ES1050 24-25 Fall Project Phase 1 1 Phase 1 Overview Phase 1 of the Fall Project is focused on the design and development of a diffuser (an example can be seen in the white component in Figure 1) for the wellness lamp. By the end of Phase 1, each student will have individually designed a 3D model of a diffuser in Onshape for submission (assignment due Oct 21) and to share with their group to support their group diffuser design that will be 3D printed in Phase 2. Figure 1: ES1050 Wellness Lamp Prototype 2 Diffuser Design Diffusers can be made from any material(s) that scatters light to soften and direct it as needed but must include 3D printable component(s), fully modelled in Onshape. Designs should consider how to ensure enough lux is transferred to meet light therapy requirements for the different modes along with providing an even diffusion (distribution along the diffuser). Constraints Table 1: Constraints and Measures for Diffuser Constraints Measures Maximum height of 110mm Height in mm of 3D Onshape model Cannot hang over the base (no wider and no longer than the base) Length and width in mm of the top view of the 3D Onshape model Must connect to the base using a single M3x6 screw to the top of the light tower Connection to base using single M3x6 screw at the top of the light tower Must have 3D printable component(s) Clearly indicated design elements in 3D Onshape model including materials if proposing a composite material design Objectives Table 2: Objectives and Measures for Diffuser Objective Measure Maximize esthetics Unique and simple design with consideration to colour, shape, contour, balance and evoking meanings for users Note: 3D printing of group diffuser designs in phase 2 will be limited to white or transparent PETG filament. This should not limit your individual diffuser design Minimize UV light Review to detect material absorption of UV light Maximize even light diffusion Review to detect material absorption and even distribution of light in direction of light therapy to the front of the lamp (such as thickness of material, type of material, etc.) subject to the clear intent of the design aesthetics 3 Wellness Lamp Base A 3D model of the major components of the lamp base is provided in the Western Engineering Onshape application in the ES1050 24-25 class under documents (it will also be part of your Diffuser design assignment on http://westernengineering.onshape.com). Groups will have access to fabricated bases along with calipers to review and measure during lab sessions. Students should note that there will be minor variations in the fabrication of each unit due to limitations of the fabrication or assembly and should plan their own designs accordingly. 4 Deliverables Each student shall submit their individual diffuser design 3D. This is an individual assignment. Students need to create their design in the assignment posted on http://westernengineering.onshape.com and then submit a model link and some screenshots to Gradescope for grading. By accessing the assignment through the Onshape assignment, students will be start with an Onshape document preloaded with the base component parts. You should see the parts shown in the image to the right pre-existing in the model you are building your diffuser in. Figure 2: Lamp Base Parts Students are expected to: • Model their own Diffuser (following good modelling practices and satisfying the objectives and constraints listed above) • Create an assembly fastening all the base components provided in their nominal locations as modelled • Add their diffuser to the assembly demonstrating how it is mounted to the Lamp Base • And fasten it in place using an 6mm M3 screw imported from the Standard Content library included in Onshape (see Figure 3 below for illustration of how to add in standard content models). Figure 3: Inserting standard content in Onshape Assemblies The Group diffuser design will not be submitted for grading now but will be submitted for 3D printing in Week 7. 4.1 Submitting Diffuser Model Gradescope assignment link:https://www.gradescope.ca/courses/18379/assignments/98570 . 1. Click the Submit button to the right of your model title on the Onshape modelling webpage (top right in this image). Do NOT close the Onshape modeling tab or navigate away as you will need to get a link to share with us as well from this website for Step 2! Note: the button changes to Resubmit once successfully submitted: 2. Copy and submit to Gradescope Q1 the html link showing in your browser immediately AFTER clicking submit (and while it still shows “Resubmit”). Note 1: you are copying the correct link if you see the word “submission” to the right of your title. Note 2: if you missed the link then click on the icon highlighted in yellow in the immediately above image and select the most recent “Submission” model document from the list and then recopy the link in your browser bar. Table 3: Phase 1 & 2 Lab Schedule Week Expected Elements Phase 1 3 Develop team charter, set up OneNote, familiarize yourselves with the project details, and start to ideate value added. 4 Start to ideate diffuser designs individually and share with group to inspire variations. 5 Translate individual diffuser design to Onshape (reverse engineering) and identify assumptions and risks for your solution. Phase 2 6 Share final individual diffuser designs with group, evaluate to identify top solution (or combined solution) and finalize top solution design in Onshape. 7 Develop individual and group 3D diffuser slicer printing model in PrusaSlicer and submit group file for 3D printing. 5 Individual Diffuser Rubric Due 9pm, Oct 21st. A base score for the diffuser design will be awarded for satisfying the following design requirements: Marks Requirement 1 Correct submission to Western Engineering Onshape and Gradescope 1 Maximum height 110mm above the base 2 Profile does not hang over the base (width and depth of top view) 2 Sufficient clearance inside diffuser to avoid interfering with the lighting and wiring components included in the tower 2 Diffuser design shows: (0) no, (1) some, or (2) significant effort to be aesthetically pleasing 2 Diffuser design is likely to: (0) not block UV and unevenly distribute light, (1) partially block UV and uniformly distribute light, or (2) block UV and uniformly distribute light towards viewer observing the front of the lamp 2 Ensure proper orientation/front of the diffuser is clearly obvious during assembly 3 Assembly model illustrating the completed lamp includes all the provided base components and your diffuser part(s) properly assembled using an imported M3 6mm screw part Marks will be deducted for poor modelling practices used while creating your Diffuser designs: • Sketches o Sketch name(s) not representative of what was modelled in it – Sketches should not be left as default Sketch # o Sketch(es) that are not fully defined (black lines only) and show blue lines or red (over-defined) • 3D Features o Features are not done logically, e.g. many individual chamfers instead of one chamfer applied to multiple edges in one operation o Features that aren’t named logically (if you extrude a rod, then call it a rod extrusion.) • Parts o Any parts that are not solids and are instead hollow or shells • Mates o The assembly must have the main Base component fixed, so it doesn’t slide around when dragging on components o All mates should be named so it is clear what is being mated to what and the nature of the mate
DIPLOMA IN MANAGEMENT STUDIES FINANCIAL ACCOUNTING INDIVIDUAL ASSIGNMENT (30%) Instructions: Read the instructions in your Student Portal, Course Outline, CA Outline and your Blackboard portal carefully. If you still have queries read the FAQ first and then email queries via your student portal. You will be penalized with marks deduction if the instructions are not strictly followed. You are to upload your assignment by the due date through the student portal account. After the due date, your submission will not be entertained. Write your FULL Name AND your NRIC/FIN number as in the register on a CA cover. You should a keep a copy of assignment submitted. All workings must be shown. The submitted report must show evidence that this is your own work. No marks will be awarded if there are no workings or reasonable explanations. This report must be type written and submitted in word format. Please be reminded that plagiarism and collusion is a serious offence, and all cases will be referred to the administration. Grades will be withheld if the submission is suspected for plagiarism or collusion till investigations are completed. Penalty Marks for Late Submission of Assignment By one day: 20% to be deducted from total marks More than one day: submission will NOT be graded You may appeal via [email protected] CA Submission CA 1 must be submitted online via student portal. Please read instructions provided in the portal carefully. Deadline: 23 Oct, 11.59 am Please be reminded that plagiarism and collusion are serious offences, and all cases will be referred to the administration. You may be penalized leading to failure and termination from the DMS programme. APPENDIX A FORMAT OF WRITTEN ASSIGNMENT Please note the following technical requirements: a. Typed on word processor such as M/S Word. b. Use Times New Roman font, size 12. c. Paragraphs of text are to be double spaced; d. Financial statements and tables can be single spaced e. Color: Black (for text) f. Paper: White g. Individual Assignment Submission form. to be attached at the FRONT of the assignment, with your full name as per student ID. Important Note: Students caught for Plagiarism and/or Collusion will be subjected to heavy penalties. Plagiarism & Collusion The university considers plagiarism & collusion as serious offences that could lead to expulsion from the programme. Students should ensure that the assignments submitted are their own work. Students should check every page and verify that it is their own work. What is Plagiarism: It is the use of someone else’s work in its entirety or some parts in exact form. or in very close form, as your own without acknowledgment to original author(s). Examples of plagiarism in assignments include the use of other authors: phrases, facts and illustrations, statistics, and assembled materials, without acknowledging them. What is Collusion: It is the use of other person’s work or ideas with the consent of the other person(s), without formally acknowledging them in your own work. Although students can discuss their ideas and group projects freely with anyone, when it comes to writing the report, each student or each group must use their own words to produce their respective reports. Sharing the same phrases or paragraphs or sections of texts and illustrations (without any acknowledgments) in different group reports constitute collusion. INDIVIDUAL ASSIGNMENT (100 marks) Question 1 (100 marks) Bennie, the owner of Bibi Trading, deals in vehicle accessories. Its unadjusted trial balance as at 31 August 2024 is given as follows: Unadjusted Trial Balance as at 31 August 2024 Accounts Titles Dr ($) Cr ($) Plant and machinery 780,000 Office equipment 228,000 Accumulated depreciation as at 1 September 2023 - Plant & machinery 212,500 - Office equipment 88,000 Sales 1,545,500 Returns 18,000 21,000 Rent received 76,000 Utilities expense 70,000 Advertising expense 76,000 Freight inwards 28,000 Freight outwards 32,000 Purchases 923,000 Insurance expense 14,000 Salaries and wages expense 146,000 Commission income 8,000 10% Bank Loan, due in 2034 300,000 Trade payables 180,000 Trade receivables 240,000 Capital – Bennie 300,000 Drawings – Bennie 33,610 Inventory – 1 September 2023 118,000 Cash at Bank 28,000 Discounts 12,146 15,756 2,746,756 2,746,756 The following additional information was extracted from the records towards the end of the financial period. 1. Advertising of $16,000 included in the trial balance was for period from 1 July 2024 to 31 October 2024. 2. A customer, Clarissa, has paid a deposit of $5,000 for goods to be delivered on 2 September 2024. The receipt was recorded as sales. 3. The 10% bank loan was taken on 1 June 2024. The interest expense has yet to be accounted for. 4. N Ltd. owed Bibi Trading $30,000 and settled the amount early by cheque and was given a 5% cash discount. This transaction was omitted. 5. A purchases invoice of $34,000 was wrongly recorded as $43,000. 6. Bennie took $5,500 for personal use from the bank account. No entries had been made in the books. 7. Commission income of $3,700 for July 2024 was yet to be received. 8. Annual depreciation on fixed assets were as follows: Office equipment - $18,300 Plant & machinery - $31,800 9. A physical count on 31 August 2024 revealed stocks on hand to be $140,600. Required: (a) Prepare the necessary general journal entries to record transactions (1) to (8). Narrations are not required. (Hint: For some transactions, you will need to create new accounts which are not shown on the trial balance.) (40 marks) (b) Prepare the following financial statements for Bibi Trading: (i) Statement of Comprehensive Income for the year ended 31 August 2024 (ii) Statement of Financial Position as at 31 August 2024 (60 marks)
ACCT6003 Fundamental Analysis for Equity Investment Week 10 Assignment on Financial Ratio Analysis Marks: 6/100 Deadline for submission: Before the lecture of Week 11. In this assignment, you are required to analyse the profitability of Woolworths Group Ltd during 2012-2017, using the provided reformulated statements of Woolworths in the Excel spreadsheet that is available on Canvas. Required: 1. In the Excel worksheet named ‘Q1. Profitability’, you are required to use the provided template to perform profitability analysis for Woolworths during 2013-2017 using the reformulated statements, for the following ratio decompositions: • ROCE decomposition in operating, financing, and minority interest parts. • ROCE decomposition as RNOA, FLEV, Spread, MILEV and MISpread. • RNOA decomposition as ROOA, OLLEV and OLSpread. • RNOA decomposition asATO and OPM. • OPM decomposition as GPM and individual operating expense ratios. • ATO decomposition as inverse of individual operating turnover components. • Analysis of the operating cash-to-cash cycle. You may need to add more rows in some decompositions to complete the above analysis. You are required to perform checks and round the checks to the nearest fourth decimal point as indicated in the template example using the Excel formula ROUND(cell,4). You are also required to document any assumptions that you need to make in the ‘Notes’ area at the end of the worksheet. [2 marks] 2. In the worksheet named ‘Q2. Insights’ and in less than 300 words, discuss what you consider to be the two most important business insights from this profitability analysis. You are required to use ratio analysis to make the case why the insights are very important for Woolworths and then support your arguments using evidence from the annual reports to explain the movement in ratios and why these are important for Woolworths. [2 mark] 3. Consider that you are an analyst in 2017 who is responsible for issuing an investment recommendation for Woolworths at year-end 2017. You are using the Residual Operating Income (ReOI) valuation model, and you plan to project pro-forma statements for 2018-2022 for the finite forecasting horizon. You have access to these reformulated financial statements and the accompanying profitability analysis. In the worksheet named ‘Q3. Projection’ and in less than 300 words, explain how you could use this historical data to help you project informed pro-forma statements and apply the ReOI model. [2 mark]
SUSTAIN 2GS3 - MIND MAP ASSIGNMENT ofFinalGradeGrade BreakdownMind Map (75%); Reflection/Desc th2025Due DateMarch 27, 2025 @ 4:00pmEST
Portfolio for Safety-Directed Design of a Brake-By-Wire System for Car Coursework for 661985 - Safety Critical Systems The Portfolio explores the iterative design of a Brake-By-Wire (BBW) system for cars. There are two parts to this assignment. Part 1 is worth 40% of the assignment and Part 2 is worth 60% of the assignment. You will analyse this architecture using Fault Tree Analysis and Markov Models and you will be asked to reflect on results. The tasks involve logical analysis and a small component of programming. The proposed architecture for the system is given in Figure 1 below: Figure 1. The proposed architecture of the BBW system System Specification • The BBW features separate braking on each wheel. • All components of the system are powered by a common power supply (PS). • An electromechanical pedal (PL) receives the braking demand from the driver and sends this as message (PLm) to three pedal nodes PN1, PN2, and PN3. • From each pedal node PNX (where X:1…3) two replicas ofthe message PNXm are sent by the pedal node to busses B1 and B2. • Wheel nodes WN1 and WN3 each read the three messages PNXB1m from bus B1 and Wheel nodes WN2 and WN4 read the three messages PNXB2m from bus B2. • As long as one of the messages is received a wheel node can create the braking output applied to the corresponding wheel (WN1b ... WN4b). Failures Each component in this system has only one failure mode that shares the name of the component. For example: • The failure mode of component PS is PS • The failure mode of component B1 is B1 The failure mode of each component leads to omission of all outputs. For example: • If PS fails, you get O-p (Omission of p) • If PN1 fails, you get O-PN1m on both busses In the absence of component failures, all four wheels apply the braking output and the car brakes correctly. When components fail, the system may fail to brake on one or more wheels. The effects vary depending on the number of wheel failures. For example: • If one wheel fails to brake, or three wheels fail to brake, the car is likely to skid off its course. In this case, to correct the skidding failure, an electronic stability program could release the wheel that is diagonal to the wheel that fails to brake. The car then brakes slowly, and the stopping distance is increased. • If all wheels fail, then the car experiences catastrophic loss of braking. The assignment tasks follow in two parts: • Part 1: Safety Analysis and Iteration of Design. This part assesses the material taught by Prof. Papadopoulos in the first part of the course • Part 2: Reliability Analysis and Iteration of Design. This part assesses the material taught by Dr Aslansefat in the second part of the course. Part 1 - Safety Analysis and Iteration of Design Part 1 is worth 40% of the Portfolio mark. Based on the design given for the BBW in Figure 1 and its specification: 1. Draw, or alternatively specify clearly using a set of logical expressions, a fault tree for the event “Omission of braking output by WN1”, i.e. for the event O-WN1b (10 marks). 2. Calculate the minimal cut-sets of the fault tree (10 marks). 3. Identify components that are single point of failure (5 marks). 4. Based on the cut-sets, describe weaknesses and strengths ofthe system (5 marks). 5. Draw, or alternatively specify clearly using a set of logical expressions, a fault tree for the “Loss of braking in all three wheels W1, W2 and W3” that will cause skidding. Name the top event “OW123” (5 marks). 6. Calculate the minimal cut-sets for this tree (5 marks). Notes: • Explain your solutions in [1-6] above with a short paragraph of text to show your understanding. Avoid verbosity. Up to 30% of marks will be deducted for lack of explanation. • Fault trees should be constructed systematically by traversing the model of the system architecture and applying the algorithm taught in the course. Unsystematic, simplified, fault trees that somehow capture the failure logic correctly will be awarded less marks. If the calculation of cut-sets that follows from such simplified fault trees is trivial, it will be awarded less marks. • For clarity, in your fault trees, use the names of components, messages and component failure modes as displayed in Figure 1. Marks will be deducted if you use names that don’t correspond to the figure. • To avoid repetition of branches, expand the branch that is repeated only once and use references to the top event of this branch elsewhere. Marks will be deducted if you unnecessarily expand repeated branches. • You may use HiP-HOPS or any other tool available free on the internet to construct the fault tree or calculate cutsets. However, make sure that you answer the questions. Fault trees must be drawn as graphs using the guidelines given above. Calculations of cutsets must be explicit, contain all logical steps, and explained. Tools will not necessarily do these things for you. • Graphs could be produced in a fault tree analysis or drawing tool. However, hand-drawn images photographed and carefully embedded in a report are acceptable as long as they are clear, and any symbols or text are clearly readable. Part 2 -Dynamic Reliability Analysis of the BBW Part 2 is worth 60% of the Portfolio mark. Based on the design given for the BBW in Figure 1 and its specification, you will analyse the architecture using Markov Models. Calculation of reliability involves some coding. Note that the system description, failure modes, and behaviours in conditions of failure (e.g. Skidding) remain exactly as described earlier in the specification of the system. Further assumptions that underpin reliability analysis are as follows: • It is assumed that all components have two states Operational and Failed. • It is assumed that the system is completely healthy at the starting point. • The failure distribution of all components is exponential with a constant failure rate. Based on this design and the assumptions solve the following tasks: 7. Only consider the independent failure modes ofthe 4 Wheels in the BBW, and assume that the rest of the system is perfect. Each single wheel failure leads the BBW to hazardous states of asymmetrical braking. In each of the 4 cases, skidding prevention is applied by locking the diagonal wheel leading the system to a corresponding recovery state with reduced braking capacity. We assume that the skidding prevention mechanism is perfect, i.e. the probability of its failure is zero. We also assume that any further wheel failure from asymmetrical braking or recovery states will lead the BBW to a single terminally failed state. Draw a Markov model and explain the model construction procedure (10 marks). 8. Consider that in [7], all wheels have the same failure rate of 0.0001 failures per hour. Provide a Python code to calculate and visualise the reliability curve for 2000 hours (10 marks). 9. Only consider the failure modes of PL, PN1, PN2, PN3 and PS, assuming that the wheels are perfect. Draw a Markov model which shows how the system moves into a state of complete loss of braking and explain the model construction procedure (10 marks). 10. Consider that in [9], all failure modes have the same failure rate of 0.000623 failures per hour. Provide a Python code to calculate and visualise the reliability curve for 900 hours. (10 marks). 11. Consider only failure modes of B1 and B2, and assume that all other components are perfect. Also, assume that the busses are repairable with a failure rate of 0.0002 failures per hour, and a repair rate of 0.01 repairs per hour. Construct a Markov model to evaluate the Availability and MTBF of the bus subsystem of the two busses. Provide a Python code for steady-state availability and MTBF calculation (10 marks). 12. Consider only the failure modes of PN1, PN2 and PN3. Assume that all other components are perfect. Only focus on the reliability of pedal nodes, and explain how it can be improved using a reconfigurable Triple Modular Redundancy (TMR) architecture with one hot standby redundancy (see Figure 2). Apply the fixed failure rate of 0.000432 failures per hour to all components. Construct a Markov model to evaluate the reliability of the Pedal Node subsystem consisting of the three PN nodes with the new architecture. Provide a Python code for reliability calculation and visualise the reliability curve for 3850 hours (10 marks). Figure 2, Reconfigurable TMR with Hot Standby Spares Notes: • Explain your solutions in [7-12] above with a short paragraph of text to show your understanding. Avoid verbosity. Up to 30% of marks will be deducted for lack of explanation. • For computational problems [8, 10, 11 and 12], submit your Python code in separate files. These files should be named according to the question number (e.g., Question8.py, Question10.py, etc.). Please ZIP the files with the final report and submit it as a single-file submission. • Ensure your code is runnable. If your code cannot be executed due to errors, it will be examined manually, and marks will be awarded based on the effort and correctness of the approach.
STATS 726 STATISTICS Time Series SEMESTER TWO 2023 1. With the convention that B is the backshift operator, we define where b is a complex number and is its complex conjugate. We have b = reiη, where and i 2 = −1. Equivalently, we can write b = r (cos(η) + isin(η)). Elementary calculations lead to β(B) = 1 − 0.8B + 0.4B2 . Note that you do not need to prove that the expression of β(B) given above holds true. All processes that we consider in this question are defined for t ∈ Z, where Z is the set of integers. Let {Vt} ∼ WN(0, 1) and {Wt} ∼ WN(0, 4), with the property that Cov(Vs, Wt) = 0 for all s and t. We define {Xt} and {Yt} as follows: Xt = β(B)Vt , Yt = Xt + Wt . Answer the following questions. (a) Decide if the MA process {Xt} is invertible (or not). Justify your answer. [5 marks] (b) Let γX(h) be the autocovariance function of {Xt}. Show that [6 marks] (c) Let γY (h) be the autocovariance function of {Yt}. Similarly, γW (h) is the autocovari-ance function of {Wt}. Show that γY (h) = γX(h) + γW (h), for all h ≥ 0. Use this result and the result from part (b) in order to write down the numerical values of γY (h) for h ≥ 0. [8 marks] (d) For h ∈ {1, 2, 3, 4}, the partial autocorrelation function αY (h) of {Yt} can be computed by using the steps of the Durbin-Levinson Algorithm that are presented below. Note that, for h ∈ {0, 1, 2, 3}, vh = E, where denotes the best linear predictor of Yh+1 given Y1, . . . , Yh. Copy to your answer the steps of the algorithm and replace ? with the correct numerical values. Use the results from part (c). Show your working. For h = 1, For h = 2, For h = 3, For h = 4, [12 marks] [Total: 31 marks] 2. Consider again {Vt}, {Wt}, {Xt} and {Yt}, which have been defined in Question 1. Now we define the processes {Zt} and {St}, for t ∈ Z: β(B)Zt = Wt , St = Zt + Vt , where β(B) is the same as in Question 1. Answer the following questions. (a) Decide if the AR process {Zt} is causal (or not). Justify your answer. [3 marks] (b) Let ρZ(k) be the autocorrelation function of {Zt} at lag k. It is known that ρZ(k) = 0.8ρZ(k − 1) − 0.4ρZ(k − 2) for k ≥ 1. Write down the characteristic equation for the homogeneous equation given above. Then write down the general solution for the homogeneous equation. [7 marks] (c) Show that the following identity is true for all t ∈ Z: β(B)St = Yt . [5 marks] (d) By using the the autocovariance function of {Yt}, it is possible to find the following representation (for all t ∈ Z): Yt = θ(B)εt, where θ(B) = 1 − 0.19B + 0.07B2 and εt ∼ WN(0, 5.59). Use this result together with the result from part (c) in order to conclude that {St} is an ARMA(p, q) process. Find the values of p and q. [5 marks] Hint: In your answer you may use the fact that one of the roots of the polynomial 1 − 0.19z + 0.07z2 is , where i2 = −1. (e) Let ρS(k) be the autocorrelation function of {St} at lag k. Use the result that you have obtained in part (d) in order to write down the general homogeneous difference equation for ρS(k). Use this equation and the result from part (b) for writing a short comment about the differences and similarities between ρZ(k) and ρS(k). [7 marks] (f) In Figure 1 are displayed the autocorrelation function and the partial autocorrelation function for {Xt}, {Yt}, {Zt} and {St}, for lags 1, . . . , 5. For each panel (a), (b), (c), (d), identify the process whose autocorrelation and partial autocorrelation functions are represented in that panel. Justify your answer by using the results from Question 1 and from the previous parts of Question 2. [12 marks] [Total: 39 marks] Figure 1: The autocorrelation function and the partial autocorrelation function for {Xt}, {Yt}, {Zt} and {St}, for lags 1, . . . , 5. 3. Let n = 200. We have the observations x1, x2, . . . , xn of a zero-mean time series X1, X2, . . . , Xn. After applying the formulas from Chapter Introduction, the observa-tions x1, x2, . . . , xn gave the following values for the sample autocorrelation function: Answer the following questions. (a) Assume that the zero-mean time series X1, X2, . . . , Xn is actually an IID sequence. As n is large, this assumption leads to the conclusion that the sample autocorrelations (h), h > 0 are approximately IID N(, ). Replace with the correct numerical values. Justify your answer. Then use this result in order to find the bounds of the interval where approximately 95% of sample autocorrelations should fall. Compare the values of (1), (2) and (3) with the bounds that you have found. Based on these comparisons, write a short comment in which to discuss if we have evidence against the hypothesis that the observed time series is a realization of an IID process. [8 marks] (b) Assume that the zero-mean time series can be modeled as the AR(2) process Xt = φ1Xt−1 + φ2Xt−2 + εt , where {εt} ∼ IID N(0, σ2). Use the Yule-Walker equations in order to find the estimates and . Explain why it is not possible to find a numerical value for the estimate . [14 marks] Hint: The following result might be useful. Let a, b, c, d ∈ R such that ad − bc ≠ 0. We have the following identity: (c) In connection with the estimation problem from part (b), we know that (for n large), we have approximate Normality of the estimators: In the equation above, replace ? with the correct matrix. Compute the entries of the matrix; you may reuse expressions from part (b) where this is helpful. [8 marks] [Total: 30 marks]
MEDA 37028. Post-Production Supervisor Post-Production Manual: Track Allocation Chart Brief A track allocation is how the timeline should look at the Pix Lock stage and upon delivering to the Online & Audio Post. Generate a track allocation chart for your editor who is cutting a BFTV project so that they know what the Pix Lock version should end up looking like. This helps with consistency between editors. Deadline Due end of Week 9 March 14th, 2025 by 11:59pm - Submit as an Excel or PDF document onto Slate: (Assessments > Assignments > Track Allocation) - Save as: Last name_Track_Allocation Components - Depending on the project, list the visual components on the desired final video tracks. (see the track allocation sample) - Assign Primary Audio to 4 audio tracks - Assign Secondary Audio to 2 tracks - Include a Voice Over or ambient Track. - Allocate a minimum of 4 tracks for Music. - Allocate a minimum of 4 tracks for SFX. - Colour code, each element differently, on the tracks - Include a title at the top of the chart (e.g. name of the production) - Use font style/font / alignment that is legible Objectives Practice using Excel Think through project elements Pay close attention to details Evaluation: The assignment is worth 2% of your final grade: This assignment is due on the above date during your section. Late submissions will result in a penalty of 10% per day. If delivered after 7 calendar days (1 week late), it will result in a zero. All components must be completed individually.
48436 Assignment Introduction Your assignment is aimed at adding current interesting information to the material provided in class. You need to provide enough detail so that other students can replicate your work. This is a group work assignment. Three students are in a group. You can choose a topic from the attached topic list to work on. You need to submit your Assignment Proposal as an upload by the end of Week 6. You can still update the proposal after week 6 with the permission of your tutors. The Assignment Report is due in Week 11. You need to give a short presentation (15 mins) in the last week lab session. The whole assignment is worth 30% and marked out of 100 marks which are allocated as follows · The proposal takes 5 marks. · The report takes 75 marks, where o the general part is 30 marks o the detail part is 45 marks. · The presentation takes 20 marks. Note that although this is a group assessment, your contribution is assessed by your peers. See the Peer Participation document. You may not receive the same mark as your peers. Every group just needs to submit one set of documents, i.e., proposal, report and presentation slides. Please clearly state group members in every document. Marking Breakdown Proposal (5 marks): · The topic outline. · The group members and a schedule of their work from weeks 7 to 10. · Confirm with screenshots that you can obtain, install and run the major Apps and/or VMs you intend to use. · Some detail on what will be covered. Name any apps that you think important. · Detail marking. You are expected to develop and clarify your own details based on the given samples in the topic list. Report – General (30 marks): We do not have report template. You can use your favourite template and reference style. Expected report length for marking 15 - 25 pp. Add additional reference material as an appendix as required to add value for future use. (5 marks) Report Layout, such as colour front page, contents page which relates to assessment items, page numbers, use of formatting, tables, charts, screenshots and interesting images. (5 marks) How we ran the project. Issues encountered and overcome. (5 marks) Executive Summary that summarises the methods used and the main findings of your assignment. (What we Did and What we Found). (5 marks) General discussion about Forensics, Reflection and conclusion. (5 marks) Quality References used with summaries of their usefulness to Digital Forensics. (5 marks) Report Detail Currency: You are expected to explore the latest tools and technologies. Report Detail (45 marks): Choose only one of the options listed below. 1) Three other Browsers, e.g., Firefox, Ice Weasel and Safari, on other systems, e.g., MacOS. (10 marks) Describe with screenshots how to locate cookie and history data on the device for each browser. (20 marks) Describe how the browser handles tracking information and where you can find such evidence. (10 marks) Where are the cache files on these devices? Can you find anything of forensic interest in the cache files? (5 marks) What would you recommend as sound business practice to secure these Browsers? 2) Document or email Metadata. Office documents, PDFs and Camera files may contain useful forensic evidence. (10 marks) Explain how such documents contain metadata such as dates and authors and data structures such as embedded scripting. (20 marks) Describe popular tools to locate and recover metadata and scripts. Some tools use a scripting language such as python. Describe how to use these tools. (10 marks) Describe, with examples, how a malicious user embeds malware in a document and fools a target into opening the document so as to infect their PC. (5 marks) What would you recommend as sound business practice to secure document metadata? 3) Web Analytics. (10 marks) Explain how a company uses User tracking to improve their sales. (10 marks) Describe how Google Analytics works with screen shots. (20 marks) Describe how other current Web Analytics tools work. Demonstrate such a tool with screenshots. (5 marks) What would you recommend as sound business practice to manage web analytics of your site by competitors? 4) Windows and Linux Artifacts. (10 marks) Describe in some detail what you would look for in a full Windows and Linux Live Analysis (add to week 7/8). (20 marks) Describe such an analysis on target machines or VMs of your choice (not your laptop or UTS Workstation). Indicate the tools used and the reasons for choosing them. (10 marks) Describe a scripting tool that automates Live Analysis. What are its Pros and Cons? (5 marks) What would you recommend as sound business practice for the use of a Windows System to combat unauthorised forensics? 5) Social Media Security (10 marks) It is possible to exploit social media in a number of ways. Collecting data and impersonation are some such methods. Describe the common methods of collecting data. (15 marks) Give some examples of the operation of tools which can collect this data. (10 marks) Include samples of collected data that removes anonymity. (5 marks) What would you recommend as sound business practice for the use of social media. (5 marks) What would you recommend for enforcing company phone security? 6) Unique Group proposal (45 marks) As agreed with the Tutor. Presentation (20 marks): The presentation will be assessed from the following aspects · Time management · Presentation structure · Presentation clearness · Technical soundness · Audience engagement · Overall performance
Electrical Engineering & Computer Science EECS 281: Data Structures and Algorithms Midterm Exam Written Questions 1. Reverse a Linked List You are given a singly-linked list, where each Node is defined as follows: struct Node { int val; Node *next; Node() : val{0}, next{nullptr} {} Node(int x) : val{x}, next{nullptr} {} Node(int x, Node *next_in) : val{x}, next{next_in} {} }; Write a program that reverses this singly-linked list. Return the new head node after you’re done. Example: Given the head node of the following list 1->2->3->4->nullptr You would return the following list 4->3->2->1->nullptr Complexity: O(n) time and O(1) auxiliary space, where n is the length of the list. Implementation: Implement your solution in the space below. You may NOT use anything from the STL. Line limit: 15 lines of code. Node * reverse_list(Node *head) { 2. Remove Duplicates from Sorted Linked List You are given a sorted linked list, where each Node is defined as follows: struct Node { int val; Node *next; Node() : val{0}, next{nullptr} {} Node(int x) : val{x}, next{nullptr} {} Node(int x, Node *next_in) : val{x}, next{next_in} {} }; Write a function that deletes all duplicates in the list so that each element ends up only appearing once. Example: After passing the list 280->280->281->370->370 into the function, the final list should be 280->281->370. Complexity: O(n) time and O(1) auxiliary space, where n is the length of the list. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 15 lines of code. Node * remove_duplicates(Node *head) { 3. Previous Greater Element You are given a non-empty vector of distinct elements, and you want to return a vector that stores the previous greater element that exists before each index. If no previous greater element exists, -1 is stored. Example 1: Given vec = [11, 16, 15, 13], you would return [-1, -1, 16, 15]. Example 2: Given vec = [19, 18, 12, 14, 13], you would return [-1, 19, 18, 18, 14]. Complexity: O(n) time and O(n) auxiliary space, where n is the length of the vector. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 15 lines of code. vector prev_greatest_element(vector &vec) { 4. Merging Intervals You are given a collection of intervals. Write a function that merges all of the overlapping intervals. Example 1: Given vec = [[1, 3], [2, 6], [8, 10], [15, 18]], you would return [[1, 6], [8, 10], [15, 18]]. Example 2: Given vec = [[4, 5], [1, 4]], you would return [[1, 5]]. Complexity: O(n log(n)) time and O(n) auxiliary memory, where n is the length of the vector of intervals. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 20 lines of code. struct Interval { int start; int end; }; vector merge_intervals(vector &vec) { 5. List Addition You are given two non-empty linked lists representing two non-negative integers. The most signi cant digit comes first and each of their nodes contains a single digit. Add the two numbers and return the result as a linked list. You may assume the two numbers do not contain any leading 0's except the number 0 itself. The structure of a Node is provided below: struct Node { int val; Node *next; Node() : val{0}, next{nullptr} {} Node(int x) : val{x}, next{nullptr} {} Node(int x, Node *next_in) : val{x}, next{next_in} {} }; Example: Given the following two lists: 1->9->4->7->nullptr 9->3->9->nullptr you would return the list 2->8->8->6->nullptr. Complexity: O(n) time and O(n) auxiliary space, where n is the combined length of the lists. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 30 lines of code. Node * add_lists(Node *list1, Node *list2) { 6. Single Element in Sorted Array You are given a sorted array consisting of only integers where every element appears exactly twice, except for one element which appears exactly once. Write a function that returns the single element. Example: Given vec = [1, 1, 2, 3, 3, 4, 4], you would return 2. Complexity: O(log(n)) time and O(1) auxiliary space, where n is the length of the vector. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 15 lines of code. int find_single_element(vector &vec) { 7. Merging Lists You are given k sorted linked lists. Write a program that merges all k lists into a single sorted list. The structure of a Node is provided below: struct Node { int val; Node *next; Node() : val{0}, next{nullptr} {} Node(int x) : val{x}, next{nullptr} {} Node(int x, Node *next_in) : val{x}, next{next_in} {} }; Example: Given the following four lists: 1->5->7->nullptr 4->9->nullptr 3->6->8->10->nullptr 2->nullptr you would return the list 1->2->3->4->5->6->7->8->9->10->nullptr. Complexity: O(nk log(k)) time and O(n) auxiliary space, where n is the length of the longest list. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 25 lines of code. Node * merge_lists(vector &lists) { 8. Shifting Zeros You are given a vector of integers, vec, and you are told to implement a function that moves all elements with a value of 0 to the end of the vector while maintaining the relative order of the non-zero elements. Example: Given the initial vector [0, 1, 0, 4, 3], you should rearrange the contents ofthe vector so that the final ordering of elements is [1, 4, 3, 0, 0]. Complexity: O(n) time, O(1) auxiliary space, where n is the length of the vector. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 15 lines of code. void shift_zeros(vector &vec) { 9. Warmer Temperatures You are given a vector of integers, temps, that stores the daily temperature forecasts for the next few days. Write a program that, for each index of the input vector, stores the number of days you need to wait for a warmer temperature. If there is no future day where this is possible, a value of 0 should be stored. Example 1: Given the following vector: [55, 62, 46, 52, 51, 50, 51, 53, 63] you would return the vector [1, 7, 1, 4, 3, 1, 1, 1, 0] since you would need to wait 1 day on day 0 for a warmer temperature (55 → 62), 7 days on day 1 for a warmer temperature (62 → 63), and so on. Example 2: Given the following vector: [74, 74, 73, 75, 74, 73, 72, 71, 70] you would return the vector [3, 2, 1, 0, 0, 0, 0, 0, 0] Your program should run in O(n) time. You may use extra space to store your output, but the rest of your program must use O(1) auxiliary space. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 20 lines of code. vector warmer_temperatures(vector &temps) { 10. 2-D Matrix Search You are given a m × n matrix in the form of a vector of vectors that has the following properties: • integers in each row are sorted in ascending order from left to right • integers in each column are sorted in ascending order from top to bottom Write a function that searches for a value in this matrix and returns whether the element can be found. Example: Given the following matrix: [ [ 1, 4, 7, 11, 15], [ 2, 5, 8, 12, 19], [ 3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30] ] and a target value of 5, you would return true. Given a target value of 20, you would return false. Complexity: O(m + n) time, O(1) auxiliary space. Implementation: Implement your solution in the space below. You may use anything from the STL. Line limit: 20 lines of code. bool matrix_search(vector &matrix, int target) {
MEDA 37028. Post-Production Supervisor Post Production Manual Brief As post-production supervisor on a BFTV project you will be generating a manual containing documents that are useful throughout the production, post-production process and upon final delivery. Use the portfolio project or, if you are in 3rd year a production you have worked on in any capacity. Use that project to fill out these elements for the Post Manual (or Post Binder). Deadline - All documents can be submitted as a Word or Excel document onto Slate: Slate > Assessments > Assignments > Relevant Folder based on task Components — Editing Track allocations 2% Due: Week 9 March 14th 2025 by 11:59pm — Post-production schedule 5% Due: Week 10 March 21st 2025 by 11:59pm — Breakdown Edit structure 3% Due: Week 11 March 27th 2025 by 11:59pm Remaining components 10% Due: Week 13 April 11th 2025 by 11:59pm — Music Cue Sheet (w/ TC) 3% — Final Script. Transcript. (w/ TC) 3% — Supers / Titles / List (w/ TC) 2% — Final Credits list 2% Objectives Practice using Excel Think through project elements Pay close attention to details Follow instructions Manage the post team Deliver post-production components Evaluation: The assignment is worth 20% of your final grade: This assignment is due on the above date during your section. Late submissions will result in a penalty of 10% per day. If delivered after 7 calendar days (1 week late), it will result in a zero. All components must be completed individually.
BECO011 Economics for Business Tutorial Week 1: Law of Demand and Supply and Market Equilibrium BECO011 Week 1 Worksheet Tutorial A Activity 2 - 1 Quantity Demanded and 3 Demand Students will be divided into 5 groups (face to face class). Each group will consist of 3-4 students. Every group is assigned to one of the following items: § Sony Playstation 5 - Group 1 § Doyle’s Fish and Chips - Group 2 § Dyson Vacuum Cleaner - Group 3 § Fitness First Yoga Classes - Group 4 § All Sydney Tow Truck Services - Group 5 Task 1 (15 minutes) It was noticed that each of the above items had experienced an increase in sales. For each item above, identify the possible reasons for the increase in the quantity demanded/ demand. Each group should create a table below with the columns. Each group is given 15 minutes to discuss. Identify the factor(s) and complete your answers in the table below. § Sony Playstation 5 - Group 1 § Doyle’s Fish and Chips - Group 2 § Dyson Vacuum Cleaner - Group 3 § Fitness First Yoga Classes - Group 4 § All Sydney Tow Truck Services - Group 5 No Increase in quantity demanded of *the assigned item* is caused by a change in ___________ Increase in demand of * the assigned item* is caused by a change in ___________ Only one (1) factor needed Use your creativity to think about the three (3) possible factors. 1 2 3 4 5 Task 2 (15-minute sharing session) Upon returning to main session from your Breakout Rooms. Choose a representative from your group. Share your answers with other students by doing a 2-minute presentation to the whole class. For example, you could start off by explaining - Based on our discussion, we found that The increase in quantity demanded in Sony Playstation 5 is due to *your answer*, on the other hand, the increase in the demand for Sony Playstation could be due to three factors - (1) rise in the income of the consumers (assume Sony Playstation 5 is a normal good). As average income of rises, more people will demand for Sony Playstation 5. (2) (3) (4) (5) Please also provide a simple explanation to go with the factors chosen. Activity 3 Changes in Quantity Supplied and Supply Task 1 (10 minutes) Using the groups formed in Activity 1. Discuss and answer the questions amongst the group members. You have 10 minutes. GrainCorp is one of the leading barley farming and processing companies in Australia, GrainCorp operates across multiple Australian states, including New South Wales and Queensland, and is a significant exporter of barley to international markets, particularly in Asia. (i) Besides the price of barley itself, identify and briefly explain three (3) other factors that may have influenced or determined the supply of barley. (ii) Given the other factors, will the supply of barley curve shift or will it be a movement along the supply curve? Why? Task 2 (10-minute sharing session) Choose a representative from your group. Share your answers with other students by doing a 2-minute presentation to the whole class.
CSSE3100/7100 Reasoning about Programs Week 10 Exercises Exercise 10.1. A unique number allocator is required to allocate unique thread ids in an operating system. The specification of a class for the allocator is given below. (Note that the notation x !in s means x is not a member of set s, and s + t is the union of sets s and t.) class UniqueNumberAllocator { ghost var used: set ghost predicate Valid( ) reads this constructor ( ) ensures Valid( ) && used == {} method Allocate( ) returns (n: nat) requires Valid( ) modifies this ensures Valid( ) && n !in old(used) && used == old(used) + {n} method Reset( ) requires Valid( ) modifies this ensures Valid( ) && used == {} } Implement the class using a single variable, next, which holds the next number to allocate. next should initially be 0 and increment on each call to Allocate. Hint: Use a quantifier to express the abstraction relation. Exercise 10.2. The classes CoffeeMaker1.dfy and CoffeeMaker2.dfy developed in last week's lectures are on the Learning Resources page of Blackboard (under Week 9). Add ChangeGrinder and InstallCustomGrinder methods to CoffeeMaker2 based on those in CoffeeMaker1, but updated to reflect the fact that Grinder is a composite object. Challenge: Specify and implement a method for CoffeeMaker1 that removes and returns the grinder of a coffee maker, replacing it with a new one that the method allocates. Make sure your specification allows the following test harness to be verified: method RemoveGrinderHarness( ) { var cm := new CoffeeMaker( ); var grinder := cm.RemoveGrinder( ); cm.Restock( ); grinder.AddBeans( ); } Exercise 10.3. A bounded queue is a sequence of up to N elements (N > 0) where users can insert elements one at a time, and then remove them one at a time in the same order that they were inserted. For example, if the user inserted the element A, then B, then C, they would first remove A, then B, and so on. One way to implement a bounded queue is with a circular array. A circular array consists of an array and two pointers, wr and rd, to array indicies. Elements are inserted (i.e., written) at array index, wr, and removed (i.e., read) at array index, rd. That is, wr denotes the first empty space in the array (if any), and rd denotes the first full space (if any). Below are two examples of this implementation at some time during its execution. Note that when wr reaches the end of the array, another insertion will make it wrap back to the start. Therefore, wr can be less than rd as in the second example. When wr == rd the queue is either empty or full. An additional Boolean variable empty is used to denote whether it is empty or full. Initially, wr and rd are both 0 and empty is true. (a) Provide the abstract and concrete state variables for the above design of a bounded queue. (b) Provide the class invariant as a ghost predicate Valid(). (c) Provide specifications and implementations for the constructor and the methods Insert, which inserts an element into the bounded queue, and Remove, which removes an element from the bounded queue.
STATS 726 Time Series (Exam) SEMESTER TWO, 2022 1. Let Z be the set of integers, which means that Z = {. . . , −2, −1, 0, 1, 2, . . .}. Consider the following process: Xt = φ2Xt−2 + εt , where t ∈ Z, 0 < φ2 < 1 and {εt} is Gaussian white noise. More precisely, we have {εt} ∼ IID N(0, 1). It is known that E(Xt) = 0 for all t ∈ Z, and the autocovariance function γ(k) of {Xt} has the following expression for k ≥ 0: Use the results provided above in order to answer the following question. For h ∈ {0, 1, 2, 3}, the best linear predictor of Xh+1 given X1, . . . , Xh has the expression where φh 1, . . . , φh h are computed by using the steps of the Durbin-Levinson Algorithm that are presented below. Remark that = 0. Additionally, vh = E for h ∈ {0, 1, 2, 3}. Copy to your answer the steps of the algorithm and replace ? with the correct quantities. Each quantity can be either an expression that involves φ2 or a numerical value. For h = 1, For h = 2, For h = 3, [Total: 15 marks] 2. Consider again the process defined in Question 1: Xt = φ2Xt−2 + εt , where t ∈ Z, 0 < φ2 < 1 and {εt} ∼ IID N(0, 1). Answer the following questions. (a) With the notation from Question 1, we consider the following innovations: Use these identities together with the expressions of that you have obtained in Question 1 in order to find the entries of the matrix C, which is defined in the equation below. Copy to your answer the matrix C and replace ? with the correct quantities. Each quantity can be either an expression that involves φ2 or a numerical value. Justify your answer. [12 marks] (b) Let With the notation from part (a), we have: where I is the identity matrix. With the convention that Θ = C − I, we get Use the result obtained in part (a) in order to find θt t−j for t ∈ {1, 2, 3} and j ∈ {0, . . . , t − 1}. Copy to your answer the matrix Θ and replace θt t−j for t ∈ {1, 2, 3} and j ∈ {0, . . . , t − 1} with the correct quantities. Each quantity can be either an expression that involves φ2 or a numerical value. Do not replace the symbols *. Justify your answer. [3 marks] (c) An alternative solution for finding θt t−j for t ∈ {1, 2, 3} and j ∈ {0, . . . , t − 1} is to apply the Innovations Algorithm. Copy to your answer the steps of the algorithm that are presented below and replace ? with the correct quantities. Each quantity can be either an expression that involves θ or a numerical value. For t = 1, For t = 2, For t = 3, [15 marks] (d) Confirm that the values of θt t−j for t ∈ {1, 2, 3} and j ∈ {0, . . . , t − 1} are the same as those obtained in part (b). [2 marks] (e) Confirm that the values of Xe2 1 , Xe3 2 , Xe4 3 are the same as those obtained in Question 1. [2 marks] [Total: 34 marks] 3. Let {Xt} and {Yt} be two invertible MA(1) processes which are defined as follows: Xt = Zt + αZt−1, α = 0.9, {Zt} ∼ WN(0, 1), (1) Yt = Vt + βVt−1, β = 0.5, {Vt} ∼ WN(0, 1). (2) We assume that Cov(Zs, Vt) = 0 for all s and t. Furthermore, we define {St}: St = Xt + Yt for all t. It is known that E(St) = 0 for all t, and the autocovariance function γ+S(k) of {St} has the following expression for k ≥ 0: Straightforward numerical calculations lead to Use the results provided above in order to answer the following questions. (a) It follows from the autocovariance function of {St} that we have the following repre-sentation: St = εt + θεt−1, for all t, (3) where θ ∈ R and εt ∼ WN(0, ). For all lags k, let ρS(k) be the autocorrelation function of {St}, which is computed by employing (3). Use the identity to find the value of θ such that the process in (3) is invertible. Then find the value of . [7 marks] (b) For all t, we define the processes {Ft}, {Gt} and {Ht} as follows: Ft = −αFt−1 + Vt , Gt = −βGt−1 + Zt , Ht = Ft + Gt . Note that α is the same as in (1), {Vt} is the same as in (2), β is the same as in (2) and {Zt} is the same as in (1). With the convention that B denotes the backshift operator, calculate (1 + αB)(1 + βB)Ht . Express the result by using {∈t} (see part (a)). [7 marks] (c) Use the result in part (b) in order to demonstrate that {Ht} is an ARMA(p, q) process. Find the values of p and q. [3 marks] (d) Let ρH(k) be the autocorrelation function of {Ht} at lag k. Use the result in part (c), to find the values of µ1 and µ2 in the following equation: ρH(k) = µ1ρH(k − 1) + µ2ρH(k − 2) for k ≥ 2. Justify your answer. [4 marks] (e) Write down the characteristic equation for the homogeneous equation given in part (d) and then write down the general solution for the homogeneous equation given in part (d). [4 marks] [Total: 25 marks] 4. Annie found the following question in a textbook: “Let n = 100. Suppose that x1, . . . , xn are observations of a time series {Xt} that can be modeled as the causal AR(2) process Xt = φ1Xt−1 + φ2Xt−2 + εt , where {εt} ∼ IID N(0, σ2). For h ∈ {0, 1, 2}, the sample autocovariances are computed under the assumption that the mean of {Xt} is known to be zero by applying the formula and the following values are obtained: Use these values to find the estimates of φ1, φ2 and σ2.” Answer the following questions. (a) Annie wants to obtain the Least Squares (LS) estimates for φ = [φ1 φ2] > by using the linear regression model y = Xφ + ∈, where the entries of the vector ∈ are IID N(0, σ2). To this end, she considers three different selections for the pair (yy, X). For each pair (yy, X), the answer should be expressed as follows: In your answer, replace ? with the correct quantities, for each pair (yy, X). Do not compute explicitly the inverse of the matrix that appears in the answer. The pairs (yy, X) considered by Annie are: i Linear regression for the original time series ii Linear regression for the time series padded with zeros after the last observation iii Linear regression for the time series padded with zeros before the first observation and after the last observation [20 marks] (b) As Annie knows only the values of (0), (1) and (2), and she does not know the values of the observations x1, . . . , xn, she can use only one of the three linear regression models that are listed in part (a). Decide which is the model that Annie can use. Justify your answer. [3 marks] (c) After doing all the calculations, Annie obtains = 1.32 and = −0.634. Use these values in order to find . [3 marks] [Total: 26 marks]
Module: BENV0151 Energy and Environmental Systems Fundamentals Sustainable Built Environments, Energy and Resources BSc/MEng SECTION A: CORE ASSESSMENT DETAILS Coursework Title: Energy and Environmental Systems Challenges Weighting: 100% of your marks for this module Enquiries: [email protected]. Please ensure you include your name, Student ID, and the Module Code in any email Coursework Issued: 23/01/2025 Expected Workload: 30 hours Deadline: 11:00am, 25/04/2025 Word Limit: 3000 Page Limit: N/A SECTION B: COURSEWORK INFORMATION Coursework Brief: For this coursework, you are requested to solve 5 problems that involve applying the developed knowledge into practice, focusing on the balance between energy demand and generation in (building) systems [Module Learning Objective #3]. The problems are set at different scales, ranging from simple architectural and service elements to whole buildings, so you will have to identify the corresponding challenges to meet specific energy and environmental performances [Module Learning Objective #2]. For each problem, you will be asked to include a brief discussion section, where you will have the opportunity to express your understanding of the interaction at play in each problem between the building/element, the “human factor”, and the context [Module Learning Objective #1]. For each of the problems listed, please develop your response using the following seven-step problem-solving approach. Each “step” should be a corresponding sub-heading of your response to all the 5 problems to solve. The use of calculators or spreadsheets is allowed for this coursework. Step 1: Problem Statement In your own words, briefly state the problem, the key information given, and the quantities to be found. This is to make sure that you understand the problem and the objectives before you attempt to solve the problem. Step 2: Schematic Draw a sketch of the physical system involved and list the relevant information on the figure. The sketch does not have to be something elaborate, but it should resemble the actual system and show the key features (you can either use a graphic editor to generate it, or sketch it by hand, scan it, and copy-paste it into the document). Indicate any energy and mass interactions with the surroundings. Listing the given information on the sketch helps one to see the entire problem at once. Step 3: Assumptions and Approximations State any appropriate assumptions and approximations made to simplify the problem to make it possible to obtain a solution. Justify the questionable assumptions. Assume reasonable values for missing quantities that are necessary. Step 4: Physical Laws Apply all the relevant basic physical laws and principles and reduce them to their simplest form by utilizing the assumptions made. Step 5: Properties Determine the unknown properties necessary to solve the problem from property relations or tables. List the properties separately, and indicate their source (i.e., references in a bibliography section), if applicable. Step 6: Calculations Substitute the known quantities into the simplified relations and perform. the calculations to determine the unknowns. Pay particular attention to the units and unit cancellations and remember that a dimensional quantity without a unit is meaningless. Also, don’t give a false implication of high precision by copying all the digits from the calculator—round the results to an appropriate number of significant digits. Step 7: Reasoning, Verification, and Discussion Check to make sure that the results obtained are reasonable and intuitive and verify the validity of the assumptions. This is your chance discuss your understanding of the interaction at play in the given problem between the building/element, the “human factor”, and the context. This section may include references to literature, which you can report in the Bibliography. The coursework should include a general Bibliography section at the end of the document (Harvard style. for references is required for cited literature), covering all sources used in the compilation of this coursework (e.g., tables for values/coefficients, scientific papers mentioned in the different discussion sections of each problem, etc.). ***PROBLEMS TO BE SOLVED*** Problem #1 A warehouse in London has a floor area of 200 m2 and an average height of 5 m. The mechanical ventilation system guarantees a ventilation rate of 0.36 ACH. Determine the heat transfer rate associated with ventilation, knowing that there is a 10-degree Celsius difference between the temperatures inside and outside of the warehouse. Assuming that the ventilation system is in operation for 10 hours a day, and that the heat loss needs to be compensated for by means of an electric heater, determine its weekly cost if the electricity price in that area is £0.061/kWh. Discuss: • What kind of activities and occupancy level would be acceptable for the given ventilation rate? Why? • What are the sustainability implications of compensating heat losses via the proposed approach? Problem #2 Consider a 3-m-high, 6-m-wide, and 0.3-m-thick wall made of exposed bricks. On a certain day, the temperatures of the inner and the outer surfaces of the wall are measured to be 16°C and 2°C, respectively. Determine the rate of heat loss through the wall on that day. After that, assume you apply on the bricks wall a 10-cm-thick layer of rock wool insulation and a 2-cm-thick layer of plaster: these two materials have a thermal conductivity of λ = 0.05 and λ = 0.4, respectively. Determine the U-value (air-to-air) for this newly built multi-layer wall and the new rate of heat loss through the wall under the same temperature conditions. Discuss: • After applying the new materials, is the performance of the wall under consideration adequate for a residential building in England? Why? • How is sustainability related to adequate insulation in buildings? How does insulation impact energy consumption in buildings? Problem #3 A fixed aluminium-framed window with glass glazing is being considered for an opening that is 1.2 m high and 1.8 m wide in the wall of a house that is maintained at 22°C. Determine the rate of heat loss through the window when the outdoor air temperature is 10°C, if the window is selected to be: (a) 3-mm single glazing, or (b) double glazing with an airspace of 12 mm. Assuming now that outdoor there is a wind speed of 3 m/s, and the consequent convective heat transfer rate is 160 W, determine the surface temperature of the external glazing, knowing that the outdoor temperature of (undisturbed) air is still 10°C. Discuss: • How are the two glazing scenarios different in terms of performance? • How do such different glazing options impact sustainability, by considering energy efficiency and occupants’ comfort? • What are the implications for thermal bridges if a material other than aluminium was selected for the window frame? The dimensions of a concrete wall of a building located in Rome (Italy) are 5*4 m. It has a surface temperature of 24°C. Calculate the radiative heat transfer from the wall to the outdoor environment in a typical day of January. Furthermore, knowing that the building is a rectangular prism with four such walls with a U-value of 2.0 W/m²·K, that the building has a square floor plan of 25 m2, and floor and roof have U-values of 1.0 and 0.7 W/m²·K respectively, then calculate an approximation of the buiIding’s heat transfer coefficient. Discuss: • How would the radiative heat transfer value change if a typical day in April was taken as a reference, instead of January? • For radiative heat transfer, discuss the implications of using materials other than concrete in world regions with different climates include a city of your choice (e.g., your hometown, or a city you would like to visit) as an example. Problem #5 A UCL cafeteria (V = 400 m3) that normally hosts 35 students from the SBEER Programme during their breaks is to be air-conditioned with window air-conditioning units of 5 kW cooling capacity each. A student at rest may be assumed to dissipate heat at a rate of 360 kJ/h. The lighting system in the room consists of 20 lightbulbs, each providing a radiative heat transfer of 100 W. The rate of heat transfer to the classroom through the walls and the windows on a summer day is estimated to be 15,000 kJ/h. If the room air is to be maintained at a constant temperature of 21°C, determine the minimum number of window air-conditioning units required. Discuss: • Assuming the classroom had extra seats capacity, how would the increasing number of students affect the need for additional air-conditioning units? • What is the impact on sustainability of the need for additional air-conditioning units, under different configurations of energy supply from the grid? • Based on the content you have been taught in the lighting session, consider how different types of bulbs may achieve similar brightness in lumens. • Considering that an average reverberation time of 0.5 s has been measured in the cafeteria, discuss what residual acoustical capacity the space may still have and how this could be increased.
MA 575 – Fall 2022. Midterm Exam Some useful formulas • The Gaussian distribution If X ∼ N(µ, σ2), we have E(X) = µ, Var(X) = σ2. • If X = (X1, . . . , Xp)′ ∼ Np(µ, Σ), and A ∈ R k×p , for some k ≥ 1, then AX ∼ N(Aµ, AΣA′). • In a simple linear regression model yi = β0 + β1xi + ϵi , 1 ≤ i ≤ n, where the errors are independent, and have mean zero and variance σ2, the estimates of β0, β1 and σ2 are given respectively by where ˆyi = ˆβ0 + ˆβ1xi , and where as usual denote the true values of the parameters, we have Furthermore the R2 of the model is Problem 1: Consider the multiple linear regression model y = Xβ + ϵ, where ϵ is modeled as having the distribution N(0, σ2 In). Suppose that we fit the model to a dataset and obtain the following summary in R. Call: lm(formula = y ˜ X1 + X2 + X3 + X4, data = dataset) Residuals: Min 1Q Median 3Q Max -90.531 -20.855 -1.746 15.979 66.571 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1045.9715 52.8698 19.784 < 2e-16 *** X1 4.4626 10.5465 0.423 0.674 X2 1.6379 2.3872 0.686 0.496 X3 -3.6242 3.2154 -1.127 0.266 X4 -2.9045 0.2313 -12.559 2.61e-16 *** --- Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 Residual standard error: 32.7 on 52 degrees of freedom Multiple R-squared: 0.8246,Adjusted R-squared: 0.809 F-statistic: 52.88 on 4 and 52 DF, p-value: < 2.2e-16 (a) (2pts) What does the column ’Estimate’ represent? How is it computed? (b) (2pts) What does the column ’Std. Error’ represent? How is it computed? (c) (2pts) What does the column ’t value’ represent? How is it computed? (d) (2pts) What does the column P r(|t| >) represent? How is it computed? (e) (2pts) What does the F-statistic represent? How is it computed? Problem 2: Consider a simple linear regression model yi = β0 +β1xi +ϵi , for i = 1, . . . , n, where the error terms ϵi’s are assumed independent and identically distributed with distribution N(0, σ2 ). Let ˆβ0, ˆβ1 denote the least squares estimators of β0 and β1 respectively, and let σˆ 2 be the usual linear model estimator of σ2. See formulas on page 1. Answer TRUE or FALSE, and explain your choice if asked. (a) (2pts) The fitted regression line x 7→ ˆβ0 + ˆβ1x always goes through the point (¯x, ¯y). Explain. (b) (2pts) The estimators (ˆβ0, ˆβ1) and ˆσ2 are always independent. (c) (2pts) The vector of residuals of the model is always orthogonal to the vector of fitted values. Explain. (d) (2pts) The T distribution with ν degree of freedom is obtained by dividing a standard normal random variable by the square root of a random variable that follows a chi-square distribution with ν degree of freedom. (e) (2pts) The R2 of the model equals to one means that the linear model is the best possible regression model for the data. Problem 3: Consider the simple linear regression model yi = βxi + ϵi , 1 ≤ i ≤ n, where the error terms ϵi’s are assumed iid with distribution N(0, σ2). The true values of β, σ2 are denoted respectively β⋆, and σ⋆2. (a) (3pts) Suppose that we combine all the n observations together to write the model in a matrix form. as y = Xβ + ϵ, where y = (y1, . . . , yn)′. What is X, β and ϵ? Deduce the expression of the least squares estimate ˆβ of β. (b) (2pts) Find an estimator for σ2. (b) (5pts) The residual sum of squares of the model can be written as as Use this to show that
ACCT 2301 Northeastern University Summer 1 2025 Due Weds June 11, 2025 11:59 PM ET on Turnitin in Canvas Rory Gilmore is the CEO of Stars Hollow Inc., which distributes consumer healthcare products including nutrition supplements, OTC pharmaceuticals, and personal care products to various market segments. Rory has worked for Stars Hollow from the beginning and is proud of the company’s growth and success. She has worked diligently on developing supply chain channels and fostering relationships with her various market segments. However, as Stars Hollow has grown, Rory has come to realize that she doesn’t understand the profitability of the company in the detail that she desires. Without this understanding, Rory believes that she is not well equipped to try to improve profitability and strategize for the future. Rory has always been an outgoing person (she takes after her mother Lorelai), and she has tried to focus on customer service. As a result, she really enjoys working with the independent stores. She feels that this is a market segment that is often overlooked by the bigger consumer health care distributors. However, Rory is not sure if this market segment is the most lucrative. Rory has reached out to you for your help. You both took managerial accounting together, but Rory did not focus on the material as well as you did. She is hoping that you can advise her on her business. You think that this is a great opportunity for you to put your managerial accounting skills to work in an advisory role. Knowing the power of managerial accounting data, you have asked Rory to put together some sales and cost data by market segment. You also specifically asked Rory to talk with her employees to get a handle on what activities are driving costs. She explained to you that a customer places an order for one or more various product lines. A product line is a single product like Pantene Pro V Shampoo. Each product line is delivered in one or more separate boxes depending on the size of the purchase order. Stars Hollow employees deliver the boxes and put the product on the customer shelves. Each delivery includes one or more boxes of product to the customer. Rory is really proud of serving the customers and so she does not charge the customer for stocking the shelves but luckily not all the customers take advantage of this service. Rory has provided you the data you requested in Tables 1 - 3. Rory is anxious to meet with you to get your insight. In preparation for the meeting with Rory, you should prepare cogent answers to the following questions, draw relevant insights and provide any supporting exhibits and/or graphs that you believe will illuminate your analysis. You should use Excel for your analyses. In your advisory role, you need to prepare for your meeting with Rory by providing a professional analysis. REQUIRED QUESTIONS 1. Rory has been assessing the profitability of each market segment using gross margin percentage. Compute the gross margin percentage for each of the market segments. 10 points 2. Rory wants to try to allocate operating costs to each market segment but she is not confident in her managerial accounting skills. She really wants to keep it simple so she has asked you to consider allocating operating costs using cost of goods sold as the driver. Calculate the allocation rate. Allocate the operating costs using cost of goods sold as the allocation base and compute the operating income of each market segment. 20 points 3. Use the activity-based costing information to calculate the allocation rates. Allocate the operating costs to each of the market segments using activity-based costing and compute the operating income of each market segment. 25 points 4. Based on all of the data you were provided and your analyses, what insights have you gained on the profitability of each market segment? Based on your analyses in the above questions, provide recommendations to Rory to help improve the profitability of Stars Hollow. Be specific and note the benefits, costs and potential risks to the recommendations that you are proposing. 35 points DELIVERABLES You should provide a written report that addresses each of the above questions to Rory Gilmore. Think about your audience and purpose for this report. Your report should be professional and include both a written analysis and tables in one file. This report should be uploaded to Turnitin on Canvas by 11:59 PM ET on Weds June 11, 2025. I want you to upload one file that I will grade. It will make it easier for me to grade one file. Therefore, you can embed your tables into a word doc or pdf making sure that it looks professional. Note that your tables should be clear with titles, labels… You should also upload your excel file with all of your supporting work if I need to refer to it. The excel file should also be uploaded to Turnitin in Canvas by 11:59 PM ET on Weds June 11, 2025. QUALITY OF WORK 10 Points Your report will be graded based on the thoughtfulness, thoroughness and depth of your analysis. Careless and superficial work will be penalized. You must follow the directions and provide the deliverables as outlined above with a professional report that includes clear tables/visuals.
ICS 33 Spring 2025 Exercise Set 8 Due date and time: Friday, June 6, 11:59pm Final late work deadline: Late submissions are not accepted Getting started First of all, be sure that you've read the Reinforcement Exercises page, which explains everything you'll need to know, generally, about how the reinforcement exercises will work this quarter. Make sure you read that page before you continue with this one. Problem 1 (3 points) Earlier this quarter, we saw that Python provides a built-in decorator @classmethod, which specifies that a method in a class shouldn't be subject to the usual rules that it be called on an object of that class and that this target object be passed into a leading self parameter. Instead, the class is passed into a leading cls parameter. When we first learned about this technique, it was somewhat magical; we had no way to explain how it might work, because we lacked the understanding of the details that underlie it. However, we're not in that position anymore, so it's worth revisiting that idea to make sure we understand how it relates to things we've learned in the weeks since. What better way to understand how it works than to implement it using the techniques we've since learned? Write a decorator named @class_method that, when used on a function defined within a class (i.e., a def statement nested immediately within a class statement), converts it into a class method, meaning two things. The method can be called on the class as a whole, rather than on an object of that class. Whether called on the class as a whole or an object of that class, its first parameter will be the class, rather than an object of that class. In other words, rather than having a self parameter, it has a cls parameter. When you've finished with it, you'd expect it to work as follows. >>> class Thing: ... @class_method ... def foo(cls, x, y): ... return (cls.__name__, x + y) ... >>> Thing.foo(11, 7) ('Thing', 18) >>> Thing().foo(11, 7) ('Thing', 18) It's safe to assume that your @class_method decorator will only be used on methods (i.e., on def statements immediately nested within class statements). It is irrelevant how it works when it's used anywhere else. Limitations The Python standard library is entirely off-limits in this problem. Your function must not require any module to be imported. Built-in decorators, such as @classmethod or @staticmethod, are also off-limits, since that's what we're asking you to implement here. What to submit Submit one Python script. named problem1.py, which contains your decorator and nothing else. Neither docstrings, comments, nor type annotations are required, since we've all agreed already on what problems we're solving here. There is no credit being offered for writing automated tests — though you certainly might want to, since that's a great way to ensure that your code works as you expect — and we'd prefer you not submit them even if you do. Problem 2 (2 points) During our conversation about Class Design, we learned about three dunder methods that allow a class to modify how attribute lookup rules are applied to its objects: __getattr__, __setattr__, and __delattr__. One difference that emerged between them is the circumstances in which they're used; we could summarize that difference as follows. __getattr__ is called only if looking up an attribute in an object's dictionary fails (i.e., if that attribute is not present). __setattr__ and __delattr__ are called regardless of whether the attribute is present in the object's dictionary. In no more than a couple of sentences, briefly explain why you think Python handles __getattr__ differently from __setattr__ and __delattr__, rather than handling all of these dunder methods identically. What to submit Submit one PDF named problem2.pdf, which contains your answer to this question. Problem 3 (3 points) Write a class named LimitedString meeting the following requirements. Constructing a LimitedString requires one positional argument that specifies a maximum length. This maximum length must be a non-negative integer; anything else should cause a ValueError to be raised. A LimitedString object is a descriptor that can be used to enforce that an object attribute's value is a string, and that its length is no longer than the maximum length. If an optional keyword argument can_delete is passed when constructing a LimitedString, it controls whether an attribute described by it can be deleted from an object — True if it can, or False if it cannot. (If can_delete is False, deleting the attribute causes an AttributeError to be raised.) After you're finished, you would expect the following behavior. from it. >>> class Thing: ... name = LimitedString(10) ...
CS CM121/221 Final Problem 1 Pseudoalignment [30 points] Consider the two following isoforms: t1 = AGGAT A t2 = AT GAT A t3 = T T GAT A In this problem, assume we are only generating data from the forward strand, so you don’t need to consider the reverse strand. Why? Because I am nice, dammit. (a) Draw a transcript. de Bruijn graph with k = 3. You can pick colors if you’d like, otherwise, annotate the equivalence classes with labels 1, 2, or 3. (b) Assume reads are of length 4 and a read can start at any position (given sufficient length, of course). What are the possible equivalence classes for possible reads from (a)? Further, generate a table with the equivalence class label, and the number of occurrences from possible reads of length 4. (c) Does your answer in part (b) qualitatively change if the reads are of length 5? Please explain. (d) Draw the transcript. de Bruijn graph with k = 4 and generate a table like you in did (b) for this graph. (e) Do you think using a larger k = 4 helps disambiguate reads of length 4 in this case? Problem 2 Expectation-Maximization Algorithm [30 points] Let there be two isoforms, tA and tB with known sequences sampled by RNA-seq and unknown abundances θA and θB. Isoform. tA has effective length l and isoform. tB has effective length 2l. And now, the problem: (a) Consider three reads, (r1, r2, r3). r1 is compatible with both tA and tB. r2 is compatible only with tA and r3 is compatible with only tB. Using the standard RSEM algorithm described in class, derive one iteration of the EM algorithm updates assuming you start with abundance θA = θB = 1/2. (b) Implement the EM algorithm with the following input specification: 1. a compatibility matrix with each row being a read, and each column being an isoform. 2. effective lengths of the isoforms 3. a starting proportion for each transcript. 4. an integer for number of iterations Output: relative abundances (θ). (c) Run the EM with the configuration from (a) for 100 iterations where l = 10. (d) Run the EM with the configuration from (a) for 100 iterations, but with effective lengths equal to each other (both are 10). (e) Interpret the results from (c) and (d). Problem 3 Non-linear dimension reduction [50 points] There is some data on BruinLearn in final/tsne.tsv you need to load for this problem. You don’t need to know the generating process for the data, but in case it is helpful, here it is. Rows 1 to 100 correspond to the first ‘cluster’ and rows 101 to 200 correspond the second ‘cluster’. The data is generated by: xi ∼ Normal2(µk(i) , I2), where k(i) = 1 for i = {1, 2, . . . , 100} and k(i) = 2 for i = {101, 101, . . . , 200}. µ1 = (0, 0) and µ2 = (10, 10). You are going to implement some components of t-SNE to get some intuition about how different components of the algorithm work. Please add a screenshot of your code, or a notebook printout anytime you are asked for an implementation. Finally, everything you need to know is in the non-linear dimension reduction slides. (a) (Page 33) Implement the pj|i matrix. Do yourself a favor and make it a function because you’re going to use it quite a bit. You can make your function take a single shared = σ 2 . Sanity check: each row should sum to 1. Side note: if you decide to do the extra credit (see (k)), you should allow your algorithm to utilize different otherwise you’re gonna have a bad time. For completeness, the equation, (b) (Page 33) Implement the pij matrix. Sanity check: the entire matrix should sum to 1. Again, the equation, where N is the number of samples (200 in this case). (c) Using σ2 = 1, plot the entire dataset and color the points based on their probability relative to the first data point. To be rigorous: p1j is the vector of probabilities of “j picking 1 as its neighbor”. A reasonable color scale might be: wj ∝ p1j/maxk(p1k). Your plot should show a change of color away from the first data point. Do the same for σ 2 = {0.1, 10, 100}. Each plot might look something like this: (d) (Page 35) Implement the qij matrix. Sanity check: the entire matrix should sum to 1. The equation: (e) Using yi = xi (the original data is projected using the identity), plot the entire dataset and color the points based on their q1j probability relative to the first data point. How is it different than the p1j plot from (c) when = 1? (f) (Page 25) Implement the KL-divergence. Note, the contribution of {ij} is zero when pij = 0. Please use log-sum-exp and logs where appropriate. (g) Using the real data as the low-dimensional projection, compute the KL-divergence when: i. σ2 = 0.1. ii. σ2 = 1. iii. σ2 = 100. Any thoughts on what might be happening? (h) Summarize your thoughts on how these hyper-parameters matter. (i) Extra credit (3 points): Using σ2 = 1, can you find a projection that reduces the KL-divergence? Note, there are plenty linear or non-linear ones. The easiest might be to do might be ‘move’ one cluster. Plot the projection and report the KL-divergence. (j) Extra credit (5 points): implement the Perplexity and recompute the KL-divergence from the previous projections you made using the you get for Perplexity {5, 25, 50, 100}. To implement the Perplexity, find the value of that approximately satisfies the equa-tion Perplexity(Pi) = 2H(Pi) where Pi is the i-th row in the pj|i matrix and H(Pi) is the Shannon entropy. Plot a histogram of your values and how did your results change?
