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110389 Advanced Taxation

SECTION A

All amounts are expressed in New Zealand currency. All taxpayers are New Zealand tax residents and where relevant, the taxpayers have a standard balance date of 31 March. All scenarios are hypothetical and are set up for the purpose of this examination.

Use the following scenario for Questions 1, 2, 3, 4 and 5.

Gwyn Paltrow works as a beauty consultant for Zoop Ltd and receives an annual salary of $75,000 p.a. She is currently in a long-term relationship with Chris Marty, and they have plans to get married in the near future. Gwyn owns 70% of Zoop Ltd and the other 30% is owned by the Marty Family Trust. The trustees of the Marty Family Trust are Chris, his brother Steven and their solicitor Kevin, and the benefi ciaries are Chris and his three children from a previous marriage. The Marty Family Trust has not distributed any benefi ciary income for more than four years, including the current year.

Zoop Ltd owns a Rimu writing table which cost $1000 and could be sold to the public for $1,500. However, instead of selling it, the company decided to gift the table to Gwyn’s sister. Zoop Ltd also recently provided an interest-free loan of $200,000 to the Marty Family Trust.

During a trip to Amsterdam to attend a beauty makeup course, Gwyn visited a diamond factory and became captivated by the diamonds. Consequently, she invested in some diamonds and upon her return to New Zealand, her close friend Pascoe Hunt who is a jeweller, expressed interest in buying the diamonds from her. Gwyn has now decided to sell the diamonds to Pascoe. As they met at a café to discuss their respective businesses, Pascoe also suggested that Gwyn consider using a look-through company for her beauty business.

[TOTAL FOR SECTION A: 20 MARKS]

Question 1

Advise Zoop Ltd whether there are any FBT or dividend implications for gifting the table to Gwyn’s sister. (4 marks)

Question 2

Briefl y explain to Zoop Ltd the fringe benefi t tax implications of the interest-free loan to the Marty Family Trust. (4 marks)

Question 3

Advise Gwyn on the income tax implications when she sells the diamonds to Pascoe. (4 marks)

Question 4

Advise Gwyn on whether Zoop Ltd qualifi es for election as a look through company based on the counted owner test. You are required to show how you work out the number of look through counted owners. (4 marks)

Question 5

Briefl y explain whether electing to become a look-through company is advantageous for Gwyn and the Trust from a tax perspective. Provide 2 reasons to support your explanations. (4 marks)

SECTION B

All amounts are expressed in New Zealand currency. All taxpayers are New Zealand tax residents and where relevant, the taxpayers have a standard balance date of 31 March. All scenarios are hypothetical and are set up for the purpose of this examination.

Use the following scenario for Questions 6, 7, 8 and 9.

Jordan, Jasmine, Jack and Jamie, who are best friends, have reached out to you for guidance on the income tax implications related to the sale of their individual properties.

a) Jordan’s father has been involved in the land development business since 2001. In May 2015, Jordan himself acquired a residential rental property and is currently contemplating selling it in November 2023.

b) Given the thriving property market in the past few years and Jordan’s endorsement of real estate as a sound investment, Jasmin, took out a bank loan to help finance his purchase of a residential property that cost $1.8 million and a commercial property that cost $2.5 million. Both properties were in Taranaki and purchased on 1 April 2022. Both properties are currently rented out. Jasmine has provided you with the following details:

Residential Property

– it is a residential rental property that generates an annual rental income of $46,400.

– the mortgage interest amounts to $54,000 per annum and other tax-deductible expenses total $10,000 per annum.

Commercial Property

– it generates an annual rental income of $100,800.

– the mortgage interest is $90,000 per annum and other tax-deductible expenses amount to $19,000 per annum.

c) Jack purchased a residential property for $950,000 on 14 February 2020 when the sale and purchase agreement was signed. The title of the property was transferred to Jack’s name on 10 March 2020. Initially, Jack rented out the property but later decided to sell it. The sale and purchase agreement was signed on 15 November 2022. The title of the house was registered in the buyer’s name on 15 January 2023.

d) In March 2019, Jamie bought a three-storey house constructed in 1995. Jamie resides on the third fl oor while the other 2 floors are rented out. However, Jamie intends to migrate to Australia and plans to sell her three-storey house in November 2023.

[TOTAL FOR SECTION B: 20 MARKS]

Question 6

Jordan wants to know the income tax implications of selling his residential property in 2023. Briefl y explain to him the income tax consequences under sections CB 6, CB 10 and CB 6A/CZ 39. (6 marks)

Question 7

Jasmin wants to determine taxable income from her two properties. You are required to show her all the calculations for the net rental income or loss for each of her rental properties and the resulting taxable income for her in 2022-23. (6 marks)

Question 8

Jack wants to know whether the bright-line rule applies to the sale of his residential property. You are required to briefl y explain to him whether he is subject to the bright line rule, showing all the relevant dates. (5 marks)

Question 9

Briefl y explain to Jamie whether the sale of her three-storey house will be exempted under the bright line rule. (3 marks)

SECTION C

Use the following scenario for Questions 10, 11, 12 and 13.

Mona and Lisa are partners in a limited partnership that commenced its business operations on 1 April 2022, focusing on selling cleaning products. In this limited partnership, Mona is a limited partner and is entitled to 70% of the partnership’s net income. On the other hand, Lisa serves as a general partner and her share is 30% of the net income.

At the beginning of the partnership, Mona contributed $40,000 in capital. However, during the 2022-23 income year, Mona made an additional capital contribution of $20,000. For the year ended 31 March 2023, the limited partnership’s income amounted to $50,000 with allowable deductions totalling $150,000.

Mona has other investments including some investments in a multi-rate portfolio investment entity (MRP). In 2022-23, Mona’s return from her PIE investment is $10,000. Mona has also invested in a widely held superannuation scheme (which is not a PIE). Mona’s marginal tax rate is 39%.

Lisa’s brother Leonardo is the sole owner of Davinci Ltd, a company that provides engineering services exclusively to one particular organisation only. Davinci Ltd does not have substantial business assets. Leonardo, being the sole employee, carries out these services through Davinci Ltd. The income and expenses of Davinci Ltd in 2022-23 are as follows:

[TOTAL FOR SECTION C: 20 MARKS]

Question 10

Briefl y explain the maximum amount of loss that Mona can offset against her other income in the 2022-23 income year (show all calculations). (5 Marks)

Question 11

Claiming losses against Mona’s other income means that it will lower her tax liability. Briefl y explain whether structuring the business as a limited partnership and utilising the losses against her other income would be viewed as a form. of tax avoidance. (4 marks)

Question 12

Provide a brief explanation to Mona on the following:

how the $10,000 return from her investment in the MRP is treated for income tax purposes

what are the two advantages of investing in MRP

the income tax implications when she receives a lump sum payment from the superannuation scheme on her retirement. (6 marks)

Question 13

i. Briefl y explain to Leonardo whether he will be subject to the personal services attribution rule in relation to the business conducted by Davinci Ltd.

ii. Assuming that Leonardo is subject to the personal services attribution rule, calculate the amount of income derived by Davinci Ltd that will be attributed to Leonardo in 2022-23 under the personal services attribution rule. (5 marks)

SECTION D

All amounts are expressed in New Zealand currency. Where relevant, the taxpayers have a standard balance date of 31 March. All scenarios are hypothetical and are set up for the purpose of this examination.

[TOTAL FOR SECTION D: 20 MARKS]

Question 14

Briefl y explain the rationale behind the implementation of the CFC rules in New Zealand. (3 marks)

Question 15

Garfi eld, a New Zealand resident, owns 41% of the shares in Piazza Ltd, a foreign company located in Pizza Island. The four other shareholders, who are not associated with Garfi eld or with each other, are not New Zealand tax residents and they each hold 14.75% of the shares. Piazza Ltd has derived $600,000 active income and $1,500 passive income. In the following year, Piazza Ltd distributed dividends to its shareholders.

Briefl y explain whether

Piazza Ltd is a CFC under the New Zealand Income Tax Act. (3 marks)

any income will be attributed to Garfi eld under the CFC rules. (3 marks)

Garfi eld will be required to pay tax in New Zealand on the dividend received. (2 marks)

(8 marks)

Question 16

On 5 April 2021, Wilson Ltd, a New Zealand resident company bought 15,000 shares in Jon Ltd for $5 per share. Wilson Ltd has held these shares and made no sales. Jon Ltd is an incorporated listed company in Bermuda and is not a NZ resident company.

Briefl y discuss whether Wilson Ltd is liable to pay any Foreign Investment Fund (FIF) income in the tax years 2021-22 and 2022-23. Wilson Ltd holds less than 10% interest in Jon Ltd. No calculations are required. (4 marks)

Question 17

On 5 April 2022, Stan Lee, a New Zealand tax resident individual, bought 15,000 shares in Jon Ltd at $5 each and has not sold any of these shares. On 30 September 2022, Stan bought another 10,000 shares in Jon Ltd at $4 each. The closing market value of the shares on 31 March 2023 is $105,000. He holds less than 10% of the interest in Jon Ltd.

Briefl y explain whether Stan is liable to pay any FIF income in 2022- 23? Show your calculations. (5 marks)

SECTION E

All amounts are expressed in New Zealand currency. Where relevant, the taxpayers have a standard balance date of 31 March. All scenarios are hypothetical and are set up for the purpose of this examination.

[TOTAL FOR SECTION E: 20 MARKS]

Question 18

a. Identify and explain two strategies employed by multinational corporations to circumvent tax payments via foreign enterprises. (4 marks)

b. Briefl y explain the measures implemented by the New Zealand government to counteract such strategies. (4 marks)

(8 marks)

Question 19

Goody Ltd, a profi table NZ resident company intends to expand its operations by purchasing 100% shares of Badee Ltd, a manufacturing company incorporated in the United States. The projected profi t of Badee Ltd for the 2022-23 income year is $5 million.

a. Briefl y explain whether the profi ts of Badee Ltd will be taxable in New Zealand.

b. If Goody Ltd establishes a branch in the United States, briefl y explain whether the profi ts generated by the US branch of Goody Ltd will be subject to tax in New Zealand. (5 marks)

Question 20

Verrie Wealthy who is a NZ resident, has invested $200,000 in a foreign bank term deposit, and $100,000 in Australian-listed shares. In 2022-23, Verrie Wealthy derived the following returns from his investments: interest of $10,000 gross (foreign tax paid $1,000), dividends of $7,300 gross (foreign tax paid $1,100) and also earned a salary of $60,000.

Calculate the amount of foreign tax credit that Verrie can claim in New Zealand in 2022-23. You are required to show all calculations. (7 marks)

Problem Set 4, PL Trees

Due: July 1, 2025

1. Use PL trees to answer the following questions.

(a) Is the following argument valid? If not, read a counterexample off the tree. (2)

((A Λ ¬B) → C), A : ¬ (A → (B Λ C))

⃝ Valid.

⃝ Not Valid.

(b) Are the following propositions equivalent? If not, read a counterexample off the tree. (3)

((A Λ ¬B) → C), (¬ (A → B) → C)

⃝ Equivalent.

⃝ Not equivalent.

World History, Part 2

Syllabus

Course Description

This course focuses on the origins, battles, and results of World War I and World War Il. Students will study the rise of totalitarian states and the political environment in which they emerged. In addition, this course includes an in-depth study of the modern global situation, and the independence many former colonies now enjoy. Finally, students will examine the economical state of countries throughout the world and discuss why some have thrived and others have suffered.

Course Learning Outcomes

By the end of this course, you should be able to do the following:

1. Analyze and explain imperialism and revolutions in nations around the world-leading up to the Great War, or Word War I.

2. Investigate causes, impacts, and events in World War I and explain the occurrence of total war.

3. Examine economic and governmental theories and approaches and analyze how they led to the Great Depression.

4. Discuss the causes and events that led to World War Il, how these events diminished colonization around the world, and the various theaters of WWII.

5. Analyze the process of many nations in Africa and Asia becoming independent and relate those events and World War Il to the lead-upl to and unfolding of the Cold War.

6. Explain the relationship of nations as the Cold War dragged on, and discuss nations in terms of contemporary challenges, including nationalism and terrorism.

Marketing

Syllabus

Course Description

Students who complete this course will understand the key principles and practical application of marketing found in the workplace setting. Students will analyze the seven core functions of marketing and practice the creative problem-solving process in project-based skill assignments. The course will provide opportunities to understand and apply the following marketing concepts:

the seven core functions of marketing

the 4 P’s of the marketing mix

the marketing environment

marketing Terminology

target marketing

marketing information management

pricing decisions

pricing strategy

product service management

product life cycle

promotion

advertising media

the channel of distribution

the selling process.

Course Outcomes

As students complete the course assignments, they will increase their knowledge, improve 21st-century skills, and develop an attribute.

Knowledge: Business Marketing

In this course, knowledge refers to the subject matter and content students will learn while completing the readings, practices. quizzes, and assignments.

On successful completion of this course, students will be able to do the following:

1. Define marketing and the marketing terminology.

2. Identify and describe the purpose of the seven core functions of marketing.

3. Apply knowledge in hands-on marketing projects.

21st-Century Skill: Creativity—Creative Production and Innovation

As students complete this course’s assignments, they will gain skills in Creativity and Innovation. This skill is part of Creativity.

Attribute: Resilience

Attributes This course focuses on developing the attribute of Resilience in Marketing.

MSIN0041 – Individual Coursework 1

General instructions: Please submit your work in a PDF file to the designated submission dropbox on Moodle by 1 pm, 26 October 2022.

Problem 1. Conjoint Analysis

(5 marks) What are the steps in designing a conjoint study? Explain the first step in the context of a specific company or industry that could implement conjoint designs to improve product designs or pricing decisions.

Problem 2. Market Simulator

Download the conjoint.R script posted to the Moodle page and start by running the first three sections of code. That is, load the bayesm package and its camera data, load the custom functions, and estimate the conjoint model using rhierMnlRwMixture() from bayesm. If bayesm is not installed on your device, run install.packages(“bayesm”) to install the required package. The script. defines a custom function mktsharesim()that sim- ulates the market shares of products in a given scenario using estimation results from a conjoint model. Read the function’s documentation to understand what the function does.

From its marketing research, Canon learns that young people enjoy taking selfies and there is an increasing trend of making video blogs. To appeal to this potential customer base, Canon comes up with a camera that is selfie-friendly and has good picture and video quality. Specifically, the camera has a sensor with 16 megapixels (high), 6× zoom (low), 1080p video (high), has swivel screen, and no Wi-Fi. Assume the marginal cost is 0.5 ($50).

Through additional marketing research, Canon learns that there are mainly four compet- ing products in the market. The three other cameras are produced by Sony, Nikon, and Panasonic respectively. These cameras are very similar: they all have low specs (ie low megapiexels, low zoom level, low video quality, no swivel screen, and no Wi-Fi) and are priced at 2 ($200).

You are now tasked to find the optimal price for the product.

a. (2 marks) Use the seq() function to create a sequence of prices (called price) from 0.5 to 5 ($50–$500) with an interval of 0.1 ($10). Print the first ten values of the price sequence. Show your R code.

b. (10 marks) Now simulate Canon’s profit for each candidate price in the price sequence you generated in (a). To do this, create a vector called profit with its length equal to the length of the price sequence. There are multiple ways to do so. For example, you could just create a copy of the price sequence and assign it to profit, or you could create a vector of zeros with double() or rep().

Consult the following pseudocodes to calculate profit for each candidate price:

for i in 1:length(price) do

create a matrix X representing the choice set

# Use defaults for function arguments with default values.

# Remember to correctly index the output from mktsharesim()

# for you simulation.

use mktsharesim() to simulate market shares with

Canon’s price set to price[i]

Compute the profit in the current choice scenario

and save it to profit[i]

end for

Make sure to show your R code. Include set.seed(1012) at the top of your code for replication of your results.

c. (5 marks) Plot profits against the price range. Draw a vertical line at the optimal price. Show your R code and display the figure below. Both the x- and y-axes should be labelled. What is the profit maximizing price?

d. (3 marks) Canon is thinking about adding the Wi-Fi feature to the device so that users can transfer photos to phones for Instagram posts. Assume including this new fea- ture raises the marginal cost to 0.55 ($55), what is the optimal price and profit for this new product? Would you recommend that Cannon further include the Wi-Fi feature to the camera? Make sure to show you R code. Include set.seed(1026) at the top of code for replication of your results.

Problem 3. Multinomial Logit Model

In this problem, you will be guided to derive an important empirical prediction by the stan- dard multinomial logit model on consumers’ substitution pattern.

Assume every customer faces the choice set where Xk is product k’s specifica-tions and pk is its price. The standard multinomial logit model assumes that every customer shares the same preference parameter vector β over the product specifications and price parameter θ for the price. According to the model, the market share of sj in the choice set is

a. (3 marks) What is the cross elasticity of demand for product j with respect to pk for some n ≠ j in the choice set, ie ? Your result should be expressed with respect to θ, pn, and Sk. Remember to show your steps. (Hint: you may find this fact useful: )

b. (4 marks) Suppose there are three different cereal products in the choice set: X1, X2, and X3 . Among these products, X1 is an adult cereal product, and X2 and X3 are two kid cereal products. The two kid cereal products are similar in ingredients, nutrition, and tastes, and often considered good substitutes for each other.

Assume you have estimated a standard logit model for cereal products. Based on the estimated model parameters, you deduced that = 0.5. Using this information and your finding in the previous part, if p2 rises by 1%, ie the price of the first kid cereal product rises by 1%, how much do you expect S3, the demand for the other kid cereal product, to change in percentage? Explain your answer. (Hint: in the hint for the previous part, are the required parameters in your answer about product j?)

c. (3 marks) Do you find your answer about the substitution pattern between the cereal

products in the previous part empirically or intuitively realistic? Why or why not?

Comparing a Flywheel vs Supercapacitor Power Buffer System to Enable Deployment of Fast EV Chargers in Weak Grids

Area: Electrical, Power conversion, Energy storage

Subarea: Power Electronics

Nature: Modelling – Simulation

Distinctive skills to be gained: Understand the principle of power electronics, energy conversion and energy storage how to model the losses and determine conversion efficiencies

Background: Electrical energy can be transported and converted with high efficiency into other type of energy (such as mechanical in case of vehicles) but its storage is still a problem. The most known electrochemical storage device is the battery, but this has disadvantages such as a limited lifetime/number of charging/discharging cycles and a long charging and discharging time (hours) at a very limited current which is obviously not suited for EVs on road.

Fast charging is a technique developed for such cases but handling short time (minutes) / large currents/powers (100+A/100kW) is very demanding both for the existing power grid which may not be designed to handle significantly higher powers. Using an intermediary energy/power store embedded with the EV charger may offer the solution to reduce the grid power peak and provide fastest recharge of EV battery but supercapacitors (electrochemical storage) or flywheels (mechanical storage) need to be used.

Developing an efficient power converter able to perform the AC/DC conversion (in the grid side converter that needs to control active power whilst maintaining grid side current sinusoidal and balanced, may only have unidirectional power flow unless it may be required to also support local grid during grid faults) and DC/DC conversion (convert constant DC to variable DC voltage as seen across the battery or supercap stack or to interface with a variety of vehicles having different battery voltage and power ratings, that needs to control the power flow into the supercap stack) power conversion and its associated control to implement the required power and energy management (limit the recharge power of supercap between EV charges from grid and implement power sharing grid/storage sys during fast charging) . The other option is to design a flywheel and a high performance AC machine (permanent magnet of induction type) electric drive to interface the main DC bus of the EV charger to the fast mechanical flywheel storage system. The following directions of research are relevant to above topic and may be explored in more detail:

a. Investigate the particularities of implementing a large supercapacitor stack vs implementing the flywheel storage in terms of physical size and the required power electronic/electrical drive interface

b. Investigate and evaluate the potential advantages offered by wide-band gap switching devices over conventional silicon-based semiconductor devices

c. Investigate the advantages offered by a modular converter design

d. Investigate the possible advantages offered by smart prioritization of multiple vehicle charging depending on power available, urgency/need of certain vehicles/price premium

e. Investigate a large installation such as a parking lot that is equipped with renewable energy, and the possibility of having energy stored on parked vehicles for longer durations to support other needs (airport, grid etc.)

Project Aims: This project will investigate the implementation of the simulation models for power loss evaluation and control for a multi -stage AC/DC and DC/DC power converter with embedded supercapacitor or battery energy storage.

Project Objectives (a shorter selection will be agreed with supervisor after the literature review stage is completed and the exact direction of research decided) :

1) Understand requirements for EV fast charging (derive V/I/P/energy ratings and times)

2) Review latest developments in the field of energy storage devices (batteries and supercaps) relative to the specification of fast charging

3) Review power converter topologies able to implement the fast charging functionality (DC/DC and A/DC DC/AC)

4) Implement simulation models for AC/DC rectifiers and DC/DC converter using the example models provided in PSIM or PLECS and build an EV charger model for the system (AC/DC + DC/DC) and also of the electric drive (AC motor + AC/DC inverter) . This study can be augmented by implementing design of magnetic components (interface inductors) and estimation of semiconductor losses (thermal model) which can then be used if exploring (a) or (b)

5) Investigate smart management techniques relevant to multicar simultaneous charging (c) or large car park with renewable generation (d)

P1: Navmesh Pathfinding
Introduction
In this programming assignment you will need to implement in Python a bidirectional A* search algorithm to solve the problem of finding paths in navmeshes created from user-provided images. The program to build the navmeshes from images as well as a template code containing the prototype of the function you have to implement are provided. The input parameter is a navmesh and the output is an image showing the path from a source and destination. Both the source and the destination are defined interactively through a given python program. The next section shows an example on how to define the source and destination points as well as how to visualize the output of your algorithm.
Example (Assuming you are in the /src folder)
In order to test your pathfinder you need to execute the following command (assuming you are in the /src folder):

$ python nm_interactive.py ../input/homer.png ../input/homer.png.mesh.pickle 2

Where the parameters represent an image file to display (must be a PNG), a binary file containing the navmesh representation of the given image (.mesh.pickle) and a subsampling factor. The subsampling factor is an integer used to scale down large images for display on small screens. When you run this code you should see a new window showing the image you gave as parameter. You can interact with this window using your cursor. If you click on any region of the image, it should appear a red circle. This first circle represents the source point. You can click on the image once again in order to define the destination point. Figure 1 shows what you should see after each of these steps.

Figure 1: Screenshots of the execution of nm_interactive.py. Before the first click, after the first click and after the second click, respectively

After the second click, nm_interactive.py calls the find_path function that is defined in the nm_pathfinder.py file. Since this function is not yet implemented, nm_interactive.py can’t calculate the path and hence can’t show it. Your job is to implement an A* bidirectional algorithm inside this function. When you finish your implementation, you should see the following image after the second click:

Base Code Overview
The provided base code is composed by input data (/input) and three python files (src/), which are described as follows:
– src/nm_interactive.py
This is the main program of this project and it is the one you have to run to test your solution. It takes three command line arguments: an image file to display (must be a PNG), the filename of a pickled mesh data structure (.mesh.pickle), and a subsampling factor. The subsampling factor is an integer used to scale down large images for display on small screens.
– src/nm_meshbuilder.py
This program can build navmeshes for user-provided images. This is the program that produces the ‘.mesh.pickle’ files used by nm_interactive.py. “Pickle” is the name for Python’s serialized binary data format. See the OPTIONAL steps at the end of this document for how to make your own maps.
– src/nm_pathfinder.py
This file contain only one function called “find_path”, which is the one you have to implement. The parameters and the return values are described in comments inside the function. Note that this function is being called in nm_interactive.py, so to test your solution you just have to execute nm_interactive.py as described in Section “Example”.
-input/homer.png.mesh.pickle
This is a binary data file created by nm_meshbuilder.py. Once unpickled (this is done for you in nm_interactive.py), this file yields a dict. The mesh dict has two keys: ‘boxes’ and ‘adj’: the former is a list of non-overlapping white rectangular regions in homer.png. Think of these as the nodes in a graph. Boxes are defined by their bounds: (x1, x2, y1, y2). From your perspective, (x1,y1) is the top left corner and (x2,y2) is the bottom right. ‘adj’ is a dict the maps boxes to lists of boxes. Think of these as the edges in a graph. Although there is a geometric relationship between boxes, a distance value is not given in the mesh (because we don’t know which point on the border of a box you’ll be using to enter or leave). It may be the case that a box has no neighbors. However, for the example homer map, every box has at least one neighbor in ‘adj’.

Suggested Workflow
Identify the source and destination boxes.
●Scan through the list of boxes to find which contains the source point. Do this as well for the destination point. Instead of returning a list indicating that you haven’t visited any boxes, return a list of these two boxes.

Implement the simplest complete search algorithm you can.
●Starting with the source box, run breadth-first search looking for a sequence of boxes that reaches the destination box. If no such path can be found, make sure your program can report this correctly (such as by printing out “No path!” in the console). To earn the point, the “No path!” message needs to only show when there really isn’t a path. Complete search algorithms buy us the ability to report this confidently. You can also use this to evaluate your A* outputs!

Modify your simple search to compute a legal list of line segments demonstrating the path.
●Instead of doing your search purely at the box level, add an extra table (dict) to keep track of the precise x,y position within that box that your path with traverse. In the solution code, we call this table ‘detail_points’, a dictionary the maps boxes to (x,y) pairs. This diagram illustrates why midpoints of boxes will not work for this assignment:

●When considering a move from one box to another, copy the x,y position within the current box and the constrain it (with mins and maxes) to the bounds of the destination box.

Note: In the coordinate system of this problem set, the origin is the top left corner, while x and y grow towards the bottom right corner.

●Use the Euclidean distances between these two points as the length of the edge in the graph you are exploring (not the distance between the midpoints of the two boxes).
●When the search terminates (assuming it found a path), construct a list of line segments to return by looking up the detail points for each box along the path. In this assignment, the order of the line segments is not important. What matters is that the line is legal by visual inspection of the visualization it produces.

Modify the supplied Dijkstra’s implementation into an A* implementation.
●We have supplied an implementation of Dijkstra’s forward search as a starting point together with a maze environment and an example maze for testing it.
●Find the part of the code that puts new cells/boxes into the priority queue.
●Instead of using the new distance (distance to u plus length of edge u–v) as the priority for insertion, augment this with (add to it) an estimate of the distance remaining. If you already produced a helper function to measure the Euclidean distance between two detail points, you can use this function to measure the distance between the new detail point and the final destination point.
●When you are dequeuing boxes from the priority queue, remember that their priority value is not a distance. You’ll have to recover the true distance to the just-dequeued box by looking it up in your distance table.
●To make sure A* is implemented correctly, try to find a path along a straight vertical or horizontal hallway. The A* algorithm should mostly visit boxes between the two points. Dijkstra’s however, will also explore in the opposite direction of the destination point up to the radius at which it found the destination. In the example Homer map, there is a nice vertical hallway just outside of the circular chamber at the top-right.

Modify your A* into a bidirectional A*.
●Make a copy of the code you have working now for reference.
●Where you had tables recording distances and previous pointers (‘dist’ and ‘prev’), make copies for each direction of the search (‘forward_prev’ and ‘backward_prev’). Don’t, however, duplicate the queue.
●Find the part of your code where you put the source box into the priority queue.
●Instead of just enqueuing the source box, also enqueue the destination box (which will be used to start the backwards part of the bidirectional search). In order to distinguish the two portions of the search space, instead of just enqueuing boxes, you should also indicate which goal you are seeking.
●Example:
○heappush( (0, source_box, ‘destination’) )
○priority, curr_box, curr_goal = heappop(queue)
●Modify the rest of your queue operations to use this extra representation that keeps track of the goal. Use the goal to decide which set of ‘dist’ and ‘prev’ tables to check and update.
●If you are implementing bidirectional A*, change which point you are using as an estimate based on the stated goal you dequeued. This strategy is called front-to-back bidirectional A*. (Front-to-front bidirectional A* measures the distance to the closest point on the opposite frontier — it’s more complex than you need here.)
●Instead of terminating the search when you dequeue the destination box, stop EVEN EARLIER when the just-dequeued node is known in the table of previous pointers for the other search direction. In other words, stop when either direction of search encounters territory already seen by the other direction.
●Adjust your final path reconstruction logic to build segments from both parts of the path your algorithm discovered.
Requirements
●Implement a function to compute a path from a source to destination point in a navmesh using A* bidirectional algorithm.
●Test your implementation in a new navmesh created from an image provided by you.
Grading Criteria
●Are the mesh boxes containing the source and destination points identified? So long as these both show up in the set of visited boxes that your algorithm returns, you are good. Beyond this, whether the set of visualized boxes represents boxes you have actually dequeued or the larger set of boxes you have enqueued is up to you.

●Does the program behave properly in the following cases:
-When there is no path, report it via message in the console
-When the path is degenerate, draw a line between the start and the destination
-When the path is between only two adjacent cells (of the navmesh)
-When the source and destination cells are separated by one additional cell

●Where there is a path, is it found and drawn in a legal manner? Legal means forming a single connected polyline from the source to destination point that never veers outside of the bounds of mesh box contained within the set of visited boxes.

●Is the A* algorithm implemented correctly?

●Is a bidirectional search algorithm (or better) implemented correctly?
Submission Instructions
Submit via Canvas a zip file named in the form of “Lastname-Firstname-P1.zip” containing:
●The nm_pathfinder.py file implementing the function find_path.
●An image file named test_image.png containing a new image you tested your solution with
●A mesh representation of that image named test_image.mesh.pickle

Also, put your name and your partner’s name in the Comment field of the submission form

Creating a Custom Map
Here’s how to create your own test map:

STEP 1: Find some image that you think will be easy to turn into a black-and-white occupancy map. Save it as a PNG file. nm_interactive can only display PNG files.

ucsc_banana_slug-orig.png

STEP 2: In your favorite photo editor, create a black-and-white version (e.g. by desaturating and then applying brightness and contrast operators). Save this in a lossless format like PNG.

ucsc_banana_slug.png

STEP 3: Run the navmesh builder program. You must have SciPy (http://www.scipy.org/) installed for this program to work.

$ python nm_meshbuilder.py ucsc_banana_slug.png
Built a mesh with 711 boxes.

This will produce two files. The first is the mesh as a pickled Python data structure: ucsc_banana_slug.png.mesh.pickle. The second is a visualization of the rectangular polygons extracted by the navmesh builder:

STEP 4: Run your pathfinding program giving the original PNG file, the pickled mesh data, and some subsampling factor. A factor of 1 displays the image at original size, while a factor of 4 will scale the image down by a factor of four in each dimension for display (pathfinding will still be done at the full resolution).

$ python nm_interactive.py ucsc_banana_slug-orig.png ucsc_banana_slug.png.mesh.pickle 1

ELEC9714 Assignment 1, t2 2025 page 1

ELEC9714

Electricity Industry Planning + Economics

School of Electrical Engineering and Telecommunications

University of NSW

Assignment 1

This assignment will be distributed to you in week 3 via the course Moodle. It is due on Sunday

midnight of week 5 (just before the start of flexibility week). The assignment must be submitted via

Moodle as a single pdf file. Aim to make your assignment look like a professional consultancy report

and paste in Excel plots and calculation tables. The assignment must be submitted individually and

must be your own work. The UNSW policy on student plagiarism can be found on the

www.unsw.edu.au website. Note also the information on plagiarism detailed in the elec9714 Course

Outline which is available on the course Moodle. Note that UNSW uses automated plagiarism

software. Because of this, all text and tables need to be ‘searchable’ within the pdf – ie. not pasted in

as graphics. Again, the only acceptable pasted graphics are the plots, not any tables and not any of

your discussion. If the marker spots text graphics your assignment will not be marked. You are also

required to upload your Excel Spreadsheet or similar working file. This will not be marked but may be

checked if there are concerns about assignment similarities across two or more students. Be sure to

include the standard EE&T assignment coversheet.

The assignment will be marked out of 100, with an overall marks breakdown for each part. For each

part, 25% of the marks is for explaining how you undertook the analysis, 50% of the mark is for your

answers, and 25% of the mark for your discussion of the findings. If you don’t discuss your results

then you can only get maximum 75% of the assigned mark, assuming you explained your method and

got the right answer. Finally, no spurious precision please. You are modelling industry costs in 2050

using heroic assumptions. I expect 3 digits maximum (eg. $2.15b rather than $2,147,362,014.32).

Keep this mind during analysis – you might want to make simplifying assumptions in your estimations

rather than trying to get your calculations exact.

The two assignments over the course are in total worth 25% of your final assessment. This

assignment therefore contributes 12.5% of your final mark. Note that late submission without good

reason will see you lose 10% of your mark per day it is late. I suggest you contact me prior to the

submission date if you expect to be late in order to discuss arrangements.

An Excel spreadsheet is available on the Moodle. It provides data from the CSIRO Gencost report. It

also contains 30 minute demand data and representative State utility PV and wind traces, using

actual NEM data from calendar year 2024 (provided by NEMSight).

You are strongly encouraged to use Excel or a similar spreadsheet package to undertake this

assignment – indeed, you will need to use some form of data analysis software. You will also want to

spend the time to work out how to automate the calculations as much as possible. There are lots of

parts to this assignment that extend the initial analysis – make it easy to change key parameters such

as the carbon price by making it an external parameter which your formulas references, rather than

hard-coding it in. A little automation will make your life much easier, and it is very valuable to have

good Excel skills – it is the one techno-economic energy modelling tool that you can guarantee will be

available to all power system engineers in whatever role they have.

ELEC9714 Assignment 1, t2 2025 page 2

As an energy policy analyst working for the Queensland Government you are part of a team intended

to advise the State Government on what to do given the former State Government’s ambitious

decarbonization targets for 2050, concerns regarding renewables by the current government and the

current energy crisis across the Australian National Electricity Market due to coal and gas market

pricing shocks, and an aging coal and gas generation fleet in the State.

Note that the State Government is concerned that the National Electricity Market is incapable of

providing the State with secure affordable power and is actively considering ‘going it alone’ including

government funding of generation investment, and no reliance on interconnector flows with NSW or

any of the other States. Coal generation investment is now again under active consideration.

You have been given the responsibility to estimate the optimal ‘new build’ generation plant mix for

the Queensland Electricity Industry in 2050. This will be an input into Government decision making

on what types of generation deployment they should be facilitating over the coming 25 years. Note

that you can assume that no current plants in Queensland will still be operating at that time.

The Gencost database provides estimated technical and economic characteristics for a range of

potential new build plant including overall capital costs, economic life, fixed O&M costs, variable

O&M costs, efficiency, fuel costs as well as CO2 emissions intensity and CO2 storage costs where

relevant. Note that these are summarized for technologies relevant to Queensland in the assignment

spreadsheet. These numbers have been modified from the latest (December 2024) Gencost

estimates for several technologies in the assignment.

A particular challenge is assessing the impact of a future carbon price on emissions from the

electricity sector in Australia. Rather than making a (large) assumption, you will consider two

scenarios of carbon price – $0/tCO2 which is the present situation in Australia, and $100/tCO2 which

is roughly the current carbon price in the EU that applies to the electricity sector. While a carbon

price might seem unrealistic at present, we can only hope that serious carbon pricing is implemented

over the coming two decades. And State governments could of course choose to ‘shadow’ price

carbon for planning purposes even in the absence of concerted Federal Government or international

progress. Keep in mind that when generators pay a carbon tax, then the government earns revenue.

This revenue can be used to reduce other taxes and, arguably, therefore doesn’t actually represent

an industry cost. However, carbon pricing also reflects, at least in part, the damage costs associated

with each tCO2 (ie. the government may need those revenues to pay for the overall economic

damage that climate change is causing).

Another challenge for the team is that the government is not yet clear if it will have to make the

investment directly, or whether it will aim to incentivize private market participants to invest in the

‘optimal’ generation mix. The State government can effectively borrow money at 5%, while private

market participants argue that they can only finance projects at 10%. To date, state governments in

Australia have undertaken some investment directly, but also contracted to buy power purchase

agreements from private providers.

The potentially relevant generating plants for your analysis are provided in the assignment

spreadsheet. You’ll note there is no brown coal or biomass or new hydro costings given that brown

coal is not relevant in Queensland and there are only very limited new biomass and hydro

opportunities in the State Of course, not all these plants are fully dispatchable and capable of

operating at up to 100% Capacity factor over the year so you will need to think carefully about which

plants you include for part a) and consequent analysis.

ELEC9714 Assignment 1, t2 2025 page 3

Annualised fully dispatchable technology costs:

(a) Plot the total annual costs ($/MW/yr) for each of the appropriate ‘new build’ plants available

for Queensland with the capacity factor of the plants varying from 0 to 1 over a year

(representing 0 to 8760 hours of operation in a year) for two scenarios, 5% discount rate and

$100/tCO2, and 10% discount rate with no carbon price. Use the capital, economic lifetime

and O&M, plant efficiency, and fuel costs provided specifically for the State in the

spreadsheet. Note that these are based on the 2030 Gencost estimates given the challenges

of projecting longer-term future costs, even though you are solving the optimal generation

mix for 2050. Cost forecasts have proven pretty hopeless over just a few years, let alone

decades. You will need to calculate fixed ($k/MW/year) for each relevant generation option

for the two interest rates (5% and 10%) and variable ($/MWh) costs (for no carbon price and

$100/tCO2) for each technology. The assignment spreadsheet provides you with a plotting

template to assist you in drawing these plots once you have calculated these costs for each

technology for each of the two scenarios.

Note that the solar thermal cost is higher than in Gencost because it has been adjusted to be

capable of 100% capacity factor operation. In practice this is very challenging as these plants

need clear skies. However, no generation technologies offer 100% CF operation in practice

over extended periods due to maintenance, forced outages etc. Also, note that the hydrogen

engines are zero emissions because it is assumed the hydrogen is from renewable sources.

Highlight the economically optimal (ie. lowest annual cost) plant type as capacity factor increases

from 0 to 1 and estimate or calculate the ‘break point’ capacity factors.

Think carefully about which technologies can actually be included in such analysis – the ability to

operate the plant at any overall annual capacity factor up to 1 (ie. plant runs at rated output for

the entire year) and to definitely be available when needed (such as those peaking plants which

won’t run often but have to be there when there is high demand)) is key here. Discuss briefly both

how you undertook this analysis (ie. explain what you did with the data to get the plots), and

what these findings highlight about comparative technology costs and the impacts of carbon

pricing and interest rates on these. You might also want to consider the implications of including

currently technical unproven technologies in your analysis. Note that this discussion is not

optional – engineers need to explain how they do their quantitative (numerical) analysis, yet also

what it means. Remember, your client here is the Queensland Government – the senior executives

will generally not have engineering backgrounds. (20 marks)

Optimal dispatchable generation mix:

AEMO has provided you with estimated half hourly demand data for Queensland for the calendar

year 2024. They estimate that electricity demand will increase by 30% to the year 2050 as businesses

and households move from using gas to electricity for heating (space and water) and cooking, and

industry also electrifies more processes currently using gas, coal or oil. You can, however, assume

that the general ‘shape’ of the demand profile won’t change over that time (ie. you can just scale the

30 minute data to estimate a 2050 demand trace for Queensland). We will come back to this

question of load profile later.

(b) Using this data and growth projection, estimate and plot a load duration curve for

Queensland for the year 2050, ordered from highest to lowest demand over the year. (5

marks)

ELEC9714 Assignment 1, t2 2025 page 4

(c) From this load duration curve, and economically optimal plant capacity factor estimates from

(a) above, estimate the optimal plant capacity mix for Queensland for the 5% discount rate

and $100/tCO2 carbon price scenario for 2050. Ignore issues of existing Queensland

generation plant (much of which can be expected to be retired over the next 25 years or so).

You can also assume that all new build generating plant is 100% reliable.

Again, think carefully about which technologies can actually be included in such analysis. You can

eyeball your generation plot against the load duration curve as shown in the lectures or convert

the breakpoint capacity factors to the 30 minute dispatch across the year (capacity factor X 17520

30 minute dispatches). Discuss briefly how you undertook this analysis (ie. explain what you did

with the data to get the plots), and what these findings highlight about Queensland likely ‘least

cost’ new build generation mix with a significant carbon price. You will also want to provide your

generation mix results in a Table. (15 marks).

d) Now estimate the total annual cost ($m/yr) of the electricity industry in 2050 for the 5%

discount rate and $100/tCO2 scenario. Include of course annualised capital costs, the

associated fixed O&M costs, and the variable O&M, fuel and carbon costs associated with

actual operation of the plants. Also estimate the total electricity industry greenhouse gas

emissions.

An easy way to estimate operating costs is by measuring the areas under the load duration curve

(LDC) for each of the technologies in the optimal mix. That gives you hours X dispatch MW with

an associated variable cost $/MWh for each plant. You really should spend the time to work out

how to automate this as you will be doing more of these annual industry cost calculations in the

assignment. Think of how to automate the process of taking your generation mix estimates (MW

of each technology) and then breaking down the dispatched energy in the LDC by which

generation technology is providing it. (10 marks).

Fully dispatchable and non-constrained variable renewables:

With sufficient energy storage, it might be argued that wind and solar can be made fully dispatchable

and non-energy constrained plant, in a similar way to the solar thermal plant. For wind and PV this

would involve oversizing wind and solar and adding a lot of battery storage. If you had a PV site with

full sunshine every day, close to the equator so you get 12 hours of sun per day regardless of season,

then assuming 6 hours of full sunshine a day (yes a big assumption), the PV plant will generate 1MW

for those 6 hours and store 18MW for later use in the other 18 hours. For a slightly more realistic

example, let’s assume a 1MW 100% capacity factor PV plant would require 5MW of PV and 36MWh

of battery storage (three full nights of storage for the 1MW plant to cover occasional cloudy days and

losses.) Assume battery costs of $150k/MWh, which seems very plausible given current price falls

(although CSIRO’s Gencost report doesn’t agree) and a total fixed O&M cost of $150k/MW/year for

this plant with no variable O&M. For simplicity assume a 20 year economic life (very long for battery

energy storage plants its true, but short for the PV which is about half the capital cost)

e) Add this dispatchable generator to your generation options plot and present it here. Would such a

PV plant capable of 100% CF operation be part of the optimal generation mix under the 5% and

$100/tCO2 carbon scenario? Discuss your findings for this ‘extreme’ case of making variable

renewables equivalent to full dispatchable and non-constrained plant. (10 marks)

ELEC9714 Assignment 1, t2 2025 page 5

Incorporating demand side participation (DSP):

AEMO estimates that Queensland might have around 3GW of price responsive demand in 2050.

Effectively, this demand will choose not to run if the price is very high (here we assume $5000/MWh

(which is well below the current market ceiling price but does represent an extraordinary electricity

price for many industry participants). AEMO estimates capital costs to create such load flexibility of

on average $100k/MW with no fixed or variable O&M costs and an economic life of 20 years. You

might consider this equivalent to a peaking generator that has very low capital costs, but a

$5000/MWh operating cost. Assume again the 5% discount rate and $100/tCO2 scenario.

g) Estimate how many MW and how many hours a year this demand side participation might

actually be called upon in the Queensland electricity industry in 2050. Briefly discuss your

findings, and their implications for the value of demand side participation. You can add this DSP

as another generation technology in your plot to see over what range of capacity factors it’s the

least cost ‘generation’ option. Do not include the dispatchable PV plant in this calculation You’ll

want to check how many MW of demand will optimally be met by DSP – is the projected 3GW

enough? (5 marks)

Incorporating variable wind and PV:

AEMO has also provided you with 30 minutes traces of well performing PV and wind generation in

Queensland. These have been normalized as 1MW of PV and wind capacity profiles.

By assuming that PV and wind have sufficiently low operating costs that they will always be fully

dispatched (unless spilling), you can create a residual load duration curve for different penetrations of

PV and/or wind, which you then use to determine the optimal dispatchable generation mix.

h) Estimate the optimal generation mix of the Queensland electricity industry when adding 8GW of

PV and 8GW of wind. Do not include the dispatchable PV plant or DSP calculated above. What %

of wind and solar generation is spilt? Assume the 5% discount rate and $100/tCO2 scenario.

Recall that the traces you are given are for 1MW of solar and 1MW of wind so you will need to

scale accordingly.

i) Estimate the optimal generation mix of the Queensland electricity industry when adding 12GW of

PV and 12GW of wind. What % of wind and PV generation is spilt?

Briefly discuss your findings – in particular, does wind and/or PV reduce overall industry costs?

How much spill of wind and solar are you seeing? (15 marks).

Incorporating high renewables and storage:

Are you interested to know what the whole mix might look like with high renewables as well as

storage to avoid at least some of that renewables spill, and avoid having to run as much conventional

generation? Estimate the total annual cost of the Queensland electricity industry for the case where

there is 12GW of utility solar and 12GW of utility wind for the 5% $100/tCO2 scenario in 2050.

However, the State also installs 5GW of battery energy storage, with 6 hours of storage (ie. 30GWh

energy capacity). Assume again this storage costs $150k/MWh, ignore O&M costs, and there are no

roundtrip losses (actually around 10% losses with Li-ion energy storage). Does the storage make

economic sense in terms of reducing total industry costs? Do not include the dispatchable PV plant or

DSP calculated above.

ELEC9714 Assignment 1, t2 2025 page 6

There are many ways to model such storage but the simplest is to assume that you’ll operate the

storage to reduce the periods of highest demand, while charging during the periods of lowest

(negative demand). With 6 hours storage you might assume that over the year the plant charges for

around 2000 hours and discharges for 2000 hours. So you effectively have 5GW of extra load for 2000

hours of lowest (ideally negative) demand and 5GW of generation for another 2000 hours of the

highest demand. You can estimate a new residual load duration curves and solve the least cost mix of

dispatchable generation. More complex techniques are to solve actually battery plant dispatch for

the 30 minute demand trace over the year but I don’t suggest you try this unless you enjoy linear

programming. (10 marks)

Incorporating EV charging:

l) Discuss how you might incorporate EV charging into the analysis. Let us assume that rapid

transport electrification means that there are 4 million EVs in Queensland in 2050. Assume also

each vehicle typically charges at 3kW (note that typically they already charge at around 7kW for

household charging, let alone supercharging). Each vehicle drives around 40km/day (around

14600km/year), consuming around 6kWh/day or 2.2MWh/year (EV efficiency around

150Wh/km). Total daily consumption charging these EVs is therefore around 24GWh. Consider

two extreme cases for vehicle charging.

1) on average vehicles charge between 6-10pm every day, starting when people get home from

work. This effectively adds a block of new Queensland demand of say 6GW for that 4 hours.

2) all vehicles charge between 10am-2pm every day, utilizing a wide range of work based and

public charging infrastructure. Again, there is additional Queensland demand of 6GW for those 4

hours every day.

For both cases, estimate the optimal generation mix for the 5% discount rate and $100/tCO2

carbon price scenario and 12GW of wind and 12GW of utility solar. Don’t include the demand-

side participation, dispatchable PV or utility PV in the analysis. Calculate the total industry cost.

What is the difference in total annual industry cost depending on which charging profile is used.

And does the average $/MWh for electricity increase or decrease for each scenario. Briefly

discuss the value of thoughtful EV battery charging.

Think of ways to modify the load duration curve given this new load, and then reordering to get a

‘residual’ duration curve that you can then use to determine the optimal generation mix. There is

a useful demand profile tool in the assignment spreadsheet that allows you to enter a daily

controllable load profile, which then gets scaled up over the entire year. (10 marks)

Assignment-1 Briefing Sheet (2024/25 Academic Year)

Weighting %:

25%

Target for returning coursework:

2 weeks from the date of the submission

Authorship:

Individual

Number of hours you are expected to work on this assignment:

15 hours

This Assignment assesses the following Learning Outcomes:

I. To demonstrate knowledge and understanding of cloud architecture including different platforms, models, and services.

II. To demonstrate knowledge and understanding of the benefits and issues of cloud computing.

III. To evaluate Cloud Computing systems in terms of general quality attributes and possible trade offs presented within the given context.

A) Assignment Title:

Mini-Research on Cloud Computing Topics

B) Assignment Purpose:

This assignment aims to deepen students’ understanding of cloud computing through research and analysis. By examining selected survey papers on specific topics, students are expected to gain insights into the current state and future directions of cloud computing technologies. The report will also allow students to develop and demonstrate their ability to critically analyse academic literature and articulate their thoughts and understanding clearly.

C) Topics and Reading Materials:

Students will choose one topic from the provided list. Each topic is supported by a set of survey/review papers which they must read as part of their research. The topics cover a broad spectrum of cloud computing, from technological foundations like virtualisation to broader implications like taxonomy and open-source platforms. The list is as follows:

• Topic 1: Virtualisation

i. Bhardwaj, A. and Krishna, C.R., 2021. Virtualization in cloud computing: Moving from hypervisor to containerization—a survey. Arabian Journal for Science and Engineering, 46(9), pp.8585-8601.

• Topic 2: Traditional Distributed Computing to Cloud Computing

i. Sadashiv, N. and Kumar, S.D., 2011, August. Cluster, grid and cloud computing: A detailed comparison. In 2011 6th international conference on computer science & education (ICCSE) (pp. 477-482). IEEE.

• Topic 3: A Taxonomy of Cloud Computing

i. Sharma, Y., Javadi, B., Si, W. and Sun, D., 2016. Reliability and energy efficiency in cloud computing systems: Survey and taxonomy. Journal of Network and Computer Applications, 74, pp.66-85.

• Topic 4: Cloud Computing – A Hardware Approach

i. Hong, C.H., Spence, I. and Nikolopoulos, D.S., 2017. GPU virtualization and scheduling methods: A comprehensive survey. ACM Computing Surveys (CSUR), 50(3), pp.1-37.

• Topic 5: Open-Source Cloud Platforms

i. Kozhirbayev, Z. and Sinnott, R.O., 2017. A performance comparison of container-based technologies for the cloud. Future Generation Computer Systems, 68, pp.175-182.

You can directly download them from the link below on OneDrive (note that you will need to log in with your UH account):

https://tinyurl.com/cloud-assignment-1

D) Report Structure and Questions:

The 5-page report should be structured to address specific aspects of the chosen topic:

1. Overview of Topic:

o Purpose: Introduce the topic and explain its relevance in the realm of cloud computing.

o Key Points: Highlight the critical aspects covered in the survey papers and any foundational concepts.

2. Critical Analysis:

o Main Findings: Summarize the primary conclusions of the survey papers. What are the significant trends or breakthroughs discussed?

o Literature Comparison: Discuss any contrasting views or methodologies presented in the papers. Are there conflicting findings or consensus?

3. Implications:

o Challenges: Identify the main challenges or issues revealed in the literature. What are the obstacles to progress in this area?

o Opportunities: Suggest potential opportunities for innovation or further research that could address these challenges.

4. Personal Insight:

o Future Directions: Propose where the field might go based on the papers’ findings. What are the upcoming trends?

o Impact: Reflect on how advancements in this topic could impact the broader IT and cloud computing landscape.

5. Conclusion:

o Summary: Briefly recap the key points discussed and any conclusions drawn.

o Reflection: Share any personal learning or insights gained through this assignment.

Submission Requirements:

The assignment has to be submitted online via StudyNet. Please submit your report as a PDF file.

Note:

The Module leader reserve the right to conduct an oral examination with the student about the subject matter in his/her assessment submission.

Marks awarded for:

Assignment 1

Assessment Criteria

Mark Available

Mark out of 100%

Understanding of Topic:

• Assesses how well the student grasps and explains the topic’s significance

and foundational concepts.

5

20

Analysis of Literature:

• Evaluates the depth of the literature

review and the ability to identify key

messages and compare perspectives.

5

20

Insight into Challenges and Opportunities:

• Looks at the student’s ability to

discern and articulate the practical implications of the topic.

5

20

Originality and Depth of Insights:

• Measures the creativity and depth of the student’s personaI insights and outlook on the topic.

5

20

Quality of Writing and Adherence to Report Guidelines:

• Checks for the overall organisation, clarity, grammatical correctness, and adherence to the report format and page limit.

5

20

Overall Comments and marks

25

100

Homework 2

Legal assumptions

• You may assume any of the following without proof: the laws of algebra are valid, the sum or difference of two integers is an integer, the product of two integers is an integer.

• Additionally, you may use any facts about modular arithmetic/algebra without jus-tification, such as the rules of modular addition and multiplication. This includes facts about algebra on even and odd numbers, such as even + dd = odd, even · dd = even, etc. (since these are equivalent to addition and multiplication mod 2).

Definitions and Notation

• An integer x is divisible by d if there exists an integer k with x = dk.

• An integer x is rational if there exist integers a, b with x = a/b. Otherwise, it is irrational.

• An integer x is prime if x ≥ 2, and there do not exist integers j ≥ 2, k ≥ 2 with x = jk.

• An integer x is even if there is an integer k with x = 2k, or odd if there is an integer k with x = 2k + 1. If convenient, you may also use that x is even if x ≡ 0 (mod 2), or odd if x ≡ 1 (mod 2).

Mechanical Problems

1. Even Stevens [14 points]

Consider the proposition: for all integers x, y, if 3xy + 4x + y is odd then x is odd or y is odd. Give three separate proofs, using:

(a) a proof by contrapositive

(b) a proof by contradiction

(c) a proof by cases on whether x is even or odd.

2. Rooting For You [14 points]

Prove that for all odd integers a, b, c, the equation ax2 + bx + c = 0 does not have any solutions where x is an integer.

3. Bad Id34 [14 points]

(a) Prove that √3 is irrational.

(b) Note that √4 = 2, which is rational. What step in your proof would go wrong if you used the same proof strategy to show that √4 is irrational? Cite a specific step or claim from your previous answer, and explain in a sentence or two why it is incorrect for √4.

4. It’s A Very Very … Mod World [12 points]

Calculate 7203 mod 5. Show your work. Your solution should not contain any numbers greater than 50 except for exponents.

Bad Proofs

Each of the following propositions may or may not be true, but we have given an incorrect “proof” that attempts to show that it is true. Identify the specific logical error made in each proof by citing a sentence, equation, step, or missing part of the proof, and briefly explain why it is wrong.

5. Irrational Inaccuracy [8 points]

Proposition. √6 is irrational.

Incorrect Proof. We have √6 = √2 · 3 = √2 · √3. We proved in class that √2 is irrational, and we proved previously in this homework that √3 is irrational. So √6 is the product of two irrational numbers, so it is irrational.

6. Parity Ploy [8 points]

Proposition. For all integers x and y, if one of the variables is even and the other is odd, then their sum is even.

Proof. We use a proof by contrapositive. Switching the order of the if-then and negating each side, we get:

“For all integers x and y, if their sum is odd, then one of the variables is odd or the other is even.”

Letting x and y be any integers whose sum is odd, we must either have that x is even and y is odd, or that x is odd and y is even. In either case it holds that one of the variables is odd or the other is even, so the proposition is proved.

Discovery Problems

7. Lucky Seven [15 points]

(a) Prove that any positive integer n is divisible by 9 if and only if the sum of its digits is divisible by 9.

(b) For which integers 2 ≤ d ≤ 7 is it true that a number is divisible by d if and only if the sum of its base-7 digits is divisible by d? Give a complete list of these integers, and explain how you might change your proof from the previous part to show this property for the integers in your list.

For full credit you must include all integers with this property in your list, but you do not need to prove that your list is indeed complete.

8. Prime Pairs [15 points]

The twin prime conjecture is a famous unsolved problem, which asks for a proof or dis-proof that there are infinitely many pairs of prime numbers whose difference is exactly 2 (for example: (3, 5),(5, 7),(11, 13),(17, 19)). We will investigate two related (but solved) problems:

(a) Prove or disprove: there are infinitely many pairs of prime numbers whose difference is exactly 3.

(b) Prove or disprove: there are infinitely many pairs of prime numbers whose difference is a nonzero multiple of 3.

Note: We proved in lecture that there are infinitely many prime numbers; you can use this without re-proving it. If you’re having trouble, try listing some small primes and noting which pairs have a difference that is a multiple of 3. Do you notice a pattern?

COMPSCI5100

DEGREES OF MSc, MSci, MEng, BEng, BSc, MA and MA (Social Sciences)

Machine Learning & Artificial Intelligence for Data Scientists

Question 1: Regression (Total marks: 20)

Consider using regression to predict the world population growth rate using the data shown in the following figure:

Figure 1.1. Size of training data used in machine learning models from 1950-2023. Source: Modified from https://ourworldindata.org/grapher/artificial-intelligence-number-training-datapoints

(a) A rescaling method was used to rescale the years to values displayed in Figure 1.2. Describe which rescaling method was used (with enough details of the procedure), and why you think it was applied.

Figure 1.2: Size of training data used in machine learning models with rescaled years.

[4 marks]

(b) Consider fitting the data with a polynomial regression of order 2, identify the two most likely poorly fitted data points (use years in Figure 1.1 as reference) and explain why. [6 marks]

(c) Consider fitting the data in Figure 1.1 with a regression with the radial basis function:

Outline one advantage and disadvantage of using this radial basis function over polynomials with the data in Figure 1.1. [4 marks]

(d) Suppose we use the radial basis function in (c), with μk set to be xn and s = 10, to fit the data. We used two fitting strategies, namely ridge regression and lasso, and obtained the following fitting models in Figure 1.3 A and B. Identify which fitting strategy is used in each figure and explain why and how the chosen fitting method could have generated the result. (note, each method is used only once). [6 marks]

Question 2: Classification (Total marks: 20)

(a) Assume the following training data in the two-dimensional plane of X1 and X2 is available (Figure 2.1). The target variables for the points in the red and blue are +1 and -1. We summarise the data as the following tuples: <(2,0), 1>, <(0,2),-1>, <(0,2),-1>, <(3,0),1>, and <(-1,0), -1>, respectively. (Note, you can use LATEX notation, for example X_1, X_2, \alpha_1, \alpha_2 and etc)

i. Design a k-NN classifier with k=1 and write down the equations that specify the decision boundary between the two classes. [6 marks]

ii. Using the classifier above, determine the class variables C1, C2, and C3 for the following test data points: <(0,0), C1>, <(0.7,0), C2 > and <(0.3,0), C3 > [3 marks]

(b) In the same data set in Figure 2.1, we apply a linear SVM model with the predictor y(X1, X2) for classification.

i. Which data points are the support vectors? Write down the equation for y(X1, X2) (Hint: First visually assess the data to determine the decision boundary and the support vectors. Observe the constraints for the margin and SVM classifier.) [4 marks]

ii. Specify the Lagrange multipliers a1, a2, a3, a4, a5 for each of the data points in the training data (2,0), (0,2), (0,-2), (3,0), and (-1, 0), respectively. [5 marks]

iii. Which k-NN or SVM classifiers (designed above) will be more accurate? Explain your answer in up to two sentences. [2 marks]

3. Unsupervised learning question (Total marks 20)

Consider using the K-means algorithm to perform. clustering on the following scenario Figure 3.1 A. We expect to form. three clusters as shown in Figure 3.1 B.

(a) Outline what would happen if we directly apply K-means with Euclidean distance to this data. Can it achieve the clustering objective? How will it split/group the data and why? [3 marks]

(b) An alternative approach is to use Kernel K-means. Would kernel K-means could help in this dataset and why? [2 marks]

(c) An alternative approach is to use mixture models. Would mixture models help to better classify this dataset than K-means and why? [3 marks]

(d) The plot in Figure 3.2 shows some 2D data. PCA is applied to this data. Explain how the first principal component would look if it is overlaid on the plot. Explain your reasoning. (Hint: if you cannot draw, indicate points/axis on the grid)

[2 marks]

(e) Similar to the previous question, explain what the second principal component would look like and why. (Hint: if you cannot draw, you could refer to the x, y-axis for reference) [2 marks]

(f) Explain how you would choose the number of clusters in an application of mixture models. [3 marks]

(g) Explain how you could detect an outlier point with mixture models. Write a high-level pseudo code and describe each step. (Hint: Start with the expectation-maximization algorithm and how it can facilitate the detection) [5 marks]

Team Term Project (TTP) Part 1

What’s the rationale for investing in a new in-house brewery?

MET AD715 – Quantitative and Qualitative Decision Making – A4

October 22, 2024

Executive Summary

The primary purpose of this report is to determine the feasibility of the opening of Allston Aleworks, a new craft brewery in Allston, Boston.

1 Introduction

The craft beer industry in the United States has seen substantial growth in recent years, as consumers start to prefer unique local brews over beer that are mass produced (Statista, 2023). Consequently, there is a growing opportunity for craft breweries to capitalize on this increase in demand, especially in areas where beer consumption is relatively high. Targeting a younger and more trend-driven demographic, Allston Aleworks aims to tap into this market by introducing a new brewery in the Boston area, as well as housing its production in the city outskirts.

The target location, Allston, as well as the surrounding area of Fenway and Brighton has a population of 111,979 as of 2022 (Data USA, 2022). Allston’s population mostly consists of students, young professionals, and academics, owing to the proximity of several academic institutions, including Harvard University, Boston University, and Boston College. This report aims to assess the viability of opening Allston Aleworks by examining the market, operational and financial factors.

1.1 Problem Statement

The main objective of this report is to determine whether Allston Aleworks as a business opportunity is viable, by utilizing and analyzing the market as well as the operational logistics, marketing strategy, financial sustainability, and competitive landscape. Although Allston has a promising client base, we must also take into account the significant entry barriers that exist such as start-up costs, legal regulations and local competition that could play a role in the success of Allston Aleworks.

Due to the highly competitive nature of the craft beer industry in Boston, Allston Aleworks has to be strategic in its marketing and financial approach so as to be able to succeed. Hence, in this report, we will also aim to investigate whether there is sufficient demand, whether the brewery will be operationally profitable and whether it can achieve this profitability within a reasonable timeframe.

1.2 Overall Goals and Objectives

In order to assess the feasibility of Allston Aleworks it is important to highlight some key assumptions made about the market conditions and operation of the business. We shall consider the fact that the brewery will have 20 tables with a 4 square seating capacity each, as well as an additional 20 seats at the bar counter. The hours of operation at the brewery will be from 4pm – 2am everyday, with an anticipated turnover of 3 seatings per day for both table and bar seats. We will also be operating on an assumed occupancy rate of 60%. On average, each customer is expected to consume 1.5 pints of beer during their visit. This number is adjusted and accounts for customers who may not drink as well for customers that will drink more than 1 pint, bringing the assumed average to 1.5 pints.

The price for a pint of beer will be assumed to be at $X, though the actual price might vary slightly for different types of beer, for the sake of simplicity, we will assume that all the ingredients and differences between the types of beer is negligible. As a result, the production costs, including material and labor costs will be evenly distributed among our beers. For the primary ingredients, we have identified two primary cost drivers being; malt and hops. With this, malt is expected to cost around $X per ton and hops at $X per ton. Based on this, the approximate material cost for a gallon of beer would be $X, and thus for a pint, $X. It is to be noted that although yeast and water are also key ingredients in the brewing process, their cost per pint is too insignificant and thus negligible (See Appendix 1). Labor and other costs such as packaging will also be consider and will be accounted for in the table below:

Product Name

Material per pint ($)

Labor per pint ($)

Other Costs ($)

Price per Pint ($)

Pilsner

Bavarian Lager

Light Wheat

Red Wheat

Pale Ale

Nut Brown Ale

Stout

Bock Dark

In regards to staffing, Allston Aleworks aims to employ 1 critical marketing personnel and 1 critical technical personnel for the first two fiscal years (FY1 & FY2), and expand to 2 persons for each team by fiscal year three (FY3). We will be solely relying on sales of beer for our revenue without any other revenue streams such as food or merchandise. We must also take into note that there are 4 competitors in the Allston area that must be taken into consideration when accessing market dynamics.

With these assumptions, the primary objective of this report is to determine whether Allston Aleworks is a sound financial investment and whether it is sustainable and profitable. This report aims to analyze whether the brewery will be able to generate enough demand and revenue in-order to cover operational expenses and whether it can break-even within a reasonable timeframe. The report will also assess whether the operational logistics, marketing plan, staffing and pricing model are sufficient for Allston Aleworks to gain and maintain long term profitability within its current business conditions.

1.3 Report Structure

This report will consist of two main parts, being the managerial decision process per each functional area and the application of decision tools per each functional area. The two functional areas that we have identified to be of critical importance and will need to be evaluated are marketing management and financial management, as these will directly affect the brewery’s operation and financial feasibility.

2. Managerial Decision Process for Marketing and Financial Functional Areas

2.0 Methodology for Analysis of a Functional Area

2.1 Marketing Management and Decision Making

2.2 Financial Management and Decision Making

3. Application of Decision Support Tools per Functional Area

3.0 Methodology for Applying Decision Tools per Cycle

3.1 Functional Area Marketing Management

3.1.1 SWOT Analysis

Strengths

Two Distribution Channels: By offering two different channels for distribution (wholesale & retail), Allston Aleworks diversifies its revenue streams. This allows us to have access to a broader range of customers as wholesale streams offer us a connection with local restaurants, bars and liquor stores and retail allows us to send directly to the end consumer. This diversification better prepares us for market fluctuations and demand changes.

Locational Advantage: Allston Aleworks is located in the neighborhood of Allston where there is a young vibrant community that consists primarily of students and young professionals (Boston Planning & Development Agency, 2017). This demographic is highly susceptible to high beer consumption, offering Allston Aleworks a consumer base within its very neighborhood. On top of this, Allston is also home to many live music venues, attracting even more young people to the neighborhood that could prove to help with Allston Aleworks’ customer traffic.

Flexibility to adapt & innovate: Due to the fact that Allston Aleworks is a new brewery, it is still capable and able to experiment with its product line and new flavors as it is not tied to any existing product or niche. This ability to change allows Allston Aleworks to tailor its beers to the customer’s preferences and can introduce new changes and products to match the current consumption trends.

Weaknesses

New Establishment: As Allston Aleworks is a new entrant to the craft beer market, it will lack the brand recognition and customer loyalty that older and more established brands/breweries have. This fact could make it more difficult for Allston Aleworks to attract customers initially as customers may not find any reason or drive to switch over from their current brand/breweries.

Limited Parking: Boston is notorious for its difficulty in finding parking. This can be attributed to its historical layout and narrow streets as the city was built before the rise of modern transportation. As a result, Allston Aleworks will struggle to attract customers who do not reside in the immediate area as the parking difficulty will deter those who live further away.

Transient Population: Allston’s large student population can prove to be a double-edged sword. Although a high student population means that Allston Aleworks will see a lot of foot traffic, they experience significantly less traffic during school holidays as students return home. On top of this seasonal demand, many students will move out of the area after they graduate, thus making it even more difficult for Allston Aleworks to build long-term customer loyalty.

Opportunities

Post Pandemic Recovery: As the world continues to recover from the Covid-19 pandemic, there is a greater push and demand for social gatherings. This allows for Allston Aleworks to present itself as a local place where people can gather and socialize.

Health-Conscious Consumption: According to CNN, there’s a rise in demand for lower-alcohol beverages as consumers grow more health-conscious (Howard, 2024). This shift sees consumers pulling away from traditionally harder liquors and opting for lighter alcohol beverages like pilsners or wheat beers. This shift can prove to be advantageous for Allston Aleworks, as consumers pivot to beer as a less alcoholic-intensive beverage.

Threats

Inflation: As the ingredient costs for malt, hops and yeast increase due to inflation, this would also ultimately increase the brewery’s operating expenses. As a result, profit margins will start to shrink with the rising prices. Allston Aleworks can choose to increase its prices to dampen the loss but this will deter more price-conscious consumers.

Supply Chain Disruptions: Global economic instability and geopolitical tension continue to complicate supply chains, with a prevalent example being the Russia-Ukraine war. As Ukraine is one of the world’s top barley producers, the on-going war in Ukraine will decrease global barley supply (Council of the European Union, 2024; U.S. Department of Agriculture, Economic Research Service, 2024). Furthermore, the worsening drought conditions in Europe also disrupts the supply for hops, one of Germany’s biggest exports (Leuenberger et al., 2023). These factors ultimately created shortages and price increases for key ingredients such as hop and barley, increasing the production costs for beer. For Allston Aleworks, this increase can be reflected in a lower profit margin or a need to switch over to alternative ingredients that could affect the price and quality of its products.

3.1.2 Decision Tools (Applied After the Submission of a Cycle)

D-Analysis

From the

3.2 Functional Area Financial Management

3.2.1 PESTEL Analysis

Political Factors

3.2.2 Decision Tools (Applied After the Submission of a Cycle)

4. Summary and Recommendations

Reference

Boston Planning & Development Agency. (2017). Allston trends report. Boston.gov. https://www.bostonplans.org/getattachment/360909b1-97da-46db-be3a-6cc7131f984e

Council of the European Union. (2024). Ukrainian grain exports explained. Consilium. https://www.consilium.europa.eu/en/infographics/ukrainian-grain-exports-explained/

Data USA. (2022). Boston City (Allston-Brighton-Fenway PUMA), MA [Data Profile]. Data USA. https://datausa.io/profile/geo/boston-city-allston-brighton-fenway-puma-ma

Howard, J. (2024, April 1). Non-alcoholic sober bars are growing in popularity, as part of the ‘sober curious’ movement. CNN. https://www.cnn.com/2024/04/01/health/non-alcoholic-sober-bars-dry-january-wellness-cec/index.html

Leuenberger, M., Gfeller, A., Schläpfer, A., & Wilmes, S. B. (2023). Low-temperature microhydration promotes macromolecular conformational changes and dynamic processes. Nature Communications, 14, 41474. https://doi.org/10.1038/s41467-023-41474-5

Statista. (2023). Craft beer market in the U.S. – statistics & facts. Statista.

https://www.statista.com/topics/1809/craft-beer/

U.S. Department of Agriculture, Economic Research Service. (2024, May). Ukraine’s rise in grain and sunflower seed market share limited by ongoing war. Amber Waves. https://www.ers.usda.gov/amber-waves/2024/may/ukraine-s-rise-in-grain-and-sunflower-seed-market-share-limited-by-ongoing-war/

Question 1 – Qualitative characteristics of financial information (50 marks, around 400 words)

On London Stock Exchange website >> Prices and Markets page: https://www.londonstockexchange.com/live-markets/market-data-dashboard/price-explorer, filter by clicking ‘Sector’. Select a sector of your interests and click ‘Apply filters’. Then in ‘Market cap (£m) tag’, select ‘Highest-lowest’. Explore the ranking list. (1) Choose a company which has a relatively large market capital size/higher ranking one; and (2) choose a much smaller company as the comparison/much lower ranking one. Use the Table below as a guided structure to analyse the financial reporting quality of both companies, from the four enhancing qualitative characteristics of financial reporting perspectives. You are required (1) to find the relevant statements in their annual reports and (2) to paraphrase or summarise them, to evidence the quality of reporting, from the four perspectives respectively, and (3) to make suggestions to the company, which may report with a lower quality, to improve. You could write in four paragraphs, instead of using a table. One statement is required for each box to be concise.

The larger company: company name 1

The smaller company:

company name 2

Suggestions for improvement

Comparability

Verifiability

Timeliness

Understandability

This question is to assess the module Learning Outcome 4 (LO4, mapping with Course LO1 and LO5): apply critical thinking skills to various financial accounting and analysis scenarios.

Question 2 – Creative accounting (50 marks, around 600 words)

Find the reports and materials published online and in press about a corporate scandal (excluding the Enron scandal) of your choice in a country where IFRS applies (check here: https://www.ifrs.org/use-around-the-world/use-of-ifrs-standards-by-jurisdiction/). You are required to analyse the accounting scandal and the consequential company failure.

You are required to answer the following two questions:

1) Identify two specific accounts manipulation problems of your chosen accounting scandal and explain the seriousness of them (e.g. a fraud or creative accounting, illegal or unethical). Cite the relevant research literature where necessary. See the lecture contents to understand the difference between fraud/illegal accounting practice and creative accounting/earnings management.

2) Reflect on the role of professional ethics in financial reporting, what are the ethical implications and impacts of this scandal on society? In other words, what could be done to prevent such scandals from happening, from the application of the fundamental qualitative characteristics of financial reporting principles perspective?

Guidance:

You are required to use AI language generator (e.g. ChatGPT) as a research assistant where applicable to help you to contextualise the question and the possible draft answers. However, any texts generated by any AI language generator in your research and analysis process are required to be submitted in an Appendix attached to your answers to the above two questions, which are not included in the word count nor being marked. You need to show the improvement in your final answers, from the AI generated texts, To:

· Include the page number of the referenced parts of the annual reports and other references that you used;

· Summarise or paraphrase the AI generated texts to evidence your learning;

· Correct the AI generated texts with reference to the academic references or the latest information that is missing from the AI used database.

· Improve the expression, being more relevant to the question context with specific examples and the appropriate application of principles.

This question is to assess the module Learning Outcome 2 (LO2, mapping with Course LO3 and LO4): evaluate the ethical implications of financial accounting disclosure practices for various external user groups. Specifically, this question is to assess your understanding on:

i. How poor financial reporting practices (i.e. companies insufficiently fulfill the qualitative characteristic of financial reporting requirements) would affect and/or interact with the companies’ adoption of creative accounting/earnings management practices?

ii. What are the different forms of creative accounting/earnings management in practice? What are the differences between illegal accounting practices and creative accounting practices?

iii. The importance of accounting professional ethics.

Please note that accounting scandal and company failure would not necessarily mean that this company went bankruptcy. The companies may still exist, yet the accounting scandals have been reported and the wrong doings have been penalised.

General Requirements to Question 1 and 2:

Your answers are to be your own work. You are to use Harvard referencing style. to reference any material you have directly or indirectly taken from other sources. Accounting standards may be cited by simply giving the abbreviation for the standard (IAS, IFRS, etc.), its number and the paragraph to which you refer. There is no lower- or upper-word count limits for each of your answers to the questions. The overall word count is suggested to be 1,000 words +/- 10%. You will not get penalised if you write longer than 1,000 words, up to 2,000 words.

Marks will be awarded according to the University of Sussex Business School Generic Assessment Criteria 2020. Please make sure you watch the video under Marking Scheme(s) on https://canvas.sussex.ac.uk/courses/28288/pages/assessment-information and read the ‘Expected at level 6’ carefully before writing up your answers. Marks will be given based on the quality of your writing from 5 perspectives including: (1) Knowledge & Understanding, (2) Application, (3) Critical Thinking, (4) Reading & Research, and (5) Presentation & Style. (Teamwork criterion is irrelevant to this assessment.) Your submission will be checked for plagiarism automatically using the Turn-it-in.

Homework 1

Reminders

• The integers are the set {. . . , −2, −1, 0, 1, 2, . . . }. The real numbers are the set of all (non-imaginary, non-infinity) numbers, including all the integers, e, π, √2, −0.203, etc.

• The notation ∃ means “there exists,” and ∀ means “for all.”

• An integer x is even if there exists an integer k with x = 2k. An integer x is odd if there exists an integer k with x = 2k + 1.

• An integer k divides an integer x, written k | x, if there exists an integer j with x = jk.

• The greatest common divisor of two or more integers is the largest integer that divides all of those integers.

• A real number x is rational if there exist integers a and b (where b ≠ 0) with x = a/b. Otherwise, x is irrational.

• You may assume any of the following without proof: the laws of algebra are valid, the sum or difference of two integers is an integer, the product of two integers is an integer.

1. Collaboration and Support [3 points]

(a) Give the names and uniqnames of 3 of your EECS 203 classmates (these could be members of your homework group or other classmates).

(b) When you have questions about the course content, where can you ask them? Where are you most likely to ask questions?

(c) Name one self-care action you plan to do this semester to maintain your overall well-being.

Mechanical Problems

2. Quantifier Quandary [14 points]

For each of the following propositions, state whether it is true or false when the domain of each quantifier is (i) the integers, and (ii) the real numbers. Justify each of your answers by either naming specific variable settings or by writing one sentence that suggests a general argument, as appropriate.

(a) ∃x(x3 = −1)

(b) ∃x(x2 = −1)

(c) ∃x(x4 < x2 ) (d) ∀x(2x > x)

(e) ∀x∃y(x2 − y = 0)

(f) ∀x∃y(y2 − x = 0)

(g) ∀x∃y(y2 = x or y2 = −x)

3. Pairwise Properties [9 points]

(a) Prove or disprove: there exist three integers x, y, z where the minimum of all three is 1, but for each pair of integers (x, y), (x, z), and (y, z), the minimum of that pair is not 1.

(b) Prove or disprove: there exist three integers x, y, z where the greatest common divisor of all three is 1, but for each pair of integers (x, y), (x, z), and (y, z), the greatest common divisor of that pair is not 1.

4. Sum Stability [12 points]

(a) Prove or disprove: for all rational numbers x and y, x + y is rational.

(b) Prove or disprove: for all irrational numbers x and y, x + y is irrational.

In either part, you may use without justification that any integer is rational and that the number √2 is irrational, but you should include justification if you claim any other numbers to be rational or irrational.

5. Number Theory Negations [6 points]

Write the negation of each of the following propositions. Simplify as far as possible by pushing “not” (or similar words) inside logical expressions.

(a) There exists an integer a where a is not negative and a is not positive.

(b) For all integers b, b is rational or irrational.

(c) For all integers c, if c is even, then c + 1 is odd.

(d) For all integers d, d is positive if and only if d is not negative.

(e) There exists an integer e1 such that for all integers e2, e1 · e2 = e1.

(f) For all integers f1, there does not exist an integer f2 such that f2 > f1 and f2 ≤ f1.

6. For-All Flip [8 points]

Let P(x, y) be an unknown predicate.

(a) If ∀x∃yP(x, y), must it also be true that ∃y∀xP(x, y)?

(b) If ∃y∀xP(x, y), must it also be true that ∀x∃yP(x, y)?

For each part, either explain in a sentence or two why the proposition must also be true, or give a counterexample of a predicate P where it is false.

Bad Proofs

Each of the following propositions may or may not be true. We have given a “proof” that is correctly formatted, but which contains a logical error. Identify the error by citing a sentence, equation, or step, and briefly explain why it is wrong.

7. Oddness Oversight [6 points]

Proposition 1. For all odd integers n, we have 4 |(n2 − 1).

Incorrect Proof. Let n be any odd integer. Since n is odd, we have n = 2k + 1 for some integer k. Since 4 |(n2 − 1), we have n2 − 1 = 4j for some integer j. So

(2k + 1)2 − 1 = 4j

4k2 + 4k + 1 − 1 = 4j

4k2 + 4k = 4j

k2 + k = j.

So since k is an integer, k2 + k is an integer, which agrees with the fact that j is an integer, so the proof is complete.

8. Positivity Prank [6 points]

Proposition 2. For all even integers x and odd integers y, we have xy ≥ 0.

Incorrect Proof. Let x be any even integer and let y be any odd integer. Since x is even, we have x = 2k for some integer k. Since y is odd, we have y = 2k + 1 for some integer k. So

since a square is always 0 or larger.

Since x, y are both integers, xy is an integer. All integers larger than −1/4 are at least 0, so xy ≥ 0.

9. Set Slip [6 points]

Proposition 3. Let a, b be integers and let S be a finitely-large set of integers such that

∃s1 ∈ S a|s1 and ∃s2 ∈ S b|s2.

Then ab divides the product of all the integers in S.

Incorrect Proof. We can list the elements of S as S = {s1, s2, . . . , sc} , where we choose to write s1 (divided by a) first and s2 (divided by b) second. So we have s1 = ak1 and s2 = bk2 for some integers k1 and k2. The product of all the integers in S is

s1s2s3 . . . sc = (ak1)(bk2)s3 . . . sc

= (ab) · (k1k2s3 . . . sc).

Since k1, k2, s3, . . . , sc are all integers, we have that k1k2s3 . . . sc is an integer, which shows that ab divides the product of the integers in S.

Discovery Problems

10. Threepeat/Thirteen [15 points]

A threepeat is a positive integer that has exactly six digits, and where the first three digits are the same as the last three digits. For example, 203203 is a threepeat.

Which threepeats are divisible by 13? Is it all of them? None of them? Only the even ones? Only those that are large enough? Something else? Choose one of the following three propositions, and then give a proof of the proposition you choose:

• All threepeats are divisible by 13.

• No threepeats are divisible by 13.

• Some threepeats are divisible by 13, and others are not. A threepeat t is divisible by 13 if and only if

(if you choose this option, fill in the blank to complete a proposition).

11. Consecutive Counting [15 points]

A positive integer h is happy if the sum of any h consecutive integers is divisible by h. For example, 203 is happy if the number 1 + 2 + 3 +· · ·+ 203 is divisible by 203, and the number 2 + 3 + 4 + · · · + 204 is divisible by 203, and so on.

Which positive integers are happy? Is it all of them? None of them? Only the even ones? Only those that are large enough? Something else? Choose one of the following three propositions, and then give a proof of the proposition you choose:

• All positive integers are happy.

• No positive integers are happy.

• Some positive integers are happy, and others are not. A positive integer h is happy if and only if

(if you choose this option, fill in the blank to complete a proposition).

Groupwork

1. Diag Squirrels [15 points]

Sammy and Sapphire the Diag Squirrels are playing a game. Sammy and Sapphire take turns, starting with Sammy. There is a row of 5 holes, each starting with 203 acorns in it. On each turn, a squirrel picks a hole, eats exactly one acorn from it, then places up to 3 new acorns in each hole to the right of that hole. If none of the holes have any acorns left, meaning the squirrel can’t eat any acorns on their turn, they lose.

The goal of this question is to prove that Sammy can play the game in a way that guarantees they will win.

(a) Prove that if all holes have an even number of acorns, then all legal moves leave at least one hole with an odd number of acorns.

(b) Prove that if at least one hole has an odd number of acorns, then there exists a legal move that leaves all holes with an even number of acorns.

(c) Prove that there exists a strategy that Sammy can use to play the game to guarantee they will win. (Note that the leftmost hole can only be picked 203 times, and the next hole can only be picked 203 + 203 · 3 times, and so on, so the game always ends. You may assume this without further proof.)

2. Lying and Politics [15 points]

There are two kinds of people in the world: knights and knaves, where knights always tell the truth and knaves always lie. There are three people, Alice, Bob, and Charlie, and one of them is the city mayor.

• Alice says “I am not the city mayor.”

• Bob says “The city mayor is a knave.”

• Charlie says “All three of us are knaves.”

Is the city mayor a knight or a knave? Explain your answer.

SPRING 2024

1.Consider a second-order hidden Markov model, in which Xt generally depends on both Xt-1 and Xt-2.The initial distribution is Pr(Xo,X₁),transition probabilities are Pr(Xt|Xt-1,Xt-2)for t≥2, and observation probabilities are Pr(E|Xt)for t≥1.

(a)Circle either true or false for each of the conditional independence statements below that are guaranteed to hold in the second-order HMM.

(b) Give a minimal expression for Pr(X₁,…,X₅,e₁,…,e₅) using the HMM parameters. (Multiplica- tion of CPTs will be interpreted as multiplication of factors.)

(c) Suppose we have αt=Pr(Xt-1,Xt|e1:t)and we want to compute αt+1 =Pr(Xt,Xt+1|e1:t+1). Give a minimal expression for αt+1 using at and the HMM parameters,normalizing if necessary.

2. Flying during the holidays can be a stressful time,since so many things can go wrong. Bad weather (W) or mechanical airplane problems (M) can delay your flight (D); mechanical problems can also affect the chances of your baggage (B) being lost. Suppose you have a probabilistic model of the relationships between these Boolean events as follows:

(a) Draw a representative Bayesian network of this model. Be sure to label your nodes and indicate directionalityon the edges.

(b) Are weather (W) and whether your baggage (B) makes it back safely with you independent of each other?

(c) Suppose you are sitting at the airport and you tell your family that your fight was indeed delayed. Given this information,are weather and baggage arriving safely conditionally independent of each other?

(d) Write an analytical expression for Pr(W,B|D=+d), the joint distribution of weather and baggage given that your flight is delayed.Your expression should only include sums,products, and/or quotients of terms fro the model described above.

(e) Numerically compute Pr(+w,+b,+d),the joint probability that bad weatheroccurred,your bag- gage got lost,and your flight was delayed.

3. A recycling robot is trying to classify the objects that it sees as bottles(B=+b)or notbottles (B=-b).The robot considers three binary features:whether the object is rounded(R=+r)or not (R=-r),whether it is made of glass(G=+9)or plastic(G=-9),and whether it is small (S=+8) or large(S=-s).The robot is given a labeled data set as follows:

(a) Suppose we learn a naive Bayes classifier from this data.Find the numerical parameters that would be learned usingα=1 smoothing. Please write your answers as reduced fractions.

(b) Using the learned model,how does the robot classify the feature set (一r,-g,-s)?

(c) Suppose our data set did not include the class labels.If we were to learn a naive Bayes model using expectation-maximization,are we guaranteed to recover the maximum-likelihood parameters learned from the labeled data set?Why or why not?

(d) Convert the features to numerical values by treating +as +1 and-as-1.Consider a linear classifier that predicts B=-b if fw(x)≤0 and B=+b otherwise.What is the classification accuracy on the data set given a model with weight vector w=(1,1,0,1)?

(e) Again starting from w,compute the update made to w using the perceptron learning rule after the first mistake made on the data set.

(f) A sigmoid activation function would still yield the same predictions and same classification accu- racy as the hard threshold function described above.Give two different advantages that a sigmoid function has over the hard threshold.

(g) Suppose we pass our data set through the neural network below,where x is R,y is G,and z is S. Find the individual outputs of each forward pass.