STATS 763 (10/06/2021 17:30) Adv Regression Methodology (Exam) Question 1: [Total: 30 marks] The relationship between BMI and various other factors was investigated by Noh et al. (2016) using 2012 data from the Korean Longitudinal Study of Aging. Data on 7730 individuals aged 51 and over was available. A BMI of 25 or more corresponds to an Overweight status, and a BMI of 30 or more to an Obese status. We are interested in the efect of Age on the Overweight and Obese indicators. The relationship between Age and BMI by biological Sex is depicted in the figure below. a) [10 marks] We are interested in the efect of Age for each biological Sex (i.e. the efect of Age*Sex) on the probability of being Overweight. We assume that adjusting for unemployment status (Unemployed= 1) and Marital status accounts for all confounding. The following model is fitted using all the data in data frame df; note the identity link: mod .ow | t | ) (Intercept) 0 .5593657 0 .0504992 11 .077
Coursework assignments 100% out of 100% total mark Offshore Jacket Structures Course Title: Offshore Structural Design Course Code: EA50JG Assignment 1 (25%): Preliminary design of Jacket structures Assignment 2 (25%): Loading and computational analysis Assignment 3 (25%): Design of tubular joints and foundation Assignment 4 (25%): Computational design of Jacket structures Assignment 1 (25%): Preliminary design of Jacket structures The coursework project includes: • Coursework P1: Framing and bracing configurations and preliminary sizes. Assignment 2 (25%): Loading and computational analysis The coursework projects include: • Coursework P2: Hydrodynamic and wind loading and preliminary analysis. • Coursework P3: Modelling the initially sized jacket in P1 and applying the assumed vertical permanent and variable loading as well as the lateral loading derived in P2. Assignment 3 (25%): Design of tubular joints and foundation The coursework projects include: • Coursework P4: Design of tubular joints. • Coursework P5: Foundation design. Assignment 4 (25%): Computational design of Jacket structures The coursework project includes: • Coursework P6: Designing the jacket members using the more accurate computational forces incorporating piles and check for fatigue. The project is aligned with IStructE Chartered membership exam: https://youtu.be/lDdOdF2aSFs?si=IrK_Cx3tfg-rzhvA Submissions: Through submission links in MyAberdeen. You are required to keep your own electronic and/or ‘hard’ copy of any work submitted. Assessment criteria: The assessment of the course works will be based on various items include: • A complete package of calculations from concept design to detailed design. • Effective presentation, conveyance and communication of the information (2CGS marks for each of the assignments) . As a structural Engineer in design offices, you need to present your calculations to other members of the design team and your calculation results will be used by other Engineers to continue the work until the stage of construction and completion of the project. The way you present your calculations should flow and must be very clear to everybody not just yourself. You need to use sketches, drawings, and diagrams throughout the calculations. • Accuracy of the calculations is also very important for the same reason as above. • A sample calculation (2CGS marks for each of the assignments) covering the whole process of the design is required for all the hand-calculations. The repetitions can be tabulated. Missing each of the above criteria may result in reduction of marks by one grade bande.g. if the calculations are complete and accurate but presentation is not satisfactory the grade maybe dropped to a B band. All calculations can be handwritten or typed in the provided calculation sheets or a structured format of your own choice. The general project description: The client requires the conceptual design of an offshore substructure to support a well head platform in a water depth of approximately 34.5m (to LAT). Other alternative concepts have already been ruled out for this site, leaving steel jacket structures as the only viable alternative. This assignment covers a range of integrated design courseworks that are required in the conceptual design of a jacket. Design data for the jacket structure is included accordingly in this assignment. The substructure is required to provide lateral support toten 0.762 m diameter conductors spaced at a minimum of 1.3 m centres. All conductors should be located within the conductor bay outline shown in figure below. Functional loading: The topside loads on the wellhead platform. topside consist of dry loads, operating loads and live loads. The wellhead deck should be assumed to have a dry load of 2200 te and operating load of 1500 te. The centre of gravity for the dry and operating loads should be assumed to beat the centre of the topside at 26.5 m above LAT. The laydown area is shown below and should be assumed to have a load limit of 15 kN/m2. Tidal levels for the platform. are given below. MSL = LAT + 1.87m HAT = LAT + 3.60m The storm stillwater levels for different return periods are: SWL (1 year) = MSL + 1.23 m SWL (100 year) = MSL + 2.01 m Assignment 1- Coursework P1 (100%), Framing/bracing configurations and preliminary sizes: Prepare adesign appraisal with appropriate sketches indicating between three to four distinct and viable structural solutions for the proposed substructure (i.e., from seabed to the +21m level) complying with the requirements of the platform framing configurations (20% marks). The different schemes should consider aspects such as: the batter angle; the number of bracing bays, and the pattern of the frame. bracing. Preliminary framing and bracing sizes (70% marks) of at least three comparable choices (recommended choices are: 3 and 2-bay, X- bracing compared with 3 and 2-bay, diagonal bracing systems using the same batter angle for all the choices) should lead to and justify (10% marks) selection of one preferred scheme based on weight comparison of 4-sided jacket (i.e., the whole structure), structural performance and practical issues. Assignment 2- Coursework P2 (50%), In-place loading and preliminary analysis: For the platform. layout given in the general description and the preferred jacket outlined in P1: a) Draw the wave and current velocity profiles. b) Calculate wave, current, wind and vertical forces applied to the jacket. c) Calculate the maximum base shear and overturning moment that must be resisted by the jacket and transferred to the pile foundation. The design parameters are given in Tables as below. Assume marine growth of 100 mm below SWL100. Platform location: 052°47'11"N, 003°09'36"E Air Density = 1.24 kg/m3 Sea Water Density = 1025 kg/m3 Design wave parameters: Return period Wave height (m) Wave period (s) 1 year 10.7 10.2 100 year 15.5 12.2 Design current profile: Depth Current velocity (m/s) 1 year 100 year Surface 1.4 1.6 25% of water depth 1.4 1.6 50% of water depth 1.4 1.6 80% of water depth 1.2 1.5 95% of water depth 1.1 1.2 1m above Seabed 0.95 1.1 Wind design parameters: Return period 1 hr wind speed at 10 mabove Sea level (m/s) 1 year 27 100 year 33.5 Assignment 2- Coursework P3 (50%), Computational modelling/analysis: Simulate the initially sized jacket in P1 with beam elements employing a finite element software: apply the given permanent and variable loads to the topside platform. and input the environmental wave, current and wind loading tabulated in P2. Compare the base shear and overturning moment derived from the computational analysis to those in Coursework P2 approximated by hand calculations for wave + current + wind loads and discuss (20% marks) the possible reasons for the difference in results (check with and without the effect of pile sleeves in hand calculations). Report the computational work using graphics from the final model views, applied loads (detailed input parameters and tables for wave, current, wind and vertical loads) (20% marks) and analysis results including deformed shapes under vertical and lateral loads (20% marks), axial forces (filled diagrams for vertical and lateral load cases at 0, 45, 90-degree directions) (20% marks) and support reactions (show values) (20% marks). Assignment 3-Coursework P4 (50%), Design of tubular joints: For the preferred platform. jacket outlined in P1 and analysed in P3: Select and classify the most critical joint at the bottom plan level, based on the most critical load combination, comprising all the in-plane braces at that joint (10% marks). Check the joint detailing and validity range criteria are satisfied (10% marks) and calculate the utilisation factor for at least one set using an appropriate LRFD code of practice (80% marks). For braces classified as K% and Y% joints, a combined K/Y effect should be accounted for through the corresponding strength and chord force factors (i.e., Qu=K% × Quk + Y% × QuY and qA=K% × qAk + Y% × qAY). The angles between the braces should betaken from your computational model. The joint detailing should be checked accounting for eccentricity/overlap of the braces based on a chosen/measured gap. If the joint found to be over-utilised, or the joint detailing and validity check criteria are not satisfied, provide a solution supported by engineering joint detailing sketches of an update to the joint geometry that will enable it to resist the applied loads and satisfy the specified detailing criteria. Assignment 3-Coursework P5 (50%), Design of pile foundations: For the preferred platform. jacket outlined in P1 and analysed in P3 and based on the maximum axial and shear forces taken from the computational analysis results considering all the ASD load combinations: Select a pile diameter and thickness to resist the maximum compressive pile head axial and lateral forces calculated in P3 with an interaction ratio between 1.0 and 1.33. Assume moderate to good pile driving condition (5% marks). Design the most critical pile using the soil profile shown below, assuming both plugged and unplugged failures and discuss the governing failure. Use a single pile foundation per leg (generally a smaller number of larger diameter piles reduces the installation time) (80% marks). For both the plug and unplugged designs plot the variation in the soil-pile tension and compression capacity to a depth of 70 mbelow seabed (15% marks). Design soil profile: Assignment 4-Coursework P6 (100%), Computational design: For the simulated and analysed jacket in P3 perform. the design iteration inputting appropriate load combinations for full 360-degree wave approaches: - Incorporate the piles (designed in P4) into the computational simulation employing springs for axial and lateral stiffness based on appropriate t-z, Q-zand p-y soil-pile interaction characteristics. Design the most efficient jacket sections with piles (50% marks) with expected demand to capacity ratios (DCRs) of the legs and face braces being greater than 0.7 while lower DCRs may be acceptable for plan braces. The legs and face braces maybe grouped at each bay for practicality purposes. - Check and redesign the jacket members and piles based on updated dimensions/number of the piles to achieve a topside maximum lateral deformation of the minimum of 100 mm and 80% of the initial deformation under the operating environmental load with 1-year return period (40% marks). - Compare the initial and updated jacket and pile designs and discuss the most efficient solution based on minimum weight and practicality (10% marks). Report the above computational work using 2D views of the designed sections and their design to capacity ratios of ALL the elevations and plans as well as tables and sketches for comparing the designs. Note: Local buckling should be avoided for all the designs following the D/t limitations instructed in the preliminary sizing of the sections.
ECON6012 / ECON2125: Semester Two, 2024 Tutorial 3 Questions A Note on Sources These questions and answers do not originate with me. They have either been in uenced by, or directly drawn from, other sources. Key Concepts Compact Sets, The Heine-Borel Property, The Heine-Borel Theorem. Tutorial Questions Tutorial Question 1 Use the Heine-Borel Theorem to show that S2 ={(x, y) ∈ R2 : d((x, y), (0, 0)) = 1} is compact in R2 . Tutorial Question 2 Use the Heine-Borel Theorem to show that [—1, 1] × [—1, 1] is compact in R2 . (You may use the fact that the functions fi : R2 —→ R defined by f1 (x, y) = x and f2 (x, y) = y are both continuous.) Tutorial Question 3 Consider a consumer whose preferences are defined over the consump- tion set X = R2+. This consumption set consists of bundles of non- negative quantities of each of two commodities. Denote atypical con- sumption bundle by (x1 , x2), where x1 is the quantity of commodity one in the consumption bundle and x2 is the quantity of commodity two in the consumption bundle. Suppose that this consumer faces a budget constraint of the form. p1 x1 + p2 x2 ≤ y, where p1 > 0 is the linear price per unit for commodity one, p2 > 0 is the linear price per unit for commodity two, and y > 0 is the consumer’s income. The consumer also faces non-negativity constraints on his or her con- sumption of each commodity. This means that x1 > 0 and x2 > 0. 1. What is the consumer’s constraint set? 2. Is the consumer’s constraint set a subset of his or her consump- tion set? 3. Is the consumer’s constraint set a proper subset of his or her consumption set? 4. Is the consumer’s constraint set non-empty? 5. Is the consumer’s constraint set a compact set? Justify your answer. Additional Practice Questions Additional Practice Question 1 Use the Heine-Borel Theorem to show that S3 ={(x,y, z) ∈ R3 : d((x,y, z), (0, 0, 0)) = 1} is compact in R3 . Additional Practice Question 2 Use the Heine-Borel Theorem to show that [—1, 1]n is compact in Rn. (You may use the fact that the functions fi : Rn —→ R defined by f1 (x, y) = xi for each i ∈ {1, 2, · · · , n} are all continuous.)
Assessment 2: Research Project (60%) Word Limit: 2,500 words Submission date: Thursday 30th January 2025, by 3pm. Students will devise a research question that can be answered using a digital methods approach, using Zeeschuimer and 4CAT. Other data collection tools are not permitted. The research project MUST be approved by the module convenor in advance, by completing this form. before 9am, December 17th. The student will undertake the relevant research and produce a report which summarises the research and findings and the methods used. The report will reflect on the strengths and limitations of the chosen tool and methods, the extent to which they shape the research questions that can be asked and the data that can be found, and the ethical challenges and implications of using these methods. Students should use the following structure for their project report. 1. Title 2. Introduction (200 words). Brief presentation of research topic and research problem. 3. Relevant literature & Research Question (300). Briefly review relevant literature and conclude with the presentation of your specific research question. 4. Data, Methods and Ethics (800). Consider the following issues: · What data have you collected and analysed? · Why is the data relevant to your research question? · How did you gather the data? Describe the sample period if relevant. · What analysis have you carried out? · Explain the reasons why your analytical techniques were the best way to address your research question. · Discuss the ethical issues connected to the research. 5. Findings and Discussion (600): present your findings (with paraphrased quotes, visualisations, tables if relevant). 6. Conclusion (600). Use these prompts as a guide: · What answer can you provide to your research question? · How does this answer compare to existing research on the topic (do your findings align with existing research or does it suggest new developments)? · What limitations are there in your research (critically discuss possible flaws in the methodology)? · What possible ways could the research be developed and improved in the future?
Independent Study ANTH 101L: Biological Anthropology Lab Course Notes and Assignments Module 1 Course Notes (Chapters 1 and 17) Chapter 1 – Introduction to Biological Anthropology What is anthropology? And what is biological anthropology, in particular? Have you thought about it before? Anthropology, in short, is the study of all people in all places and times. Studying people everywhere and everywhen. Anthropology (in the United States, anyway) is divided into four major subfields: cultural anthropology, archaeology, linguistics, and biological anthropology. Across all of these areas of study, we employ four approaches to research: holism, comparison, dynamism, and fieldwork. Of these, fieldwork is what you have likely heard about the most. Lab work aligns with fieldwork in that it provides hands-on application of the concepts. Let me break this down a bit further. Cultural anthropology is the study of living cultures. Culture is the main way that we adapt to our environment (we are not polar bears packing on extra body fat and thick fur in preparation for winter . . . instead we invent shelters, means to heat them, and warm clothing). The main way cultural anthropology studies are conducted is through participant observation. This means researchers, after doing a huge amount of background research, are living among the people they are studying, interacting with them, observing them, and often participating in daily activities. This is fieldwork and often extends for many months at a time, sometimes a year or more. Archaeology, near and dear to my heart, is the study of past cultures through the things they leave behind. This means either their artifacts or, sometimes, their bodily remains. Artifacts are anything created or affected by humans, so, objects, roads, structures, storage pits, pyramids . . . these are all of interest to archaeologists. Linguistics is everything you ever wanted to know about language but were afraid to ask. Linguists study modern languages, ancient languages, languages that are written, languages that are spoken only, how language is acquired, how languages are similar and how they have changed over time. Finally, biological anthropologists are the body folks. They study how we are similar, how we are different, and how things have changed over time. Yes, we change physically but that is over long time-frames. Remember that culture is the main way we adapt to our environment, and cultural changes can happen very quickly. Each of these four major subfields has many many subspecialties. Some anthropologists talk of a fifth major subfield, though it really relates to each of the four so I don’t consider it a fifth subfield: applied anthropology. Applied anthropology is the practical application of any anthropological subfield to real-world issues. An example would include forensic anthropology, which is a subdiscipline of biological anthropology. Biological anthropology (sometimes shortened to bioanth) has also been called physical anthropology. You will see many references to this and it’s often a factor of the time period the author learned it in school. Often physical anthropology is an older term, though both biological anthropology and physical anthropology are valid terms for the same thing. Biological anthropology has numerous subfields within it including: primatology (think Jane Goodall), paleoanthropology (looking at ancestors waaay back), molecular anthropology (looking at genetics and DNA), biological archaeology (examining human remains from archaeological settings . . . fascinating stuff), human biology (looking at modern adaptations and variations), medical anthropology (difficult to define succinctly but the application of anthropology to medical issues), and paleopathology (looking at usually skeletal pathology in ancient specimens). Anthropology seeks to apply the scientific method. You should be familiar with it already, but if you are not here it is in a nutshell: essentially a researcher would make observations, decide on a testable hypothesis, test it, obtain the results, and revise the hypothesis as needed. Chapter 17 (in the Appendices) – Osteology This week please read Appendix A in the textbook. Page 635 is a good reference for the complete human skeleton. It is important to have a basic understanding of osteology (the study of human bones) since this is a critical part of the material examined in biological anthropology. This unit gives a good overview of the human skeletal system. One note of clarification: Some people confuse osteology with faunal analysis. While osteology is the study of human bones, faunal analysis is the study of animal bones, usually from archaeological contexts. The human skeleton can tell us a lot about people right now, from a few hundred years ago, or from thousands of years ago. Soft tissues do not usually survive from the past (though there are certainly exceptions) but, because of their mineral content, bones preserve surprisingly well. Burial context and preservation is important and that is a whole other topic. For now, understand that we see very poor preservation in very acidic burial contexts. As the text mentions, there is standardized anatomical terminology used to describe anatomical positions, features, directions, and movements. The anatomical position (see p. 676) is the standard way of laying out a human body or skeleton so that no bones are twisted around, and directional planes are taken from this position. It is important to understand what anterior, posterior, distal, superior, medial, lateral, inferior, proximal, robust, and gracile (robust means what it sounds like, bigger and thicker; while gracile means thinner and leaner) mean. Also, understand what cranial skeleton vs. post-cranial skeleton indicates (head and everything below the head). Note the directions in Figure A.3 on p. 628. Pp. 629-630 and Figure A.4 give an explanation of bone structure and remodeling. Bones are generally considered one of five shapes including: long, short, flat, sesamoid, and irregular. There is a typo on p. 634. The fifth line of text should read “against the force of gravity, . . . “ Note the discussion of the axial vs. appendicular skeleton on pp. 634-5. The text gives a good tour of the head and there are good illustrations on p. 637 Figure A.13 that will be worth referring back to this semester. Note the foramen magnum shown in Figure A15 and its position beneath the cranial base. On p. 645 there is a brief discussion of teeth. Each tooth type has a particular shape and function. The flat incisors in the front of the mouth are excellent for slicing into food, such as a piece of fruit or a vegetable. The canines (vampires, dogs, and cats have hyper-developed canines) are good for puncturing or grasping food for tearing. The premolars (sometimes called bicuspids) and molars are good for grinding and tenderizing food prior to swallowing. Teeth can be, and often have been, used for tools as well. We can learn a lot about an animal’s diet by looking at its tooth count and type. Alligators have one kind of dentition, goats have another. Also note that human deciduous teeth (the baby teeth that fall out) are a bit different from our permanent teeth. Think about what that means for us and our diet. We’ll look at teeth a bit closer later. The vertebral column is a fascinating stack of bones which support our upright posture, provide a framework for attaching ribs which provide protection for vital organs, and which is designed to flex as we locomote. There are seven cervical (neck), twelve thoracic (upper torso), five lumbar (lower back), five sacral –and these are fused (back of the pelvis), and three or four coccygeal (tailbone) vertebrae. Note that “vertebra” is the singular form, “vertebrae” is the plural form. Each type has typical morphologies specific to its region. The text has very good labeled illustrations. Note the different spinal curvatures that help maintain stability. On pp. 651-2 there are a couple of typos. The text on p. 651 references Figure A.31 but there appears to be no Figure A.31. On p. 652 the text should read, “The humerus is the bone of the upper arm.” (Note, there is no “o” in humerus) The appendicular skeleton (arms, legs, hands, feet) contains numerous long bones that are important in determining age at death, height, musculature, and often reveal signs of disease or injury. The pelvic girdle is the most important site in a skeleton for determining sex. Please note that in anthropology, sex and gender are not necessarily the same things. Sex is biological and is determined by chromosomes (more on that in a later chapter) while gender is a socially constructed role, though that’s more in the domain of cultural anthropology than our study of biological anthropology right now. There are a few features in the pelvis that can also be used for helping to determine age at death, depending on how well preserved they are. There is another typo on p. 658. The text should read, “There are two bones of the lower leg: . . . “ There is a brief discussion of adult skeletons vs. subadult skeletons and of comparative anatomy also. Module 1 Assignment Please fill in the osteology of the skeleton and the skull worksheets found below and submit them. Answer the following questions about the bones indicated on the diagram on the previous page using the correctly spelled scientific terms. A. This is often one of the best preserved portions of a skeleton. B. This bone supports strong muscles in the upper arm. C. These support the torso and, working together with the other bones in this stack, give the body stability when upright. D. These two bones articulate with other bones at the elbow and the wrist. and E. This portion of the head articulates with the upper bones of the head near the ear. F. These two bones articulate with other bones at the knee and at the ankle. and ___________________ G. This entire circular structure is important for determining biological sex of a skeleton and helps to support the internal organs. H. This is the strongest bone in the body and is difficult, though not impossible, to break. ______________________ I. This little bone is not usually present in newborn babies but develops in the first couple of years of life. J. These bones articulate with the fingers and the bones of the wrist. Use the correctly spelled scientific terminology to answer the questions below. "Skull illustration, lateral view - Axial Skeleton Visual Atlas, page 17"byRob Swatskiis licensed underCC BY-NC 2.0 A. The angle of this bone is one method of determining biological sex from the skull within a population. Its angle is an important feature of early hominins. B. This is the general term for where two bones come together, usually forming a joint. We say two bones here. C. This paired bone is a major bone of the head and meets in a center line called the sagittal suture. It also forms part of the lambdoid suture at the posterior of the head. D. This bone forms the lower portion of the lambdoid suture and figures prominently in Neanderthals skulls. E. The robusticity of this boney projection is another method of determining biological sex from the skull within a population and can be readily felt behind the ear. _______________________ F. This bone forms the cheek bone. G. This boney projection is well-developed in modern Homo sapiens sapiens, not so much in early hominins. H. This bone resides above the ear. "Skull illustration, anterior view - Axial Skeleton Visual Atlas, page 9"byRob Swatskiis licensed underCC BY-NC 2.0 A. The bones of the top of the head meet in a midline connection here. B. This boney area’s size is one method for determining biological sex from a skull within a population and is quite prominent in Neanderthals. C. This rounded area protects the eyeball. D. This is where the upper teeth are found. E. This is the lowest part of the skull and is where the lower teeth are found. F. These prominent boney projections form. the cheek. G. These little holes allow for the passage of nerves and blood vessels. Module 2 Course Notes (Chapters 3 - 5) Chapter 3 – Molecular Biology and Genetics In Biological Anthropology, ANTH 101, we looked at the principles of inheritance including Mendelian inheritance where we have single-gene recessive or dominant alleles. Remember that in this case heterozygous indicates the inheritance of two different alleles for a gene, while homozygous indicates the inheritance of two of the same alleles for a gene. Mendel famously studied pea plants and noted a number of different characteristics for which he was able to determine dominant and recessive traits. When a heterozygous gene carries a recessive and a dominant allele, the dominant allele will be expressed in the phenotype. The same is true for a homozygous gene carrying two dominant alleles. A homozygous gene carrying two alleles is required for the recessive trait for that trait to be expressed. Examples of Medelian traits found in humans includes mid-digital hair (hair on the middle segment of your fingers), tongue rolling (the ability to roll the sides of the tongue into a tube), earlobe attachment, interlocking fingers and thumbs (placing the left thumb over the right is the dominant condition), earwax color, and a cleft chin (dimple in the chin). Remember in the Explorations online textbook we looked at a number of different inheritance patterns including incomplete dominance and codominance. There is also a sex-linked inheritance pattern where a trait is carried on the X chromosome. Since females have two X chromosomes (XX), an allele on a single X chromosome will not necessarily be expressed or expressed in full, whereas since males have an X and a Y chromosome (XY), if they carry the proper allele, it will be expressed. This can have serious health consequences with diseases such as hemophilia, which is carried by females but is most commonly expressed in the male offspring. Some members of Queen Victoria’s royal lineage in royal families in Europe experienced this devastating disease. You’ll read more about different modes of evolution in part of this week’s assignment. Module 2 Assignment Complete the Punnett Square assignment (below), the Gene Flow assignment, and the Genetics Discussion and submit them. Punnett Squares: Gene Flow Assignment: In Biological Anthropology, ANTH 101, we looked at some of the ways allele frequencies change so we take a tangible view of what that might look like. For this assignment you will need a group of multi-colored candies or small pieces of paper about the size of a dime (think M&Ms or Skittles, or something like that . . . you can use crayons but that’s not as much fun). You need anywhere from 30-100 candies/colored pieces of paper and you need more than four colors but fewer than ten, your choice. Make sure your hands are clean and have a separate piece of paper for notes. 1. Place a piece of paper (regular notebook or printer paper is fine, this is not for notes) on your desk in front of you. Dump all the candies into one pile together and mix them up. Record how many total candies you have. The different colors represent different alleles. Randomly divide your pile into two equal groups (call one Group A and the other B) and set one aside. These groups are your gene pools. Record how many of each color you have in each group. 2. Draw two “islands” on your paper then randomly populate both islands with the candies from your group that you did not set aside (Group A). Count the numbers of each color on each island and record your results. These are your starting populations for these islands. Now push the candies from both islands together and mix them. You have introduced new genetic material and this illustrates gene flow, what happens when two populations experience any admixture of new alleles. Record your total numbers of each color in this newly mixed group. 3. Now randomly place your hand over top of this population and remove approximately a third of the pile (no need to count, just approximate a third of your pile and push it aside). Eat these candies (or share with your friends/family). You have just experienced a catastrophe of a natural disaster or disease. Record your numbers for the remaining group. How have your allele frequencies changed? Did you greatly reduce any one particular color? As your population numbers get smaller, you have a more limited gene pool from which to draw genetic material. This could potentially lead to health issues as the chances of deleterious genes being expressed increases. 4. Now set what remains of Group A aside and pull out your original Group B. Be sure you have recorded how many of each color you have for this group. Eat (or share) all of your favorite color of candies from Group B. This represents Natural Selection, because you selected them out of the population due to some particular trait (in this case, color). Record how many of the eaten candies there were and how many remain of each of the other colors. This has again changed your allele frequencies and has removed (and represents a lack of) those alleles from your populations. The eaten candies might represent a hair color or an eye color, or perhaps lactase persistence (the ability to digest milk and milk products after childhood), etc. 5. Finally, push all of your candies from both groups together. Record your numbers (total and numbers of each color). Now randomly take one in every five candies and squish it a bit with your thumb. This represents random mutation, which may occur in DNA replication. This may not have a deleterious effect on the population or, on the other hand, it could reduce the “success” of that part of the population, meaning that segment of the population will not successfully reproduce and have fertile offspring. This exercise has illustrated some of mechanisms of allele frequency change. Please type up your numbers and discuss how allele frequencies changed (or didn’t) with each step (minimum half a page of discussion). Genetics Discussion Final part of the assignment for this module: Please write your responses to the question below. The more examples you can give, the better. What are the ramifications of a service like 23andMe? What kind of information can an individual learn from genetic testing? Is this good or bad or ??? Who should have access to this information? Why? If it helps, you can visit the website of a genetics testing company to see what services they offer before answering these questions. Module 3 Course Notes (Chapters 5 and 9) Chapter 5 – Meet the Living Primates This week read the chapter in the text to better inform. you for the primate assignment below. Your assigned primate depends on when you were born! Jan/Feb = human, Mar/Apr = chimpanzee, May/June = orangutan, July/Aug = gorilla, Sept/Oct = ring-tailed lemur, Nov/Dec = baboon. Chapter 9 – Early Hominins Along with these course notes, take a quick look at the overview of bipedalism in the ANTH 101 Explorations text on pp. 327-330, especially the illustration in Figure 9.5 and the list in Figure 9.6. Here we turn our attention to bipedalism, its associated biological morphology, and behavioral changes it precipitates. What is bipedalism and why is it such a big deal in biological anthropology? Bipedalism is the act of walking on two legs as opposed to quadrupedalism, which is the act of walking on four. Bipedality distinguishes humans from all other modern hominins in that we are the only ones who can locomote comfortably in a bipedal manner; indeed, we use habitual bipedalism which means it is our most comfortable, efficient, and easiest method of locomotion. Certainly apes can and do use bipedalism at times but their gate is not smooth, and is more of a waddle from side to side. Also, it is not the most comfortable or frequently used form of locomotion among the apes. We have talked about different anatomical parts of the skeleton and when examining fossils for signs of possible bipedality, we must look at specific areas of the skeleton for clues, often taking more than one feature into account. The foramen magnum is located very differently in a bipedal human than it is in a quadruped such as a great ape. Even though apes spend a lot of time in a seated position, locomotion is frequently quadrupedal which means the head needs to be held where the animals can comfortably see where they are going whether locomoting slowing or quickly. The foramen magnum of an ape, then, is located fairly posteriorly which facilitates keeping the head in a horizontal orientation during quadrupedal locomotion. The foramen magnum of a human, on the other hand, is located much more towards the center of the inferior portion of the skull in order to balance it atop the spinal column which is the optimum orientation for bipedalism. The human vertebral column is S-shaped with a curve in the upper portion of the spine (the cervical curve) and a curve in the lower portion of the curve (the lumbar curve). These two curves act as a giant shock absorber and keep the weight balanced over the knees and feet in a midline of a bipedal human. The vertebral column in an ape is straighter which causes the weight to be carried more forward when standing. The pelvic girdle is short and broad in bipedal humans forming a bowl shape, and it supports the internal abdominal organs. (see the illustration on the next page) The gluteal muscles attach to the posterior surface of the ilia and help to stabilize the hip and maintain balance when one foot is off the ground during a stride. The left gluteal muscles balance the left leg and hip while the right foot is striding and the right gluteal muscles balance the right leg and hip while the left foot is striding. The pelvic girdle of apes is very different. It is tall and narrow, and forces the center of gravity to the anterior of the body. The gluteal muscles allow forward motion but are not positioned to balance the animal in an upright position when one leg is off the ground so they cannot balance on one leg like humans can. One other difference between a human pelvis and an ape pelvis is the size of the inlet or large hole in the middle. The inlet of an ape pelvis is quite large in comparison to that of a human. Ape infants easily pass through this inlet, which means that childbirth is much easier for an ape. The large inlet easily allows the passage of the infant ape whereas the smaller inlet in the human pelvis, which is a function of its shape, makes childbirth much more difficult in humans since the size of a human infant’s head (the largest circumference feature of a human infant) is very close to the size of the human pelvic inlet. On occasion, a human infant’s head is too large to pass through the mother’s pelvis which necessitates Cesarean delivery. This is thought to be an anatomical tradeoff for bipedality. The angle of the femur and how it articulates with the top of the tibia at the knee is also different from apes. Apes tend to have straight knee articulation whereas human bipeds tend to have the knees angled inward to better balance the pelvis above the knees, this is known as the valgus knee. The foot also is different in that the ape toes (phalanges) are long for grasping (prehensile) and the big toe (hallux) is divergent, meaning it splays sideways to the medial aspect of the foot. The foot in the bipedal human has short phalanges with a large, non-divergent hallux that bears a great deal of weight. Along with the powerful calf muscles, the human hallux is used to propel the foot. Both ape and human feet have a transverse arch which runs medially to laterally, but only humans have a longitudinal arch running from the toes to the heel. You can see evidence of this in your own foot if you look at footprints you leave with your bare feet in soil or as a wet footprint on a solid surface (such as after a dip in a pool or after getting out of the bathtub or shower). So how does bipedalism change human behavior. over that of an ape? Well, habitual bipedalism means that we spend less time in trees than apes do. Our feet and legs are not as well suited to climbing trees as are the feet and legs of apes, and we do not brachiate on a regular basis (unless we spend a fair amount of time on jungle gyms). Apes are able to easily traverse branches in trees, often traveling from one tree to another through quadrupedal movement, using prehensile toes, leaping, and brachiating. Humans, however, use habitual bipedalism and spend a vast majority of their time terrestrially. Advantages of bipedalism include the ability to carry things (objects and infants), hunting since the hands are freed up to engage in hunting activities, gathering from higher terminal branches than from the ground level, thermoregulation since less of the torso is directly exposed to the sun and the head is elevated above the heat reflected from the ground, the ability to traverse long distances using less energy since quadrupedal locomotion requires much more energy than bipedalism, and surveillance of prey or predators from a higher location than from a quadrupedal elevation on the ground.
PMGT5205_2024S2 Professional Project Practice A2 - Team Report (20% of course assessment) PART A - 5 of 10 Questions. Part B to be released in Wk9. The following questions are based on Pacificano Markets scenario and should be worked on as a team activity and answered in your report. See Canvas Discussion Thread for details! 1. Team Profile (10 Marks) a) The format and presentation of your report should look like it came from a project consultancy and will be assessed for its professionalism and incorporation of your team name/branding. b) Briefly describe your team members and team building activities by providing: • A portrait/picture and short bio of each member of your group including your DISC (*) profile • A summary of your Team Charter and WOW, or Way of Working! • Describe the team building activities you undertook and their effectiveness • Provide a RACI matrix showing the responsibility for/ contribution to this assignment c) From your team building experiences, suggest a (ideal/ better) team activity that the Pacificano Markets team might undertake to quickly establish a good working environment. (*) See this website: https://www.123test.com/disc-personality-test/ 2. Rich Pictures (10 Marks) a) Run a workshop with your team members to develop and then draw/ submit TWO separate high-level Rich Pictures (not too many words please) that visually highlight/capture the key stakeholders, and the interactions between them, in: • The “current state” of Pacificano BEFORE the strategic decision to establish weekly markets • The “future state” of Pacificano AFTER the introduction of the weekly markets b) Use the two drawings above to list the changes required to establish/ manage the weekly markets. 3. Stakeholder Analysis (10 Marks) Undertake a team-based stakeholder identification/ analysis, potentially using the Rich Pictures above and your understanding of the scenario. a) Create a Stakeholder Register that: • Identifies the five major stakeholders in this project – start with the most important external stakeholders - DO NOT include the project manager/ team. • Briefly describes the main concerns/ interests for each stakeholder. • Explainshow you might manage the stakeholders’ concerns to ensure project success. b) Use a Power/ Interest matrix to: • Position each of these stakeholders on at the start of the project. • Describe briefly how would you manage each stakeholder’s concerns and interests. • Explain/discuss any stakeholders that would move positions on the matrix during the project 4. Business Case (10 Marks) Undertake a team-based exercise to define the main sections that should be included in a compelling business case to justify the Pacificano Markets idea. a) Provide a brief SWOT analysis of Pacificano Markets strategy and represent it in a simple table b) Use McKinsey’s three time-horizons model to describe your understanding of the Pacificano Markets Scenario explaining what might take place in each time-horizon c) Write a representative SMART objective for each of the time-horizons TH1 – short-term, TH2 – medium-term, TH3 – long-term. d) Apply the User Story format/ template* to capture four (4) key User Stories related to the project/ stakeholders identified in the scenario (*) As a I need to so that I can 5. Work Breakdown Structure (10 Marks) Based on their understanding of the scenario (extended by discussions on Canvas) the PM and project team developed the following preliminary high-level WBS for estimating the first launch of Pacificano Markets: a) Review/ critique the above (preliminary Level-2) WBS and use the definition and/or the project scenario to identify: • At least two positive (good) things about the WBS above, and, • At least two negatives (bad/weak/missed) things about the WBS. Note: You may need to “interview” the Pacificano Mayor (via the Canvas Discussion Thread) to better understand the WBS above. After confirming with lecturers, teams have the flexibility to adjust the structure/headings so long as it does not change the scope. b) Use your team’s amended WBS to identify at least 2 to 4 (max) realistic work packages under each of the above (Level-2) work breakdown to show (at least 12) Level-3 work packages. c) Present the WBS in a table and for each of your Level-3 work packages: o Briefly describe/ explain (~10 words or less) the product/service that would be provided/ delivered by that work package o Identify some relevant activities that would need to be conducted to deliver that product/service
MENG 4019 - Practical 4 – 2022 Task: design and simulate the operation of a hydraulic curcuit. Two hydraulic cylinders: First hydraulic cylinder: stroke 2000 mm, D piston 100 mm, d rod 50 mm angled 75 degrees from horizontal is lifting a mass load of 500 kg. Pulll external force 8000 N, push external force 10000 N. Second cylinder: stroke 1000 mm, D piston 100 mm, d rod 50 mm. Pulll external force 10000 N, push external force 15000 N. Sequence: First cylinder extends, command by a push button. Once first cylinder reaches limit of stroke, after 3 seconds, the second cylinder extends. After the second cylinder reaches limit of stroke, and after 4 more seconds, first cylinder retracts, then second cylinder retracts Use PLC to control the sequence First, we build the conceptual circuit: 1. Open Automation studio, select and insert the following components from the Hydraulic set of components. 2. Edit the valve – change the internal distribution Then copy/paste the valve: select and ctrl + drag it 3. Connect circuit as shown below. You can name the cylinders: 4. Set the parameters for the hydraulic cylinders 5. Check the circuit - Select the Simulation tab and run a Normal Simulation. Then, Stop Simulation and run a Slow-Motion Simulation. Click on the valves to change position. Check that all connections are set and are correct: 6. Set the PLC for the control of the circuit. From the Ladder for Allen-Bradley PLC/ Ladder for AB PLC drag a Rung in the model: 7. We see that the surface of the sheet is too small. Right click on the document, select Document Properties and change the size to A3: 8. Click on the rung and move it in a suitable position. Then from Electrical Control (JIC Standard), from PLC cards, select and place the PLC Input Card and PLC Output Card, as shown: 9. From the Electrical Control (JIC Standard) insert the power supply in the PLC input and output cards. Insert the push button and call it START. 10. Set the solenoid for Cylinder 1 in the output bank (SOL_1), an Examine if Closed (XIC) contact and an OTE (Output Energise). Link them: XIC to the IN0 input, the OTE to the OUT0 output, the SOL_1 to the valve’s solenoid and the solenoid between OUT0 and the power supply: 11. We check that the rung operates correctly and the cylinder 1 is correctly being actuated with the push button 12. We seal-in the solenoid as the push button is pressed. We use a program instruction reference between the output and the input: 13. We check if it works – all seems correct: 14. We also insert a push button – STOP – connected to IN1 and an Examine if open (XIO) contact in the first rung 15. We check the START/STOP functionality – all seems correct 16. We set the proximity sensor on the first cylinder, we insert a normally open proximity switch, and we connect it to IN2, we insert an XIC contact into the next free rung and a timer. We set the timer at 3 seconds (time base 0.1 s, preset counter – 30) 17. We connect the Done output of the timer to an XIC input and the OTE to the second solenoid 18. We check functionality. All seems to be working well: 19. We need to set the proximity sensor on the second cylinder, link it to a normally open proximity switch, link the proximity switch in the input, link it to an XIC and a timer in the PLC. If the number of rungs is insufficient, click on the last rung and pull it down gently Connect all components, add two XIO contacts before the B3:0/0 and OUT2. Note: ensure the connections are with the DN of the second timer – check code of the timer 20. Check the functionality of the circuit. All seems to be in order. Save the circuit, then try alternatives. Add functionality and test. Document your work.
LING 226 Assignment 2, 2023 Short Program and Written Reflection 2 (25% of total grade) The goal of this assignment is to ask and answer a question about the linguistic profiles of different texts. The question being asked should be motivated by your understanding of and possible assumptions about the texts. These motivations and assumptions do not necessary have to be correct, but they should be logical/reasonable/justifiable. For example, we could assume that children’s books are written with less sophisticated vocabulary when compared to adult books – this is a reasonable assumption. We might also expect a horror novel to include more negative language when compared to a romance novel. In both cases, we can test these questions by constructing a linguistic profile of the texts and comparing them. For the child/adult book comparison, we may want to create a lexical profile of frequency, diversity, concreteness, and potentially other measures of complexity. For the horror and romance comparison, we may want to construct a profile based on emotional vocabulary, sentiment, and other measures related to affect. In both cases, more than one measure would be employed to compare the texts (hence creating a linguistic profile). If more than one text is used for each category, we would calculate an average score for each category, and compare the results. Your job is to generate and a research question which you answer through calculating and comparing the linguistic profiles of different categories of texts. Specifically, please generate and test one question related to: 1. A small corpus of your own design which contains at least two categories of texts 。 A good minimum for your corpus will be ten texts per category, with two categories, with approximately equal total words per category. 。 You are free to use texts from anywhere, including data provided by Stephen, questions from The Current, or elsewhere. In addition to developing and comparing the linguistic profiles of your texts, you need to further complicate your analysis by examining the nature of your results when accounting for at least one distributional or syntactic property of the texts. This means information such as part of speech, collocations, or word vs. phrase-level measures (ngrams) should be incorporated into your research questions. For example, instead of just comparing the lexical sophistication between children and adult books for all words in a text, you would instead run separate analyses for nouns and verbs. Or, you might be interested in profiling the nature of collocations and/or ngrams for different measures. The choice is yours and might further interact with your research question (e.g., you might find that sentiment ratings of adjectives pattern with specific nouns that follow). Comparison of lexicon and distributional/syntactic information Lexicon Information Distributionaland Syntactic information Sentiment & Emotion Ratings Bigrams, ngrams Age of Acquisition Part of speech Concreteness Collocates Your Python Code You should create code cells and functions which: • Load in and preprocess your text(s) ◦ (The specific choices you make for preprocessing should be appropriate for your analysis) • Analyse your data for various lexical and syntactic features • Output your analysis either into the notebook, or written to file in a spreadsheet/text document • You data should be made available either by reading it in through URL or provided with your submission Just as before, the course notebooks have everything you need to create these functions. You can reuse any and all of the functions in the course notebooks to create your program. You will however likely need to make modifications in order to adapt these functions / code cells to your particular analysis. Your Written Reflection In your notebook, you should prepare a report describing on your analysis, which should include these sections: • Research Questions ◦ Clear statements of your research questions ◦ The rationale behind your research questions ◦ Predictions of what you will find • Data ◦ Explanation of the data and what categories it represents ◦ How you gathered the data for your own corpus • Analysis ◦ Description the linguistic profiles ◦ Decisions about preprocessing and other preparations of the texts ◦ Which lexical features were included, and why? • Results & Discussion ◦ Interpretation and discussion of your results (i.e., answering your research questions) ■ Did your expectations hold? Why or why not? ◦ Any remaining questions / limitations based on what happened during your analysis Your report should be about 500-600 words long (up to 900 if attempting challenge). You should submit your assignment as a .ipynb notebook file in Nuku/Canvas by the due date. You should also provide your corpus data (or load the data in via URL). Your notebook should have a text cell at the start with includes your name, your student ID, and whether you are attempting to complete the challenge (see below). The notebook should include all of the code cells, plus your written report as text cells. You are free to mix code and text cells as you deem appropriate. Marking Guidelines A-level papers will contain two clearly articulated research questions and the rationale behind the questions. There are clearly stated decisions behind why certain linguistic features are chosen to construct the linguistic profiles, as well as well as the choice(s) behind distributionaland syntactic measures. The presentation and interpretation of the results are used to provide direct answers to the research questions. The report also reflects on any limitations or remaing questions. A link and/or data files are provided for the corpus. All of the code cells will work properly. The paper includes a successful attempt at the challenge. B-level papers will contain two research questions and provide some rationale for the questions. The decisions behind why certain lingusitic features were chose may be unclear, as are the reasons for choosing particular distributionaland syntactic measures. Answers to the resarch questions are provided. A link and/or data files are provided for the corpus. All of the code cells will work properly. A challenge may be attempted, but to limited success. C-level papers will contain unclear research questions and/or research questions with unclear motivation or justification. The linguistic profiles may be under explained and/or weakly connected to the research questions. Data presentation and interpretation will lack detail and/or not clearly connect to the research questions. Some attempt is made to answer the research questions. A link and/or data files are provided for the corpus. All of the code cells will work properly. No challenge is attempted. D-level papers will have unclear research questions and/or poorly motivated linguistic profiles. Attempts are made to answer the research questions, which may be only partially successful. Data may not be included, and some code cells may not work. No challenge is attempted. A-level Challenge A-level papers need to go above and beyond the rest. Students need a way to play to their strengths. The challenge provides that opportunity. Students can either flex their computer science skills, showcase their critical thinking abilities and/or domain knowledge outside of computer science, or some combination of both. In either case, you should be driven by a desire to have your assignment used as an exemplar for next year’s cohort of students. I want to leverage my computer science skills: Just as in assigment 1, expand the boundaries of your program beyond the level of the code provided in the notebooks in order to provide more sophisticated presentation and analyses of your data. You might want to explore different visualisations in Python, and/or play around which some classification functions (e.g., some machine learning or statistical comparisons). You would still write a report which meets the criteria of A. I want to leverage my non-computer science knowledge: Include more justification and external research for your research questions and analysis. You might conduct your anaysis as a replication of some published research, or instead continue a research direction already established in prior literature. Your interpretation of your results is connected not only to your data, but also results of previous studies.
LING 226 Assignment 1, 2023 Short Program and Written Reflection 1 (25% of total grade) The goal of this assignment is to develop a program to read in text data, perform. some preprocessing on the data, and then compare the effects of different preprocessing on various text metrics. You should construct a program with these functions: • a function to preprocess text data which can: ◦ remove punctuation ◦ remove stopwords ◦ lowercase all words ◦ remove words below/above a certain frequency • a function (or functions) to calculate these text metrics: ◦ total number of words ◦ overall lexical diversity of the text ◦ average lexical diversity of text sentences ◦ top ten most frequent words The course notebooks have everything you need to create these functions. You can reuse any and all of the functions in the course notebooks to create your program. After creating these functions, you need to conduct an experiment. The goal of your experiment is to compare the effects of preprocessing on the different text metrics. To do so, you need to use data from at least two sources: 1. One of the built-in NLTK corpora resources (e.g., Brown, State Union) 2. Data from The Current (data from at least two questions) Using this data, look for trends and consistent effects that preprocessing has on various text metrics. Also look to see if there are any texts more or less immune to the effects of preprocessing. After conducting your experiment, write a short report (500-600 words) reflecting on your results. You should detail the comparisons and analyses that you conducted, what results you found, and your interpretation of the results. Specifically, you should focus on what happens to these metrics under different preprocessing conditions, and focus on making conclusions about their implications for text analysis in general. You should submit your assignment as a .ipynb notebook file in Canvas by the due date. Your notebook should have a text cell at the start with includes your name, your student ID, and whether you are attempting to complete the challenge (see below). The notebook should include all of the code cells, plus your written report as text cells. You are free to mix code and text cells as you deem appropriate. Marking Guidelines A-level papers will run a number of comparisons and report the differences between text categories in a clear and descriptive manner. The written reflection will be equally descriptive and include insightful reflections and deductions on how preprocessing affects these text metrics. These reflections and deductions will be clearly connected to the data and results from the student’s analysis. All of the code cells will work properly. The paper includes a successful attempt at the challenge. B-level papers will run the comparisons and note the differences between text categories. The written report will be partially descriptive but also include reflections and deductions on how preprocessing affects these text metrics. There are some connections made to the results of the student’s analysis. All of the code cells will work properly. A challenge is attempted to limited success. C-level papers will run few comparisons and make note of important differences between text categories. The written reflection will be mostly descriptive. All of the code cells will work properly. No challenge is attempted. D-level papers will run one or few comparisons between texts, make note of some differences between the texts, and include a written reflection which is too short and too descriptive. Some of the code cells may not work properly. A-level Challenge A-level papers need to go above and beyond the rest. Students need a way to play to their strengths. The challenge provides that opportunity. Students can either flex their computer science skills, showcase their critical thinking abilities and/or domain knowledge outside of computer science, or some combination of both. In either case, you should be driven by a desire to have your assignment used as an exemplar for next year’s cohort of students. I want to leverage my computer science skills: Go nuts with your program, but in a way that stays within the confines of the assignment prompt. You might want to develop new text metrics or improve upon the ones used in the notebook. You might find a way to efficiently compare data from multiple sources, combining the results computationally as a way to more empirically demonstrate the effects of preprocessing on text. You would still write a report which meets the criteria of A. I want to leverage my non-computer science knowledge: Write a report which blows my mind in its ability to make connections between your results and the assignment prompt, but also goes a step further to consider other contexts and domains. You may want to draw from your domain knowledge in languages, linguistics, or other content areas to discuss what might happen in otherlanguages or domains beyond the data used in this assignment. You might even go out and find some additional research or papers on the topic and integrate them into your assignment.
MCS304 Assessment 2: Critical Essay This critical essay (2000-2500 words)should be submitted by 1pm Thursday,Week 12. Choose one of the following questions: How does food justice work try to re-imagine the food system?Choose one example of food justice work to closely examine and evaluate. "All cuisine is'nationalcuisine".How far do you agree? Is working class cuisine andfood culture pathologised?In what ways?With what effect? Doeseveryone have a 'right to food'?Critically discuss this in relation to food justice work. How is globalisation fed by food culture?Discuss the ways in which global imaginaries and discourses connect with food culture,using theory and examples. How have feminists critiqued food culture? 'All foodbanks should be closed down'.Do you agree?Can food insecurity be solved with food charity? How far is food culture a matter of 'taste'?Discuss in connection with concepts of social class. How significant is gender in food culture and food practices? 'Human history is replete with borrowed edibles'.What happens to food culture when it moves? You may develop your own essay question if you wish,but you must consult withthe Module Convenor and get the question wording formally approved.
CHEN E4010 Mathematical Methods in Chemical Engineering Syllabus and Lectures Schedule – Fall 2024 Welcome! CHEN E4010 Mathematical Methods in Chemical Engineering is a rigorous course that is an important component of the foundations of your graduate education in chemical engineering. I love math's inherent beauty and awesome power to solve practical problems in almost any field. In this course, you will be able to appreciate this in the context of chemical engineering problems. 1. CHEN E4010 Math Methods in Chemical Engineering - 3.0 pts Prerequisites: CHEN E3120 and E4230, or equivalent, or instructor's permission. Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems. (http://www.columbia.edu/cu/bulletin/uwb/) 4. Textbook and Materials (required and supplemental): a. Textbook (Required): Rice, Richard G. and Duong D. Do Applied Mathematics and Modeling for Chemical Engineers 2nd Edition, New York, Wiley 2012. ISBN-13: 978- 1118024720 | ISBN-10: 1118024729 (Suggested): Francis B. Hildebrand, Advanced Calculus for Applications, 2nd Edition, Prentice-Hall (1976). ISBN-13: 978-0130111890 | ISBN-10: 0130111899 b. Materials(required): 1. CHEN E4010 CourseWork's web site https://courseworks2.columbia.edu/welcome/ c. Materials (supplemental) 1. Reference books and internet sites Abramowitz, Milton and Irene A. Stegun, Handbook of Mathematical Functions with th Formulas, Graphs, and Mathematical Tables, New York: Dover, 1965 9 printing. Billo, E. Joseph, Excel for Scientists and Engineers, Numerical Methods, Hoboken, NJ: Wiley, 2007 Fogler, H. Scott, Elements of Chemical Reaction Engineering 4th Edition (3rd Printing), New York: Prentice Hall, 2006 Fong, C.F. Chan Man, D. De Kee and P.N. Kaloni, Advanced Mathematics for Applied and Pure Sciences, Canada: Gordon Breach Science Publishers, 1997. (http://cuit.columbia.edu/mathematica-students accessed Jan 5, 2017) (http://www.mathworksheetsgo.com/trigonometry-calculators/inverse-cosine- calculator.php accessed Jan 5, 2017) (http:// http://integrals.wolfram.com/index.jsp accessed Jan 5, 2017) Aris, Rutherford, Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover Publications Inc. 1962. Stewart, James, Calculus Concepts and Contexts, New York: Brooks/Cole Publishing. 1998, P402 -408, Section 5.6 Integration by parts Strang, Gilbert, Introduction to Linear Algebra, Wellesley-Cambridge Press and SIAM, Fifth Edition (2016). An excellent introduction to the subject. Zill, Dennis G. and Warren S. Wright, Advanced Engineering Mathematics, Burlington, MA: Jones and Bartlett Learning LLC, 2014. Engineering mathematics textbook. 2. Other supplemental material, notes, and problems will be posted on the CourseWorks web page and updated throughout the course. 5. Course Objectives: a) Be able to mathematically describe chemical engineering problems and the application of selected methods for their solution. b) Apply general modeling principles, including model hierarchies. c) Solve linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. d) Solve partial differential equations in Cartesian and curvilinear coordinates to solve chemical engineering problems. e) Hopefully, to learn to love and admire mathematics for its inherent beauty and almost magical power in solving practical problems. 6. Classroom Procedures: a) What you should bring to class: A calculator, writing implement, a notebook, textbook, and computer laptop as desired. b) What not to bring to class: Anything that could disturb others around you. Anything that would distract you or others from the guest speaker, such as but not limited to a plate of food, computer games, any device that makes sounds, coursework from another class, social media connecting devices, etc. c) Be on time for class and actively participate. Being on time for class means you are seated, ready to take notes, solve problems, listen to lectures, and take other classroom instructions before the start time. You are also expected not to chat and be distracted. This standard is adopted to provide the best class experience possible. Class participation is part of your grade. You must be in class and seated, ready to go at the start time. If you are found to be a distraction, you may be asked to leave. d) Web Site. The website for this class contains important administrative and scheduling information and is located at the Columbia Course Works website: https://courseworks.columbia.edu/welcome/; I will update the site with lecture slides and links to articles and resources as appropriate. 7. Course Grade: The final grade in this course will be based on points awarded according to the following system: a. Final grade: 50 % midterms (two midterms, 25% each) + 50 % Final exam b. Rules for Exams: All exams are closed books and closed notes. You are not allowed to use any books or notes of any sort during the exams, except for a “crib sheet” (one page, 8.5 x 11 inches, for midterms, and two pages for the final exam) as a concise set of notes used for quick reference. You are not allowed to use cell phones, calculators, computers, or any device that allows for data storage during the exams. c. Final Exam: This is like the midterms, except it will be two hours long and covers all aspects of the course. 8. Homework: Homework problems will be assigned, and completion dates suggested. However, homework will not be collected or graded. You are ultimately responsible for knowing all aspects of the problems. To help you learn, homework solutions will be made available through the TA one week after the homework has been posted. Copying solutions will not help you learn the material and is against Columbia University's Policy. (http://bulletin.engineering.columbia.edu/policy-conduct-and-discipline). The re-distribution of the homework solutions in CHEN E4010 is not authorized. The TA has office hours should you need assistance or clarification with the homework or exams. While the homework in the math methods course is not graded, the homework is still an assignment for a student in the course and is assigned to help your learning. In all exams, at least one question from the homework will be asked. This can be seen as an incentive to do the homework regularly and diligently.
CS 3800 Fall 2024 Homework 11 1. [10 Points] Language problems. Let E = {⟨M⟩ | M is a DFA that accepts some string with more 1’s than 0’s} Show that E is decidable. (Hint: Theorems about CFLs are helpful here). 2. [14 Points] Explicit mapping reduction. Let Σ = {0, 1} (a) Consider the following languages A, B ⊆ Σ ∗ : A = {w ∈ Σ* | w has the substring 1110111} B = {w ∈ Σ* | w does not have the substring 1110111} Show that A ≤m B by defining an explicit reduction f from A to B. (b) Is it always the case that A ≤m A for languages A ⊆ Σ ∗ ? Prove your statement (use results from lecture for a simplest proof). 3. [6 Points] Reductions from decidable languages. Let A, B ⊆ Σ ∗ and assume that A is decidable. For each of the following statements give either a proof or a counterexample. For full credit, use results from class, when available. (a) A ≤T B (b) A ≤m B 4. [13 Points] Mapping reductions. (a) Show that for each Turing machine M there exists a Turing machine Mc such that – M never prints a blank – L(M) = L(M) (b) Consider the problem of determining whether, started on a blank tape, a Turing machine will ever print a blank. Formulate this problem as a language and show that it is undecidable: use a mapping reduction from Accept-Empty (lecture 22b). 5. [15 Points] Mapping reductions. An unreachable state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any unreachable states. Formulate this problem as a language and use a reduction from Accept-Empty to show that it is undecidable. 6. [10 Points] Mapping reductions to ATM. Let Σ = {0, 1}. Which, if any, of the following languages are mapping-reducible to ATM ? Give simplest proofs using results from lecture or homework (a) L1 = {< M >| M is a TM that accepts at least one string consisting only of 1’s} (b) L2 = {< M >| M is a TM that accepts no input} 7. [12 Points] Languages in NP that aren’t NP-complete Give two languages that are in NP but are not NP-complete. Explain why these languages aren’t NP-complete. 8. [20 Points] Sudoku. The game of Sudoku takes as input a n2 × n2 grid partitioned in blocks of size n × n. Each cell of the grid is to be filled with an integer from 1 to n2 so that each row, each column, and each block contains all of the integers from 1 to n2. Some of the cells have been pre-filled, so that the question is whether or not the other cells can be filled so as to satisfy all conditions. (a) Does the following Sudoku problem have a solution? If yes, show that solution, if no explain why there is no solution. (b) Explain why Sudoku ∈ NP (the input is a partially filled n 2 × n 2 array). Your explanation may be based on the informal definition of NP, on its expression with an existential quantifier, or on nondeterministic machines. Given that SAT is NP-complete and Sudoku ∈ NP, we have Sudoku ≤p SAT. The next few questions construct an explicit reduction from Sudoku to SAT. For simplicity we do this in the case of 4 × 4 grids. That is, for each partially filled 4 × 4 grid S, we construct a CNF ΦS such that S has a solution iff ΦS is satisfiable. ΦS uses variables xi,j,k (1 ≤ i, j, k ≤ 4) that are true iff the cell in row i and column j contains value k. ΦS will be the conjunction of several clauses, each representing a condition that must be satisfied. (c) Write a CNF Φpre that is true if and only if the prefilled cells have the content indicated in the figure of part (a). (d) Next, we must ascertain that each cell contains a number. Write a clause Φij that is true iff the cell in row i and column j contains a number. (e) We should also write a CNF Φrow i guaranteeing that no two cells in row i (1 ≤ i ≤ 4) contain the same number. Φrow i is obtained as conjunction Φrow i = Φrow i, 1 ∧ Φrow i, 2 ∧ Φrow i, 3 ∧ Φrow i, 4 where Φrow i, k is a CNF expressing that no two different cells in row i have value k. Write the CNF Φrow i, k. (f) Similarly, write a CNF Φcol j, k expressing that no two different cells in column j have value k. (g) Lastly, no two cells in the same block should contain the same number. Write a CNF Φblock 1,1,k ensuring that no two different cells in the top-left block (containing cell (1, 1)) have value k. (h) Do we need to add a CNF preventing a cell from containing two different numbers? (i) We obtain ΦS as conjunction of expressions of the above types. What is the total number of clauses in ΦS? Explain your count by giving the number of clauses of each type (c) through (g).
HCA 2006 Full Firm Valuation: Deal Financing Practice Case Overview You will be assisting Taylor Murphy in determining if her group of bidders can justify topping the $51 per share offer for HCA from the management-led consortium. Your valuation should take place as of December 31 2006 which will be the time any potential takeover could be closed. As a result, your valuation should be based on the projected free cash flows starting in 2007. The forecasts for year end 2006 numbers given in Exhibits 3 and 5 (denoted “2006E”) should be treated as the best possible approximations for the actual final balance sheet and income statement for 2006. Assignment Questions 1. Project HCA’s free cash flows. Base your projections on management’s forecasts given in Exhibit 5 for the years 2007-2011. You should project free cash flows beyond 2011 until the steady state is reached (i.e. when estimated FCF growth becomes constant going forward). To do this, use the following information: Revenue: After 2011, revenue growth is expected to average 4.5% annually into the foreseeable future. Other Operating Income The forecasts in Exhibit 5 include “Other Operating Income” which refers to income (net of expenses) generated from HCA’s operations that are not related directly to patient care such as hospital cafeteria sales, hospital gift shop sales, medical research grants and hospital parking garage fees. In the historical income statements given in Exhibit 2 this income is included as part of “Revenue”. Operating Margins: By 2011, operating margins will have reached their steady-state, long run levels. That is, EBIT will grow at the same rate as revenue after 2011. Tax Rate: HCA will face a tax rate of 37.5%. Non-Operating Income (net): In Exhibit 2 and Exhibit 5 “non-operating income (net)” refers to interest income and gains and losses related to HCA’s investments in cash and cash equivalents. Net Property Plant and Equipment: After 2011 Net Property Plant and Equipment is expected to grow at the same rate as revenue. Other Current Assets: Included in the balance sheet information in Exhibit 3 are “Other Current Assets”. These refer to HCA’s Prepaid Expenses. Amortization of Fees: For tax purposes the $910M banking “Fees and Expenses” (see Exhibit 7) as well as the $300M breakup fee will be amortized straight line over four years starting in 2007. These fees will be incurred at the time of the deal: December 31 2006. This projected amortization is not included in the projections in Exhibit 5. Recall that for the purposes of calculating free cash flow that amortization should be treated in the same way as depreciation (it is a non-cash expense but does generate a tax shield). Working Capital: The “Increase in Working Capital” in Exhibit 5 refers to the change from the previous year in the level of working capital where working capital is defined as: Working Capital = Accounts Receivable + Inventory + Other Current Assets – Accounts Payable – Accrued Expenses Note that this definition of working capital is incomplete because it does not include the reduction in the deferred tax liability (“reduction in deferred taxes”) that are listed separately in Exhibit 5 and relate to projected changes in the deferred income tax liability (“deferred income taxes”) on the balance sheet in Exhibit 3. You should think carefully about whether a reduction in a deferred tax liability represents an increase or a decrease to free cash flow when incorporating it in your forecasts. Beyond 2011 all items in working capital (i.e. including the level of deferred income taxes) are expected to grow at the same rate as revenue. 2. Estimate HCA’s optimal capital structure. Note that the proposed capital structure to finance the deal (Exhibit 7) might not be the optimal capital structure for HCA going forward. You expect that HCA will move towards the optimal capital structure going forward. Estimate what ND*/EV should be optimally for HCA. To do this, use the following information: The current proposed offer of $33,310M is an offer to buy all the equity AND debt of HCA. Put differently, it represents how much the buying group is prepared to pay to acquire all of the assets of the firm (Enterprise value and Cash). Use this information to form. your initial estimate of the enterprise value of HCA for your OCS calculations. When estimating the OPMRWC you should take into account how management’s forecasts of future operating profit margins (from Exhibit 5) compare to the margins that have been obtained over the last 10 years. If you are expecting margins to be higher or lower on average in the future than the minimum OPM that has been realized historically should be adjusted accordingly to forecast what OPMRWC is likely to be in the future. Use your own judgement in deciding how to do this and justify the choice you make. There is no one “right” way to do this. You will need to estimate the yield that HCA will pay on its debt (rD) at the optimal capital structure. To do this use the information on debt ratings and yields in Exhibit 9 and 11. Specifically, estimate HCA’s bond rating by computing the actual coverage ratio HCA would have had in 2006 if it had been at its optimal capital structure. Compare this to the information on “EBIT Interest Coverage (x)” in Exhibit 11 to estimate how HCA will be rated in the future. Justify each of the judgments you make in arriving at your estimate for the optimal capital structure. 3. Estimate the weighted average cost of capital. You should estimate the WACC for HCA at the optimal capital structure. Choose comparable firms from those listed in Exhibit 10 to estimate the asset beta for HCA. Information on HCA’s own equity beta is not included in the case. Justify your choice of comparable firms. Assume that there are no non-operating assets at these comparable firms. 4. Estimate HCA’s residual value. You should estimate two different residual values for HCA: Growing Perpetuity Assume that the free cash flows grow at a constant rate consistent with your forecasts. To do this you will need to find the year when, according to your forecasts the free cash flows begin to behave like a growing perpetuity (i.e. grow from that year forward at a constant rate). Enterprise Value/EBIT Multiple Estimate the residual value using a EV/EBIT multiple based on comparable firms (in Exhibit 10). Justify which firms you use for your analysis. Do this to form. an estimate of the residual value at the same point in time as the other two residual value estimates. Hint: when applying this method the data in Exhibit 10 will produce a trailing multiple (Enterprise Value in year t divided by EBITt). In words they will give you an estimate of the enterprise value at a point in time as a multiple of the level of EBIT in the year leading up to that point in time. You should apply the multiple you get from these comparables to HCA’s forecasted EBIT in a consistent way. Refer to Lecture 9 if you need a refresher on this. 5. Valuation and Recommendation. Using each of the two residual values, estimate the value of the firm and the value of HCA’s equity. What is the share price implied by each valuation? Would you recommend that Roary make a bid for HCA above the current offer of $51 per share? Explain.
COM1005 Machines and Intelligence Weeks 10-11 Lab Question Sheet Robotics & Layered Control Architectures Instructions Complete your copy of the lab question sheet, as instructed below. Download the completed file as a .docx file and rename it to ‘layered_control_lab.docx’ before submitting. Base model Implement the base layered control model (Elowen), according to the given specifications. Adjust the tumble rate to match the ‘one tumble every 5 seconds’ rule, depending on how quickly the periodic control loop runs on your machine. Perform. a series of trials with Elowen in the phototaxis world, where you let her run in the environment and record the number of steps it took her to run out of energy. For each run, record how many boosters were consumed and how many tumbles were made. In the event of Elowen falling down on the floor, all the trial data should be discarded, as this indicates a problem with the ‘safety’ layer (which should be further improved). Elowen: Base Data Run # 1 2 3 4 5 6 7 8 9 10 Steps Boosters Tumbles Elowen: Statistics # of trials Steps: Min Steps: Max Steps: Median Steps: Mean Steps: St. Dev. 10 Modified model In the L4 ‘Tumble’ layer of Elowen’s base model, the tumble frequency is fixed and the tumble angle probability distribution is uniform. Implement, describe and evidence a more complex implementation of this layer, which would increase Elowen’s step count, on average, before she runs out of energy in the given environment. (For example, you can use the tumble frequency as a function of the surrounding brightness; and/or you can introduce a more complex probability distribution for tumble angles). Your final MiRoCODE program should support running both models. You can use the ‘modified’ boolean variable provided in the template as a toggle to select which model to run. Answer individually and in your own words. Use of GenAI tools is NOT allowed. Answer in no more than 200 words. Be specific and include formulas. Provide figures, tables and/or screenshots if necessary. You can use the steps and tumbles as two useful metrics when comparing the base model to the modified model.
ECO3011 Intermediate Microeconomic Theory: Assignment 1 Total points: 100 Due Date: February 17 (Monday) 11:59pm Please show detailed steps for ALL the questions. 1. (7 pts) Professor Goodheart gives 3 midterm exams. He drops the lowest score and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her first exam. Let x2 be her score on the second exam and x3 be her score on the third exam. If we draw her indifference curves for scores on the second and third exams with x2 represented by the horizontal axis and x3 represented by the vertical axis, explain how you determine the shape of her indifference curve through the point (x2, x3) = (50, 70) and display in a plot. In your graph, label the numerical values of important points that characterize the indifference curve. 2. (14 pts) Sammy and Jimmy are twin brothers. Each gets a weekly allowance of ✩2. Sammy’s preferences for baseball cards (quantity denoted as x) and “famous economists” cards (quantity denoted as y) can be represented by the utility function u(x, y) = xy. Suppose that both goods are ✩1 per unit, and x and y can be any non-negative real numbers. (a) (2 pts) Solve for Sammy’s optimal consumption bundle. (b) (3 pts) Suppose the price for baseball cards, px, rises to ✩2. What is Sammy’s new optimal consumption bundle? (c) (5 pts) How much would his parents have to increase his allowance in order to leave him exactly as well off as he was originally? Save your final result to 2 decimal point. (d) (4 pts) Jimmy’s preferences are represented by v(x, y) = ln(x) + ln(y). Answer questions (a), (b) and (c) for Jimmy. Compare the result with Sammy. Explain why you have such result. 3. (23 pts) People buy all sorts of different cars depending on their income levels as well as their tastes. Industrial organization economists who study product characteristic choices (and advise firms like car manufacturers) often model consumer tastes as tastes over product characteristics (rather than as tastes over different types of products). We explore this concept below. Suppose people cared about only two different aspects of cars: the size of the interior passenger cabin and the quality of handling of the car on the road. Compare three car models: a Chevrolet Minivan, a Porsche 944, and a Toyota Camry. Porsche’s do not have much space in the interior but they handle well at high speeds. Minivans have tons of interior space but don’t handle that well at high speeds. And Toyota Camrys are somewhere in between — with more space than Prosche’s but not as much as minivans, and with better handling at high speeds than minivans but not as good as Porsches. (a) (3 pts) Putting x1 = “cubic feet of interior space” on the horizontal axis and x2 = “speed at which the car can handle a curved mountain road” on the vertical, based on the above information, draw the three types of cars in a plot assuming that they will fall on one line. (b) (6 pts) Suppose we considered three different individuals whose preferences (over space and ma-neuverability) satisfy basic assumptions and are monotonic and strictly convex, and suppose each person owns different one of the three types of cars. Suppose further that each indifference curve from one person’s indifference map crosses any indifference curve from another person’s indiffer-ence map at most once. (When two indifference maps satisfy this condition, we often say that they satisfy the single crossing property.) Consider the case that the indifference curves through Toyota Camry for the three individuals all intersect at the Toyota Camry. Now suppose you know person A’s MRS at the Toyota Camry is larger (in absolute value) than person B’s, and person B’s MRS at the Toyota Camry is larger (in absolute value) than person C’s. Who owns which car? Draw a plot to show their indifference curves through the Toyota Camry and explain your result. (c) (4 pts) Suppose we had not assumed the “single crossing property” in part (b). Would you have been able to answer the question “Who owns which car” assuming everything else remained the same? Explain with a plot. (d) (2 pts) Suppose you are currently person B and you just found out that your uncle has passed away and bequeathed to you his 3 children,aged 4, 6 and 8 (and nothing else). This results in a change in how you value space and maneuverability. Is your new MRS at the Toyota Camry now larger or smaller (in absolute value)? (e) (3 pts) Suppose that the tastes of persons A, B and C can be represented by the utility functions uA(x1, x2) = x α 1 x2, uB(x1, x2) = xβ1x2, u C (x1, x2) = xγ1x2 respectively. Calculate the MRS for each person. (f) (5 pts) In the above utility functions, assuming α, β and γ take on different values, is the “single crossing property” defined in part (b) satisfied? Given the description of the three persons’ preferences in part (b), what is the relationship between the values of α, β and γ? Explain all of your results in details. 4. (16 pts) Dudley’s utility function is U(C, R) = C − (12 − R)2, where R is the amount of leisure he has per day and C is the quantity of all consumption goods. He has 16 hours a day to divide between work and leisure. He has an income of ✩20 a day from nonlabor sources. The price of consumption goods is $1 per unit. (a) (2 pts) If Dudley can work as many hours a day as he likes but gets zero wages for his labor, how many hours of leisure will he choose? (b) (4 pts) If Dudley can work as many hours a day as he wishes for a wage rate of ✩10 an hour, how many hours will he choose to work? Write down his budget constraint. (c) (6 pts) If Dudley’s nonlabor income decreased to $5 a day and wage rate is still ✩10 per hour, how many hours would he choose to work? Explain your result. Draw in a graph the old budget constraint, the new budget constraint, and indifference curves. Also display Dudley’s optimal choices under the old and new nonlabor income. Label important points in your graph. (d) (4 pts) Suppose that Dudley has to pay an income tax of 20 percent on all of his income (labor and nonlabor), and suppose that his before-tax wage remained at $10 an hour and his before-tax nonlabor income was $20 per day. How many hours would he choose to work? 5. (14 pts) There are two goods in the world, pumpkins (x1) and apple cider (x2). Pumpkins are $2 each. Cider is $7 per gallon for the first two gallons. After the second gallon, the price of cider drops to $4 per gallon. (a) (4 pts) Peter’s income is $54. Draw his budget constraint. Clearly show in the plot the intercepts on the axes, the kink in the budget line and the slope of each segment of the budget constraint. (b) (3 pts) Peter’s utility function is u(x1, x2) = x1 + 3x2. Sketch some indifference curves in your graph. Find Peter’s optimal consumption bundle (x*1 , x*2). (c) (4 pts) Paul’s income is $22. Draw his budget constraint in a new graph. Clearly show in the new plot the intercepts on the axes, the kink in the budget line and the slope of each segment of the budget constraint. (d) (3 pts) Paul’s utility function is u(x1, x2) = min{3x1, 2x2}. Sketch some indifference curves in your graph for Paul. Find Paul’s optimal consumption bundle (x*1 , x*2). 6. (26 pts) I have two 5-year old girls — Ellie and Jenny — at home. Suppose I begin the day by giving each girl 10 toy cars and 10 princess toys. I then ask them to plot their indifference curves that contain these endowment bundles on a graph with cars on the horizontal and princess toys on the vertical axis. Assume they are both rational. A. Ellie’s indifference curve appears to have a marginal rate of substitution of -1 at her endowment bundle, while Jenny’s appears to have a marginal rate of substitution of -2 at the same bundle. (a) (2 pts) Can you propose a trade that would make both girls better off? (b) (2 pts) Suppose the girls cannot figure out a trade on their own. So I open a store where they can buy and sell any toy for ✩1. Illustrate the budget constraint for each girl in two separated plots. (c) (6 pts) Will either of the girls shop at my store? If so, what will they buy? Explain your result with indifference curves displayed in the plots you drew for part (b). (d) (4 pts) Suppose I do not actually have any toys in my store and simply want my store to help the girls make trades among themselves. Suppose I fix the price at which princess toys are bought and sold to $1. Without being specific about what the price of toy cars would have to be, illustrate, using final indifference curves for both girls on the same graph, a situation where the prices in my store result in an efficient allocation of toys. (e) (1 pts) What values might the price for toy cars take to achieve the efficient trades you described in your answer to (d)? Explain. B. Now suppose that my girls’ tastes could be described by the utility function u(x1, x2) = xα1x12 −α , where x1 represents toy cars, x2 represents princess toys and 0 < α < 1. (a) (2 pts) What must be the value of α for Ellie (given the information in part A)? What must the value be for Jenny? (b) (4 pts) When I set all toy prices to $1, what exactly will Ellie do? What will Jenny do? Assume that it is possible to trade fractions of toys. (c) (1 pt) Given that I am fixing the price of princess toys at $1, do I have to raise or lower the price of car toys in order for me to operate a store in which I don’t keep inventory but simply facilitate trades between the girls? (d) (4 pts) Suppose I raise the price of car toys to $1.40, and assume that it is possible to sell fractions of toys. Have I found a set of prices that allow me to keep no inventory?
COMPSCI 753 COMPUTER SCIENCE Algorithms for Massive Data SEMESTER TWO, 2022 1 Locality-Sensitive Hashing Given three documents S1, S2 , S3 and a customized query document q: S1 = {0, 1, 2}, S2 = {0, 3, 4}, S3 = {1, 3, 4}, q = {h(y), 3, 4}; h(y) = y mod 5. where y is the first digit of your Student ID. For instance, suppose my Stu- dentID=6xxxxx, my query document would be q= {1, 3, 4}, where 1 = (6 mod 5). 1.1 Computing MinHash Signatures 1. Generate the bit-vector representation for {S1, S2 , S3 , q} in shingle space {0, 1, 2, 3, 4}. [2 marks] 2. Generate the MinHash matrix for {S1, S2 , S3 , q} using the following four MinHash functions. [4 marks] h1 (x) = (2x +1) mod 5 h2 (x) = (3x +3) mod 5 h3 (x) = (x +5) mod 5 3. Among the hash functions, h1 , h2 , h3 , which one gives the true simulated permutation? [1 mark] 4. Consider the query q and estimate the signature-based Jaccard similari- ties: J(q, S1 ), J(q, S2 ), and J(q, S3 ). [1 mark] 1.2 Tuning Parameters for rNNS In our lecture, we have learnt to formulate the collision probability (i.e., S- curve) given the number of bands b and the number of rows per band r as follows: Pr(s) = 1 − (1 − sr )b. Consider three sets of parameters (r=2,b=10), (r=1,b=10), (r=10,b=50). The collision probabilities for similarity s in range of [0,1] for each (r ,b) are pro- vided accordingly as in Table 1: 1. Which settings give at most 5% of false negatives for any 60%-similar pairs? Briefly explain the reason. [3 marks] 2. Which settings give at most 20% of false positives for any 20%-similar pairs? Briefly explain the reason. [3 marks] Table1.: Collision Probabilities 1.3 c-Approximate Randomized rNNS Consider a family transformation from (d1 , d2 , p1 , p2 )-sensitive to (d1 , d2 , 1 − (1 − p1(k))L , 1 − (1 − p2(k))L )-sensitive, where k and L refer to the number of hash functions and the number of hash tables, respectively. 1. Briefly describe steps to achieve such transformation. [4 marks] 2. What is the expected impact on probability bounds after the transfor- mation with the k and L, respectively? [4 marks] 3. Consider hash table size l = 10, MinHash functions k = 5, and 534 news articles. In phase one hashing, I generated signature matrix for l times. In phase two hashing, I constructed LSH hash tables of size l × m (m: the number of buckets). For each hash table lj, I computed the collision distribution for all articles across m = 600 buckets and reported a heatmap plot as follows (i.e., m: x-axis, l: the y-axis). The values at (mi, lj) is the number of colliding articles at bucket mi and table lj . What is the summation of (mi, lj) ∀mi ∈ [0, 599] for each hash table lj? [3 marks] 2 Data Stream Algorithms 2.1 Bloom Filter 1. How can Bloom Filter improve the false positive ratio? Why does that work? [4 marks] 2. Suppose we have n bits of memory available and set S has m members. Instead of using k hash functions, where each mapping an element to a bit in the main memory, we could divide the n bits into k subarrays (assume n is divisible by n), and then use the i-th hash function, i ∈ [1, k], to the i-th subarray. As a function of n, m and k, what is the probability that a bin has at least one ball in the new framework? [2 marks] 3. How does the new framework compare with using k hash functions into a single array? [4 marks] 2.2 Misra-Gries Algorithm 1. Given the data stream below, perform the Misra-Gries algorithm with k = 3 counters and present the summary, including the elements and its counter values, when the execution of the algorithm is finished. [2 marks] S = {4, 46, 14, 46, 57, 46, 22, 57} 2. Recall in Assignment 2, there was a request to “report the average number of times the decrement triggered by Misra-Gries over a data stream” . What expected number of times has the Misra-Gries summary triggered the decrementsteps after processing the given stream? Please derive your answer as a function of m and k. [3 marks] 2.3 Count Sketch Algorithm Consider the same data stream S and hash functions below. Given the sign hash functions below, perform. the Count Sketch algorithm and present the (i) hash table, (ii) counter matrix, and (iii) estimated frequency of each element in a stream after processing all elements. [10 marks] h1 (x) = x mod 3 s1 (x) = ((2x +1) mod 3) mod 2 h2 (x) = (3x +1) mod 3 s2 (x) = ((3x +2) mod 3) mod 2 h3 (x) = (5x +2) mod 3 s3 (x) = ((4x +2) mod 3) mod 2 3 Algorithms for Graphs 3.1 PageRank Given a directed graph G: 1. Give the column-stochastic adjacency matrix of the above graph G. [2 marks] 2. Compute the PageRank of the above graph G without teleport. [4 marks] 3. If teleport is applied, each node has (1−β) chance to teleport to all other nodes. What changes will be observed on the ranking of the four nodes when (1 − β) increases. What if β = 0? Explain your answer. [4 marks] 3.2 Community Detection 1. Draw an example graph of four nodes, on which the three graph cut criteria (i.e., MinCut, RatioCut and NormalizedCut) produce the same bi-partitioning. [4 marks] 2. Compute the edge betweenness for each edge in the graph below. Which edge is to be removed? [8 marks] 3.3 Influence Maximization What is the most probable set of influenced nodes by running the Indepen- dent Cascade model on the seed set S = {v1 }? Explain your answer. (Hint: Consider the probability of each deterministic sub-graphs. There could be multiple deterministic sub-graphs that result in the same set of influenced nodes.) [8 marks] 4 Recommender Systems 4.1 Collaborative filtering Given the following user-item interaction matrix of 4 users and 5 items: Apply the user-based collaborative filtering algorithm that considers the global bias bg, user bias bi(user) and item bias bj(item) . Use Pearson correlation coefficient to compute the user similarities. Give the top-1 recommended item to user u3 . [8 marks] Note: The predicted ratings should round to one decimal place. 4.2 Factorization Machines 1. Explain the difference between tensor decomposition and factorization machines in context-aware recommendation, in terms of the computation cost and the way of modeling correlations among features. [4 marks] 2. A tourism recommender system is to be upgraded for the support of travel package recommendations. Each travel package is a non-empty set of landmarks. Users can post their ratings on a single landmark or the whole travel package. The table below shows all ratings exist in the database. (a) Describe a memory-based collaborative filtering algorithm that can recommend new travel packages (e.g., {l1 , l3 }). [2 marks] (b) Convert each of the above rating records as an input feature vector for factorization machines. Explain how factorization machines rec- ommend new travel packages based on your input feature vectors. [4 marks] (c) List one advantage of factorization machines compared to the memory- based collaborative filtering algorithm in travel package recommen- dation. [2 marks]
CO 327 Winter 2025: Assignment 1 problems Due: Wednesday January 15, 11:59pm EST Assignment problems. A1-1. LP formulation and Gurobi The Let It Grow company is preparing to sell plant fertilizers for the spring and fall seasons. There are three main components of a fertilizer: nitrogen, phosphorous and potassium. A fertilizer often has a NPK rating consists of three numbers a−b−c, representing the percent-age of nitrogen, phosphorous and potassium in the fertilizer, respectively. For example, in 1 kilogram of a fertilizer with NPK rating of 20 − 10 − 5, there are 200 grams of nitrogen, 100 grams of phosphorous, and 50 grams of potassium. The remainder of the fertilizer consists of materials that are freely available (e.g. water, soil, etc.). Let It Grow wants to make 7 different types of fertilizers that are designed for different purposes. Their NPK ratings and their selling price are listed in the following table. The company has a limited supply of the three chemicals: 3000 kilograms of nitrogen, 1000 kilograms of phosphorous, and 1500 kilograms of potassium. The goal is to maximize the total value of the fertilizers that are produced. (a) Formulate this problem as a linear program. Make sure you clearly explain your vari-ables, objective function and constraints. (b) Using Gurobi, implement the linear program from part (a) and solve it. Include the program you input into the software, and the output that includes the optimal solution and optimal value. State separately the optimal solution and value to the word problem. (c) Suppose the company is testing different prices for all purpose fertilizers. Experiment with Gurobi to see how does the optimal solution vary according to changes in the price of all purpose fertilizers. For each possible optimal solution, write down the range of possible prices that result in that solution. You do not need to be exact on the prices, though they should be pretty close. Include some work on how you have determined the solutions. (Hint: The attribute “obj” for a variable can be useful. If v represents the variables of your model, then v[0].obj = 5 sets the coefficient of the variable at index 0 in the objective function to 5.) A1-2. Review: Duality and complementary slackness (a) Let (P) be the following linear program. Write down the dual (D) of (P) using y as the vector of dual variables. (No justifications required.) (b) Write down all the complementary slackness conditions for (P) and (D). (c) Let ¯x = (3, 0, −2, 0, 7)T . Use the Complementary Slackness Theorem to prove that ¯x is optimal for (P). In particular, you need to determine a possible optimal solution for (D). (d) Use the Weak Duality Theorem to give an alternate proof that ¯x from part (c) is optimal for (P).
I S 300: Introduction to Information Systems Course Description and Objectives: Modern information technologies have dramatically transformed the economic and social structures of our society. Understanding the role of information technology (IT) is critical for firms to provide competitive advantage in today’s competitive environment. These days over 50% of capital expenditures made by firms are IT-related. Knowing how to effectively manage IT is a prerequisite for successful business managers, CIOs, and CEOs. This course is designed to be an important step towards building your IT knowledge base on the road to becoming a successful manager. The course consists of both lectures and lab sessions. The lectures will teach you the language, key concepts, and frameworks for the management of Information Systems (IS). You are expected to gain an understanding of the strategic value of IT/IS as well as their applications in today’s business environment. You will also be able to develop basic IT project management skills such as system analysis and design, project planning, implementation, and testing. The lab sessions emphasize using computers to analyze, coordinate, and solve organizational decision-making problems by providing a hands-on environment to learn various business computer applications such as Microsoft Excel, R, and MySQL. At the end of this course, I expect my students to be comfortable taking an active role in today’s dynamic IT business environment and understand the role of management in IT solutions. Course Materials: • Required Textbook: Management Information Systems: Managing the Digital Firm, 17th Edition, by Kenneth Laudon and Jane Laudon • A computer with webcam, microphone, and high-speed internet access. Grading: Your final grade is comprised of seven components: a midterm exam, a final exam, a team project, your class participation, quizzes, and the computer lab. More detailed requirements and specifications about them will be provided in class. The composition of your final weighted grade is: 1. Exam 1 ................................................................................................................. 20% 2. Exam 2 ................................................................................................................. 20% 3. Team Project (Business Plan Based on an Emerging Information Technology) 20% 4. Participation .......................................................................................................... 10% 5. Quizzes (Pre-chapter 6%, in-class 4%) ................................................................. 10% 6. Computer Lab ....................................................................................................... 20% Total: 100% Please ignore any Canvas calculations as they might reflect the wrong weight / grades. Curve: There will be no individual exam or assignment curves. If a curve is needed on the final weighted course grades, it will be applied. If the class average is low, I typically curve up. If the class average is too high, I might curve down to satisfy the requirements of the Dean’s Office, but I have never needed to curve down the grades before in my career. Grading Appeals / Regrading: Any grade appeals should be summarized in an email and sent to your grader/TA or me. A written appeal is mandatory to request a regrade. If you’re emailing me, clearly indicate your class/section, name (if different than Canvas), which assignment should be regraded, and why. Do not use any other method (such as Canvas comments) for such communication. Appeals must be filed within seven days after the graded item has been returned to you. In case of a grade appeal, I regrade the entire assignment, not just the objected (appealed) part. Exceptions to this policy may apply in the case of the final exams / projects due to deadlines for UW grade submissions. Extenuating Circumstances (missed assignments and exams): Unexpected events happen in life. If you miss an exam or assignment for a documentable extenuating circumstance, I typically count the average of the same grade category for the missed exam or assignment. For example, if a student misses the midterm exam for an extreme emergency, he or she can have the final exam grade count for the missed exam. This arrangement will only be given to students who are able to produce an official document within a reasonable time (within 7 days.) Examples of official extenuating circumstances are medical issues, traffic accidents, participation in university activities at the request of university authorities, death of a first-degree family member, and other compelling verifiable circumstances beyond the control of the student. Please note that work, interviews, training, vacations, friend weddings, or medical issues of second-degree relatives are not considered extenuating circumstances. Official documents should be written in English and must cover the exam date. All non-United States documents must be authenticated and verified. I evaluate these instances on a case-by- case basis. Requesting this policy is inherently a risky move and I don’t recommend it unless there is a documented case. Exams (individual): There will be two exams. Exams will be in-class, in-person, on computer, and in a mixed (multiple-choice and essay) test format unless announced otherwise before the exam. Book chapters to be tested in exams are not cumulative. Team Project (group): Throughout this course, you and your team will develop a business plan based on an emerging information technology of your choice. There will be small deliverables every other week to ensure progress. You will present these business plans towards the end of the course. This team project is specifically designed as open-ended to enhance your creativity and teamworking skills. I expect you to combine the theoretical material you learned in this course with a practical concept that you find appealing. In this project, it is essential that you choose an “emerging” information technology but not a stagnant or declining one. It is also important that you identify an “information-related technology” but not something like biotechnology or pure mechanical-technology. Last but not least, the technology of your choice needs to be suitable for business use. Some examples of emerging information technologies are: • Adaptive Machine Learning • Internet-of-Things • Wearable User Interfaces • Edge Large Language Models • Blockchain (NFT, cryptocurrency) • Digital Twin of a Customer • Disinformation Security • Gamification • Spatial Computing • 6G cellular network What is a business plan based on an emerging information technology? A business plan is a formal statement of a set of attainable business goals and the plan to reach those goals. Emerging information technologies are contemporary advances and innovations in the information technology (IT) field. Emerging technologies provide competitive advantage for those who can come up with innovative business ideas using them. A business plan based on an emerging information technology combines these two notions to create a plan around an IT product or a service. Business plans are decision-making tools. There is no fixed content for a business plan. Rather, the goals and audience determine the content and format of the business plan. A business plan represents all aspects of the business planning process declaring vision and strategy alongside sub-plans to cover marketing, finance, operations, human resources as well as a legal plan, when required. A business plan is a summary of those disciplinary plans. Typical structure for a business plan presentation includes: • Mission and vision statements • Business description (A brief statement that explains what the product or service is and why it will be successful) • Business environment analysis • SWOT analysis • Industry background • Competitor analysis (Understand competitors and substitutes. Explain why your idea is different.) • Market analysis (Identifies the market, the business's position in it, and the competitors. It also assesses the competition and identifies market trends. Best market analyses are supported with data.) • Go-to-market strategy • Operations plan (May include supply chain and production plans) • Management summary • Financial plan (Includes financial projections, start-up costs, funding, and investor pitches. It may also include forecasted income statements, balance sheets, cash flow statements, and capital expenditure budgets) • Timeline and milestones Typically, business plans are developed to attract investors. To do so, I strongly recommend identifying a competitive product or service. Give it a cool name. Make sure it has potential. And finally, figure out the financials: decide on how much investment you need / would like. At the end of the course, you will submit peer evaluations for your team members. Your individual grades may be adjusted based on these peer evaluations. Participation (individual): I will not take attendance every class. However, you will learn better if you are in class daily to listen, take notes and have your questions answered. Course participation will be a part of your final grade. There might also be pop quizzes as a portion of the participation grade. For participation, things I view positively include: • asking insightful questions about assigned readings • redirecting a discussion when the current point has been adequately covered • good analysis supported by case facts or your own experience • summarizing or reconciling previous comments • constructive disagreement • synthesizing and advancing the discussion • a good sense of humor • drawing generic learning points from a particular case Factors I view negatively include: • lack of involvement – absence, silence, detachment or disinterest • leading our discussion into unrelated topics • spending undue amount of time on minor points • long, rambling comments • making undue noise, or disturbing the lecture • disrespectful attitude towards the instructor and classmates • being unprepared, or passing on a cold call Here are some guidelines for assessing class participation, especially when I ask a question: Grade Criteria 91-100 • Gives the right answer or disagrees with my answer. Then, explain and elaborate why. • Demonstrates analysis of readings exceptionally well, relating it to other course material. • Consistent involvement: keeps focus, responds thoughtfully to others’ comments. 81-90 • Gives the right answer, without an explanation of why, sometimes using a single phrase. • Shows thorough knowledge of case and readings, has thought through implications. • Ongoing involvement: responds to others in a constructive way, thinks through own points. 71-80 • Gives the wrong answer but shows some knowledge of case and readings. • Builds on others’ contributions. Shows some evidence of trying to interpret or analyze facts. • Uneven involvement: demonstrates mediocre evidence of critical thinking. 61-70 • Gives the wrong answer and does not demonstrate any knowledge of our readings. • Helps move along the discussion in an incremental manner (e.g., repeats some content.) • Peripheral involvement: Not much new thought; rephrases, underlines earlier comments. 51-60 • Skips answering. Does not demonstrate preparation. • Present in class. Not disruptive. • States straight facts from the content when called on or directly asked. 1-50 • Present, but demonstrates no evidence of preparation. • Shows lack of interest or respect for other’s contributions. • Obviously did not prepare. 0 • Absent. • If present, engages in disruptive behavior. • Misses quizzes. Peer Evaluations (for your own teammates): Any group assignment grade is not your individual grade until peer evaluations are counted at the end of the course. Please note that this can be especially controversial if you expect the same grade as your teammates without showing reasonable effort. In order to create an incentive for a fair work environment in teams, I adjust group grades with peer evaluations. To do so, I need your help to collect data on the performance of each teammate. Here is how it works: Each of the N members of a project team will be given 100×(N-1) points to allocate among the other members of the team. Everyone will distribute those points among their team members EXCLUDING themselves. The individual’s peer weight will be the average of the allocations from his or her team members (usually 100). An individual’s project grade will be the team project’s score weighted by the individual’s peer weight. Peer evaluations suggest that peers should be evaluated on: • Prompt and reliable attendance at scheduled meetings or working periods • Getting individual sub-tasks completed on time • Taking on difficult tasks • Contributing ideas on a regular basis • Contributing specialized skills or knowledge • Facilitating effective team interaction • Keeping attitudes positive throughout the process For example, let us assume you are in a five-person group and your teammates are John Smith, Jane Brown, Mike Lee and Mary Martinez. This means you have 400 points to allocate among your teammates (because 100x(N-1) is 400, where N=5) • If you believe everyone contributed equally, write “John Smith: 100, Jane Brown: 100, Mike Lee: 100, Mary Martinez: 100” in the assignment submission section. (This is generally the most common peer evaluation.) • If you believe Jane contributed significantly more than anyone, you can write “John Smith: 75, Jane Brown: 175, Mike Lee: 75, Mary Martinez: 75.” • If you believe Jane did no contribution and/or hindered your team performance, you can write “John Smith: 133, Jane Brown: 0, Mike Lee: 133, Mary Martinez: 134.” • Please note that all examples above add up to 400 points. Last names are required. Your sum can be different based on the team size. After making sure you allocate points, feel free to add any notes or comments you’d like to share with me about the group performance. Additional comments are optional. Warning/clarifications: • Include the full (first, middle and last) name of your teammates, as it’s shown on Canvas. For example, if your teammates’ name is John Smith, don’t shorten it to Joe, or even John, just write the full name as John Smith. • If you do not submit peer evaluations, or do not follow the directions above, your grade in team assignments may be deducted. Quizzes (individual): Unless otherwise announced in class, there will be four quizzes. Quizzes will be in-class, on Canvas, and in a multiple-choice test format. Follow announcements carefully. Computer Lab Sessions (individual): Hands-on practice is an essential part of this course and the information systems field overall. Teaching assistants will conduct lab sessions to improve your skills in contemporary information technologies and tools. I recommend adding these skills to your resume. AoL Quiz Requirement: You are required to complete an Assurance of Learning (AoL) quiz for this course, which measures how the Foster School of Business is delivering Assurances of Learning. Assurances of Learning help the Foster School evaluate how well we are teaching you and they allow us to fine-tune the curriculum to make sure we are meeting goals and objectives of the course. Additionally, the overall results help the Foster School remain accredited through the Association to Advance Collegiate Schools of Business (AACSB). The quiz is administered by the Undergraduate Program’s Office through Canvas. An email announcement will be sent out by the last week of the quarter. You should complete the quiz as diligently as possible so that the results are significant and impact the Foster curriculum. Thus, you should approach the quiz as a closed note, closed book test. You should not seek assistance from other students or faculty. Please do not discuss the quiz with fellow students.
