Module code/name MSIN0023 Computational Thinking Academic year 2024/25 Term 1 Assessment title Assignment 3: Code, discuss and analyse an algorithm applied to a management problem Individual/group assessment Individual Submission deadlines: Students should submit all work by the published deadline date and time. Students experiencing sudden or unexpected events beyond your control which impact your ability to complete assessed work by the set deadlines may request mitigation via the extenuating circumstances procedure. Students with disabilities or ongoing, long-term conditions should explore a Summary of Reasonable Adjustments. Students may use the delayed assessment scheme for pre-determined mitigation on a limited number of assessments in a year. Check the Delayed Assessment Scheme area on Portico to see if this assessment is eligible. Return and status of marked assessments: Students should expect to receive feedback within 20 working days of the submission deadline, as per UCL guidelines. The module team will update you if there are delays through unforeseen circumstances (e.g. ill health). All results when first published are provisional until confirmed by the Examination Board. Copyright Note to students: Copyright of this assessment brief is with UCL and the module leader(s) named above. If this brief draws upon work by third parties (e.g. Case Study publishers) such third parties also hold copyright. It must not be copied, reproduced, transferred, distributed, leased, licensed or shared with any other individual(s) and/or organisations, including web-based organisations, without permission of the copyright holder(s) at any point in time. Academic Misconduct: Academic Misconduct is defined as any action or attempted action that may result in a student obtaining an unfair academic advantage. Academic misconduct includes plagiarism, self-plagiarism, obtaining help from/sharing work with others be they individuals and/or organisations or any other form. of cheating that may result in a student obtaining an unfair academic advantage. Refer to Academic Manual Chapter 6, Section 9: Student Academic Misconduct Procedure - 9.2 Definitions. Referencing: You must reference and provide full citation for ALL sources used, including AI sources, articles, text books, lecture slides and module materials. This includes any direct quotes and paraphrased text. If in doubt, reference it. If you need further guidance on referencing please see UCL’s referencing tutorial for students. Failure to cite references correctly may result in your work being referred to the Academic Misconduct Panel. Use of Artificial Intelligence (AI) Tools in your Assessment: Your module leader will explain to you if and how AI tools can be used to support your assessment. In some assessments, the use of generative AI is not permitted at all. In others, AI may be used in an assistive role which means students are permitted to use AI tools to support the development of specific skills required for the assessment as specified by the module leader. In others, the use of AI tools may be an integral component of the assessment; in these cases the assessment will provide an opportunity to demonstrate effective and responsible use of AI. See page 3 of this brief to check which category use of AI falls into for this assessment. Students should refer to the UCL guidance on acknowledging use of AI and referencing AI. Failure to correctly reference use of AI in assessments may result in students being reported via the Academic Misconduct procedure. Refer to the section of the UCL Assessment success guide on Engaging with AI in your education and assessment. Content of this assessment brief Section Content A Core information B Coursework brief and requirements C Module learning outcomes covered in this assessment D Groupwork instructions (if applicable) E How your work is assessed F Additional information Section B: Assessment Brief and Requirements Code, discuss and analyse an algorithm applied to a management problem Introduction: Consider a problem we have covered from this module or from any other module (e.g. from Data Analytics I or Mathematics II) involving non-trivial algorithms. You are also free to consider any other algorithmic topics we may not have covered e.g. image-processing. The problem should relate to a management problem or business-idea that requires the use of algorithms. A non-trivial algorithm uses loops and will be of at least linear complexity. The more complex your algorithm the more opportunity you will have to demonstrate increased understanding and more sophisticated analysis, providing enhanced potential of a good grade. You may wish to continue with the same algorithm/problem you presented in your Assignment 2 essay or choose a different algorithm or problem. Example algorithms: Here are some examples of non-trivial algorithms you could consider: · Data Analytical Classification algorithms including Decision Tree Induction and Nearest Neighbour · Data Analytical Clustering algorithms including Hierarchical Clustering and K-Means Clustering · Matrix Row Reduction algorithm to solve systems of simultaneous equations or to find inverse matrices · Simplex Linear Programming algorithm · Search and Graph Analysis algorithms, including shortest-path algorithms · Exhaustive Enumeration and Greedy/Heuristic Algorithms for any NP-Complete problem (eg travelling salesman, knapsack packing problem, wedding banquet seating …) Report Format and Structure: The main body of your report has a word count limit of 2000 words, consisting of a number of sections, as detailed below. In addition, you should include as appendices: all your code appropriately commented; your test run outputs; and extracts from your test data. There is no word limit on the appendices, which will be assessed alongside the main body of your report. You are required to submit two files, with a third optional data file: 1. A single PDF document containing your full report, including all the appendices. 2. A single supplemental code file, which can either be in the form. of a standard python code file (.py) or a Jupyter notebook file (.ipynb). This code will not be marked, but may be required to validate that the code you have provided as an appendix can be executed, as claimed. 3. An optional data file (.csv), if this is required to run your supplemental code file. The requirements of the code and code appendix are provided first in these instructions as this forms the primary focus of this assignment. This is followed by instructions for each of the sections of main body of the report. CODE APPENDIX: Provide working python code that solves your problem (30%) Provide, as an appendix to your report, your completed coded. Embed in your code comments that describe each function in terms of its purpose, inputs and outputs. Additional comments should also be included to help explain key steps in your algorithms, and examples of particular techniques you have used. You are not required to have written all the code yourself. There are plenty of examples of python code on the Internet that provide solutions to any problem you are likely to consider. Please feel free to use such code, providing suitable references to these sources. Any code you do re-use should fully implement your chosen algorithms, so that you can identify and comment on how the code implements these algorithms. You are not allowed to use python modules that directly implement your algorithm in such a way that you cannot see exactly how the code implements the algorithm. You can though use standard python modules to provide appropriate data representations for your algorithm (eg numpy for matrix data or networkx for graph data) or provide other functions that do not form. part of the core implementation of your focus algorithm (eg math, statistics, csv, random modules). You are required to demonstrate you have fully understood the code and have been able to apply it to your particular problem, using suitable test data. This is likely to require, at a minimum, that you write some additional code to run and test your algorithm code on your particular problem; maybe to load data from a csv file, enter some initial input values, and to print or plot outputs. You should add additional print statements within your code to illustrate key aspects of how the algorithm works. You should also add appropriate additional code (such as loop counters) and print statements within your code to help assess the complexity your algorithm and prepare Big(O) plots. You are required to provide code that it understandable and well designed. Code copied from the Internet is often not well designed! Don’t necessarily use the first version you find. You are likely to need to edit and potentially change any code you re-use from the Internet so that it uses clear and consistent names. You will need to demonstrate decomposition in your code (ie it should contain multiple functions, rather than one large single function). You may therefore need to decompose a large unstructured program from the Internet into smaller functions that are easier to understand. Main Report Sections: 1. System Requirements and Your Algorithm (10%) Describe your management problem or business-idea and outline the purpose of the software system/application that addresses this problem/idea in the form. of a brief set of system requirements, listing: · The functional requirements, identifying the key functions with their data inputs and outputs. · Any non-functional requirements you believe may be important for this problem. (Note: The topic of Functional and Non-functional Requirements is covered in Week 8.) Briefly introduce your algorithm, identifying: · How your algorithm works. · How your algorithm helps solve your problem. · Which functional requirements are associated with your algorithm. 2. Explain how the code works (30%) Explain the design of your code, particularly commenting on: · The overall structure of the code in terms of the key functions it contains and how the code decomposes into a hierarchy of functions. · The flow of the overall code as it progresses from loading/inputting/generating some input data to providing the final solution to your problem. · In what ways the code is generalised, i.e. in what ways can the code you are using be used to solve more other, more generalised, problems to the specific scenario problem you have applied it to? · How data is represented in your code and why it is represented in this way. · The use of any particularly noteworthy or advanced coding features such as: recursive functions, use of list comprehensions, use of dictionaries and sets, passing functions as input parameters. You must also identify and comment on which parts of the code are re-used (you must reference the source of all re-used code), any re-used code you have improved or changed (how and why), and which parts you have coded fully yourself. 3. Analyse the complexity of your code (10%) Explain how the key inputs to your problem can vary in size and nature. Assess the expected running time complexity of your code in terms of an order of magnitude of the size of your input value(s). Justify your results. Record the run time performance of your code using a range of different input size values and produce a run time Big(O) plot based on these timings. Provide additional loop-counter-based and/or theoretical Big(O) plots to support your findings. Explain you results and compare any theoretical or loop-counter-based analysis with your experimental timing results. Explain any realistic limits of your code, in regard to runtime performance. 4. Describe the data used in your code (10%) Describe the data you used to illustrate how your algorithm could solve your particular management problem or business-idea software. Did you use an open data source for this or did you create/generate the data yourself? Explain the choices you made in this regard. Explain how you selected or generated different ‘sizes’ of data to analyse the running time complexity of your code. 5. Conclusions (10%) Briefly conclude by discussing the benefits and limitations of your code. Things you may like to consider are: · Explain in what ways you believe your code follows good design principles. · Discuss any alternative approaches to solving this problem. · Suggest how your code could be improved. · Discuss whether and how you think this code can be generalised for use on different problems. · Discuss any limitations in your data and the implications for your findings
CIT 5940 - Module 1 Programming Assignment ArrayLists: Dynamic Arrays Assignment Overview In this module, you saw how an ArrayList works by performing operations using an underlying array hidden to users. In this assignment, you will modify the implementation of an ArrayList so that it uses Java Generics, as well as adding custom functionality. Learning Objectives • Understand the implementation of an ArrayList in Java • Gain familiarity with reading and modifying existing code • Verify that you can submit code to our autograding platform. Advice We highly encourage you to utilize the course discussion forum to discuss the project with class- mates and TAs. Before asking the question, please search in the forum to see if there are any similar questions asked before. Please check all suggestions listed there. For this and all other assignments in this course, we recommend that you work on your local computer using an integrated development environment (IDE) such as Eclipse, IntelliJ, Visual Studio Code, or whatever IDE you used for any prior Java courses that you are familiar with. Although you will need to upload your solution to Gradescope for grading (see the Submission Section below) and could develop your solution on that platform, we recommend using industry standard tools such as Eclipse or IntelliJ so that you become more used to them and can take advantage of their features. If you have trouble setting up your IDE or cannot get the starter code to compile, please post a note in the discussion forum and a member of the instruction staff will try to help you get started. We have provided an example JUnit test file to help check your implementation. Please read the comments and complete the code to validate your solution before submission. 1 Setup 1. Begin by downloading the CIT594-arraylists . zip archive from Canvas, then extract the contents. The main file you will work is MyArrayList . java. This contains the unimplemented methods for the code that you will write in this assignment. 2. We have also provided a JUnit test file, MyArrayListTest . java as an example of JUnit tests. Please read the comments in the file and complete the code to validate your solution before submission. 3. Compile this code before making any changes. This will ensure your local environment is configured correctly. 4. Review the current implementation. You’ll want to understand the various parts of the code and how they work together before making changes! 2 Requirements 2.1 Structure and Compiling 1. You MUST use a Java Development Kit (JDK) version of 17 or higher. This is because Gradescope is using Java 17. 2. You MAY use a JDK version higher than 17, but you MUST set the Java language level to 17 for compatibility with Gradescope. 3. You MUST NOT change any method signatures for any of the provided methods. This includes the parameter lists, names, and return value types, etc. 4. You MUST leave the MyArrayList.java in the default package. 5. You MUST NOT create additional . java source files for your solution. 6. You SHOULD create JUnit tests to help validate your code. These tests SHOULD NOT be a part of your solution. The starter code includes a partial JUnit test file as a refresher. We do expect you to test your code thoroughly with additional JUnit tests. 7. You MUST follow our directives in the starter code comments. This means if we ask you to not change a variable’s value, you MUST NOT change that variable’svalue. 8. You MAY create additional helper functions, as long as they meet the other requirements of the assignment (e.g. uses Java Generics, doesn’t crash with invalid inputs). 9. You MUST fill out the required Academic Integrity signature in the comment block at the top of your submission file. 2.2 Functionality Specifications 2.2.1 General Requirements 1. Your method MUST NOT crash if a user enters an invalid input. Remember you do not have control over what a user inputs as arguments. Your program should not throw an exception except when specified. 2. Note specifically that Java allows you to add the value null to a list of objects. Your program MUST consider null as a valid element. 3. You MUST maintain the size field. This is the number of elements in the underlying array, NOT the length of the array. 4. You MUST check for element equivalence using the equals method. 2.2.2 Java Generics 1. You MUST modify the starter code to use Java Generics instead of Strings. This includes parameters and return values. 2. Your underlying array MUST be of type Object[]. 3. As a hint, find all the references to String, these will be replaced! 4. As an example, you should be able to create an instance of the class for any type like this: // create an ArrayList that holds Integers MyArrayList> integerList = new MyArrayList();
INFO6007/INFO3333 Project Management in IT (Semester 2, 2024) INFO6007 ASSESSMENT GUIDE 1. KEY ASSESSMENTS These are the key assessments for INFO6007 during Semester 2, 2024 which are given below: Assessment Component Team-Based? Weight Due Knowledge Test No 15% Week 7 Group Project Yes 30% Week 10 Presentation Yes 5% Week 11 & 12 Final Exam No 50% Exam Period 2. SUBMISSION INSTRUCTIONS The submission instructions for the assessments are given below. Please ensure that yu to follow the guidelines before submitting the assessments to avoid being penalized. a) All the assignments are to be submitted online via the Turnitin submission portalon Canvas. No printouts of the assignments should be submitted. b) Only one team member from each group should submit the assignment online. If you experience any difficulty in submitting your work, please let your tutor know immediately c) Late assignment submissions will be penalized by a penalty of 5% per day of the total mark allocated for the assignment (if you need more details or need some sort of clarification please check with Lecturer or the teaching team). d) Individual contribution for group assignment may be taken into consideration while marking the group assessments. e) Assessment files should be named in the following format before submission Format: GroupNumber_INFO6007_AssessmentName_Sem2_2024 Example: Group1_INFO6007/INFO3333_GroupProject_Sem2_2024 3. UNIVERSITY POLICY ON ACADEMIC DISHONESTYANDPLAGIARISM The Faculty of Engineering views all forms of academic dishonesty, including plagiarism and recycling, very seriously. The University-wide policy on academic honesty is set out below. Plagiarism means presenting another person’s ideas, findings or work as one’s own by copying or reproducing them without due acknowledgement of the source. AI: Use of AI is not allowed Recycling means the submission for assessment of one’s own work,or of work which is substantially the same, which has previously been counted towards the satisfactory completion of another unit of study, and credited towards a university degree, and where the examiner has not been informed that the student has already received credit for that work. Students who submit work containing significant portions that have been copied from other sources, including published works, the internet, existing programs, works previously submitted for other awards or assessments, or the work of other students, without proper acknowledgement will be penalized. 4. KNOWLEDGE TEST (15%) There will be a knowledge test conducted for this unit in week 7. It is a Canvas-based online test. The details of the format and coverage will be provided in lectures. 5. GROUP PROJECT (30%) 5.1. TEAM STRUCTURE Students are expected to form teams of 5 students per group for the group assignment by Week 1. All the group members must be in the same tutorial group. 5.2. PROJECT TOOLS MS Project software or similar software should be used by your group project for INFO6007/INFO3333. 5.3. LEARNING GOALS In this assessment you are expected to demonstrate your understanding of the following topics: a) Project Charter b) Project Scope c) Ability to perform a literature review/research d) Work Breakdown Structure e) Project Plan andTime f) Project Cost g) Project scheduledevelopment h) Time control processes i) Budgeting and cost baseline etc. In addition to covering the learning topics, you are expected to demonstrate your leadership and effective teamwork skills and to provide self-assessment and peer review. Each group/team is expected to choose their IT project from the list of real-life project provided below or use/find any IT related project of the choice available elsewhere. Real-life Projects list links https://www.transport.nsw.gov.au/projects https://www.cityofsydney.nsw.gov.au/building-new-infrastructure https://www.eralberta.ca/projects/ https://www.development.vic.gov.au/projects?view=list https://www.freelancer.com.au/ https://www.fiverr.com/ 5.4. TASKS Based on the information presented in the projects list links, prepare a proposed plan of action, which will ultimately result in a full detailed project plan. In this assignment you would need to cover at least the following : a) Project Charter Outline Create an outline of the Project Charter for the project case as specified in the marking criteria Project Time Line: 9 - 12 months b) Scope Provide a scope statement for the project case, and milestones. c) Literature Review Conduct a literature review and identify the knowledge gaps d) Detailed Work Breakdown Structure (WBS) Prepare WBS for the project case which outlines first three levels of the structure only. e) Provide a brief description for each phase/work package and high-level activity. Detailed Project Schedule Construct a high-level visualization of project time management (e.g. Gantt chart) and provide an explanation of each milestone. Identify dependencies f) Cost Modeling Identify the type of costs for the project case. Outline the direct and indirect project cost etc. g) Communication Management h) Quality Management i) Risk Management j) Human Resource Management k) Procurement Management 5.5. PROJECT REQUIREMENTS & MARKS DISTRIBUTION (more details can be found in canvas in week 6) Assessment Element Sub-Elements Weight 1. Project Charter • Project details (Brief background and objectives) • Project deliverables (high level) • Project cost (Total cost) • Project time (Total time) • Roles and responsibilities of stakeholders. Each student act as astakeholder of the project, e.g., CEO, CIO, Director of Human Resource, etc. /10 2. Scope • Project scope statement • Milestones /10 3. Literature Review/Market Research • Appropriate literature selection • Identification of knowledge gaps • Analysis and consolidation • Summary of literature review • Citation (appropriate, extensive use) /10 4. Work Breakdown Structure (3 level) • Work Packages/ Activities/Tasks • Provide a brief description of each of the activities, put in a table format /5 5. Project Schedule/Time Modeling • Detailed schedule (Ganttchart) • Proper sequencing and task Dependencies /5 6. Cost Modeling • Detailed budget table • Identify cost types and briefly describe them • Detailed cost baseline /10 7. Communication • Communication plan, see the template provided on Canvas /10 8. Quality Management • Quality management plan, see the template provided on Canvas /10 9. Risk Management • A brief risk register, see the template provided on Canvas /10 10. Procurement Management and Human Resources Management • Plans • Resource allocation • Acquistions /10 11. Structure • Harvard referncing Style • Grammar and formatting • Number of pages: 28 - 33 pages including references • Font Size: 11 /10 Total /100 6. Presentation(5%) It will be agroup presentation and will be held in week 11 and 12. Each member from your group is expected to present. Time Allocated for the presentation is 10 minutes per group + 5 minutes Q&A. Presentation generally involves the following criteria. Further details would be provided by the lecturer. a) Contents of presentation b) Team communication during presentation c) Engaging the audience d) Confidence and ability to convince e) Q&A handling (if any)
553.420/620 Probability Assignment #04 1. We have two spinners: spinner 1 has 5 equally likely regions numbered 1 through 5, spinner 2 has 6 equally likely regions numbered 1 through 6. You spin each spinner once and note the region number the spinner landed. (a) What’s the probability you landed on at least one even number? (b) Given you landed on at least one even number, what’s the probability the other number is odd? Hint: for (a) it might be helpful to define Ei to be the event that spinner i landed even. Then E1 ∪ E2 is the event you landed on at least one even. 2. (a) Flip a fair coin twice. One of the flips is a head. What’s the probability the other is a tail? (b) The Smith family has two children. One of them is Tina – a girl. What’s the probability Tina has a brother? 3. (a) In dealing two cards, what’s the probability we get a heart followed by a red card? (b) In dealing two cards, what’s the probability you get a red card followed by a heart? (c)* In dealing five cards, what’s the probability we see a black followed by black followed by red followed by a spade followed by a heart? * just as in part (b) if we invoke some nice property of the sample space this problem is not too bad. 4. (a) Roll a 6-sided die twice. Given a 1 occurred, what’s the probability the first one shows a 6? (b) Roll a 6-sided die twice. Given exactly one 1 occured, that’s the probability the first is a 6? 5. Among two coins – one fair, the other two-headed – one is selected uniformly at random. (a) The coin is flipped twice. Let Hi be the event that we get a head on the ith flip, i = 1, 2. Are H1 and H2 independent? Justify your assertion. (b) Flip the coin n times, where n > 1 be an integer. If the selected coin came up heads on all n flips, what’s the probability the two-headed coin was selected? 6. I deal each of three people 3 cards. What’s the probability at least one person has all red cards? 7. We have two boxes each filled with 2 red and 1 black balls. Two balls are drawn uniformly at random from one other these boxes and put into the other and then two balls are drawn from this box. What’s the probability we draw 2 red balls? 8. Two dice are selected without replacement from a 4-sided and two 6-sided dice, and rolled. If the sum total on the dice is 5 compute the probability we selected both 6-sided dice. 9. Angela hits the bulls-eye of a dartboard with probability 5/1 independently from throw to throw. (a) What’s the probability with three (3) throws, Angela hits the bulls-eye all three times? (b) If Angela hits the bulls-eye exactly once in three throws, what’s the probability she hit the bulls-eye on her first throw? There’s a very intuitive answer and a more rigorous one, provide both. (c) If Angela hits the bulls-eye at least once in three throws, what’s the probability she hit the bulls-eye on her first throw? 10. (continued from problem 9.) Brendan hits the bulls-eye of a dartboard with probability 4/1 independently from throw to throw. (a) Angela and Brendan each throw one dart. If the bulls-eye is hit (by one or both of them) what’s the probability Angela hits the bulls-eye? (b) Angela and Brendan each throw one dart. If the bulls-eye is hit (by one or both of them) what’s the probability Brendan hits the bulls-eye? (c) Angela and Brendan each throw one dart. If the bulls-eye is hit (by one or both of them) what’s the probability they both hit the bulls-eye?
History of World Civilization 1 Write an essay of at least 500 words reflecting on the Lecture by Carol Symes: "The Black Death: What We Know Now". In her talk, Prof. Symes presented new conclusions scientists are drawing about the Black Death. Discuss how science is changing what we thought about the Black Death. Also reflect on her comparisons between the 14th-century plague and the COVID Pandemic, which she made in 2020. Would these comparisons still hold 4 years later? Cite the lecture like this: (Symes, The Black Death). Do not use other sources.
Simulation of Engineering Systems 3 Assignment: Position Control System for a Robotic Arm Part 2: Model & Simulation Based Design Aim Part 2 of the Simulation of Engineering Systems 3 Assignment involves the model based design of the control system for a Robotic Arm Position Control System simulation that you developed in Part 1 of the assignment. This part of the assignment involves improving the controller design for this system used in the Matlab version of your simulation. Once your control system is making your simulated system perform better, you should study the effects of changing a key system parameter through the interpolation of data. For the Robotic Arm Position Control System the key parameter is the upper arm deflection angle, θU. This document provides an overview of the control system used in this simulation followed by the Assignment Specifications for this final part of the assignment. Introduction The initial design of the Robotic Arm Position Control System, which was developed in Part 1 of this assignment, was not very good i.e. very oscillatory. The reason for this was that the design of the controller was not suitable for this system. Therefore, the first stage of Part 2 of the assignment involves the redesign of the control system so that the performance of the overall system is much improved. The second stage of Part 2 of the assignment is to test the redesigned control system by varying a key parameter that has been constant in the earlier stages of this assignment. In the case of the Robotic Arm Position Control System the key parameter is the upper arm deflection angle, θU. This deflection represents the motion of the upper arm and the variation in this value represents approximate changes in the dynamics of the upper arm. In this assignment the variation in values is achieved by interpolating data points that represent the upper angle deflection at specific time points. Problem Specification The Assignment Specification Document for Part 1 indicated that the elbow control system produces the required actuator rotation to move the forearm to a reference angle. It achieves this by comparing the actuator deflection angle, θM (radians), with the reference angle, θFref (radians). This provides indirect control of the Forearm’s deflection angle, θF (radians). A diagram of the total system is shown in Figure 1. From Figure 1 it can be seen that the Elbow Control System uses the error difference between the reference deflection angle and the actuator’s deflection angle. In this case the value for θFref (the reference angle) is taken to be 55°. The reference deflection passes through the Reference Amp which is represented by a simple gain KR. Also, the motor deflection is measured by the Actuator Sensor, Figure 1: Elbow Control System which is represented by a simple gain KS. The comparison of these signals is performed by the elbow control system. The first control system design, used in Part 1 and at the beginning of Part 2, is a proportional control system i.e. VE = Gc Δθ (1) Here Gc is the controller’s proportional gain. The performance of this control system can be improved by changing the gain value for GC. Another way to improve performance is to add an integral term into the control system i.e. it then becomes a PI controller of the following form. HereKI is the integral gain, and s is the Laplace operator. The resulting commanded voltage VE is then fed into the gear compensator and the arm, actuator and gears configuration to generate an appropriate actuator deflection angle (θM). Assignment Specification The main purpose of this second and final part of the assignment for this course is to redesign and test the control system so that the Robotic Arm Control System performs better. This involves completing the following steps: Control System Design & Implementation 1. Using your Matlab script based simulation and the parameter values in Appendix A, investigate the effect of varying the coupler gain Gc on the performance of the Robot Arm System. 2. In order to improve the performance of the Elbow Control System further it is normal practice to include an integral term within the controller for such a Robot Arm System. Use your Matlab simulation and the best value for Gc (found in step 1 above) to investigate the effect of introducing the integral term into your control system and varying the associated gain KI. Is the performance of this system improved further? Interpolation 3. So far the motion of the Upper Arm has been considered to be constant. One way to incorporate these dynamics is to vary the Upper Arm deflection, θU. Within your Matlab simulation use the data presented in Table 1 (Appendix B) to represent the change in the deflection of the Upper Arm as time progresses by using Newton’s Divided Difference interpolation method. Firstly, use this method to calculate by hand the interpolating polynomial that represents the deflection values that connect the data points in Table 1. 4. Implement the resulting interpolation polynomial within your Matlab simulation code and analyse the effect of changing Upper Arm deflection values on the Robot Arm System you have designed. Do not use the in-built Matlab interpolation functions i.e. write your own code.
Department of Computer Science Summative Coursework Set FrontPage Module Title Applied Data Science with Python Module Code CSMAD Type of Assignment (e.g., technical report, set exercise, in-class test) Set exercise 2 of 2 Individual or Group Assignment Individual Weighting of the Assignment 50% Word count/page limit Approximately 1,500 words, excluding code, code comments, captions and tables. Expected hrs spent for the assignment (set by lecturer) 20 Items to be submitted A single .zip archive, containing: 1. All final project code. 2. One fully executed Jupyter Notebook file (.ipynb), displaying code, figures, and explanations (as Markdown) 3. One HTML file (.html), exported from above Jupyter Notebook. Work to be submitted on-line via Blackboard Learn by Monday, 27 January 2025, 12:00 noon Work will be marked and returned by Friday, 14 February 2025 1. Assessment classifications This coursework assesses your ability to: • acquire and be able to apply statistical, programming, and machine learning techniques in Python for data science tasks; • evaluate, select and use state-of-the-art Python tools and platforms for solving data science problems; • design, implement, and execute solutions in Python for data science problems; and • evaluate data science solutions in Python, including their outcomes, efficacy, constraints, and uncertainty. You will gain credit for: • preparing and submitting required files as requested; • successful implementation of the requested coding tasks; • writing efficient, functional code; • providing thoughtful, clear, well-structured written analysis. Your assignment will be marked according to the marking schemes provided below. The schemes are designed so that the collectively weighted assignment mark will correspond to the following qualitative master’s degree classification descriptions. The table below describes what is typically expected of the work to obtain a given mark. Classification Range Typically, the work should meet these requirements Distinction (>=70%) Outstanding/excellent work with correct codes and results. An outstanding work should demonstrate coding proficiency with high efficiency and based on advanced techniques. Written analyses demonstrate exceptional understanding and application of the related concepts and techniques, with focused attention to details of the results. The work exhibits originality and includes critical analysis. Merit (60-69%) Good work with mostly correct results: most work has been carried out correctly. Some tasks have not been carried out or are not completely correct. Coding with average efficiency. Written analyses show a strong understanding of the subject, with clear application of sensibly chosen concepts and techniques. The work includes some critical evaluation and broad generalization of the results. Pass (50-59%) Achievement of the minimum requirements. Some significant part of the assignment is missing and/or has partially correct results. Coding lacks efficiency. Written analyses meet the basic requirements, demonstrating adequate understanding and applications of key concepts, but the work may lack depth, contain technical errors, omit specific discussion of the results, or include improperly selected techniques. Fail (
Introduction to Digital Logic Design Lab EECS 112L 1 Install The Vivado Design Suite Vivado is a software produced by Xilinx for synthesis and analysis of HDL designs. The WebPack version of Vivado is free and You can download and install it from here: https://www.xilinx.com/support/download.html 1.1 Download the Vivado Design Suite Select the appropriate version for your laptop operating system. There is no official Vivado for the Mac. If you are using Mac you need to install Vivado on a virtual machine or use Vivado on one of UCI servers. • Vivado on Windows – Example: Choose ” Xilinx Unified Installer 2020.2: Windows Self Extracting Web Installer” to download the Vivado Design Suite for Windows machine. (This is the latest version available but all 2017, 2018, and 2019 versions are ok) • Vivado on Linux – Choose ”Xilinx Unified Installer 2020.2: Linux Self Extracting Web Installer” to download the Vivado Design Suite 2020.2 for Linux machine. • Vivado on Mac – Run Windows or Linux on a Virtual Machine * Download either Windows or Linux web Installer – Use Vivado on EECS server. The current version on the EECS server is 2017.1 which is ok for the purpose of this course You need a Xilinx account to download the tool. Register with your UCI net ID and sign in to download the Xilinx toolchain. This would be a file around 248MB (for windows) which will both download and install the tool for you. 1.2 Install the Vivado Design Suite This section explains the installation process for all platforms for the Vivado Design Suite. Couple points before extracting and installing the tool: • Make sure your machine can support this toolchain. You can check this on Xilinx website. • Make sure that you have enough space on your system for this tool. It might take up to a few Gigabytes Now, let’s start the installer you have downloaded in the previous step. After you click on the installer it will extract the tool and prepare it for the installation. To install Vivado on Linux: • Open a terminal and run: $chmod +x Xilinx Unified 2020.2 1118 1232 Lin64.bin $sudo ./Xilinx Unified 2020.2 1118 1232 Lin64.bin • Vivado Installer window will appear. The instalation process is same as windows. • After installing Vivado, open a terminal and type these two commands to run the software : $source /opt/Xilinx/Vivado/2020.2/settings64.sh $vivado Click Next. A window will pop up asking about your installation type and your Xilinx account. You can use the account you have made at the beginning on the Xilinx website. Select the ”download and install now” option. Click Next. 1.3 License and Edition Selection In the next step, you would select which edition of the Vivado tool you want to install. For now, we can install the webpack version which doesnt require any license. This window asks you about the tool you want to install. Select Vivado and click Next. We are going to use the free version so, here select ”Vivado HL WebPack” . Here the default options are ok. Click Next. Accept the licencse agreement and selest all ”I Agree” boxes. Select the installation directory. Click Next. Click Install. 1.4 Download and installation The final section of the installation will start to download the full image of the Vivado tool which even with a fast internet connection will take quite a long time. Try to do this part before the class. After downloading the full image the installation process will begin. Use the Vivado software on the EECS server: Note : The most updated version Vivado on the server is 2017.1 which is still enough for this course. • Connect to one of the Servers – zuma.eecs.uci.edu – laguna.eecs.uci.edu – crystalcove.eecs.uci.edu – bondi.eecs.uci.edu • Open a terminal and loging with your username $ssh -X -Y UserName@ServerName • Type this command in the terminal to setup Vivado 2017.1 $source /ecelib/eceware/xilinx/Vivado/2017.1/settings64.csh • Type vivado to lunch the application $vivado 2 Using The Vivado Design Suite Open Vivado from your desktop. Select Create Project. Click next. Your new project needs a name, an address (location on your computer), and a collection of design source codes. This new window asks you to choose a name for your project, and specify the directory that you want to save your project in. Vivado Naming Conventions: Project names and source file names must start with a letter (A − Z, a − z) and must contain only alphanumeric characters (A-Z, a-z, 0-9) and underscores( ). This new window asks you to determine the type of your project. Select ”RTL Project” in the Project Type form. Select ”Do not specify sources at this time” (we will talk about this later). Click Next. Note: You can define different types of projects in Vivado. • RTL Project - RTL to Hardware Validation – Import RTL and IP to process design all the way to hardware – Standalone IP - Create reusable preconfigured IP module – Device exploration - Empty project to examine device resources • Post-synthesis Project Netlist to Hardware Validation – Third Party synthesis • I/O Planning Project Early I/O Exploration and Assignment – Create I/O port manually or import CSV, RTL, or XDC – Can migrate to RTL Project • Imported Project - Migrate Project from Synplify, XST, or ISE Project – Imports sources and compilation order – No synthesis or implementation result imported – No tool setting migrated • Example project – Using Vivado examples In the Default Part dialog box, you should select the family and part number of the FPGA you want to implement your code on. Since in this course we are not going to work with any FPGAs, you may skip this step and click Next. Review the project summary in the New Project Summary dialog box before clicking Finish to create the project. You see diferent windows in the Vivado software: Flow Navigator, Sources, Project summary, and etc.. The Project summary will give you the status of your project. Throughout this course we are going to use Verilog language (or System Verilog) for hardware design. We can change the target language by going to the Project Summary window and click Edit. 2.1 Design a Half Adder We want to design a Half Adder. You see the block diagram below. From the Flow Navigator window, choose Add Sources. Select ”Add or create design sources” , click Next. We want to create a new file so, click ”Create File” . Define a name for your design. Click Ok and Finish. The next window asks you to define I/O ports for your module. We are going to define them later in the code so skip this part and click Ok. Now you see your new source file (HA) under Design Sources in the Sources window. Double click on HA to open it. Below you see the Verilog code for a Half Adder. Copy and paste this code to the HA.v window. Code 1: Half Adder. module HA ( A , B , Sum , Carry ) ; input input output output assign assign A ; B ; Sum ; Carry ; Sum = A B ; // bitwise xor Carry = A & B ; // bitwise and endmodule // half_adder If you have a syntax error in this part, the line which contains error will be underlined by red color. Make sure to correct all of them. Save your code.
Carbon Storage (EAEE E4301) Fall 2024 Homework #1 (Due Monday, October 7th, 11:59 pm) Homework Guidelines: Your solutions to homework assignments will be submitted and graded through Gradescope (see the Gradescope tab on your Courseworks dashboard). You will have two options for submitting your work in Gradescope, either: 1) upload individual scanned images of your handwritten pages (e.g., using your phone), one or more per question; or 2) upload a single PDF that you create which contains the whole submission (e.g., merge files on your computer or phone with a software of your choice). Please use the naming convention Lastname_HWxx.pdf when submitting your homework assignment. You may choose to type up your calculations, in which case show all your steps and highlight your solution. Note: During the upload, Gradescope will ask you to mark which page/s each problem is on (see example here). It is important that you follow that step for grading purposes. It is acceptable to discuss problems with your colleagues, and questions are encouraged during office hours, but all work must be done independently. Make sure to clearly show all work on each problem and that your solutions are presented in an orderly fashion. It is your responsibility to make your solutions easy to grade. Topics/Chapters covered: ● Class notes: Modules 1-4 ● Rackley, Chapter 2, 11-14 and other resources mentioned in class notes (e.g., Smit book) Problem #1 (The Carbon Cycle) 15 pts In class we reviewed the box model for Earth’s carbon cycle, also shown below. The percentages in white text boxes represent the percentage of emitted anthropogenic carbon accumulated in the planet’s major reservoirs. (a) Briefly explain why the surface layer of the ocean shows an increase in concentration of CO2, but the deep ocean does not. (b) Why is there no percentage shown in the sediments and crust reservoir? How can we change this? (c) Of the 9 Gt of anthropogenic CO2 emissions, how many Gt must we offset with CCUS technologies to offset rising temperatures (e.g. the greenhouse effect)? Don’t overthink - this is a quick calculation. (d) Estimate the maximum storage capacity of 10 geologic formations with the following average properties: lateral area of 10 km x 5 km, height of 30m, porosity = 0.2, irreducible water saturation (Sw_irr) = 0.15, and in situ scCO2 density = 700 kg/m^3. Hint: Back of the envelope calculations are fine. Comment on the magnitude of this storage capacity. Problem #2 (Geology / porous media) 25 pts The porosity of a sandstone (or soil for that matter) is heavily dependent on the grain size and packing arrangement, among other factors. See the below figure. (a) Mathematically prove that the porosity associated with the simple cubic packing of equally sized spheres, shown in the above figure is ~0.48. Show your work for credit. Does this value of porosity change if the grain size changes from a radius of 0.1 mm to a radius of 1.0 mm? How about permeability? (b) Using the same logic, derive the porosity of either an orthorhombic or rhombohedral packing of equal spheres (your choice!), where the grains are shifted and porosity reduced. Show your work for credit. (c) Name 2 other factors, physical and/or chemical, that can degrade porosity in a rock formation. Briefly (in a few words) explain why. (d) Would you expect a slight increase or decrease in porosity in an over-pressured formation? Why? Microscale grain packing arrangements: Top: Cubic packing of equal spheres. Middle: orthorhombic packing of equal spheres. Bottom: Rhombohedral packing of equal spheres. Problem #3 (Geomechanics) 10 pts The below left plot is a generic Mohr–Coulomb plot with failure envelope. If you want to review geomechanics more, see Rackley Chapter 12. Imagine that this Mohr–Coulomb plot represents the key rock type in a candidate storage formation for hydrostatic pressure conditions. Your team tells you that the rock has the pore pressure properties as shown in the Pressure vs Depth plot on the right. (a) At a depth of 2000m, describe or draw how the Mohr–Coulomb plot above would change. (b) At a depth of 3500m, describe or draw how the Mohr–Coulomb plot above would change. (c) What possible scenarios may create the overpressure seen at the lower depths? Problem #4 (Fluid properties, fluid-rock interactions) 15pts A formation has similar pressures, temperatures and brine properties as the Sleipner-Utsira formation/CO2 storage pilot. Assume a completely hydrophilic caprock (e.g. completely water - wetting) of average pore size r = 100 nm. What is the maximum CO2 column height beyond which CO2 will enter the caprock through capillary forces? Now perform the same calculations for an average pore size of average pore size r = 1 micron. Comment on their differences. Problem #5 (Fluid-rock interactions) 10 pts The below figure shows the water saturation with depth (or height above 100% water saturation line or “Free Water Line”) for several geologic layers. You can assume that the other fluid in the pore space is carbon dioxide. Assume normal hydrostatic conditions (no overpressure). (a) Which layer is at residual water saturation? What does this mean for the flow of water and CO2 in this layer? (b) Rank the layers from likely highest to lowest permeability based on the character of their saturation curves. Which layers might you recommend as caprocks? Problem #6 (Geochemical interactions) 25 pts The rate r of calcite dissolution in acid, aqueous solutions in moles/m2/s can be estimated via where k = in which k is the rate constant (a function of T & pH), ar is the reactive surface area of calcite in the rock,Q is the activity product for ions in the solution (in this case Q = 0.25*[Ca2+]*[H2CO3] at low pH), KS is the equilibrium constant (use 10-5 in seawater at pH 3.5), n and m in the first expression are 1, kH is a pre-exponential constant, EH is the activation energy, R is the gas constant, T is the temperature of interest in Kelvin, T0 is the standard state temperature in Kelvin (25°C, 298.15 K), aH is the activity of hydrogen ions in solution (which we will take to be equal to [H+]) and nH is an empirical constant. For your reference, for calcite dissolving in acid water: kH ≈ 10-0.3 moles/m2/s, EH ≈ 14,400 J/mole, and nH ≈ 1. (a) What is the rate of calcite dissolution in water containing 500 ppmw Ca2+ and 150 ppmw H2CO3, at 50°C with a pH of 3.5, in moles/m2/s? (b) When Q = KS, what is the rate of calcite dissolution? If Q > KS, what should happen? (c) If the calcite dissolution rate were 2x10-4 mol/m2/s and the calcite in the rock matrix has a specific surface area of 15/mm and a density of 2710 kg/m3, what is the rate of calcite dissolution in moles/gram/s? Hint: do not overthink this problem and let the formulas and units be your guide!
Individual Assignment (25%) OFRM 2024-2 Please submit your assignment electronically via the Turnitin Assignment tool no later than Sunday, Oct 20, 2024, 11:59pm. The link for the Turnitin Assignment tool has been created for you under the Assignment page on MyUni. You will need to upload a Microsoft Word version of your assignment to Turnitin. Only one submission will be permitted. Email submission will NOT be considered. Late submission will NOT be marked. By submitting your assignment, you declare that all material in this assessment is your own work. You have also read the University's Academic Honesty Policy. Please be aware of policy and guidelines regarding plagiarism and AI use. For the data, please use ONLY the data file “OFRM Data 2024-2” provided on MyUni under the ‘Assignment’ module. Preamble: Over the last two years, the threat of inflation and expanding interest rates appear large in Australia and much of the world, presenting a different set of challenges, no less. Recent geo-political challenges have been front-of-mind aggravating macro-economic risks, with increased volatility seen in the markets. Considering the evolving macro-economic and geo-political challenges, the ability to hedge one’s investment has gained prominence. In this assessment, you will develop hedging strategies using derivatives to hedge your stock, giving due regard to the established market outlook. Assume you have AUD1,000,000 that you must invest in stocks. A. Stock valuation (5 marks) Drawing on the knowledge gained in previous courses, employ relative valuation methods to value any ONE of the given stocks using only the data provided in the Assignment Data file. Assume 5% as the risk-free rate and no dividend. Determine whether to go LONG or SHORT the chosen stock with a capital of $1.000,000. Assessment criteria: o correct employment of relative valuation methodology, o cohesive arguments to long/short the stock giving due regard to both specific stock and broader market outlook. B. Hedging with Futures (10 marks) Based on the market value of your stock on September 3 and the market environment you determined in part A., implement a futures hedging strategy for the ensuing two weeks period. You are required to, at a minimum: • Implement the futures hedging strategy. Explain the strategy and its execution, and how that is appropriate to your analyses in Part A. • Tabulate and evaluate the performance of the strategy at the end of the hedge period in terms of risk and return and recommend potential improvement. Assessment criteria: o Appropriateness of the strategy versus prevailing market environment. o Determination of hedge ratio. o Full details of transactions presented in a table with appropriate narrative of all relevant transactions that may occur in real world investment. o Effectiveness of the hedge and reasons why the hedge strategy worked/failed to work as you expect. o Discuss how the hedge can be improved considering the shortcomings you identified. C. Alternative hedging strategy (10 marks) It is often advertised that options on futures can be just as effective as the underlying futures for hedging. Given your futures hedge position in part B, determine what corresponding positions in option on futures may be taken. Detail the strategy and its execution and explain how that is appropriate to your analyses in Part B. Defend why hedging with futures contracts is preferred to hedging with options on futures. Assessment criteria: o Explain options on futures hedge transactions needed. o Determine trade positions required. o Clarify appropriateness to part B objectives. o Merits/demerits of using futures vs options on futures for hedging in this particular instance. REPORT WRITING. Your report must document a complete discussion of the process outlined above, including full details of transactions executed. Transaction costs must bear evidence that it is a realistic figure. Good structure, presentation and concise writing skills are likewise important. Your report length must have a maximum word count of 2,500 words (size 12 font, single spacing), including all discussion, graphs, tables, and references. A bonus of 2.5 marks (or 10% of the possible maximum mark for the assignment) will be awarded for early submission (by 11:59PM on Sunday, 13 October 2024). Submissions made after this time will not qualify for the bonus.
FIN2001S ECONOMICS AND MARKET INNOVATIONS WELCOME MESSAGE Welcome to this module on Economics and Market Innovations (EMI). Nowadays, markets are hardly ever cooperated by following simple rules derived from economic theory. In the traditional markets, economic theory or concept can at least serve as benchmarks and starting points for more nuanced analysis. By contrast, a rise of new business models (e.g., platform business model) that uproot traditional markets, break down industry categories, and maximise the use of scarce resources. This module will equip you with knowledge of how to understand complex markets, and come away with strong analytical and problem-solving skills, as well as business acumen necessary to succeed in the professional world. In fact, Economics can be useful for professionals in all industries, not just in business. I am sure you will be able to apply all the knowledge gained in this module to enhance your work, business as well as personal life. I look forward to embarking on this exciting learning journey with you. This module will mainly be delivered via face-to-face and online using Brightspace Zoom software only for the introduction and concluding sessions. PART 1: INTRODUCTION This Study Guide is designed to provide you with details of this module; the learning outcomes; delivery and assessment arrangements. The Study Guide consists of 6 parts. Part 1 gives background details to the subject area are provided and the broad aims of the module are set out. Part 2 consists of the module outline. In this part the (a) module learning outcomes, (b) the themes and topics to be explored are explained along with the (c) learning supports to be used. Part 3 gives details of the module delivery arrangements. It sets out the session arrangements and the expectations in relation to your prior preparation and student engagement. The provisions for online provision are outlined in terms of class delivery and any module work with classmates. Part 4 provides details of the assessment techniques used in this module explaining the assessment components, their rationale. Part 5 explains the UCD grading policy and grade descriptors drawing on the university document are given for each assessment component for the module. Part 6 presents the concluding comments. a) Accessing Brightspace Zoom This module will be delivered face-to-face and online via UCD’s integrated Zoom classroom. This is accessible via brightspace.ucd.ie To students, please login to Brightspace >> FIN2001S-Economics and Market Innovations- 2024/2025 Autumn >> My Class >> ZOOM, to join the lessons. Please always login using your UCD email address and your name. Your name should be visible to the lecturer and other students to facilitate collaboration. Please join your online session no later than five minutes before the advised time of your session. Engagement tools on Zoom Throughout the online sessions for this module, you will be frequently asked to engage with both your lecturer, and with your fellow students. The lecturer may send you into breakout groups and you discuss some class content in smaller groups before your findings are discussed with the whole class. You may use the “Share Screen” function (if enabled) to show some summary points of the breakout group discussions. If you select “Chat”, a chat window will open, and you can communicate with the whole class or with your lecturer. If you would like to send a private message to your lecturer, please select your lecturer’s name instead of everyone. By clicking on “Reactions”, another menu will open. This menu allows you to raise your hand if you have a question or would like to comment. If you see a hand icon in the left upper corner of your screen, your hand is currently raised. You can lower your hand by clicking on this icon a second time. The lecturer can also lower your hand. When you join a Zoom session, you will be muted, and your camera is turned off. But for better engagement in the class, it is advised to keep your camera turned on. Please only unmute yourself if you would like to speak to avoid background noises. You can change your audio and video setting by clicking the small arrow beside the “Unmute” or “Start Video” icon. b) Background Details The EMI module provides more than mere insights into the functioning of an economy. Completion of this module will equip students with a logical and consistent framework for understanding important economic concepts. In addition, the module examines the role of network effects in business, where adding customers attracts new customers. Rather than adding large number of a single type of customers, multisided markets focus on attracting different types of customers (direct or indirect network effects). The ability to analyse contemporary economic developments will open up many career options for the students. c) Module-Aims The module aims to provide a thorough understanding of the theory and practice of economics at an introductory level and provides the basis for all subsequent study you may undertake in economics. The first part covers the principles of microeconomics, and the second part develops a framework for understanding multisided platform business model. Throughout the module and in the seminars, we will demonstrate the usefulness of economics as an analytical tool for thinking about real world problems. The module draws on students’ prior learning and work experience, and seek to combine insights from production and costs to market strategy, government policies to market barriers, international trade to market expansion, firm behaviors and market innovation, and other areas. The assessment tasks for this module have been designed with this in mind as detailed later in the study guide.
PRINCIPLES OF SOCIOLOGY SOC1101C WINTER 2025 Course Information Class Schedule: Monday 11:30 AM to 1:00 PM Thursday 1:00 PM to 2:30 PM Location: Online Via Zoom Official Course Description Introduction to the principal fields, the concepts, and the essential methods of sociological analysis. Sociology and the other social sciences. Critical thinking and techniques of intellectual work. The craft of the sociologist. This course is intended primarily for students who are not enrolled in a program in sociology. Additional Course Description and Learning Outcomes Welcome to Sociology 1101! This is a general survey course of Sociology as a discipline, but I like to think of it as a course on critical thinking about social life. Sociological investigations range from the analysis of small groups to large social systems. Sociology explores how we as individuals and societies are shaped by our collective social experience. While it is useful to learn facts about society and human interaction (i.e., what happened, when, and who was involved), it is perhaps more important to consider these facts critically, to be careful in drawing conclusions, and to be aware of their complexity. What are the sources of our facts? Are the facts complete? Are the sources unbiased? The conclusions we reach regarding social situations are often the basis for actions that have far-reaching effects on ourselves and on others. Sociology is the scientific study of humans in groups. It provides a systematic, critical approach to considering facts and their implications for social action. In this course, our main goals will be to (1) challenge our own views of social life, and (2) acquire some intellectual tools and analytic skills to help us attempt to reach a better understanding of the effects of society on individuals and individuals on society. Teaching Methods We are all unique individuals who learn differently, and we have designed this course with neurodiversity and divergent thinking in mind. To facilitate this, we will employ a flexible environment that fosters a culture of scholarship which allows us to explore some topics in greater detail and promotes student-centered learning through a flipped classroom environment, in-class workshops, guest speakers, demonstrations, and traditional lectures. If you have concerns, comments or suggestions please feel free to bring them up in class as Iam sure other students or myself are thinking about the same issues. Please check your email and virtual campus on a regular basis for Brightspace announcements. Assessment Strategy 1. Mid-Term Examinations (2 x 25 = 50%) There will be two Mid-Term examinations scheduled during the regular class period on February 6 and March 13. The exams will take place through Brightspace using the lockdown browser. They may consist of essays, long, short, fill-in-the-blank, multi-select and objective word-choice questions. 2. In-Class Learning Exercises (20%) In the past, these exercises have taken the form of in-class work, reaction papers to guest speakers, breakout rooms and discussion boards, media analyses, and mini-research assignments and real life- scenario simulations. This will be discussed in detail during lectures throughout the term and deadlines will be posted to Brightspace. 3. Final Examination (30%) The final examination will beheld during the official examination period and will be based on all material presented in class and assigned readings during the term Name Type Weight Expected Date Midterm Exam 1 Brightspace Evaluation 25% February 6 Midterm Exam 2 Brightspace Evaluation 25% March 13 Final Exam Brightspace Evaluation 30% TBC Learning Exercises Brightspace Evaluation 20% Announced During Lectures Exams will be done on Brightspace and will use the following proctoring tools: Respondus Lockdown Browser and the use of real-time proctoring with Zoom (Zoom Live Proctoring) maybe used. These tools block access to applications and internet browsing during the exam. It is important to note that there is no recording of students during the exam and there will be no use of the Respondus Monitor. You must agree to the terms and conditions for installing the Lockdown Browser. Your camera must always be on during the exam if Zoom Live Proctoring is in use. Assessment Policies and Expectations Course notes are the responsibility of each student, and you will be responsible for all assigned readings and material presented during the term, including this outline. Class attendance is strongly recommended at the University of Ottawa. Students are also expected to read the material; take notes; ask questions; and engage in class discussions of the topics and themes that form the basis of this course. This means taking part in a professional and informed debate or discussion with one’s classmates. Occasionally, and without warning, I will call upon students to discuss a point or contribute to a discussion, so please be prepared. All students are required to have a university e-mailand internet account. Please contact the University Computing Center if you do not have one. Please ensure whatever e-mail address you choose to use is one that will work with your university account (if not this account, then your university account should be forwarded to your main account). The dates for evaluations are indicated. If you are unable to turn in any of the assignments on the dates as scheduled, it is strongly recommended that you consider taking the course at a more convenient time. Note: Students should expect a two-week turnaround for marked evaluations SUPPLEMENTAL AND GRADE-RAISING EXAMINATIONS ARE NOT AVAILABLE
ECON6012/ECON2125: Semester Two, 2024 Tutorial 5 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 Mappings, Functions, Correspondences, Domain, Co-Domain, Range (Im-age Set), Continuity of Functions, Uniform. Continuity of Functions, Lips-chitz Continuity of Functions, Compactness, Convergent Sequences, Cauchy Sequences, Convergent Subsequences. Tutorial Questions Tutorial Question 1 Prove that the function f : R −→ R defined by f (x) = x2 is continuous. Tutorial Question 2 Prove that the function f : R −→ R defined by f (x) = x2 is not uniformly continuous. Tutorial Question 3 Prove that the function f : (0, 1) −→ R defined by f (x) = x2 is uniformly continuous. Tutorial Question 4 Let (X, d) and (Y, r) be metric spaces. Prove that if X is a compact set, then all continuous functions f : X −→ Y are uniformly continuous. Additional Practice Questions Additional Practice Question 1 Prove that the function f : (0,∞) −→ R defined by f (x) = x/1 is continuous. Additional Practice Question 2 Prove that the function f : (0,∞) −→ R defined by f (x) = x/1 is not uniformly continuous.
553.420/620 Probability Assignment #05 1. Flip a fair coin 3 times. Let X be the discrete random variable that returns the length of the longest run of heads. Identify the support of this random variable and construct its probability mass function. I’ll get you started. . . 2. Identify the name of distribution of the following random variables from the descriptions. Be sure to identify the associated parameters from the description if possible and write out its pmf – don’t forget the support of the pmf. (a) We toss a fair coin once. Let X count the number of heads. (b) A box has 3 red and 2 blue marbles. Draw a marble uniformly at random, note its color and put it back; repeat until you’ve selected 3 times. Let X count the number of red marbles drawn. (c) A box has 3 red and 2 blue marbles. Draw a marble uniformly at random, note its color and do not replace; repeat until you’ve selected 3 times. Let X count the number of red marbles drawn. (d) A box has 3 red and 2 blue marbles. Draw a marble uniformly at random, note its color and put it back; repeat until you’ve selected 3 red marbles. Let Y count the number of marbles drawn. (e) Surface imperfections on a silicon chip occur at a rate of 0.5 imperfection per square centimeter. Let S count the number of imperfections on a 3 cm2 chip. 3. Show is a pdf. Then compute the CDF of an rv having this pdf. 4. If you invest $1 with an APR of I × 100%, then in one year you will have 1 + I. After n years you’ll have (1 + I)n . A computer scientist give you two options. Option 1 is they will give you an APR of I = .5, i.e, 50%, for 10 years. Option 2 is they will equally likely at random pick one of the three interest rates 25%, 50% or 75% and then lock you in at this rate for 10 years, i.e., they are telling you P(I = .25) = P(I = .50) = P(I = .75) = 3/1. Notice that E(I) = .50 in option 2 which agrees with option 1. Compute E[(1 + I) n ] under each option when n = 1, 2, and 10. What do you notice? 5. Suppose X ∼ Poisson(λ), i.e., is a discrete rv with pmf for x = 0, 1, 2, . . . . (a) Compute E(X) by definition. FYI: I am asking you to simplify The MacLaurin expansion for may come in handy. (b) Compute the MGF of X, namely, the function M(θ) = E(e θX) using the Law of the Unconscious Statisti-cian. It will turn out the this function exists and is finite for every real number θ. Answer: you should show M(θ) = e λ(e θ−1) for −∞ < θ < ∞. (c) By taking derivatives of the MGF from part (b), derive the first two moments of the Poisson(λ). Use this information to compute V ar(X). 6. In class we showed that for a discrete rv X possessing an expected value that for any real numbers a and b, E(aX + b) = aE(X) + b. You show V ar(aX + b) = a 2V ar(X). Stating the obvious here but when a = 1 this says V ar(X +b) = V ar(X), i.e., shifting the distribution by a fixed constant does not change the variance. 7. Let X ∼ geometric(p), where X is the trial of the first success in independent Bernoulli(p) trials; recall the pmf is P(X = x) = p(1 − p) x−1 for x = 1, 2, 3, . . . . (a) Derive the MGF M(θ) of X and wshow how you find the values of θ for which it exists and is finite. I’ll get you started Answer: M(θ) = 1−(1 − θp)θ/peθ for θ < − ln(1 − p). (b) By taking the first two derivatives of the MGF from part (a) [okay, I admit this is a little tedious, but is good at getting you to perform. the chain rule carefully] find the mean and variance of X. Answer: E(X) = p/1 , V ar(X) = p2/1 − p . 8. Follow-up to question 7. Sometimes the Y ∼ geometric(p) rv is thought of as the number of failures before the first success, so that Y = X − 1, where X is the trial of the first success. (a) Using the fact that Y = X − 1 and, maybe the result of a previous problem on this assignment, easily compute E(Y ) and V ar(Y ). (b) Using the result of problem 7 and the fact that Y = X − 1, easily derive the MGF of Y . Hint: E(e θY ) = E(e θ(X−1)) and you know the MGF of X... The point of this problem is so that you understand that a geometric rv has both of these interpretations and, consequently, the mean is different (but the variance is not). A similar statement can be made about the different interpretations of the negative binomial rvs.
2024 Fall - ECON 5,GLOBAL 5,POL SC 5 Prerequisite: None • Skills Advisory: Eligibility for English 1. This course surveys major analytical approaches to the study of International Political Economy and analyzes contemporary issues in world politics. The class objective is to gain a better understanding of the interaction between political and economic phenomena on an international and global scale. The role of states, international and domestic instituions, and other factors in creating and/or managing conflicts and facilitating cooperation in the international political economy. This course satisfies IGETC Area 4 (Social & Behavioral Sciences) requirements. This is an Online Education course. All assignments and exams will be conducted over the Internet. Students are responsible for their own access to the Internet and computer resources. World Politics: Intersts Interactions Institutions - Freiden, Lake, and Schultz. Norton Publishers, 4th edition The text is also available as an ebook from Norton publishers Upon completion of this course, students will: 1. Exhibit, through their behavior. and course work, strong academic behaviors, including regular attendance, timeliness, participation in class activities, and adherence to the College Honor Code, as well as a heightened sense of personal efficacy and civic responsibility, evidenced by their regular attendance, participation in class activities, and their awareness of their rights and duties as citizens of their community, their country, and the wider world. 2. Be able to explain, both orally and in writing, the structure and operation of the international system, the nature and sources of conflict and cooperation, and issues of war and peace among states in the international system. 3. Be proficient in the research, analytical, and communication skills necessary to present, orally and in writing, compelling and original arguments that advance 4. Demonstrate a level of engagement in the subject matter that enables and motivates the integration of acquired knowledge and skills beyond the classroom. Upon successful completion of this class, students will: Consider the effects of nationality, ethnicity, gender, and economic class diversity on contemporary and future world political relations. List, discuss, and assess the political values and historical events that have shaped world politics and international relations. Differentiate among and analyze competing political ideologies and scholarly approaches to the study of political Economy and international relations. Understand and evaluate the interrelationship between economics and politics. Explain and evaluate the institutions of world politics (nation-states, intergovernmental organizations, transnational enterprises, social movements). Evaluate and write clearly and systematically about contemporary world political economic issues and policies. Success in this class will depend upon your ability to: (1) think critically; (2) read and write college-level English prose; (3) master important facts about international relations and world politics; and, (4) work both independently and collaboratively in a group setting. I expect students to: read this syllabus carefully, check your email each day, log on to the class website a minimum of three times each week, read all of the assigned materials, submit all Threaded Discussion postings on or before deadline, submit "Twenty-Minute Quizzes," and complete a Midterm and Final Exam. Please note that students are responsible for their own Internet access and computing resources. A loss of connectivity is not an excuse for late assignments. Some Internet service providers (ISPs), such as America Online, are notorious for inferior, unreliable service. In previous semesters, students have lost Internet connectivity in the middle of exams. Students who wait until the last possible moment to submit an assignment also run the risk of an unanticipated service disruption that prevents timely submission. If you have any questions about the reliability of your ISP or if you encounter connectivity problems, please contact your ISP or Canvas Support Hotline 844 303-0352. Dr. Berman is not able to assist you with computing or connectivity problems. In addition, please make sure that your email client accepts incoming messages with multiple addressees. Some email services (Hot-mail, AOL) allow users to block "spam," that is, advertising messages. Such features not only block unwanted messages but they may also block my messages for the class addressed to you. My email messages to you may also be blocked if you have exceeded the data storage limit of your client service. I am not always notified when my messages fail to reach you and cannot be responsible for the proper configuration and maintenance of your email service. Grading Criteria Your grades in this class will be based on: (1) your writing assignments ; (2) "Twenty-Minute Quizzes"; (3) Simulation Quizzes; (4) a Midterm; and (5) a Final. This class uses a grading system that, unfortunately, is a bit complicated. The complications arise because: (1) there are several different types of assignments--quizzes, threads, exams; and (2) these assignments are weighted differently. Your final class grade is based on 570 points. Your midterm and final are each worth 50 points, for a total of 100 points. The Quizzes" are each worth twenty points. You may only take these quizzes once. Some of the questions on the Quizzes may appear on the Midterm and Final. The Quizzes together constitute 160 points out of the 600 total class points. I will NOT accept any late assignments - each Module is open for 6 days weeks in which time I expect that students will complete the Module's listed assignments. These assignments are discussed in greater detail, below. 80 Sim Quizzes 230 Threads 160 Twenty-Minute Quizzes 50 Midterm and Final 50 Controversy quizzes Threaded Discussion Because of the nature of this course, I have found that punctual postings are critical to both the success of the course and the success of individual students. It is impossible for me to read and respond to several hundred messages and assignments in the last week of class. Therefore I have created a grading policy that rewards both the quality and punctuality of your responses and assignments. About half of your Threaded Discussion grade will be based on the punctual completion of assignments. Thus, you could minimally fulfill the Threaded Discussion requirement (60 points) simply by turning in all of the assignments on time, assuming that your contributions demonstrate that you tried your best. Grades for threads submitted late will be penalized. Please note, that all your assignments are due according to Pacific Time Zone deadlines. Make sure that you adjust accordingly. The rest of the Threaded Discussion grade will depend on the quality of your work. Your postings should be well written and clearly address the issues being discussed. I expect each writing assignment to have: (1) An introductory paragraph that addresses directly the question posed by the instructor; (2) A body of factual examples that support your answer; these examples may be drawn from either the assigned readings or footnoted sources researched independently by the student; (3) Factual examples and the published work of others must be appropriately cited; plagiarized threads will be penalized. I strongly encourage you not to cite Wikipedia or Chat GBT, as a source for academic essays. (4) A succinct concluding paragraph. If I have some concerns or comments about your thread, I will post a response. My comments are intended to help you improve your threads. Your main Newsgroup posting should be approximately 400-500 words in length. Long, rambling, unfocused messages discourage readership and suggest fuzzy thinking. It is more difficult to express ideas in short essays than in long ones. It is not necessary to post a "perfect" essay (100 out of 100 points) to earn an "A" on the threads; neither is it necessary to earn 600 points for the semester to earn an "A" in the class. A score of 90 out of 100 points on your thread is an "A-" and the equivalent of an "A" in the class because Santa Monica College does not use a Plus/Minus grading system. Controversy and disagreement cannot be avoided in a political science class but disrespectful, insulting language and intellectual intolerance (i.e., "flaming") will not be permitted. Writing about the factors necessary for a successful, online learning experience, Rupert Wegerif (http://www.aln.org/alnweb/journal/vol2_issue1/wegerif.htm) writes: "Forming a sense of community, where people feel they will be treated sympathetically by their fellows, seems to be a necessary first step for collaborative learning. Without a feeling of community people are on their own, likely to be anxious, defensive and unwilling to take the risks involved in learning. . . This style. is democratic, respectful, open to challenges, prepared to give grounds for statements and seeking critically grounded consensus." It is possible to disagree without being disagreeable. I expect students to abide by the commonly accepted rules of academic discourse. Disagreements based on opposing interpretations of facts, including disagreements with the Instructor, are encouraged. Ad homonym attacks and name-calling, which are altogether too typical of much political discourse in America today, will be penalized. Plagiarism will be penalized. It is easy to "copy and paste" materials from the Internet and it is equally easy for instructors to detect such behavior. Your threads must be original works, with proper citation for facts and ideas drawn from the works of others. I read each posting and grade them all. I do not necessarily respond to each posting in the Threaded Discussion, however. If I do not respond to your posting, please take no offense. I respond only when I wish to advance the discussion. Also, if I respond to your post with an "Ok," it means that your thread satisfies the requirements of the assignment; an "Ok" does not mean that I personally agree with the content of your statement. With my permission a student may submit a late thread assignment. Your request for a late submission must be made BEFORE the start of the nest week's module. I do NOT accept any written assignment once the following week's Module has begun. Any late thread submission will have 10 points deducted from the total. "Twenty-Minute Quizzes" Each Saturday you will take one or more "Fifteen-Minute Quizzes," so-called because you have fifteen minutes to answer ten multiple choice questions from a particular chapter. These are "open book" quizzes. You can only take each quiz one time. Quizzes are available from 6 a.m. to 10 p.m. Pacific Time Zone. Multiple choice quizzes MUST be completed in the week that they are assigned. There are NO "make-up multiple choice quizzes. Midterm Exam The Midterm Exam will be conducted online by Saturday, November 16th.. The exam will comprise 50 multiple choice questions. Some of the multiple choice questions will come from the Online Quizzes. The Midterm will be cumulative. The Midterm will be a timed exam, lasting 50 minutes. You may begin the exam at any time between 6 a.m. and 10 p.m. (Pacific Time). If you begin the exam at 9:59 p.m., you'll only have one minute to complete it, so make sure that you give yourself at least on full hour to complete the exam. You may only take the exam one time. You may not logon to the exam, print it, logoff, work offline, and then re-logon to record your answers. Failure to follow these instruction can result in a failing grade. If you exceed the time limit for the midterm, your grade may be compromised. In past semesters, some students have been inadvertently disconnected while taking their online exams. Service disconnections cannot be restored by Dr. Berman and do not constitute an excuse for missing the exam. If you have any questions about the reliability of your Internet service, please contact your service provider or the Canvas Support Hotline - 844 303-0352 before you begin the exam. If you're concerned about Internet connectivity, you may make arrangements with the College to take the exam at one of the on-campus computer labs. Final Exam The Final Exam will be conducted online by Saturday, December 14th. The Final will be a timed exam, lasting 50 minutes. The exam will comprise 50 multiple choice questions. Some of the multiple choice questions will come from the Online Quizzes. The Final will be cumulative. You may begin the exam anytime from 6 a.m. to 10 p.m. Pacific Time. If you exceed the time limits for the final, your grade may be penalized. When emailing your instructor, always include your full name and the class in which you are enrolled. I can only contact you by using your SMC Corsair account. Please check that email every day or configure your Corsair account to forward emails automatically to your personal email account.
F24 ECE 551 HW05, Due 11PM Thu. Oct. 10 1 Pr. 1. Linear regression has a myriad of uses, including investigation of social justice issues. Demo 05/sat-regress has data collected by the College Board–the organization that runs the SAT exam for high-school students, from Lesser, 2017. This data includes average SAT Math scores for 10 different family annual income brackets. This problem uses this data to explore the relationship between income and SAT scores. Make a scatter plot of the midpoint of each income bracket versus the SAT Math score. The last income bracket says “100+” which does not have a midpoint, so just set it to be 120 (K$). Use the template code in the demo. The scatter plot suggests there is a strong correlation between income and SAT score. You are going to fit four different models to the data (one at a time) and examine the fits and the coefficients: For each of the four models, use a LLS fit to determine the β coefficient(s). (a) Make a single plot showing the data and the four fits, for incomes between 0 and 130 (K$), i.e., income = 0:130 . (We cannot predict anything for even higher incomes with this data.) Be sure to label your axes and use a legend to explain which points/lines are which. (b) Make a table to report your β coefficients that looks like this: (c) (Optional) In a statistics class, you would analyze the coefficients β1 and β2 to assess whether they are significantly different from 0 and establish evidence of a relationship. Even without formal statistics, you should be able to look at your plot and your table of coefficients and draw some conclusions about how equitable the SAT exam is. Pr. 2. Polynomial regression application Let f(t) = 0.5 e 0.8t , t ∈ [0, 2]. (a) Suppose you are given 16 exact measurements of f(t), taken at the times t in the following 1D array: T = range(0, 2, 16) Use Julia to generate 16 exact measurements: bi = f(ti), i = 1, . . . , 16, for ti ∈ T . Now determine the coefficients of the least-squares polynomial approximation of the data b for (i) a polynomial of degree 15: p15(t); (ii) a polynomial of degree 2: p2(t). Compare the quality of the two approximations graphically. Use scatter to first show bi vs ti for i = 1, . . . , 16, then use plot! to add plots of p15(t) and p2(t) and f(t) to see how well they approximate the function on the interval [0, 2]. Pick a very fine grid for the interval, e.g., t = (0:1000)/500 . Make the y-axis range equal [−1, 4] by using the ylim=(-1,4) option. As always, include axis labels and a clear legend. Submit your plot and also summarize the results qualitatively in one or two sentences. For this problem, write your own Julia code rather than using fit in the Polynomials package. (You may check your solutions using that function.) (b) Now suppose the measurements are affected by some noise. Generate the measurements using yi = f(ti) + ei , i = 1, . . . , 16, , as follows. You must use the seed to get the correct values! using Random: seed! seed!(3); e = randn(length(T)) Determine the coefficients of the least-squares polynomial approximation of the (noisy) measurements y for (i) a polynomial of degree 15: p15(t); (ii) a polynomial of degree 2: p2(t). Compare the two approximations as in part (a). Again make the y-axis range equal [−1, 4] by using the ylim=(-1,4) option. Submit your plot and also summarize the results qualitatively in a couple of sentences, including comparing the behavior. in (a) and (b). (c) Let xˆn(b) and xˆn(y) denote the LLS polynomial coeffients from noiseless b and noisy y, respectively, for a polynomial of degree n. Report the values of the residual norms ∥Axˆn(b) − b∥2 and ∥Axˆn(y) − y∥2 for the polynomial fits of degree 2 and degree 15. These residual norms describe how closely the fitted curve fits the data. Also report the fitting errors ∥Axˆn(y) − b∥2 for n = 2, 15. Arrange your results in a table as follows: Hint: the bottom left entry is between 1.6 and 1.9. (d) Explain why the residual norm for degree 2 is smaller or larger than that of degree 15. Pr. 3. (a) One use of the “vec trick” vec(AXB⊤) = (B ⊗ A)vec(X) is computing a 2D discrete Fourier transform. (DFT) of a 2D signal. The (1D) DFT of a vector x ∈ C N is the vector fx ∈ C N with entries (Here we follow linear algebra (and Julia) where the first array index is 1, whereas DSP books usually use 0, . . . , N − 1.) We can represent the above computation in matrix-vector form. as fx = FN x, where FN is the N × N DFT matrix with entries We can generate FN in Julia as follows. # N × N DFT matrix using FFTW: fft using LinearAlgebra: I F = fft(I(N), 1) One can verify that FN ′ FN = NIN , so the (1D) inverse DFT of fx can be computed as x = (1/N)FN ′ fx. We compute the 2D DFT, call it SX, of the M × N matrix X by computing the 1D DFT of each column of X followed by the 1D DFT of each row of the result (or vice versa). Explain why the following expression computes the 2D DFT of X: (b) Write vec(SX) as the product of a matrix and vec(X). (c) Show that the following expression computes the 2D inverse DFT of SX: where Y denotes (elementwise) complex conjugate of matrix Y . Hint: Use the fact that FN ′ FN = FN FN ′ = NIN . (d) Write vec(X) as the product of a matrix and vec(SX). Pr. 4. In the ordinary least-squares problem we found the (minimum norm) xˆ that minimized ∥r∥2 where r = b − Ax is the residual. We saw that the optimal x can be expressed entirely in terms of b and an SVD of A. Let A be an M × N matrix so that x ∈ F N and b ∈ FM and r ∈ FM. In applications with heteroscedastic measurement errors, we prefer to minimize ∥W r∥2, i.e., a weighted squared error, where W is a diagonal matrix having diagonal entries w1, . . . wM ≥ 0. Determine the optimal x for this weighted least-squares problem. (Again, you should express the answer in terms of b, W, and an SVD of an appropriate matrix.) Your answer must not have any pseudoinverse in it! (It may have an inverse as long as you are sure that the matrix is invertible and trivial to invert.) You may assume that W*A == zeros(size(W*A)) is false in Julia. Pr. 5. (a) Find (by hand) all solutions of the linear least-squares problem arg minx∈R2 ∥Ax − b∥2 when and (b) Describe briefly how you would modify your solution for this variation of the problem: arg minx∈C2∥Ax − b∥2. Pr. 6. Recall that the least-squares problem has the solution xˆ = A+b where A+ denotes the pseudoinverse. When A is large, it can be expensive to compute xˆ using the pseudoinverse of A. In such settings, the gradient descent (GD) iteration given by xk+1 = xk − αA′ (Axk − b), (1) will converge to a minimizer of ∥Ax − b∥2 as iteration k → ∞ when 0 < α < 2/σ1 2 (A). Note that the iteration has a fixed point, i.e., xk+1 = xk if A′ (Axk − b) = 0, which are exactly the normal equations. So any fixed point minimizes the least-squares cost function. (a) Write a function called lsgd that implements the above least-squares gradient descent algorithm. In Julia, your file should be named lsgd.jl and should contain the following function: """ x = lsgd(A, b ; alpha=0, x0=zeros(size(A,2)), nIters::Int=200) Perform. gradient descent to solve the least-squares problem: ``\argmin_x 0.5 ‖ A x - b ‖2`` # In: - `A` `m × n` matrix - `b` vector of length `m` # Option: - `alpha` step size to use, and must satisfy ``0 < α < 2 / σ1(A)^2`` to guarantee convergence, where ``σ1(A)`` is the first (largest) singular value. Ch.6 explains a default value for `alpha` - `x0` is the initial starting vector (of length `n`) to use. Its default value is all zeros for simplicity. - `nIters` is the number of iterations to perform. (default 200) Out: - `x` vector of length `n` containing the approximate LS solution """ function lsgd(A, b ; alpha::Real=0, x0=zeros(size(A,2)), nIters::Int=200) Email your solution as an attachment to [email protected]. The function specification above uses a powerful feature of Julia where functions can have optional arguments with specified default values. If you simply call lsgd(A,b) then alpha , x0 and nIters will all have their default values. But if you call, say, lsgd(A, b, nIters=5, alpha=7) then it will use the specified values for nIters and alpha and the default for x0 . Note that these named optional arguments can appear in any order. This approach is very convenient for functions with multiple arguments. (b) Use your function (after it passes) to generate a plot of log10(∥xk − xˆ∥) versus k = 0, 1. . . . , 200 using α = 1/σ1 2 (A) for A and b generated as follows. using Random: seed! m, n = 100, 50; sigma = 0.1 seed!(0) # seed random number generator A = randn(m, n); xtrue = rand(n); noise = randn(m) b = A * xtrue + sigma * noise # b and xhat change with σ Repeat for σ = 0.5, 1, 2 and submit one plot with all four curves on it. Does ∥xk − xˆ∥ decrease monotonically with k in the plots? Note that σ = sigma here is a noise standard deviation unrelated to singular values. Pr. 7. (a) For δ > 0, determine the solution of the regularized LS problem Express the answer in terms of the SVD of an appropriate matrix. Use the fact that B+ = (B′B) −1B′ when B′B is invertible to simplify the expression. Hint: Rewrite the cost function so it looks like a usual least-squares problem. (b) What does xˆ(δ) tend to as δ → ∞? Does this answer make sense? (c) Write (by hand, not code) an iteration based on the gradient descent (GD) method such that the iterates converge to the minimizer xˆ(δ). (d) Determine a condition on the step size µ that guarantees convergence of your GD method. Express the condition in terms of the original problem quantities: A, b, and δ. Non-graded problem(s) below (Solutions will be provided for self check; do not submit to gradescope.) Pr. 8. Let S and T denote subspaces of a vector space V. Prove or disprove the following. (a) If S is a subset of T or vice versa, then the union of subspaces S ∪ T is a subspace of V. (b) If the union of subspaces S ∪ T is a subspace of V, then S is a subset of T or vice versa.
Assignment 2 EDPJ5026 (Language Testing and Assessment) Due date: 13/11/ 2024, 23.59 pm Words: 2,500 Bloom’s Taxonomy Assignment 2 Overview • Title: Designing a Standardised English Test for L2 English Students • Objective: Develop a standardised English test focusing on one language skill (reading, listening, writing, or speaking) for a group of L2 English students. Clearly define the purpose of the test (e.g., selection, achievement, proficiency, diagnostic). Specify the test takers’ proficiency levels according to the CEFR (Common European Framework of Reference). • Word Count: 2500 words (±10% levy) Assignment Structure 1. Introduction (300 words) o Explain the importance of language testing and assessment. o Introduce the CEFR and link it to the chosen language skill. o Describe the context of English language learning for the target students. o State the purpose of the assignment. 2. Purpose of the Test (300 words) o Provide a clear and precise name for the test. o Describe the target students, including their age, language proficiency levels, and learning contexts. o Define the purpose of the test (e.g., selection, achievement, proficiency, diagnostic). o Explain why this purpose is important for the target group. o Discuss how the purpose influences the test design and content. 3. Test Skill Focus (400 words) o Choose one language skill to focus on (reading, listening, writing, or speaking). o Justify the choice of this skill based on the test purpose and the needs of the students. o Provide a brief theoretical background related to assessing this skill. o Specify the proficiency levels according to the CEFR (A1, A2, B1, B2, C1, C2). Refer to the CEFR website for detailed descriptions of each level 4. Test Specifications (600 words) o Test Techniques: Choose three techniques for the test (see suggestions below). o Test Sections: Design three sections using the chosen techniques. o Test Content: Focus on authentic language use scenarios. o Test Length: Specify the length of the test and the time allocated for each section. o Scoring Criteria: Explain the scoring criteria for each section and how the test will be graded.Assignment Structure 5. Test Administration (300 words) o Describe the procedures for administering the test. o Discuss logistical considerations to ensure test effectiveness (e.g., test environment, equipment needed). o Explain how to ensure fairness and reliability in test administration.Assignment Structure 6. Test Validation (400 words) o Explain the process for validating the test to ensure it measures what it is intended to measure. o Discuss methods for checking the reliability and validity of the test. o Provide two examples of how to collect and analyse data to support test validation. 7. Conclusion (200 words) o Summarise the key points discussed in the assignment. o Reflect on the importance of careful test design. o Reflect on your experience in completing this assignment. 8. References (not counted) o Include at least ten relevant references. 9. Appendix (Sample Items) o Provide examples of test items/questions for each test section. o You do not need to provide audio or multimedia texts for listening tasks. You can provide sample scripts and/or images (multimedia). o Examples of scoring rubrics you may use for constructed-response tasks in writing or speaking. Examples of Test Techniques • Reading: Multiple-choice, gap-filling, cloze, short-answer, information transfer, summary. • Listening: True-false-not given, multiple-choice, gap-filling, short-answer, diagram completion, dictation (integrative). • Writing: Error detection, sentence reordering, picture description, note-taking, personal essay, academic essay. • Speaking: Read aloud, picture description, narrative, interview, role play. • Don’t use the following classroom assessment techniques such as self-assessment, peer assessment, self-reflection, assignments, and portfolio assessment in this assignment due to the time-control nature of the standardised test. Suggested Test Length • Reading: 50 to 60 minutes • Listening: 25-30 minutes • Writing: 50 to 60 minutes • Speaking: 10 to 15 minutes Writing Style • Use an instructional and directional writing style. • Be clear and concise, providing detailed explanations and justifications. • Use headings and subheadings to organise the content. • Include references to relevant literature and theories in language testing and assessment.
553.420/620 Probability Assignment #06 1. Let X ∼ Gamma(α, β). In class we showed that E(X) = αβ. By using the same approach derive E(X2 ), and then use it to compute V ar(X). 2. Use the normalization trick to compute these integrals: (a) ∫0 ∞ x −1/2 e −x/2 dx (b) ∫0 ∞ x n e −nx dx, where n > 0 is an integer. Challenge: Label the integral in part (b) by K(n), does the limit lim n→∞ √ nenK(n) exist? If so, find it. 3. The following is a PDF: A continuous random variable X having this PDF is said to have the Beta distribution with parameters α > 0 and β > 0, and we write X ∼ Beta(α, β). Use the fact that the above is a PDF to compute each of the following: (a) ∫10 x −1/2 (1 − x) −1/2 dx (b) E(X) (c) V ar(X). Hint for part (a) is to use the normalization trick. This will also work for parts (b) and (c) after you write the integrals for E(X) and E(X2 ). 4. A continuous random variable X has the PDF f(x) = x/8 for 0 < x < 4. Compute P( √3/1 ≤ √ X < √ 3). 5. The (random) rate R a particle moves (in meters per second) has PDF f(r) = 2re−r 2 for r > 0. (a) Compute the probability the particle is slower than 1/2 meter per second. (b) Compute the probability the particle travels a distance greater than 4 meters in 2 seconds. Hint: distance = rate × time. (c) Compute E(R) the expected rate. Hint: E(R) = ∫0 ∞ r · 2re−r 2 dr, try using integration by parts. Remark. The PDF in this problem is a special case of the Rayleigh distribution. 6. When it exists, the MGF of a random variable X is MX(θ) = E(e θX) for θ in an open interval that contains θ = 0. Now consider the transformed random variable Y = aX +b. Carefully show that MY (θ) = e bθMX(aθ). 7. Suppose X is a random variable with MGF MX(θ) and let µ = E(X) denote its mean and σ = √ V ar(X) denotes its standard deviation. One consequence of problem 6 is that the MGF of the z-score, namely, the random variable Z := σ/X−µ is e − µθσ MX( σ θ ). (a) If X ∼ Poisson(λ), then write down the MGF of its z-score Z = X √− λ λ . You may need to recall the MGF you computed on the previous homework; otherwise, feel free to use the distribution sheet to recall it. (b) From your answer to part (a) what happens to this MGF as λ tends to ∞? Answer this question by formally computing the limit. It may help to recognize that in the exponent of e there should appear an e√ λ/θ − 1 and replacing this with the MacLaurin expansion should simplify the problem considerably. Remark. The resulting MGF is not an accident – it happens to be the MGF of a normal distribution with mean 0 and variance (and standard deviation) 1 – this is one manifestation of the central limit theorem. 8. Let X ∼ exp(λ) for some rate λ > 0. Recall this means the PDF of X is f(x) = λe−λx for x > 0. Show that the exponential distribution has this interesting property: for any s, t > 0, P(X > s + t|X > s) = P(X > t). Interpreting X as the lifetime of a component, then, in words, this property says given that a component has survived to time s, the (conditional) probability it survives another t is just the same as a component surviving to t; the component forgets its age! This is called the memoryless property. 9. (The Tail probability formula to compute expected values of nonnegative random variables) Show that if X is a nonnegative continuous rv with PDF f(x), then E(X) = ∫0 ∞ P(X > u) du. Hint: Since P(X > u) = ∫u ∞ f(x) dx, it would follow ∫0 ∞ ∫u ∞ f(x) dxdu now switch the order of integration and pay attention to the region you are integrating over. Remark. There is a discrete random variable version of this problem when X is a nonnegative but it requires that the random variable to also be integer-valued. In this case Here’s a proof: Using this tail probability formula here’s another way to compute the mean of a geometric(p): Since the tail probabilities are P(X ≥ k) = ∑∞x=kp(1 − p) x−1 = (1 − p) k−1 , we’d have E(X) = ∑∞k=1 P(X ≥ k) = ∑ ∞ k=1 (1 − p) k−1 = p 1 . 10. Suppose X ∼ Normal(µ, σ2 ). In class we showed using the CDF method that Y = aX +b ∼ Normal(aµ+ b, a2σ 2 ) when a > 0. Your job: Show this is also true if a < 0. Hint: Following the CDF method as we did, the support of Y is all reals, so, for real y, FY (y) = P(Y ≤ y) = P(aX + b ≤ y) = P(ax ≤ y − b) = P(X ≥ a/y −b) = 1 − ∫ y−b a−∞ e − 1 2 (x − µ ) 2 σ2 √2 πσ 2 dx. Now take derivatives to recover the pdf fY (y) of Y .
