COM1005 Machines and Intelligence Weeks 10-11 Lab Question Sheet Robotics & Layered Control Architectures Instructions Complete your copy of the lab question sheet, as instructed below. Download the completed file as a .docx file and rename it to ‘layered_control_lab.docx’ before submitting. Base model Implement the base layered control model (Elowen), according to the given specifications. Adjust the tumble rate to match the ‘one tumble every 5 seconds’ rule, depending on how quickly the periodic control loop runs on your machine. Perform. a series of trials with Elowen in the phototaxis world, where you let her run in the environment and record the number of steps it took her to run out of energy. For each run, record how many boosters were consumed and how many tumbles were made. In the event of Elowen falling down on the floor, all the trial data should be discarded, as this indicates a problem with the ‘safety’ layer (which should be further improved). Elowen: Base Data Run # 1 2 3 4 5 6 7 8 9 10 Steps Boosters Tumbles Elowen: Statistics # of trials Steps: Min Steps: Max Steps: Median Steps: Mean Steps: St. Dev. 10 Modified model In the L4 ‘Tumble’ layer of Elowen’s base model, the tumble frequency is fixed and the tumble angle probability distribution is uniform. Implement, describe and evidence a more complex implementation of this layer, which would increase Elowen’s step count, on average, before she runs out of energy in the given environment. (For example, you can use the tumble frequency as a function of the surrounding brightness; and/or you can introduce a more complex probability distribution for tumble angles). Your final MiRoCODE program should support running both models. You can use the ‘modified’ boolean variable provided in the template as a toggle to select which model to run. Answer individually and in your own words. Use of GenAI tools is NOT allowed. Answer in no more than 200 words. Be specific and include formulas. Provide figures, tables and/or screenshots if necessary. You can use the steps and tumbles as two useful metrics when comparing the base model to the modified model.
ECO3011 Intermediate Microeconomic Theory: Assignment 1 Total points: 100 Due Date: February 17 (Monday) 11:59pm Please show detailed steps for ALL the questions. 1. (7 pts) Professor Goodheart gives 3 midterm exams. He drops the lowest score and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her first exam. Let x2 be her score on the second exam and x3 be her score on the third exam. If we draw her indifference curves for scores on the second and third exams with x2 represented by the horizontal axis and x3 represented by the vertical axis, explain how you determine the shape of her indifference curve through the point (x2, x3) = (50, 70) and display in a plot. In your graph, label the numerical values of important points that characterize the indifference curve. 2. (14 pts) Sammy and Jimmy are twin brothers. Each gets a weekly allowance of ✩2. Sammy’s preferences for baseball cards (quantity denoted as x) and “famous economists” cards (quantity denoted as y) can be represented by the utility function u(x, y) = xy. Suppose that both goods are ✩1 per unit, and x and y can be any non-negative real numbers. (a) (2 pts) Solve for Sammy’s optimal consumption bundle. (b) (3 pts) Suppose the price for baseball cards, px, rises to ✩2. What is Sammy’s new optimal consumption bundle? (c) (5 pts) How much would his parents have to increase his allowance in order to leave him exactly as well off as he was originally? Save your final result to 2 decimal point. (d) (4 pts) Jimmy’s preferences are represented by v(x, y) = ln(x) + ln(y). Answer questions (a), (b) and (c) for Jimmy. Compare the result with Sammy. Explain why you have such result. 3. (23 pts) People buy all sorts of different cars depending on their income levels as well as their tastes. Industrial organization economists who study product characteristic choices (and advise firms like car manufacturers) often model consumer tastes as tastes over product characteristics (rather than as tastes over different types of products). We explore this concept below. Suppose people cared about only two different aspects of cars: the size of the interior passenger cabin and the quality of handling of the car on the road. Compare three car models: a Chevrolet Minivan, a Porsche 944, and a Toyota Camry. Porsche’s do not have much space in the interior but they handle well at high speeds. Minivans have tons of interior space but don’t handle that well at high speeds. And Toyota Camrys are somewhere in between — with more space than Prosche’s but not as much as minivans, and with better handling at high speeds than minivans but not as good as Porsches. (a) (3 pts) Putting x1 = “cubic feet of interior space” on the horizontal axis and x2 = “speed at which the car can handle a curved mountain road” on the vertical, based on the above information, draw the three types of cars in a plot assuming that they will fall on one line. (b) (6 pts) Suppose we considered three different individuals whose preferences (over space and ma-neuverability) satisfy basic assumptions and are monotonic and strictly convex, and suppose each person owns different one of the three types of cars. Suppose further that each indifference curve from one person’s indifference map crosses any indifference curve from another person’s indiffer-ence map at most once. (When two indifference maps satisfy this condition, we often say that they satisfy the single crossing property.) Consider the case that the indifference curves through Toyota Camry for the three individuals all intersect at the Toyota Camry. Now suppose you know person A’s MRS at the Toyota Camry is larger (in absolute value) than person B’s, and person B’s MRS at the Toyota Camry is larger (in absolute value) than person C’s. Who owns which car? Draw a plot to show their indifference curves through the Toyota Camry and explain your result. (c) (4 pts) Suppose we had not assumed the “single crossing property” in part (b). Would you have been able to answer the question “Who owns which car” assuming everything else remained the same? Explain with a plot. (d) (2 pts) Suppose you are currently person B and you just found out that your uncle has passed away and bequeathed to you his 3 children,aged 4, 6 and 8 (and nothing else). This results in a change in how you value space and maneuverability. Is your new MRS at the Toyota Camry now larger or smaller (in absolute value)? (e) (3 pts) Suppose that the tastes of persons A, B and C can be represented by the utility functions uA(x1, x2) = x α 1 x2, uB(x1, x2) = xβ1x2, u C (x1, x2) = xγ1x2 respectively. Calculate the MRS for each person. (f) (5 pts) In the above utility functions, assuming α, β and γ take on different values, is the “single crossing property” defined in part (b) satisfied? Given the description of the three persons’ preferences in part (b), what is the relationship between the values of α, β and γ? Explain all of your results in details. 4. (16 pts) Dudley’s utility function is U(C, R) = C − (12 − R)2, where R is the amount of leisure he has per day and C is the quantity of all consumption goods. He has 16 hours a day to divide between work and leisure. He has an income of ✩20 a day from nonlabor sources. The price of consumption goods is $1 per unit. (a) (2 pts) If Dudley can work as many hours a day as he likes but gets zero wages for his labor, how many hours of leisure will he choose? (b) (4 pts) If Dudley can work as many hours a day as he wishes for a wage rate of ✩10 an hour, how many hours will he choose to work? Write down his budget constraint. (c) (6 pts) If Dudley’s nonlabor income decreased to $5 a day and wage rate is still ✩10 per hour, how many hours would he choose to work? Explain your result. Draw in a graph the old budget constraint, the new budget constraint, and indifference curves. Also display Dudley’s optimal choices under the old and new nonlabor income. Label important points in your graph. (d) (4 pts) Suppose that Dudley has to pay an income tax of 20 percent on all of his income (labor and nonlabor), and suppose that his before-tax wage remained at $10 an hour and his before-tax nonlabor income was $20 per day. How many hours would he choose to work? 5. (14 pts) There are two goods in the world, pumpkins (x1) and apple cider (x2). Pumpkins are $2 each. Cider is $7 per gallon for the first two gallons. After the second gallon, the price of cider drops to $4 per gallon. (a) (4 pts) Peter’s income is $54. Draw his budget constraint. Clearly show in the plot the intercepts on the axes, the kink in the budget line and the slope of each segment of the budget constraint. (b) (3 pts) Peter’s utility function is u(x1, x2) = x1 + 3x2. Sketch some indifference curves in your graph. Find Peter’s optimal consumption bundle (x*1 , x*2). (c) (4 pts) Paul’s income is $22. Draw his budget constraint in a new graph. Clearly show in the new plot the intercepts on the axes, the kink in the budget line and the slope of each segment of the budget constraint. (d) (3 pts) Paul’s utility function is u(x1, x2) = min{3x1, 2x2}. Sketch some indifference curves in your graph for Paul. Find Paul’s optimal consumption bundle (x*1 , x*2). 6. (26 pts) I have two 5-year old girls — Ellie and Jenny — at home. Suppose I begin the day by giving each girl 10 toy cars and 10 princess toys. I then ask them to plot their indifference curves that contain these endowment bundles on a graph with cars on the horizontal and princess toys on the vertical axis. Assume they are both rational. A. Ellie’s indifference curve appears to have a marginal rate of substitution of -1 at her endowment bundle, while Jenny’s appears to have a marginal rate of substitution of -2 at the same bundle. (a) (2 pts) Can you propose a trade that would make both girls better off? (b) (2 pts) Suppose the girls cannot figure out a trade on their own. So I open a store where they can buy and sell any toy for ✩1. Illustrate the budget constraint for each girl in two separated plots. (c) (6 pts) Will either of the girls shop at my store? If so, what will they buy? Explain your result with indifference curves displayed in the plots you drew for part (b). (d) (4 pts) Suppose I do not actually have any toys in my store and simply want my store to help the girls make trades among themselves. Suppose I fix the price at which princess toys are bought and sold to $1. Without being specific about what the price of toy cars would have to be, illustrate, using final indifference curves for both girls on the same graph, a situation where the prices in my store result in an efficient allocation of toys. (e) (1 pts) What values might the price for toy cars take to achieve the efficient trades you described in your answer to (d)? Explain. B. Now suppose that my girls’ tastes could be described by the utility function u(x1, x2) = xα1x12 −α , where x1 represents toy cars, x2 represents princess toys and 0 < α < 1. (a) (2 pts) What must be the value of α for Ellie (given the information in part A)? What must the value be for Jenny? (b) (4 pts) When I set all toy prices to $1, what exactly will Ellie do? What will Jenny do? Assume that it is possible to trade fractions of toys. (c) (1 pt) Given that I am fixing the price of princess toys at $1, do I have to raise or lower the price of car toys in order for me to operate a store in which I don’t keep inventory but simply facilitate trades between the girls? (d) (4 pts) Suppose I raise the price of car toys to $1.40, and assume that it is possible to sell fractions of toys. Have I found a set of prices that allow me to keep no inventory?
COMPSCI 753 COMPUTER SCIENCE Algorithms for Massive Data SEMESTER TWO, 2022 1 Locality-Sensitive Hashing Given three documents S1, S2 , S3 and a customized query document q: S1 = {0, 1, 2}, S2 = {0, 3, 4}, S3 = {1, 3, 4}, q = {h(y), 3, 4}; h(y) = y mod 5. where y is the first digit of your Student ID. For instance, suppose my Stu- dentID=6xxxxx, my query document would be q= {1, 3, 4}, where 1 = (6 mod 5). 1.1 Computing MinHash Signatures 1. Generate the bit-vector representation for {S1, S2 , S3 , q} in shingle space {0, 1, 2, 3, 4}. [2 marks] 2. Generate the MinHash matrix for {S1, S2 , S3 , q} using the following four MinHash functions. [4 marks] h1 (x) = (2x +1) mod 5 h2 (x) = (3x +3) mod 5 h3 (x) = (x +5) mod 5 3. Among the hash functions, h1 , h2 , h3 , which one gives the true simulated permutation? [1 mark] 4. Consider the query q and estimate the signature-based Jaccard similari- ties: J(q, S1 ), J(q, S2 ), and J(q, S3 ). [1 mark] 1.2 Tuning Parameters for rNNS In our lecture, we have learnt to formulate the collision probability (i.e., S- curve) given the number of bands b and the number of rows per band r as follows: Pr(s) = 1 − (1 − sr )b. Consider three sets of parameters (r=2,b=10), (r=1,b=10), (r=10,b=50). The collision probabilities for similarity s in range of [0,1] for each (r ,b) are pro- vided accordingly as in Table 1: 1. Which settings give at most 5% of false negatives for any 60%-similar pairs? Briefly explain the reason. [3 marks] 2. Which settings give at most 20% of false positives for any 20%-similar pairs? Briefly explain the reason. [3 marks] Table1.: Collision Probabilities 1.3 c-Approximate Randomized rNNS Consider a family transformation from (d1 , d2 , p1 , p2 )-sensitive to (d1 , d2 , 1 − (1 − p1(k))L , 1 − (1 − p2(k))L )-sensitive, where k and L refer to the number of hash functions and the number of hash tables, respectively. 1. Briefly describe steps to achieve such transformation. [4 marks] 2. What is the expected impact on probability bounds after the transfor- mation with the k and L, respectively? [4 marks] 3. Consider hash table size l = 10, MinHash functions k = 5, and 534 news articles. In phase one hashing, I generated signature matrix for l times. In phase two hashing, I constructed LSH hash tables of size l × m (m: the number of buckets). For each hash table lj, I computed the collision distribution for all articles across m = 600 buckets and reported a heatmap plot as follows (i.e., m: x-axis, l: the y-axis). The values at (mi, lj) is the number of colliding articles at bucket mi and table lj . What is the summation of (mi, lj) ∀mi ∈ [0, 599] for each hash table lj? [3 marks] 2 Data Stream Algorithms 2.1 Bloom Filter 1. How can Bloom Filter improve the false positive ratio? Why does that work? [4 marks] 2. Suppose we have n bits of memory available and set S has m members. Instead of using k hash functions, where each mapping an element to a bit in the main memory, we could divide the n bits into k subarrays (assume n is divisible by n), and then use the i-th hash function, i ∈ [1, k], to the i-th subarray. As a function of n, m and k, what is the probability that a bin has at least one ball in the new framework? [2 marks] 3. How does the new framework compare with using k hash functions into a single array? [4 marks] 2.2 Misra-Gries Algorithm 1. Given the data stream below, perform the Misra-Gries algorithm with k = 3 counters and present the summary, including the elements and its counter values, when the execution of the algorithm is finished. [2 marks] S = {4, 46, 14, 46, 57, 46, 22, 57} 2. Recall in Assignment 2, there was a request to “report the average number of times the decrement triggered by Misra-Gries over a data stream” . What expected number of times has the Misra-Gries summary triggered the decrementsteps after processing the given stream? Please derive your answer as a function of m and k. [3 marks] 2.3 Count Sketch Algorithm Consider the same data stream S and hash functions below. Given the sign hash functions below, perform. the Count Sketch algorithm and present the (i) hash table, (ii) counter matrix, and (iii) estimated frequency of each element in a stream after processing all elements. [10 marks] h1 (x) = x mod 3 s1 (x) = ((2x +1) mod 3) mod 2 h2 (x) = (3x +1) mod 3 s2 (x) = ((3x +2) mod 3) mod 2 h3 (x) = (5x +2) mod 3 s3 (x) = ((4x +2) mod 3) mod 2 3 Algorithms for Graphs 3.1 PageRank Given a directed graph G: 1. Give the column-stochastic adjacency matrix of the above graph G. [2 marks] 2. Compute the PageRank of the above graph G without teleport. [4 marks] 3. If teleport is applied, each node has (1−β) chance to teleport to all other nodes. What changes will be observed on the ranking of the four nodes when (1 − β) increases. What if β = 0? Explain your answer. [4 marks] 3.2 Community Detection 1. Draw an example graph of four nodes, on which the three graph cut criteria (i.e., MinCut, RatioCut and NormalizedCut) produce the same bi-partitioning. [4 marks] 2. Compute the edge betweenness for each edge in the graph below. Which edge is to be removed? [8 marks] 3.3 Influence Maximization What is the most probable set of influenced nodes by running the Indepen- dent Cascade model on the seed set S = {v1 }? Explain your answer. (Hint: Consider the probability of each deterministic sub-graphs. There could be multiple deterministic sub-graphs that result in the same set of influenced nodes.) [8 marks] 4 Recommender Systems 4.1 Collaborative filtering Given the following user-item interaction matrix of 4 users and 5 items: Apply the user-based collaborative filtering algorithm that considers the global bias bg, user bias bi(user) and item bias bj(item) . Use Pearson correlation coefficient to compute the user similarities. Give the top-1 recommended item to user u3 . [8 marks] Note: The predicted ratings should round to one decimal place. 4.2 Factorization Machines 1. Explain the difference between tensor decomposition and factorization machines in context-aware recommendation, in terms of the computation cost and the way of modeling correlations among features. [4 marks] 2. A tourism recommender system is to be upgraded for the support of travel package recommendations. Each travel package is a non-empty set of landmarks. Users can post their ratings on a single landmark or the whole travel package. The table below shows all ratings exist in the database. (a) Describe a memory-based collaborative filtering algorithm that can recommend new travel packages (e.g., {l1 , l3 }). [2 marks] (b) Convert each of the above rating records as an input feature vector for factorization machines. Explain how factorization machines rec- ommend new travel packages based on your input feature vectors. [4 marks] (c) List one advantage of factorization machines compared to the memory- based collaborative filtering algorithm in travel package recommen- dation. [2 marks]
CO 327 Winter 2025: Assignment 1 problems Due: Wednesday January 15, 11:59pm EST Assignment problems. A1-1. LP formulation and Gurobi The Let It Grow company is preparing to sell plant fertilizers for the spring and fall seasons. There are three main components of a fertilizer: nitrogen, phosphorous and potassium. A fertilizer often has a NPK rating consists of three numbers a−b−c, representing the percent-age of nitrogen, phosphorous and potassium in the fertilizer, respectively. For example, in 1 kilogram of a fertilizer with NPK rating of 20 − 10 − 5, there are 200 grams of nitrogen, 100 grams of phosphorous, and 50 grams of potassium. The remainder of the fertilizer consists of materials that are freely available (e.g. water, soil, etc.). Let It Grow wants to make 7 different types of fertilizers that are designed for different purposes. Their NPK ratings and their selling price are listed in the following table. The company has a limited supply of the three chemicals: 3000 kilograms of nitrogen, 1000 kilograms of phosphorous, and 1500 kilograms of potassium. The goal is to maximize the total value of the fertilizers that are produced. (a) Formulate this problem as a linear program. Make sure you clearly explain your vari-ables, objective function and constraints. (b) Using Gurobi, implement the linear program from part (a) and solve it. Include the program you input into the software, and the output that includes the optimal solution and optimal value. State separately the optimal solution and value to the word problem. (c) Suppose the company is testing different prices for all purpose fertilizers. Experiment with Gurobi to see how does the optimal solution vary according to changes in the price of all purpose fertilizers. For each possible optimal solution, write down the range of possible prices that result in that solution. You do not need to be exact on the prices, though they should be pretty close. Include some work on how you have determined the solutions. (Hint: The attribute “obj” for a variable can be useful. If v represents the variables of your model, then v[0].obj = 5 sets the coefficient of the variable at index 0 in the objective function to 5.) A1-2. Review: Duality and complementary slackness (a) Let (P) be the following linear program. Write down the dual (D) of (P) using y as the vector of dual variables. (No justifications required.) (b) Write down all the complementary slackness conditions for (P) and (D). (c) Let ¯x = (3, 0, −2, 0, 7)T . Use the Complementary Slackness Theorem to prove that ¯x is optimal for (P). In particular, you need to determine a possible optimal solution for (D). (d) Use the Weak Duality Theorem to give an alternate proof that ¯x from part (c) is optimal for (P).
I S 300: Introduction to Information Systems Course Description and Objectives: Modern information technologies have dramatically transformed the economic and social structures of our society. Understanding the role of information technology (IT) is critical for firms to provide competitive advantage in today’s competitive environment. These days over 50% of capital expenditures made by firms are IT-related. Knowing how to effectively manage IT is a prerequisite for successful business managers, CIOs, and CEOs. This course is designed to be an important step towards building your IT knowledge base on the road to becoming a successful manager. The course consists of both lectures and lab sessions. The lectures will teach you the language, key concepts, and frameworks for the management of Information Systems (IS). You are expected to gain an understanding of the strategic value of IT/IS as well as their applications in today’s business environment. You will also be able to develop basic IT project management skills such as system analysis and design, project planning, implementation, and testing. The lab sessions emphasize using computers to analyze, coordinate, and solve organizational decision-making problems by providing a hands-on environment to learn various business computer applications such as Microsoft Excel, R, and MySQL. At the end of this course, I expect my students to be comfortable taking an active role in today’s dynamic IT business environment and understand the role of management in IT solutions. Course Materials: • Required Textbook: Management Information Systems: Managing the Digital Firm, 17th Edition, by Kenneth Laudon and Jane Laudon • A computer with webcam, microphone, and high-speed internet access. Grading: Your final grade is comprised of seven components: a midterm exam, a final exam, a team project, your class participation, quizzes, and the computer lab. More detailed requirements and specifications about them will be provided in class. The composition of your final weighted grade is: 1. Exam 1 ................................................................................................................. 20% 2. Exam 2 ................................................................................................................. 20% 3. Team Project (Business Plan Based on an Emerging Information Technology) 20% 4. Participation .......................................................................................................... 10% 5. Quizzes (Pre-chapter 6%, in-class 4%) ................................................................. 10% 6. Computer Lab ....................................................................................................... 20% Total: 100% Please ignore any Canvas calculations as they might reflect the wrong weight / grades. Curve: There will be no individual exam or assignment curves. If a curve is needed on the final weighted course grades, it will be applied. If the class average is low, I typically curve up. If the class average is too high, I might curve down to satisfy the requirements of the Dean’s Office, but I have never needed to curve down the grades before in my career. Grading Appeals / Regrading: Any grade appeals should be summarized in an email and sent to your grader/TA or me. A written appeal is mandatory to request a regrade. If you’re emailing me, clearly indicate your class/section, name (if different than Canvas), which assignment should be regraded, and why. Do not use any other method (such as Canvas comments) for such communication. Appeals must be filed within seven days after the graded item has been returned to you. In case of a grade appeal, I regrade the entire assignment, not just the objected (appealed) part. Exceptions to this policy may apply in the case of the final exams / projects due to deadlines for UW grade submissions. Extenuating Circumstances (missed assignments and exams): Unexpected events happen in life. If you miss an exam or assignment for a documentable extenuating circumstance, I typically count the average of the same grade category for the missed exam or assignment. For example, if a student misses the midterm exam for an extreme emergency, he or she can have the final exam grade count for the missed exam. This arrangement will only be given to students who are able to produce an official document within a reasonable time (within 7 days.) Examples of official extenuating circumstances are medical issues, traffic accidents, participation in university activities at the request of university authorities, death of a first-degree family member, and other compelling verifiable circumstances beyond the control of the student. Please note that work, interviews, training, vacations, friend weddings, or medical issues of second-degree relatives are not considered extenuating circumstances. Official documents should be written in English and must cover the exam date. All non-United States documents must be authenticated and verified. I evaluate these instances on a case-by- case basis. Requesting this policy is inherently a risky move and I don’t recommend it unless there is a documented case. Exams (individual): There will be two exams. Exams will be in-class, in-person, on computer, and in a mixed (multiple-choice and essay) test format unless announced otherwise before the exam. Book chapters to be tested in exams are not cumulative. Team Project (group): Throughout this course, you and your team will develop a business plan based on an emerging information technology of your choice. There will be small deliverables every other week to ensure progress. You will present these business plans towards the end of the course. This team project is specifically designed as open-ended to enhance your creativity and teamworking skills. I expect you to combine the theoretical material you learned in this course with a practical concept that you find appealing. In this project, it is essential that you choose an “emerging” information technology but not a stagnant or declining one. It is also important that you identify an “information-related technology” but not something like biotechnology or pure mechanical-technology. Last but not least, the technology of your choice needs to be suitable for business use. Some examples of emerging information technologies are: • Adaptive Machine Learning • Internet-of-Things • Wearable User Interfaces • Edge Large Language Models • Blockchain (NFT, cryptocurrency) • Digital Twin of a Customer • Disinformation Security • Gamification • Spatial Computing • 6G cellular network What is a business plan based on an emerging information technology? A business plan is a formal statement of a set of attainable business goals and the plan to reach those goals. Emerging information technologies are contemporary advances and innovations in the information technology (IT) field. Emerging technologies provide competitive advantage for those who can come up with innovative business ideas using them. A business plan based on an emerging information technology combines these two notions to create a plan around an IT product or a service. Business plans are decision-making tools. There is no fixed content for a business plan. Rather, the goals and audience determine the content and format of the business plan. A business plan represents all aspects of the business planning process declaring vision and strategy alongside sub-plans to cover marketing, finance, operations, human resources as well as a legal plan, when required. A business plan is a summary of those disciplinary plans. Typical structure for a business plan presentation includes: • Mission and vision statements • Business description (A brief statement that explains what the product or service is and why it will be successful) • Business environment analysis • SWOT analysis • Industry background • Competitor analysis (Understand competitors and substitutes. Explain why your idea is different.) • Market analysis (Identifies the market, the business's position in it, and the competitors. It also assesses the competition and identifies market trends. Best market analyses are supported with data.) • Go-to-market strategy • Operations plan (May include supply chain and production plans) • Management summary • Financial plan (Includes financial projections, start-up costs, funding, and investor pitches. It may also include forecasted income statements, balance sheets, cash flow statements, and capital expenditure budgets) • Timeline and milestones Typically, business plans are developed to attract investors. To do so, I strongly recommend identifying a competitive product or service. Give it a cool name. Make sure it has potential. And finally, figure out the financials: decide on how much investment you need / would like. At the end of the course, you will submit peer evaluations for your team members. Your individual grades may be adjusted based on these peer evaluations. Participation (individual): I will not take attendance every class. However, you will learn better if you are in class daily to listen, take notes and have your questions answered. Course participation will be a part of your final grade. There might also be pop quizzes as a portion of the participation grade. For participation, things I view positively include: • asking insightful questions about assigned readings • redirecting a discussion when the current point has been adequately covered • good analysis supported by case facts or your own experience • summarizing or reconciling previous comments • constructive disagreement • synthesizing and advancing the discussion • a good sense of humor • drawing generic learning points from a particular case Factors I view negatively include: • lack of involvement – absence, silence, detachment or disinterest • leading our discussion into unrelated topics • spending undue amount of time on minor points • long, rambling comments • making undue noise, or disturbing the lecture • disrespectful attitude towards the instructor and classmates • being unprepared, or passing on a cold call Here are some guidelines for assessing class participation, especially when I ask a question: Grade Criteria 91-100 • Gives the right answer or disagrees with my answer. Then, explain and elaborate why. • Demonstrates analysis of readings exceptionally well, relating it to other course material. • Consistent involvement: keeps focus, responds thoughtfully to others’ comments. 81-90 • Gives the right answer, without an explanation of why, sometimes using a single phrase. • Shows thorough knowledge of case and readings, has thought through implications. • Ongoing involvement: responds to others in a constructive way, thinks through own points. 71-80 • Gives the wrong answer but shows some knowledge of case and readings. • Builds on others’ contributions. Shows some evidence of trying to interpret or analyze facts. • Uneven involvement: demonstrates mediocre evidence of critical thinking. 61-70 • Gives the wrong answer and does not demonstrate any knowledge of our readings. • Helps move along the discussion in an incremental manner (e.g., repeats some content.) • Peripheral involvement: Not much new thought; rephrases, underlines earlier comments. 51-60 • Skips answering. Does not demonstrate preparation. • Present in class. Not disruptive. • States straight facts from the content when called on or directly asked. 1-50 • Present, but demonstrates no evidence of preparation. • Shows lack of interest or respect for other’s contributions. • Obviously did not prepare. 0 • Absent. • If present, engages in disruptive behavior. • Misses quizzes. Peer Evaluations (for your own teammates): Any group assignment grade is not your individual grade until peer evaluations are counted at the end of the course. Please note that this can be especially controversial if you expect the same grade as your teammates without showing reasonable effort. In order to create an incentive for a fair work environment in teams, I adjust group grades with peer evaluations. To do so, I need your help to collect data on the performance of each teammate. Here is how it works: Each of the N members of a project team will be given 100×(N-1) points to allocate among the other members of the team. Everyone will distribute those points among their team members EXCLUDING themselves. The individual’s peer weight will be the average of the allocations from his or her team members (usually 100). An individual’s project grade will be the team project’s score weighted by the individual’s peer weight. Peer evaluations suggest that peers should be evaluated on: • Prompt and reliable attendance at scheduled meetings or working periods • Getting individual sub-tasks completed on time • Taking on difficult tasks • Contributing ideas on a regular basis • Contributing specialized skills or knowledge • Facilitating effective team interaction • Keeping attitudes positive throughout the process For example, let us assume you are in a five-person group and your teammates are John Smith, Jane Brown, Mike Lee and Mary Martinez. This means you have 400 points to allocate among your teammates (because 100x(N-1) is 400, where N=5) • If you believe everyone contributed equally, write “John Smith: 100, Jane Brown: 100, Mike Lee: 100, Mary Martinez: 100” in the assignment submission section. (This is generally the most common peer evaluation.) • If you believe Jane contributed significantly more than anyone, you can write “John Smith: 75, Jane Brown: 175, Mike Lee: 75, Mary Martinez: 75.” • If you believe Jane did no contribution and/or hindered your team performance, you can write “John Smith: 133, Jane Brown: 0, Mike Lee: 133, Mary Martinez: 134.” • Please note that all examples above add up to 400 points. Last names are required. Your sum can be different based on the team size. After making sure you allocate points, feel free to add any notes or comments you’d like to share with me about the group performance. Additional comments are optional. Warning/clarifications: • Include the full (first, middle and last) name of your teammates, as it’s shown on Canvas. For example, if your teammates’ name is John Smith, don’t shorten it to Joe, or even John, just write the full name as John Smith. • If you do not submit peer evaluations, or do not follow the directions above, your grade in team assignments may be deducted. Quizzes (individual): Unless otherwise announced in class, there will be four quizzes. Quizzes will be in-class, on Canvas, and in a multiple-choice test format. Follow announcements carefully. Computer Lab Sessions (individual): Hands-on practice is an essential part of this course and the information systems field overall. Teaching assistants will conduct lab sessions to improve your skills in contemporary information technologies and tools. I recommend adding these skills to your resume. AoL Quiz Requirement: You are required to complete an Assurance of Learning (AoL) quiz for this course, which measures how the Foster School of Business is delivering Assurances of Learning. Assurances of Learning help the Foster School evaluate how well we are teaching you and they allow us to fine-tune the curriculum to make sure we are meeting goals and objectives of the course. Additionally, the overall results help the Foster School remain accredited through the Association to Advance Collegiate Schools of Business (AACSB). The quiz is administered by the Undergraduate Program’s Office through Canvas. An email announcement will be sent out by the last week of the quarter. You should complete the quiz as diligently as possible so that the results are significant and impact the Foster curriculum. Thus, you should approach the quiz as a closed note, closed book test. You should not seek assistance from other students or faculty. Please do not discuss the quiz with fellow students.
Food Entrepreneurship and Business Start-up 7HO519 Description of the assessment Component 1: COURSEWORK Summary of Assessment Method: An individual 15 minute presentation to a panel of school stakeholders, where students develop and present their own business proposal idea. Students will develop their business start-up idea through extensive research and show critical awareness of the range of challenges facing the industry. Followed by 5 minutes question-answer (Q&A) session. Weighting: 100 % Delivery: 15 minute presentation (+/- 10%) and 5 minute question-answer (Q&A) session. Assesses Learning Outcomes: 1, 2, 3 and 4 Relationship to Programme Assessment Strategy The program's learning outcomes are distinct yet complementary, ensuring that no overlap occurs. A range of assessments, such as academic presentation in case of Food entrepreneurship and Business Startup, presentations, reports and essays for other subjects, offer students a well-rounded learning experience. The assessment in the Food Entrepreneurship and Business Start-Up module can link contextually with some components of the Sustainability, Social Responsibility, and Ethics module through shared topics like circularity practices in food product design and business conceptualization. Both assessments, though distinct in format, allow students to incorporate sustainability principles into the creation of their standalone business concepts. For example, ideas learned about reducing waste or ethical sourcing can be directly applied to designing business models that prioritize environmental responsibility and social impact. This cross-pollination of ideas encourages students to develop entrepreneurial ventures that are not only feasible but also can potentially align with sustainable and ethical values in the culinary industry. Attributes and Skills Skills Links to useful resources v Critical thinking □ Communication Presentation https://libguides.derby.ac.uk/presentations □ Collaboration □ Creative problem solving Creative Problem Solving Guide https://libguides.derby.ac.uk/c.php?g=722340&p=5247190 v Self-direction & planning Independent Learning https://libguides.derby.ac.uk/c.php?g=704238&p=5069214 □ Numeracy, statistics & financial literacy v Digital Critical Thinking and AI https://libguides.derby.ac.uk/c.php?g=712998&p=5159995 Ethical Use of AI https://libguides.derby.ac.uk/c.php?g=712998&p=5160252 Reference Management Software https://libguides.derby.ac.uk/referencemanagementsoftware □ Resilience □ Adaptability □ Leadership & future thinking Assessment Content Each Assessment 1 will be assessed as follows: 1) KNOWLEDGE The assessment criteria include understanding of key concepts and the wider context of the assignment, i.e., interpretation of task and topic, accuracy of the content and the analysis, ability to logically justify the decisions showing coherence, evidence, reflection and application of appropriate and relevant research to guide decisions. A. Executive Summary The Executive Summary should present the key points about the business idea developed by the student as a culinary entrepreneur (business concept, brief description of the value proposition, competitor analysis results, communication and promotion strategy). B. Business Concept Description Students should develop their own concept analysis based on their Value Proposition Design Model as follows: Description of the Value Proposition (Product/Service, Gain creators, Pain relievers) and Description of the Customers profile (Customer Job(s), Gains, Pains) C. Competition analysis Competition analysis should be based on their Value Proposition Design Model (identification, description of key competitors and/or substitutes (where relevant), analysis of their Value Proposition Design). D. Communication & Promotion strategy Communication, promotion, and digital marketing strategy should be described through focusing on various (at least 3) social media channels using various (at least 10) types of content. Appendix Images of digital marketing channels and content prototypes, should be included in the appendix. The research should be supported with appropriate tables, charts, pictures, etc. 2) FORMAT Assessment takes form. of an individual PowerPoint/Canva presentation, saved and submitted in PDF. The presentation content includes text, images, graphs, figures, tables, and annotated comments. It should contain 10 slides with a minimum of the 500 words inside the slides and max 1000 words provided in the text of presentation (speak equivalent of 2,500 from the image words +/-10%), as well as the mandatory cover page and Bibliography in Harvard style excluded from the word count. It is accompanied by a 15-min business pitch and 5 min Q&A session. Oral presentation format: A 15-min business pitch and 5 min Q&A session in class, Week 10. Students are expected to demonstrate professionalism and effective communication skills (Overall presentation of the content; Style. of the material presented; Logical and clear development of argument; Consistency in presenting the argument). Visual presentation format: Submission’s compliance with the assessment brief; cover page containing the ID of the student, numbered pages; relevant appendix content where required; correct references according to Harvard Reference style. with a bibliography; clear section headings and text coherence; consistent writing style across the text; absence of spelling, grammar, and punctuation mistakes). For further guidance, please refer to “General Written Format Guidelines” at the end of the Assessment Brief section. Students will receive constant feedback on their work drafts through the entire term through tutorials and in class activities that will enable them to further improve their work and their learning experience. Original coursework submission should be developed by the student, which means that it should be written by the students entirely on their own and specifically for this module. Students will have an opportunity to submit drafts of the slides of the presentation to check the level of similarity in Turnitin prior to the final submission.
STATS 3DA3 Homework Assignment 1 Instruction • Due before 10:00 PM on Friday, January 24, 2024. • Submit a copy of PDF with your solution to Avenue to Learn. You don’t need to write the questions in your answers. • Late Penalty for Assignments: A 15% penalty will be applied for each day an assignment is submitted after 72 hours past the due date (rounded up). This includes accommodations for extended time through SAS. • Assignments submitted after 72 hours will receive a grade of zero. • Your assignment must conform to the Assignment Standards listed below. Assignment Standards • Write your name and student number on the title page. We will not grade assignments without the title page. • Quarto Jupyter Notebook is strongly recommended. • Eleven-point font (times or similar) must be used with 1.5 line spacing and margins of at least 1~inch all around. • Use newpage to write solution for each question (Question 1, 2, 3). • No screenshots are accepted for any reason. • The writing and referencing should be appropriate to the undergradaute level. • You may discuss homework problems with other students, but you have to prepare the written assignments yourself. • Various tools, including publicly available internet tools, may be used by the instructor to check the originality of submitted work. • Assignment policy on the use of generative AI – Generative AI is not permitted in the assignments, except for the use of GitHub Copilot as an assistant for coding. – Clearly indicate in the code comments where GitHub Copilot was used as a coding assistant. – In alignment with McMaster academic integrity policy, it “shall be an offence knowingly to submit academic work for assessment that was purchased or acquired from another source”. This includes work created by generative AI tools. Also state in the policy is the following, “Contract Cheating is the act of”outsourcing of student work to third parties” with or without payment.” Using Generative AI tools is a form. of contract cheat- ing. Charges of academic dishonesty will be brought forward to the Office of Academic Integrity. Question 1 Open the surface weather dataset at noaa-gsod.csv (a subset of a much larger dataset). The larger dataset is available at https://www.kaggle.com/noaa/gsod. (a) Read the documentation on this dataset. What are visib and fog variables? Hint: 1. Visit the website https://www.kaggle.com/noaa/gsod. 2. Read about the variables. 3. Then, find out what are visib and fog. (b) What are the data types of visib and fog? Use the data dictionary and the data type in function. Hint: 1. Now read the dataset at noaa-gsod.csv. Let’s call the data frame df. 2. Find the data type of visib and fog variables. (c) Use appropritate visual tools to explore the distribution of visib and fog variables, seperately. Choose an appropriate scale for the vertical axis and colors. What do you notice? Hint: 1. Find the type of visual tool for each variable. You may need to covert the variables to appropriate types. 2. Write down what do you notice from these plots (missingness, outliers, any other patterns?). (d) If there are any, replace all missing values in the visib and fog variables with explicit NaN missing values. Comment on how do you identify missing values. Hint: Missing values may be an unsual value for the variable. (e) Create the visual tools in (b) for the visib and fog variables again, ignoring any missing values. Provide a clear and concise description of the plot - this description should be cast in the context of the surface weather dataset. Hint: Describe the range of values. Describe the shape (bell shape or right-skewed or left-skewed). De- scribe the mode (peak of the histogram). Description of the plots should be written using the description of the variable found in part (a). Question 2 We will use Spotify Tracks DB dataset from Kaggle, curated using the Spotify Web API. This API provides detailed information about each track, using the Spotify URI and Spotify ID as unique identifiers. Download the SpotifyFeatures.csv file from the provided link. (a) How many observations and variables are in the dataset? Hint: 1. Go to the link Spotify Tracks DB dataset from Kaggle. 2. On this page, there is a Download option at the top right-hand side. Click it. 3. A zip file will be downloaded. Then, unzip it. 4. Move that dataset SpotifyFeatures.csv to where you have our assignment notebook. 5. Use pd.read_csv() to read the data. Let’s call it spotify. 6. Use appropritate function to find the dimension of the spotify dataset. (b) Verify that track__id is unique for each observation. Comment on your findings. If duplicates are present, how many duplicate track id entries exist? Remove the duplicate tracks from the dataset before proceeding with further analysis. Note: Duplicates may occur because a track can belong to multiple genres. Hint: • Use is.unique to check duplicated track_id. • Use duplicated and sum() to find the number of duplicated track_id. • Use drop_duplicates() to drop the duplicate track_id. (c) For each track_id, there is genre, artist_name, track_name, popularity, and some features of the track acousticness, danceability, duration in milliseconds, energy, instrumentalness, key, liveliness, loudness, mode,speechiness, tempo, time_signature and valence. Analyze and comment on the types of these variables, grouping variables of the same type together in your discussion. Hint: Use .dtypes() to find the data types. Then, comment on the data types for the above variables. (d) How many unique genres are there in the dataset? Hint: Use .nunique() to determine this, along with other techniques. Note: There may be variations in genre names due to ambiguous characters or formatting differences. (e) Calculate the average popularity for each genre and identify the five most popular genres. Select all tracks associated with these top five genres and use this subset of tracks to answer questions (f) through (h). (f) Visualize the distribution of genre using an appropriate method and interpret the plot. Ar- range the genres in ascending order of frequency in the visualization. Hint: 1. What is the data type of genre? 2. Choose the appropriate visualization method. 3. Interpret the plot. For example, which genre mostly appears in the dataset? (g) Examine the relationship between genre and popularity using an appropriate visualization method. Ensure the plot accounts for the varying number of tracks across different genres, and interpret the results. Hint: • Use the width of the boxplot proportional to relative frequency of each genre. – compute the number of tracks in each genre using .value_count(). – relative frequency = counts/len(dataframe) (h) Explore the relationship between acousticness and popularity. Use an appropriate visual- ization method to avoid overplotting for this large dataset. Interpret the association between acousticness and popularity.
STAT3906 RISK THEORY I December 15, 2022 1. It is known that N has a zero-modified Poisson distribution,with P(N=1)=0.25 and P(N=2)=0.1. (a) Find P(N=0). [5 marks] (b) Find the variance of N. [5 marks] [Total:10 marks] 2. Suppose that X follows the generalized Pareto distribution with cumulative distri- bution function given by where ξ∈(0,1)and β>0. (a) Determine the mean excess function of X,and deduce the heaviness of the tail of X. [5 marks] (b) Compare the heaviness of the tail of X with that of Y~Exp(0).[2 marks] (c) Find TVaRp,(X)for any p∈(0,1). [5 marks] [Total:12 marks] 3. The number of payments N follows the zero-modified Negative Binomial distribu- tion with parameters po=0.6,r=2,β=0.5.The amounts paid per payment Y,Y2,….,are independent and identically distributed with a common cumulative distribution function given by Assume that Yi,Y2,..are independent of N,and define the aggregate payment by S = ni=1 Yi (a) Find P(N=n)for n=0,1,2,3. [5 marks] (b) Find TVaRo.95(N). [4 marks] (c) Find P(S≤10)using normal approximation.Express your answer in terms of the standard normal cumulative distribution function Φ. [5 marks] [Total: 14 marks] 4. For an insurance coverage,claim sizes follow a distribution which is a mixture of a uniform. distribution on [0,10]with weight 0.5 and a uniform distribution on [5,1 3] with weight 0.5.For a policy with a policy limit of a,the expected payment is 6.11875.Find the value of a. [Total:10 marks] 5. You are given the following: ● In 2022,losses are exponentially distributed with mean 600. ● It is estimated that an inflation of 10%impacts all losses uniformly from 2022 to 2023. Find the median of the portion of the 2023 loss distribution above 880,i.e.,the conditional median ofX given X>880 where X is the total loss amount in 2023. [Total: 10 marks] 6. For an insurance coverage,the ground-up losses follow a Pareto distribution with parameters α=3 andθ=5000.The coverage is subject to a deductible of 500. Calculate the deductible needed to double the loss elimination ratio. [Total: 10 marks] 7. Conditional on θ=θ,the claim size X is uniform. on the interval(θ,θ+15)for each policyholder.The parameter A varies between policyholders according to an exponential distribution with mean 10. (a) Find the unconditional density function ofX. [6 marks] (b) Find the mean and variance of X. [6 marks] [Total: 12 marks] 8. For an insurance coverage,you are given: ● The number of losses follows a geometric distribution with mean 5. ● The ground-up losses follow a Poisson distribution with mean 1. ● The number of losses and loss amounts are independent. ● There is a deductible of 1 and a maximum covered loss of 3 per loss. (a) Express the payment per loss variable as a function of the loss variable.Cal-culate the expected aggregate payment per year. [6 marks] (b) Calculate the probability that the aggregate payment is greater than 2. [6 marks] [Total: 12 marks] 9. In the aggregate loss model S=X₁+…+Xn,severities Xi's have a uniform distribution on [0,100]and the distribution of the claim count variable N is given by (a) Find P(S≤50)and P(S≤150). [7 marks] (b) Find VaR0.9(S). [3 marks] [Total: 10 marks]
RQ: How can integration be used to determine the surface area of a soda bottle Introduction As a student passionate about protecting the environment, I have always been curious about how much plastic is used in the production of various bottles and the implications of their surface areas. Research indicates that plastic waste can take anywhere from 20 to 500 years to decompose, and even then, it does not fully disappear, posing a long-term threat to ecosystems. Recognizing the environmental impact of plastic, I chose to investigate the surface area of a 2-litre soda bottle. By applying calculus concepts learned both in and outside the classroom, this exploration aims to calculate the bottle’s surface area and emphasize the broader implications of plastic usage in our daily lives. Aim The aim of this experiment is to investigate using calculus about the surface area of a 2-litre soda bottle. Data Collection The Soda Bottle (2 Liter) has an overall height of 12.4” (31.5 cm) and a diameter of 4.33” (11 cm). Measurement Calculation Separate the bottle into three different parts to calculate the surface area This exploration successfully applied integration to calculate the surface area of a 2-litre soda bottle, with the focus primarily on the curved body of the bottle. The calculation revealed that calculus offers an effective tool for understanding and quantifying physical properties of real-world objects. This investigation also emphasized the importance of precise mathematical modeling and accurate data collection to achieve reliable results. From an environmental perspective, the study highlights the implications of plastic usage by providing a measurable metric—the surface area—to estimate the volume of plastic material used in bottle production. This encourages further consideration of sustainable alternatives and waste reduction strategies. Part 1 calculation: To calculate the area of Part 1, we have to derive the surface area formula that is obtained by revolution (i.e. area of surface of revolution). Mathematically, let f(x) be a differentiable and non-negative function on the interval [a, b], we wish to find the surface area by revolving the curve of y = f(x) from x = a to x= b around the x-axis (see the following diagram for reference). Using a similar strategy we learned when trying to find the area under the curve, we are going to partition the interval [a, b] into n equal sub-intervals. On every ith sub-interval (where l ≤ i ≤ n), draw a line segment from (xi-1, f(xi-1)) to (xi, f(xi)) then revolve all these line segments around the x-axis we will get the following: Notice that after revolving each line segment, we get a trapezoidal-like shape, or a band (illustrated as the shaded region in the diagram above on the right). The formal name of this geometric shape is called a frustum of a cone. Before finding the total surface area, we start by first finding the area of one frustum: Let r1 and r2 be the radii of the bottom part and upper part of the frustum, respectively. Let l be the slant height of the frustum, as shown in the following diagram. A frustum can be thought of as a complete cone but with the upper sharp part removed. Thus, we are going to calculate the total surface area of a cone minus the surface area of the top part, as shown in the following diagram. Next, we wish to express s in terms of the remaining variables r1, r2 and l. By using similar triangles, we have: Now we can substitute this expression of s to the previous equation, and we have the following: This is a huge breakthrough and we are almost there! Now back to the context of interval partition. in the formula corresponds to length of each line segment we connected from (xi-1, f(xi-1)) to (xi, f(xi), r1 and r2 represent the height of the curve at (xi-1, f(xi-1)) and (xi, f(xi)), respectively. Therefore, the “refined” surface area formula is: Since we assume our function f(x) is differentiable on [a, b], it is also differentiable on every sub-interval [xi-1, xi]. By the Mean Value Theorem, there must exist an xi* on (xi-1, xi) such that With this, we can further simplify the above formula to: Furthermore, using the Intermediate Value Theorem, there must also exist another point, say xi** ∈ [xi-1, xi] such that f(xi**) = 2/1[f(xi-1 + f(xi)]. So the above formula can be simplified again as: Hence, the total surface area can be approximated by summing over all the frustum. Mathematically Thus, the exact area can be obtained by taking the integral: And this is the formula for calculating surface area of revolution of a curve f(x) over the interval [a, b]. For the curve y= f1(x) To interpret this graph from my curve equation: The quadratic equation that passes through the points E=(7.3468347739241,14.784138488014) K=(19.8332914008764,9.1211798726049) C = (0, 17.4293972353711) y =f(x)= -0.0047x2 - 0.3254x + 17.4294 R=(-1.9372858830404,17.3491541265612) O=(28.6197020391998,4.0410369944474) x(R)≤ x ≤ x(0) Evaluation The application of integration to determine the surface area of a soda bottle demonstrated the practical use of calculus in analyzing real-world objects. The approach of dividing the bottle into three parts—the main cylindrical body, the neck, and the base—enabled the calculations to be more manageable and accurate. By using a derived quadratic equation to approximate the curve of the bottle, the calculations for Part 1 revealed a surface area of 2483.10 square centimeters. However, several factors influenced the accuracy of these results: Curve Approximation: The quadratic equation used to model the curve of the bottle is an approximation, which might not perfectly represent the actual shape. Small deviations in the shape can lead to discrepancies in the calculated surface area. Measurements: The measurements of the soda bottle were taken manually, introducing potential human error. More precise tools, such as calipers or laser measurements, could improve accuracy. Simplifications: The calculations assumed smooth transitions between different sections of the bottle. In reality, sharp edges or indentations, particularly at the base and neck, were ignored. Integration Assumptions: The formula used for surface area relies on accurate evaluation of the integral. Computational errors in handling the quadratic equation or its derivative could affect the final result. Despite these limitations, the methodology provided a reasonable estimate of the bottle’s surface area and highlighted the significant role of calculus in environmental studies. Conclusion This exploration successfully applied integration to calculate the surface area of a 2-litre soda bottle, with the focus primarily on the curved body of the bottle. The calculation revealed that calculus offers an effective tool for understanding and quantifying physical properties of real-world objects. This investigation also emphasized the importance of precise mathematical modeling and accurate data collection to achieve reliable results. From an environmental perspective, the study highlights the implications of plastic usage by providing a measurable metric—the surface area—to estimate the volume of plastic material used in bottle production. This encourages further consideration of sustainable alternatives and waste reduction strategies. Limitations Curve Modeling Accuracy: The quadratic function used to represent the bottle’s shape does not account for small imperfections or irregularities in the actual design. Precision of Measurements: Manual measurements of the bottle dimensions could introduce errors. Neglected Sections: Certain features, such as the cap and fine details of the neck or base, were not included in the calculation. Numerical Integration: Rounding errors and approximations in the integration process may affect the final values. Material Thickness: The calculation assumes the bottle is a hollow object, ignoring variations in material thickness. Areas of Further Research Incorporating 3D Scanning Technology: Using 3D scanning to capture the exact dimensions and curves of the bottle would improve the accuracy of the model. Material Usage Analysis: Extending the study to investigate the thickness and type of plastic used, providing a more comprehensive understanding of resource usage. Comparison Across Bottles: Analyzing the surface areas of different bottle designs to evaluate their environmental efficiency. Sustainability Impact: Investigating alternative materials and their respective surface areas to assess environmental benefits. Volumetric Analysis: Exploring how the surface area correlates with the bottle’s internal volume to evaluate material efficiency.
University of Bristol MSc in Data Science; DSMP (Data Science Mini Project; EMATM0050), January 2025. Problem B: Leading-edge data analytics for Level-2 financial-market data Problem owner: DrAsh Booth, Global Lead in Applied AI/ML, JP Morgan, London. The global financial markets are obvious sources of "big data". If we look at the market for only one tradeable asset, such as shares in Amazon.com, there are so many people buying and selling the asset that the share price can potentially move up or down (although typically each move is only by a small amount) several times per second for all the time that the market is open, and hence in one trading-day there could be 20,000 or more time-points for movements in the price of an asset. This would be quite a lot to process if the data of interest at each time-point was only a single value, only the share-price in dollars and cents, but very often we are interested in much more data than just the share-price for an asset. Traders in financial markets commonly work with data that summarises all bids (orders to buy) and asks (orders to sell) currently resting at the exchange: any trader looking to buy can post a "bid limit order" at the exchange, saying what price they are prepared to pay per share, and how many shares they wish to buy; similarly any seller can post an "ask limit order" showing how many shares they want to sell, and the per-share price they are seeking. Different buyers will have different price and quantity needs, as will different sellers, and so at anyone time the stock-exchange summarises all of the currently-received orders by publishing its "Limit Order Book" (LOB), sometimes also called the ladder, which shows the total quantity of units of the asset available to buy or to sell at each price which has been quoted. The LOB at anyone time will typically involve tens of different (price, quantity) pairs - and the LOB may change several times before any transaction takes place that results in achange in the share-price, so there might plausibly be 100,000 data-points in a one-daytime-series for the LOB for a highly-traded asset such as Amazon stock, and each of those data-points would be a snapshot of the LOB as it is updated, so each of the 100,000 data-points will itself be a structure involving perhaps 50 numeric values or more, so in approximate figures we can plausibly expect data-files of 5million values from anyone such stock, in anyone day. Industry practitioners refer to this whole-LOB data as "Level2 data". There are good reasons to believe that executing appropriately advanced data-analytics on Level2 time-series data could identify opportunities for usefully predicting near- term movements in price, and hence for profitable automated trading from those signals. The problem, put simply, is for you to implement and evaluate data-analytics techniques that could be useful in identifying trading signals ("buy" or "sell") in Level2 data. You will be issued with Level2 data-sets for this project, although the identity of the asset will have been deleted. Some data will be made available as soon as the project commences, for you to start work on, and then additional data maybe released at later stages in the project: that data may not be for the same asset, or the same market-period, as the initial data-set, and so it is likely not to be statistically identical to the initial data-set, so you should plan accordingly. My team has an ongoing research interest in exploring how well various reinforcement learning approaches perform. at finding good trading strategies when working with Level2 time-series data. For example, we have an interest in the A3C approach, although we recognise that there is probably not enough time in your mini-project to research, design, implement, and evaluate a full A3C system. Nevertheless reinforcement learning is a long-established field with a very large academic literature, and there maybe simpler methods, or freely-available source code-libraries, that you can use to make good progress in the time available. You might want to start by implementing an elementary time-series analysis approach such as ARIMA1,which is relatively simple and very well known, and which could serve as a useful baseline for comparing against, but our interests lie beyond such a commonly-used approach; and so should yours. Remember that we do not just want to see a system that does time-series predictions, we want to see what profit your system might generate from actually trading on the basis of its signals: you'll need to reserve some of the Level2 data as a test-set, and to write (or find) a simple trading simulatorsowe can see how well an automated trading system would do when using the signals that your analysis identifies. One final thing: the raw datasets that you will be supplied with may need some initial wrangling (cleaning, extraction, processing etc) before you can use them, and you will probably find that some initial exploratory visualization and data-mining is useful too.
Lab 4 – VHDL for Combinational Circuits and Storage Elements 1 Objectives To construct combinational circuits and circuits with basic storage elements using VHDL 2 Pre-Lab Preparation 1. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 2. To save files for this lab, create subdirectories mux, decode, encod, and johns in your work directory. 3. Enter the name of the first project, mux, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name, and click OK. 4. Open Text Editor and type the VHDL file from Figure 6.28 of the textbook. Save the file as mux.vhd. 5. Start the compiler. Fix any errors and re-compile. Once the file compiles without errors, go to the next step. Copy the file mux.vhd to a usb drive 6. Repeat steps 3-5 for the remaining examples. Use files from the following figures accordingly (see textbook): i. decod – Figure 6.30 ii. encod – Figure 6.41 iii. johns – Figure 2 (In this Manual) 7. The last example shows one of the ways of implementing the Johnson counter. The last six digits of the student identification number must be represented by a four-bit vector variable STUDENT_ID which will be displayed cyclically in sequence with Johnson counter output. Qreg is an internal signal which can be fed back to the D’s or fed out to Q. 8. Prepare a Truth Table for Johnson Counter for 6 clock cycles. 3 Laboratory Work 1. Create the subdirectory lab4 in your work directory, and copy the all the subdirectories created as part of pre-lab to this subdirectory. 2. Compile your designs and create symbols for respective projects (mux, decode, encod, and johns) and save them. 3. Create new subdirectories inside lab4 folder of your working directory with names muxModified and decodModified. 4. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 5. Enter the name of the project, muxModified, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name at top, and click OK. 6. Create a block schematic file muxModified.bdf for the project defined in (12) and implement a 4:1 multiplexer using two 2:1 multiplexer (mux symbols) as shown in Figure 6.3 of the text book. 7. Repeat the steps 11-13 for the project decodModified and implement a 3:8 decoder using two 2:4 decoders (decode symbols) as outlined in Figure 6.17 of the text book. 8. The circuit design must handle non-valid states and non-valid student identifier cases by displaying an “E” in the seven segment display on your simulated waveforms. 9. Consider the last 6 digits of the student identifier D = {d1, d2, d3, d4, d5, d6} in its general representation. Then, as an example, a student with identifier: 500435429 will follow the display sequence as 435429.LIBRARY ieee; USE ieee.std_logic_1164.all; ENTITY johns IS PORT (Clrn, E, Clkn : IN STD_LOGIC; –clrn is your reset button STUDENT_ID : out std_logic_vector(3 downto 0); Q : OUT STD_LOGIC_VECTOR (0 TO 2)); END johns; ARCHITECTURE Behavior OF johns IS signal Qreg : STD_LOGIC_VECTOR (0 TO 2); BEGIN PROCESS (Clrn, Clkn) BEGIN IF Clrn = ‘0’ THEN Qreg
Lab 4 – VHDL for Combinational Circuits and Storage Elements 1 Objectives To construct combinational circuits and circuits with basic storage elements using VHDL 2 Pre-Lab Preparation 1. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 2. To save files for this lab, create subdirectories mux, decode, encod, and johns in your work directory. 3. Enter the name of the first project, mux, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name, and click OK. 4. Open Text Editor and type the VHDL file from Figure 6.28 of the textbook. Save the file as mux.vhd. 5. Start the compiler. Fix any errors and re-compile. Once the file compiles without errors, go to the next step. Copy the file mux.vhd to a usb drive 6. Repeat steps 3-5 for the remaining examples. Use files from the following figures accordingly (see textbook): i. decod – Figure 6.30 ii. encod – Figure 6.41 iii. johns – Figure 2 (In this Manual) 7. The last example shows one of the ways of implementing the Johnson counter. The last six digits of the student identification number must be represented by a four-bit vector variable STUDENT_ID which will be displayed cyclically in sequence with Johnson counter output. Qreg is an internal signal which can be fed back to the D’s or fed out to Q. 8. Prepare a Truth Table for Johnson Counter for 6 clock cycles. 3 Laboratory Work 1. Create the subdirectory lab4 in your work directory, and copy the all the subdirectories created as part of pre-lab to this subdirectory. 2. Compile your designs and create symbols for respective projects (mux, decode, encod, and johns) and save them. 3. Create new subdirectories inside lab4 folder of your working directory with names muxModified and decodModified. 4. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 5. Enter the name of the project, muxModified, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name at top, and click OK. 6. Create a block schematic file muxModified.bdf for the project defined in (12) and implement a 4:1 multiplexer using two 2:1 multiplexer (mux symbols) as shown in Figure 6.3 of the text book. 7. Repeat the steps 11-13 for the project decodModified and implement a 3:8 decoder using two 2:4 decoders (decode symbols) as outlined in Figure 6.17 of the text book. 8. The circuit design must handle non-valid states and non-valid student identifier cases by displaying an “E” in the seven segment display on your simulated waveforms. 9. Consider the last 6 digits of the student identifier D = {d1, d2, d3, d4, d5, d6} in its general representation. Then, as an example, a student with identifier: 500435429 will follow the display sequence as 435429.LIBRARY ieee; USE ieee.std_logic_1164.all; ENTITY johns IS PORT (Clrn, E, Clkn : IN STD_LOGIC; –clrn is your reset button STUDENT_ID : out std_logic_vector(3 downto 0); Q : OUT STD_LOGIC_VECTOR (0 TO 2)); END johns; ARCHITECTURE Behavior OF johns IS signal Qreg : STD_LOGIC_VECTOR (0 TO 2); BEGIN PROCESS (Clrn, Clkn) BEGIN IF Clrn = ‘0’ THEN Qreg
Lab 4 – VHDL for Combinational Circuits and Storage Elements 1 Objectives To construct combinational circuits and circuits with basic storage elements using VHDL 2 Pre-Lab Preparation 1. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 2. To save files for this lab, create subdirectories mux, decode, encod, and johns in your work directory. 3. Enter the name of the first project, mux, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name, and click OK. 4. Open Text Editor and type the VHDL file from Figure 6.28 of the textbook. Save the file as mux.vhd. 5. Start the compiler. Fix any errors and re-compile. Once the file compiles without errors, go to the next step. Copy the file mux.vhd to a usb drive 6. Repeat steps 3-5 for the remaining examples. Use files from the following figures accordingly (see textbook): i. decod – Figure 6.30 ii. encod – Figure 6.41 iii. johns – Figure 2 (In this Manual) 7. The last example shows one of the ways of implementing the Johnson counter. The last six digits of the student identification number must be represented by a four-bit vector variable STUDENT_ID which will be displayed cyclically in sequence with Johnson counter output. Qreg is an internal signal which can be fed back to the D’s or fed out to Q. 8. Prepare a Truth Table for Johnson Counter for 6 clock cycles. 3 Laboratory Work 1. Create the subdirectory lab4 in your work directory, and copy the all the subdirectories created as part of pre-lab to this subdirectory. 2. Compile your designs and create symbols for respective projects (mux, decode, encod, and johns) and save them. 3. Create new subdirectories inside lab4 folder of your working directory with names muxModified and decodModified. 4. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 5. Enter the name of the project, muxModified, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name at top, and click OK. 6. Create a block schematic file muxModified.bdf for the project defined in (12) and implement a 4:1 multiplexer using two 2:1 multiplexer (mux symbols) as shown in Figure 6.3 of the text book. 7. Repeat the steps 11-13 for the project decodModified and implement a 3:8 decoder using two 2:4 decoders (decode symbols) as outlined in Figure 6.17 of the text book. 8. The circuit design must handle non-valid states and non-valid student identifier cases by displaying an “E” in the seven segment display on your simulated waveforms. 9. Consider the last 6 digits of the student identifier D = {d1, d2, d3, d4, d5, d6} in its general representation. Then, as an example, a student with identifier: 500435429 will follow the display sequence as 435429.LIBRARY ieee; USE ieee.std_logic_1164.all; ENTITY johns IS PORT (Clrn, E, Clkn : IN STD_LOGIC; –clrn is your reset button STUDENT_ID : out std_logic_vector(3 downto 0); Q : OUT STD_LOGIC_VECTOR (0 TO 2)); END johns; ARCHITECTURE Behavior OF johns IS signal Qreg : STD_LOGIC_VECTOR (0 TO 2); BEGIN PROCESS (Clrn, Clkn) BEGIN IF Clrn = ‘0’ THEN Qreg
Lab 4 – VHDL for Combinational Circuits and Storage Elements 1 Objectives To construct combinational circuits and circuits with basic storage elements using VHDL 2 Pre-Lab Preparation 1. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 2. To save files for this lab, create subdirectories mux, decode, encod, and johns in your work directory. 3. Enter the name of the first project, mux, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name, and click OK. 4. Open Text Editor and type the VHDL file from Figure 6.28 of the textbook. Save the file as mux.vhd. 5. Start the compiler. Fix any errors and re-compile. Once the file compiles without errors, go to the next step. Copy the file mux.vhd to a usb drive 6. Repeat steps 3-5 for the remaining examples. Use files from the following figures accordingly (see textbook): i. decod – Figure 6.30 ii. encod – Figure 6.41 iii. johns – Figure 2 (In this Manual) 7. The last example shows one of the ways of implementing the Johnson counter. The last six digits of the student identification number must be represented by a four-bit vector variable STUDENT_ID which will be displayed cyclically in sequence with Johnson counter output. Qreg is an internal signal which can be fed back to the D’s or fed out to Q. 8. Prepare a Truth Table for Johnson Counter for 6 clock cycles. 3 Laboratory Work 1. Create the subdirectory lab4 in your work directory, and copy the all the subdirectories created as part of pre-lab to this subdirectory. 2. Compile your designs and create symbols for respective projects (mux, decode, encod, and johns) and save them. 3. Create new subdirectories inside lab4 folder of your working directory with names muxModified and decodModified. 4. Start-up Quartus II. This window gives you access to an integrated suite of CAD tools 5. Enter the name of the project, muxModified, by clicking on File then Project on the pull down menu and then Name on the subsequent pull down menu. Type the Project Name at top, and click OK. 6. Create a block schematic file muxModified.bdf for the project defined in (12) and implement a 4:1 multiplexer using two 2:1 multiplexer (mux symbols) as shown in Figure 6.3 of the text book. 7. Repeat the steps 11-13 for the project decodModified and implement a 3:8 decoder using two 2:4 decoders (decode symbols) as outlined in Figure 6.17 of the text book. 8. The circuit design must handle non-valid states and non-valid student identifier cases by displaying an “E” in the seven segment display on your simulated waveforms. 9. Consider the last 6 digits of the student identifier D = {d1, d2, d3, d4, d5, d6} in its general representation. Then, as an example, a student with identifier: 500435429 will follow the display sequence as 435429.LIBRARY ieee; USE ieee.std_logic_1164.all; ENTITY johns IS PORT (Clrn, E, Clkn : IN STD_LOGIC; –clrn is your reset button STUDENT_ID : out std_logic_vector(3 downto 0); Q : OUT STD_LOGIC_VECTOR (0 TO 2)); END johns; ARCHITECTURE Behavior OF johns IS signal Qreg : STD_LOGIC_VECTOR (0 TO 2); BEGIN PROCESS (Clrn, Clkn) BEGIN IF Clrn = ‘0’ THEN Qreg
1. Create an account on HPRC (https://hprc.tamu.edu/apply/) a. Apply for Basic Allocation on Grace (20,000 Service Units) b. 20,000 Service Units (SUs) ~= 250 A100 (40G) GPU hours 2. Train a variant of GPT-2 a. Limit training time/resource to max 24 hours w/ one A100 40G GPU b. Follow instructions at https://github.com/parasol-aser/hw-reproduce-chatgpt Your Goal: train the best GPT model from scratch within the resource budget – Top 10 submissions with the highest HellaSwag accuracy will each earn 1 bonus point – Top 3 will earn 4, 2, 1 additional bonus points respectively Your Strategies: – Tune hyper-parameters guided by the scaling laws – Try different architectures, e.g.: – Group Query Attention – Replace LayerNorm by RMSNorm – Replace absolute positional encoding by RoPE – Replace GeLU activation function by SwiGLU – Drop Positional Encoding – Change KQV (e.g., merge K and Q) – Elimination or Modification of FFN Layers – Mixture of Experts (MoE) – … Submission (5pt): – Your final model checkpoint and original logs stored on Grace (2pt) – Need to share a folder with our grader – Your training code (only diff is required if based on karpathy/llm.c) (1pt) – A report that describes your solution and results (including remaining challenges and failures if any) (2pt) – Limit your report to three pages with 10pt font size
Instructions for homework submission a) For each question, please explain your thought process, results, and observations in a markdown cell after the code cells in your jupyter notebook with the name FirstName LastName HW4.ipynb b) You can use any available libraries for this homework. For the CNN model implementation, use PyTorch. Question 1: Convolution Operation (30 points) In this problem, we will use the convolution operation on the matrix using the 3×3 filter as shown below.Apply the convolution operation for all the following settings respectively, and write your answers in a LaTex generated PDF file with the name FirstName LastName HW4.pdf • Convolution with stride of 1 • Zero padding of 1 + convolution with stride of 1 • Zero padding of 2 + convolution with stride of 2 • Convolution with stride of 1 + max pooling of 3 with stride of 1 • Zero padding of 2 + convolution with stride of 1 + max pooling of 3 with stride of 1 1 Question 2: Image Classification using CNN in Pytorch (70 points) (a) Dataloader Download the MNIST train and test dataset on Canvas. Implement a data loader with batch size and validation size as arguments. (HINT: You can check the documentation here: Creating a Custom Dataset for your files) (b) Data Exploration Pick one example from each digit and visualize them. Count the number of samples per digit in the original training data. Is the data distribution balanced? (c) Data Split Split original training data into 80% for training and 20% validation datasets. (g) Inference Use the best fine-tuned model for inference on the test dataset. Save your predictions for every row of the test data in a CSV file with the name FirstName LastName Preds.csv (Do not shuffle the test data) BONUS(+10 points): Filter Visualization Randomly pick an image from the training set. Visualize the feature maps corresponding to all convolution filters after the first and last convolution layers. 2
Programming Assignment 6 1 Goal Modern cameras are unable to capture the full dynamic range of commonly encountered real-world scenes. In some scenes, even the best possible photograph will be partially under or over-exposed. Researchers and photographers commonly overcome this limitation by combining information from multiple exposures of the same scene. You will write software to automatically combine multiple exposures into a single high dynamic range radiance map, and then convert this radiance map to an image suitable for display through tone mapping. 2 Starter Code Starter code (in Python) along with the images can be downloaded from here. The package includes 2 scenes, which have been captured with two different cameras. “Chapel” is captured with a Canon 35mm SLR and “Office” is captured with a Canon 5D Mark iv. Note that, some of the expected results are included in the “Results” folder. 3 Task 1 Here, you will calculate the camera response function (CRF) from a set of images captured with different exposure times. Two scenes are provided in the “Images” folder. You need to obtain the CRFs for both these cases, and plot the CRFs like Fig. 7 (d) of Debevec’s paper. Generally you have to do the followings to estimate the CRF: • Read the images and their corresponding exposures (already done in the starter code). • Randomly select N pixels to perform the optimization. Note that, you use the same N randomly selected positions for all the images in the stack. Choosing a very large N could slow down the optimization process. Therefore, you should choose a reasonable N, e.g., N ≈ 5×256/(P −1), where P is the number of images in the stack. • Write the triangle function defined in Eq. 4 of the Debevec’s paper and discussed in the class. • Perform the optimization. This is provided in the starter code (gsolve function for Python). You just have to provide appropriate inputs to the function. Note that, the dimension of the inputs are as follows: Z (N × P), B (P ×1), l (scalar, the value provided in the main file), w (256×1). 4 Task 2 In this task, you use the calculated CRF of each scene to reconstruct the radiance of the scene. This can be done by implementing Eq. 6 in Debevec’s paper, which was discussed in the class. Once you obtain the radiance, you need to tonemap it to be able to show the results. For this, you will be implementing a global and local tonemapper. Global – Here, you will obtain a tonemapped image using gamma compression as follows: (1) Choose a γ value (less than 1) that produces the best result in each case. Local – You will implement a simple local tonemapper (similar to the one discussed in the class) as follows: • Your input E is linear RGB values of radiance. • Compute the intensity (I) by averaging the color channels. • Compute the chrominance channels: (R/I, G/I, B/I) • Compute the log intensity: L = log2(I) • Filter that with a Gaussian filter: B = filter(L). Larger standard deviations result in tonemapped images with more details. Standard deviation of 0.5 to 2 seem reasonable. • Compute the detail layer: D = L − B • Apply an offset and a scale to the base: B0 = (B − o)∗ s – The offset is such that the maximum intensity of the base is 1. Since the values are in the log domain, o = max(B). – The scale is set so that the range of output base is dR, i.e., s = dR / (max(B) – min(B)). Values around 4 or 5 for dR should look fine. • Reconstruct the log intensity: O = 2(B0+D) • Put back the colors: R0,G0,B0 = O ∗(R/I,G/I,B/I) • Apply gamma compression. Without gamma compression the result will look too dark. Values around 0.5 should look fine (e.g. result0.5). Your HDR images have zero values which will cause problems with log. You can fix this problem by replacing all zeros by some factor times the smallest non-zero values. 5 Write Up For both scenes, you should show the estimated CRF and the global and local tonemapped version of the HDR image (radiance). Describe how you implemented the assignment. Discuss any problem you faced when implementing the assignment or any decisions you had to make. 6 Graduate Credit There are no additional requirements for graduate credit for this project. 7 Deliverables Your entire project should be in a folder called “firstnamelastname”. This folder should be zipped up and submitted through e-campus. Inside the folder, you should have the followings: • A folder named “Code” containing all the codes for this assignment. Please include a README file to explain what each file does if you add any other files to the starter code. • A report in the pdf format. Make sure you write your name on top of the report. Also make sure the pdf file is under 5 MB. Make sure you exclude all the results and original images from your submission. 8 Checklist Make sure you can check all the items below before submitting your assignment. You will lose 5 points for each item that cannot be checked. The folder is named properly (“firstnamelastname”). Note between first and last name. The folder structure should be exactly as follows “firstname lastname.zip” – “firstname lastname” ∗ “Code” ∗ Report.pdf Inside the root folder, there is a folder called “Code” that contains your source code. Also make sure the report is in the root folder. The folders “Images” and “Results” are not included (you only submit your codes and a report). Name written on top of the report. The report is in pdf format and the file is under 5 MB. 9 Ruberic Total credit: [100 points] [30 points] – CRF estimation [20 points] – Radiance reconstruction [10 points] – Global tonemapping [30 points] – Local tonemapping [10 points] – Write up 10 Acknowlegements This project is partially based on James Hays Computational Photography course with permission.
Programming Assignment 5 1 Goal The goal of this project is to become familiar with the seam carving approach. Seam carving is a technique to “retarget” (smart resize) images; the technique preserves the content in order of its importance in the image (as defined by some energy function). It was introduced in 2007 (video, paper) by Shai Avidan and Ariel Shamir. Wikipedia has a good overview of the algorithm. 2 Starter Code Starter code (in Python) along with the images can be downloaded from here. Note that, expected results for a few images are included in the “Results” folder. 3 Main Task The main task involves implementing the seam carving approach. The goal is to create two resized version of each input image; 1) reduce the width by a factor of 2, and 2) reduce the height by a factor of 2. As discussed in the class, height reduction can be done by simply rotating the image (or the energy matrix) 90 degrees (you can use numpy rot90 or any other similar function for this). For this task, you only need to generate two resized images for the first three images in the package. The forth image is related to the extra credit part. In addition to the provided examples, you need to show one image of your own which demonstrates the failure case of the approach. You need to properly discuss why the method fails on your example in the report. You are free to reduce the width or height by any factor of your choosing for this extra image. To implement seam carving, you need to do the following: 1. Compute the energy matrix for your image. Use the energy function discussed in the class which is the sum of absolute gradients in x and y directions. Make sure you convert the color images into grayscale (using rgb2gray in MATLAB or a similar function in python) before computing the gradients. 2. Find the best (lowest energy) seam using dynamic programming: • Make a scoring matrix (M) the size of your image initialized with the values in the energy matrix (E), i.e., make a copy of your energy matrix. • Set the values of every entry in the matrix except for the first row by adding to it the minimal value in any of the cells above it in the seam: M(x,y) = E(x,y) + min[M(x − 1,y − 1),M(x,y − 1),M(x + 1,y − 1)], where M(x,y) is the cost of the lowest-cost seam going through that point. You’ll have to do this in an order such that M(··· ,y − 1) is defined at the time it’s evaluated – row by row works. Also beware boundary conditions. • Find the minimal value in the bottom row of the scoring matrix. This is the bottom of the optimal seam. • Trace the seam from the bottom by following the smallest value in any of the positions above it in the seam. 3. Remove that seam in the image 4. Repeat steps 1 to 3 on the new image. Note that you have to recompute the energy matrix each time to take into account new edges added by the seam removal. 4 Extra Credit 5 Write Up For each result, you should show the input image and the two resized images (reducing width and height). You also need to include one example of your own, where the method fails to generate reasonable results. You need to properly discuss why the method fails on this example. If you implement the extra credit part, show the result with and without the mask (four images) in addition to the input image on the forth example. Describe how you implemented the assignment. Discuss any problem you faced when implementing the assignment or any decisions you had to make. 6 Graduate Credit Graduate students have to do the extra credit. 7 Deliverables Your entire project should be in a folder called “firstnamelastname”. This folder should be zipped up and submitted through e-campus. Inside the folder, you should have the followings: • A folder named “Code” containing all the codes for this assignment. Please include a README file to explain what each file does if you add any other files to the starter code. • A report in the pdf format. Make sure you write your name on top of the report. Also make sure the pdf file is under 5 MB. Make sure you exclude all the results and original images from your submission. 8 Checklist Make sure you can check all the items below before submitting your assignment. You will lose 5 points for each item that cannot be checked. The folder is named properly (“firstnamelastname”). Note between first and last name. The folder structure should be exactly as follows “firstname lastname.zip” – “firstname lastname” ∗ “Code” ∗ Report.pdf Inside the root folder, there is a folder called “Code” that contains your source code. Also make sure the report is in the root folder. The folders “Images” and “Results” are not included (you only submit your codes and a report). Name written on top of the report. The report is in pdf format and the file is under 5 MB. 9 Ruberic Total credit: [100 points] [70 points] – Seam carving [10 points] – Include one example of your own, where the approach fails [20 points] – Write up Extra credit: [10 points] [10 points] – Incorporating Mask 10 Acknowlegements This project is derived from James Hays Computational Photography course with permission.
