show that f : A → B is continuous for any metric space (B, r).
STATS 763 SECOND SEMESTER, 2023 STATISTICS Advanced Regression Methodology 1. Consider the following code and output, wherein we model and test the Volume variable from the trees data seen in class. > data(trees) > head(trees) Girth Height Volume 1 8.3 70 10.3 2 8.6 65 10.3 3 8.8 63 10.2 4 10.5 72 16.4 5 10.7 81 18.8 6 10.8 83 19.7 > dim(trees) [1] 31 3 > ## Model with three free parameters > mod.free coef(mod.free) (Intercept) log(Height) log(Girth) -6.691109 1.132878 1.980412 > ## Model with fixed coefficients for log(Height) and log(Girth) > mod.fixed coef(mod.fixed) (Intercept) -6.166161 > ## Inverse link for log link > ilink ## Derivative of the link log(mu) > dlink ## Variance function V(mu)=mu^2 > vfun ## Model matrix X from model with all three parameters and outcome Y > X Y Mystery.Function1
COMPSCI 753 COMPUTER SCIENCE SEMESTER TWO, 2023 1 Locality-Sensitive Hashing [25 marks] Given four documents S1 , S2 , S3 , S4 and a customized query document q: S1 = {c, f}, S2 = {a, b}, S3 = {d, e}, S4 = {a,c, e}, q = {a,c, e}; 1.1 Computing MinHash Signatures [10 marks] (a) Generate the bit-vector representation for {S1 , S2 , S3 , S4 , q} in shingle space {a,b,c,d,e, f}. [3 marks] (b) Generate the MinHash matrix for {S1 , S2 , S3 , q} using the following four MinHash functions. [5 marks] h1 (x) = (2x + 1) mod 6 h2 (x) = (3x + 2) mod 6 h3 (x) = (5x + 2) mod 6 (c) Among the hash functions, h1 , h2 , h3 , which one gives the true simulated permutation? [1 marks] (d) Consider the query q and estimate the signature-based Jaccard similarities: J(q, S1 ). [1 marks] 1.2 Tuning Parameters for rNNS [10 marks] Recall the collision probability (i.e., S-curve) given the number of bands b and the number of rows per band r as follows: Pr(s) = 1 - (1 - sr )b Consider three sets of parameters (r=3,b=10), (r=6,b=20), (r=5,b=50). The collision prob- abilities for similarity s in range of [0,1] for each (r ,b) are provided accordingly in the table below. Please answer the following two questions. (a) Which settings give at most 5% of false negatives for any 70%-similar pairs? Please briefly explain your answer. [5 marks] (b) Which settings give at most 15% of false positives for any 30%-similar pairs? Please briefly explain your answer. [5 marks] 1.3 c-Approximate Randomized rNNS [5 marks] Recall that a family of functions H is called (d1 , d2 , p1 , p2 )-sensitive with collision probability p1 > p2 and c > 1 if the following conditions hold for any uniformly chosen h ∈ H and 8 x, y ∈ U : • If d(x, y) ≤ r , Pr[h(x) = h(y)] ≥ p1 for similar points, and • If d(x, y) ≥ cr , Pr[h(x) = h(y)] ≤ p2 for dissimilar points. (a) How can we further transform the upper bound probability approaching 1? How can we further transform the lower bound probability approaching 0? [2 marks] (b) Consider a set of movie plot articles (D), and a set of queries (Q). You have con- structed Locality-Sensitive Hashing (LSH) frameworks for varying hash sizes with k ∈ {2, 4, 8, 16}. To evaluate the impact of k on Jaccard similarity estimation, you computed the mean absolute error (MAE) for pairs of articles (di , q), where di ∈ D and q ∈ Q, and obtained the MAE plot below. Please comment on your MAE plot. (Note: You can assume that your implementation is correct.) [3 marks] 2 Data Stream Algorithms [25 marks] 2.1 Bloom Filter [6 marks] (a) Consider the following statement: “The Bloom filter can determine the existence of items, allowing the possibility of false positive responses and false negative responses.” Is it true, false or unknown? Please briefly explain your answer. [3 marks] (b) Name two approaches to reduce the possibility of false positives. Please briefly explain your answer. [3 marks] 2.2 Misra-Gries Algorithm [5 marks] (a) Consider the given data stream. Implement the Misra-Gries algorithm with k = 4 counters. Provide a comprehensive summary, including the elements and their corre- sponding counter values, once the execution of the algorithm is completed. [3 marks] S = {45, 13, 14, 45, 7, 10, 45, 6} (b) What would the theoretical number of decrement steps be triggered after processing the above stream in question (a)? [2 marks] 2.3 Count Sketch Algorithm [14 marks] Consider the same data stream S and hash functions below. Using the given sign hash functions below, apply the Count Sketch algorithm and present the following: (a) Hash Table. [5 marks] (b) Counter Matrix. [5 marks] (c) Final estimated frequency of each element once the execution of the algorithm is completed. Please comment on your estimated frequency against the true frequency. [4 marks] 3 Algorithms for Graphs [25 marks] 3.1 Web Graphs [12 marks] Given the following raw adjacency matrix A: (a) Convert A into its corresponding column-stochastic matrix M. [4 marks] (b) In the lecture, we have shown that the PageRank r = M · r is the eigenvector of the column-stochastic matrix M corresponding to eigenvalue λ = 1. Compute the PageRank of all nodes in the above graph using the eigen-equation and report the values of the r vector. [4 marks] (c) The power iteration algorithm is an iterative method to solve PageRank. Explain: 1) how does the algorithm perform updates in each iteration? 2) what are the stop criteria and required initializations? [4 marks] 3.2 Community Detection [8 marks] Given the following undirected graph: (a) Compute the edge betweeness of each edge ({ea ; eb ; ec ; ed }) using Brandes’ algorithm, only for the case when node 1 is taken as the root node. [4 marks] (b) Apart from edge betweeness and modularity maximization, spectral graph partition- ing is another method for community detection that works by solving the problem miny∈Rn yT Ly, with L the Laplacian matrix. Explain: 1) how is the Laplacian matrix calculated, 2) how can eigenvalue decomposition be used to solve this minimization problem. [4 marks] 3.3 Influence Maximization [5 marks] Given the following directed graph: (a) Consider the set S = {1} as the seed set. Compute the contingency table for the graph. [3 marks] (b) Using the contingency table calculated in the previous step, compute the influence spread under the Independent Cascade (IC) model. [2 marks] 4 Recommender Systems [25 marks] 4.1 Memory-Based Collaborative Filtering [10 marks] Given the following user-interaction matrix of users {u1 , u2 , u3 , u4 , u5 } and items {p1 , p2 , p3 , p4 }: (a) Based on these ratings from users to items, which user is most similar to user u2 if you consider cosine similarity? How does this information help you to provide recommendations to user u2 if you were to use the user-based collaborative filtering algorithm? [4 marks] (b) Calculate: 1) the global bias (bg), 2) the user bias for user u2 (bu(ser)), and 3) the item bias for item p1 (bp(i1tem)). [3 marks] (c) Suppose that you used one of the memory-based recommendation algorithms learned in lectures to calculate predicted ratings of users over item p1 . You obtained the following comparison of predicted vs. actual ratings: Calculate the root mean squared error (RMSE) metric of the above table (report the RMSE using two decimal digits). [3 marks] 4.2 Model-based Collaborative Filtering [8 marks] In the lectures, we discussed about the Latent Factor Model (LFM) as a model-based technique for approximating the user-interaction matrix, and therefore learning how to make predictions on unknown ratings. Considering the regularized optimization problem of LFM (without bias): Explain, in a few sentences: (a) What is this optimization problem of about? [3 marks] (b) How can Stochastic Gradient Descent help solve this problem? [3 marks] (c) What is the advantage of a model-based technique such as LFM as opposed to memory- based techniques such as user-based or item-based collaborative filtering? [2 marks] 4.3 Context-aware Recommendations [7 marks] Suppose you are asked to build a context-aware system to recommend events. Users {u1; u2; u3; u4} attend events from {e1; e2; e3} in groups. Events are held in one of the two stadiums s1 and s2. After attending, users assign ratings to events. The following table shows the transactions: (a) Define an encoding for groups, users, events and stadiums, and construct the input feature vectors for the factorization machine using the event transactions in the above table. [4 marks] (b) How can the information in these feature vectors along with the information about ratings be used for prediction of future ratings? Explain your answer. [3 marks]
Portfolio Selection Problem A portfolio manager in charge of a bank portfolio wants to invest a sum of up to $12 million in a number of bonds. The bonds available for purchase, as well as their respective quality ratings, maturities, and yields, are shown in the following table: Bond Name Type Moody’s Rating Bank’s Quality Rating Years to Maturity Yield to Maturity After-tax Yield A Municipal AA 2 10 4.4% 4.4% B Agency AA 2 15 5.5% 2.8% C Government AAA 1 5 5.1% 2.6% D Government AAA 1 4 4.3% 2.1% E Municipal BB 5 3 4.7% 4.7% The bank places the following policy limitations on the portfolio manager’s actions: · Government and agency bonds must total at least $4 million. · No more than $8 million can be invested in any one bond. · The average quality of the portfolio cannot exceed 1.4 on the bank’s quality scale (on this scale, a lower number means a higher-quality bond). · The average number of years to maturity of the portfolio cannot exceed 5 years. For a portfolio, portfolio-risk rating and portfolio maturity are defined as a weighted average, where the weight assigned to each bond type is proportional to the dollar investment in that bond. Assume you can invest any dollar amount in any of the bonds. a) Assume that the objective of the portfolio manager is to maximize after-tax proceeds, e.g., a 3.0% after-tax yield on a $4 million investment translates into a $0.12 million in proceeds. Formulate a linear decision model in Excel and solve it. Describe the optimal solution, which bonds are bought, in what quantities, etc. b) Assume it becomes possible to borrow up to $1 million at 4.5% interest (before taxes). Reformulate the problem and resolve. Describe how the optimal solution has changed. (Assume the tax rate is 50%, so that the after-tax cost of borrowing $1 million at say 5% would be $50,000-$25,000=$25,000.) (Hint: add a new decision variable representing the amount borrowed.) (Hint: It is often desirable to use a linear model, since the Solver is guaranteed to find the optimal solution for such a model. The maximum allowed average quality constraint and the maximum allowed average years to maturity constraint are non-linear, but they can be transformed to linear constraints. This is done as follows: say you want to write a constraint like x+y/2x+5y ≤ 3 in linear form. Then you simply transform. it to this: 2x+5y £ 3x+3y. The constraint is now linear.)
STATS 763 - 2022 - Final examination Available from 15 June 2022 at 17:00 NZST (5:00PM) Due by 15 June 2022 at 19:30 NZST (7:30PM) General instructions • This examination consists of these instructions and 3 questions on 8 pages. Attempt all questions. The exam will be marked out of 100, out of a possibility of 100. • Inspera requires you to upload a single file containing your answers to all three questions. The file size cannot exceed 1 Gb. • The duration of the examination is two hours, between 17:00 (5:00PM) and 19:00 (7:00PM) on 15 June 2022, New Zealand Standard Time. • This assessment was designed to be completed within 2 hours by a pre- pared student. However, you have 2 hours and 30 minutes in which to complete and submit it. • Submissions will be open until 19:30 NZST (7:30PM) to allow for scan- ning and uploading. It is your responsibility to ensure your assessment is successfully submitted on time. • All reasonable forms of answer file format will be accepted, including clearly scanned or photographed hand-written responses, PDF documents, Word or similar Libre Office documents, markdown files, etc. • This is an on-line open-book exam. You are allowed any resource to answer the questions except consulting another person (see Academic Honesty Declaration). Piazza will be unavailable during the examination except to address private queries to the instructors. • Computing final numerical answers is not required. It is su cient, for full marks, to produce a correct computable solution. Question 1: [Total: 30 marks] Data were collected from 696 randomly sampled women who gave birth over a 4 1/2 month period in a New Zealand hospital in 2011. The following table describes the data. The outcome of interest is the diference between the date of birth and the expected date of delivery (‘DOB - EDD ‘), measured in weeks. A moderate positive diference (late birth) is generally not an issue; a negative diference (early birth) larger in magnitude than 3 weeks identifies the baby as premature. The exposure of interest is the Number of previous pregnancies without live birth (‘n stillbirths‘) defined as Gravidity-Parity-1. (The “-1” dis- counts the current pregnancy). This number includes stillbirths and voluntary interruptions of pregnancy. Adjustments for ethnicity (binary variables eth EurOther,eth Maori,eth Pasifika and eth Asian), age group (AgeGrp), and presence of a husband or partner (HusbPart) are considered sufficient to account for confounding in this obser- vational study. a) [6 marks] We fit two linear least-squares models, A and B. Using the partial output supplied below, test the null hypothesis H0 : βGravidity = -βParity vs H1 : not H0 . Justify your answer briely. Model A: Coefficients: Estimate Std . Error t value Pr(>| t | ) (Intercept) 0 .05010 0 .38813 0 .129 0 .89734 Gravidity -0 .30532 0 .09951 -3 .068 0 .00224 ** Parity 0 .30649 0 .12137 2 .525 0 .01178 * [snip - you don’t need the missing output to answer the question] (Dispersion parameter for gaussian family taken to be 5 .159174) Null deviance: 3639 .1 on 695 degrees of freedom Residual deviance: 3523.7161 on 683 degrees of freedom Model B: Coefficients: Estimate Std . Error t value Pr(>| t | ) (Intercept) -0 .25347 0 .35700 -0 .710 0 .47796 ‘n stillbirths‘ -0 .30509 0 .09877 -3 .089 0 .00209 ** [snip] (Dispersion parameter for gaussian family taken to be 5 .151635) Null deviance: 3639 .1 on 695 degrees of freedom Residual deviance: 3523.7181 on 684 degrees of freedom b) [6 marks] According to the fitted model below, how large would the num- ber of previous pregnancies with no live birth (the ‘n stillbirths‘ co- variate) need to be for ‘DOB - EDD‘ to be more negative than -3 weeks on average, if the expectant mother is Asian with no other ethnicity, has no husband/partner and is over 40? It is su cient to set up the equation without solving it. Model B (again) Coefficients: Estimate Std . Error t value Pr(>| t | ) (Intercept) -0 .25347 0 .35700 -0 .710 0 .47796 ‘n stillbirths‘ -0 .30509 0 .09877 -3 .089 0 .00209 ** eth_Maori -0 .11255 0 .28660 -0 .393 0 .69465 eth_Pasifika -0 .32473 0 .31575 -1 .028 0 .30411 eth_Asian -0 .60485 0 .36708 -1 .648 0 .09987 . eth_EurOther 0 .15025 0 .30503 0 .493 0 .62248 AgeGrp| t | ) (Intercept) -0 .35170 0 .40251 -0 .874 0 .383 ‘n stillbirths‘ -0 .03248 0 .38871 -0 .084 0 .933 eth_Maori -0 .20279 0 .33713 -0 .602 0 .548 eth_Pasifika -0 .09238 0 .36578 -0 .253 0 .801 eth_Asian -0 .61988 0 .42384 -1 .463 0 .144 eth_EurOther 0 .31564 0 .36039 0 .876 0 .381 [snip] ‘n stillbirths‘:eth_Maori 0 .14032 0 .34115 0 .411 0 .681 ‘n stillbirths‘:eth_Pasifika -0 .46421 0 .39582 -1 .173 0 .241 ‘n stillbirths‘:eth_Asian 0 .09691 0 .48039 0 .202 0 .840 ‘n stillbirths‘:eth_EurOther -0 .34506 0 .33578 -1 .028 0 .304 (Dispersion parameter for gaussian family taken to be 5 .12995) Null deviance: 3639 .1 on 695 degrees of freedom Residual deviance: 3488 .4 on 680 degrees of freedom Test the significance of the interaction term by producing an appropriate test statistic and p-value; make sure to specify the approximate distribu- tion of the test statistic under the null hypothesis of no interaction. e) [6 marks] The distribution of premature births by maternal age group is shown below: Counts of premature births by age group, original data Premature
Measuring Data Bias, Part 2: Comparative Analysis This part of the assignment goes deeper into understanding how open-source and closed-source generative AI models handle data bias. You will compare these models to see how each responds to similar prompts and whether certain content is blocked or restricted. Instructions: Select an open-source model and a closed-source image or text generation model. Compare the two models and experiment to see whether you can increase the bias of generations. Test the closed-source model to see what it generates in similar scenarios and what types of content it blocks from generating, if any. Based on your investigation, what kind of mitigations do you think might be in place for the closed-source systems, and why? Deliverables: For part 2, please submit: The results on your evaluation set from Part 1 from both the open-source and the closed-source models. A minimum of 2-3 new contexts that demonstrate a difference in bias mitigation between the open-source and closed-source models (or, if no such difference materializes, include the new contexts and briefly describe the responses for both). A 500-word writeup of your findings when comparing the two systems on your bias evaluation set, including: Any evidence for or hypotheses about specific mitigations that either system might have Interesting outputs or surprising findings, if any, surfaced when probing for bias Your overall assessment of bias and mitigation as based on the combined results from Parts 1 and 2.
FILM 112 Film, Media, and Screen Cultures: Theory & Practice Winter 2025 Description FILM 112 offers an introduction to theoretical and critical approaches to global time-based media, focusing on the theories of film and media. Students will learn to identify an array of cinematic elements (mise-en-scene, cinematography, editing, , postcolonialism,) and apply such tools to the analysis of global time-based media. Students will pair these conversations with the process of creation, learning the production and circulation of time based-media in order to strengthen their own creative visual storytelling skills. Intended Student Learning Outcomes To complete this course students will demonstrate their ability to: 1. Apply the scope of theoreBcal and pracBcal approaches to fields of film, media, and screen cultures. 2. IdenBfy and apply cinemaBc language to analysis of global Bme-based media. 3. Deploy creaBve visual storytelling skills alongside theoreBcal comprehension. 4. Examine the historical, social, poliBcal, psychological, and cultural implicaBons of Bme-based media. Email Policy Each student will be assigned a TA, who will be in charge of questions about assignments, feedback, course content, and evaluation. You will meet your TA in tutorial where they will share their contact information. Note that your TA is not expected to answer emails after 5:00pm or on weekends, unless they so choose. Please wait 72 hours (excluding weekends) for your TA to respond before sending a follow-up email, or emailing the course coordinator. Questions regarding the FILM112 OnQ site can also be sent to the coordinator, available at [email protected]. Often if one student has a question, many other students do too. If a number of students have the same question, responses will be posted in the “Course Announcement” section of OnQ. Students with accommodations should follow the instructions of Queen’s Accessibility Students (QSAS) and use the Ventus system to submit their accommodations. Please note that accommodations will not automatically be implemented to every assignment. If you would like to use your accommodations, like extra time, for a specific assignment, please email your TA and let them know. Additionally, any students who do not have formal accommodations but become sick and need to request either extra time or to address absences, please email your TA. Please include the course code “FILM 112” in the subject title of course related emails. Course Materials Required Readings and Screenings Bordwell, David, Kristin Thompson and Jeff Smith, Film Art: An Introduction. 13th ed. Julian MacDougall, Media Studies: The Basics. 2nd ed. Available in the Queen’s bookstore. All screening materials will be available in class. Many of the films screened are not accessible online. Technology Requirements 1. Web Browsers: onQ performs best when using the most recent version of the web browsers, Chrome or Firefox. Safari and Edge are strongly discouraged as these web browsers are known to cause issues with onQ. 2. Internet Speed: While wired internet connection is encouraged, we recognize that students may be relying on a wireless connection. A minimum download speed of 10 Mbps and up to 20 Mbps for multimedia is recommended. To test your internet speed: https://www.speedtest.net/ For technology support ranging from setting up your device, issues with onQ to installing software, contact ITS Support Centre: https://www.queensu.ca/its/itsc
LIN204H5 F English Grammar I Fall 2024 COURSE DESCRIPTION Students will learn about fundamental grammatical concepts, focusing on the major grammatical categories in English and how they interact at the phrase level. They will be introduced to the main constituents of English sentences and learn about the basic relationship between tense, aspect, and modality. Students will learn to apply this knowledge as a tool to think analytically about English, evaluating various registers and styles, and gaining an awareness of their own style of speaking and writing. Depending on the instructor, this course may be delivered fully or partially online. This course counts towards only the English Language Linguistics Minor (ERMIN1200); it does NOT count towards the Linguistic Studies Minor (ERMIN0506) nor the Linguistic Studies Major (ERMAJ1850). Learning Outcomes Students will learn to: . Identify grammatical categories of English words and phrases . Perform. basic structural analysis of English sentences . Explain grammatical concepts to a general audience . Distinguish between prescriptive and descriptive rules Textbooks and Other Materials . There is no assigned textbook to purchase for this course. . Any required reading will be posted on Quercus. . Some work will be submitted on Crowdmark. . The Course will have a Discord server, but you are not required to participate in it.
MENG 4019 ‐ Practical 3 – 2022 Task: design and simulate the operation of a hydraulic curcuit. A hydraulic cylinder, stroke 2000 mm, D piston 100 mm, d rod 50 mm angled 75 degrees from horizontal is lifting a mass load of 500 kg. Pulll external force 8000 N, push external force 10000 N. The cylinder needs to be able to move at controlled speeds and stop at intermediate positions. Firrst, we build a conceptual circuit: 1. Open Automation studio, select and insert the following components from the Hydraulic set of components. The Proportional hydraulic valve is available in the Proportina Hydraulic category 2. Connect circuit as shown below: 3. Select the Simulation tab and run a Normal Simulation. Then, Stop Simulation and run a Slow‐Motion Simulation. Click on the valve to change position. 4. Note: in the neutral position, with no load on the cylinder, the rod is slowly extending due to the difference in force originating from the difference in area between the two chambers 5. Double click on the hydraulic cylinder. Open the Data tab. Ensure the star at the top of the Component Properties is unselected. Modify the characteristics of the cylinder as in the task definition and close the Component Properties: 6. We want to control the direction and speed of the cylinder. Because we have a proportional valve, the opening of the valve is proportional to the current applied to the proportionalsolenoid that controlsthe valve. We need a control device for the current – a joystick. Insert it from the Environment & Control category: 7. We need to link an axis of the joystick to the proportional valve. Link Input Signal – Proportional to the X‐axis of the joystick ‐JY‐X. The two signals are Real, i.e. continuous, proportional with the input. Double click and link them: 8. Experiment with positioning the joystick in various positions between ‐10 and 10 and examine the flow and the speed of the piston. 9. We can insert the dynamic measurement instrument and determine the proportionality between the joystick position on X axis and the speed of the piston. The maximum speed of the piston depends on the pump output, the opening of the proportional valve and the dimensions of the cylinder (piston and rod diameters). We can see in the figure below that the pressures before and after the proportional valve differ. Thisis consistent with the role and behaviour of this category of valves Note1: only the X‐axis of the joystick controls the speed of the piston. Note 2: there seems to be proportionality only for a limited opening of the proportional valve. This is true and is equivalent to magnetic saturation in electrical machines. In Hydraulics, proportionality is a property that is valid only for a small opening of the control orifices or valves. 10. We want to control the position of the piston so that it is proportional to the position (displacement) of the joystick. We need to determine the difference between the position of the joystick and the position of the piston and set it as an error that the circuit will attempt to minimise. Insert a Control Device from the Environment & Control category: 11. Break the association between the proportional valve and the joystick. Right click on the Association and click on delete link 12. We need to link the proportional valve with the joystick by using the Control Device. Double click on the Control Device and open the Output Variable option from the left: 13. In the Control Device Output tab from the left, link the output from the joystick and the position of the piston. We input the equation (Output X signal from Joystick – Output Signal position of the piston) as real values. Select the appropriate variables, determine the code assigned by AS to each device. 14. Simulate the circuit. Modify the position of the joystick as control input: The circuit works, but exactly not as expected. We need to do de‐bugging and tuning. First issue: when the joystick input is at 0 (i.e. in the middle), the piston position is fully retracted instead on being at the middle of the stroke. We need to correct this, and we modify the Control Device Output as follows: This means that when the cylinder is at the middle, (i.e. at output signal 5 on a zero to 10 scale) and the joystick is at zero, the error shall be zero. 15. There is, however, still, a relatively substantial error. In this case, the joystick is at +1 and we would expect that the position of the piston to be at 6 (middle, 5, +1) 16. We need to fine tune the system. This can be done in a number of steps. First, increase the quality of the joystick – normally a 5% hysteresis, reduce it to 0.5% 17. Increase the Proportional gain from 1 to 10 The error is reduced to less than 0.6 of the stroke or similar. 18. Adjust the gains so that you consistently minimise the error over the whole joystick input range while avoiding instability. There is a structural issue with the circuit that leads to an inherent error. This comes from the properties of the proportional valve and the open‐loop control of the circuit. This can be solved by modifying the construction of the proportional valve to achieve correct proportionality between spool position and/or with a suite of sensors and fine tuning on the circuit: 19. If you have one, you can attach a joystick to the circuit and control the valve with it Once an external joystick is attached, it will need a bit of fine tuning to align specific inputs and required outputs
Homework 4 Book problems: 6.24, 6.28 a, b, (Required to be turned in) Matlab: (Needs to be turned in separately) In this problem you have been provided a speech file sampled at 8 kHz (corrupted_speech.mat). However, it has been corrupted using two tones, i.e two sinusoids of two different frequencies, and so the speech content is not recognizable on playback. Your job is to use filtering techniques to eliminate these two tone frequencies and recognize the content of the speech file. The following steps will be helpful for this purpose. 1. Identify the frequencies of the tones corrupting the speech. 2. Design a filter/approach to eliminate the tones and recover the speech. 3. Identify the contents of the original speech file. For every step, document and support your approach. Provide plots as needed with explanation and include the code written to accomplish the task in your report.
MTH205 Introduction to Statistical Methods Tutorial 4 Based on Chapter 4 1. Measurements of total solids, in g/L, for seven wastewater treatment sludge specimens were obtained below: 20 5 25 43 24 21 32. The measurements were rounded to the nearest gram. Perform the Wilcoxon signed-rank test. (i) Can you conclude that the mean concentration of total solids is greater than 14 g/L? Use the p-value to conclude. (ii) Can you conclude that the mean concentration of total solids is less than 30 g/L? Use the p-value to conclude. (iii) It is claimed that the mean concentration of total solids is equal to 18 g/L. Can you conclude that the claim is false? Use the p-value to conclude. The distribution of total solids is assumed to be symmetric. 2. In a research on chemical reactions, the benzene conversions (in mole percent) of 24 di↵erent benzenehydroxylation reactions are reported below: 52.3 41.1 28.8 67.8 78.6 72.3 9.1 19.0 30.3 41.0 63.0 80.8 26.8 37.3 38.1 33.6 14.3 30.1 33.4 36.2 34.6 40.0 81.2 59.4 Perform the Wilcoxon signed-rank test. (i) Can you conclude that the mean conversion is less than 45? Use the p-value to conclude. (ii) Can you conclude that the mean conversion is greater than 30? Use the p-value to conclude. (iii) Can you conclude that the mean conversion di↵ers from 55? Use the p-value to conclude. . The distribution of the conversion is assumed to be symmetric. 3. This exercise shows that the signed-rank test can be used with paired data. Two gauges that measure tire tread depth are being compared. Ten different locations on a tire are measured once by each gauge. The results, in mm, are presented in the table below: Assume the di↵erences are a sample from a symmetric population with mean μ . Perform the Wilcoxon signed-rank test totest H0 : μ = 0 against H1 : μ ≠ 0. Use the p-value in your conclusion. 4. In a comparison of the effectiveness of distance learning with traditional classroom instruction, 12 students took a business administration course online, while 14 students took it in a classroom. The final exam scores were as follows. Online: 66 75 85 64 88 77 74 91 72 69 77 83 Classroom: 80 83 64 81 75 80 86 81 51 64 59 85 74 77 (i) Perform the Wilcoxon rank-sum test to determine if the mean score di↵ers between the two types of course. Use p-value in your conclusion. (ii) What assumptions are necessary for the result of the test to be valid?
