14.8: Analyzing Financial Statements
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7. How can ratio analysis be used to identify a firm’s financial strengths and weaknesses?
Individually, the balance sheet, income statement, and statement of cash flows provide insight into the firm’s operations, profitability, and overall financial condition. By studying the relationships among the financial statements, however, one can gain even more insight into a firm’s financial condition and performance. A good way to think about analyzing financial statements is to compare it a fitness trainer putting clients through various well-established assessments and metrics to determine whether a specialized fitness program is paying dividends for the person in terms of better strength, endurance, and overall health. Financial statements at any given time can provide a snapshot of a company’s overall health. Company management must use certain standards and measurements to determine whether they need to implement additional strategies to keep the company fit and making a profit.
Ratio analysis involves calculating and interpreting financial ratios using data taken from the firm’s financial statements in order to assess its condition and performance. A financial ratio states the relationship between financial data on a percentage basis. For instance, current assets might be viewed relative to current liabilities or sales relative to assets. The ratios can then be compared over time, typically three to five years. A firm’s ratios can also be compared to industry averages or to those of another company in the same industry. Period-to-period and industry ratios provide a meaningful basis for comparison, so that we can answer questions such as, “Is this particular ratio good or bad?”
It’s important to remember that ratio analysis is based on historical data and may not indicate future financial performance. Ratio analysis merely highlights potential problems; it does not prove that they exist. However, ratios can help managers monitor the firm’s performance from period to period to understand operations better and identify trouble spots.
Ratios are also important to a firm’s present and prospective creditors (lenders), who want to see if the firm can repay what it borrows and assess the firm’s financial health. Often loan agreements require firms to maintain minimum levels of specific ratios. Both present and prospective shareholders use ratio analysis to look at the company’s historical performance and trends over time.
Ratios can be classified by what they measure: liquidity, profitability, activity, and debt. Using Delicious Desserts’ 2018 balance sheet and income statement ( Table 14.1 and Table 14.2 ), we can calculate and interpret the key ratios in each group. Table 14.4 summarizes the calculations of these ratios for Delicious Desserts. We’ll now discuss how to calculate the ratios and, more important, how to interpret the ratio value.
Liquidity Ratios
Liquidity ratios measure the firm’s ability to pay its short-term debts as they come due. These ratios are of special interest to the firm’s creditors. The three main measures of liquidity are the current ratio, the acid-test (quick) ratio, and net working capital.
The current ratio is the ratio of total current assets to total current liabilities. Traditionally, a current ratio of 2 ($2 of current assets for every $1 of current liabilities) has been considered good. Whether it is sufficient depends on the industry in which the firm operates. Public utilities, which have a very steady cash flow, operate quite well with a current ratio well below 2. A current ratio of 2 might not be adequate for manufacturers and merchandisers that carry high inventories and have lots of receivables. The current ratio for Delicious Desserts for 2018, as shown in Table 14.4 , is 1.4. This means little without a basis for comparison. If the analyst found that the industry average for small bakeries was 2.4, Delicious Desserts would appear to have low liquidity.
The acid-test (quick) ratio is like the current ratio except that it excludes inventory, which is the least-liquid current asset. The acid-test ratio is used to measure the firm’s ability to pay its current liabilities without selling inventory. The name acid-test implies that this ratio is a crucial test of the firm’s liquidity. An acid-test ratio of at least 1 is preferred. But again, what is an acceptable value varies by industry. The acid-test ratio is a good measure of liquidity when inventory cannot easily be converted to cash (for instance, if it consists of very specialized goods with a limited market). If inventory is liquid, the current ratio is better. Delicious Desserts’ acid-test ratio for 2018 is 1.1. Because the bakery’s products are perishable, it does not carry large inventories. Thus, the values of its acid-test and current ratios are fairly close. At a manufacturing company, however, inventory typically makes up a large portion of current assets, so the acid-test ratio will be lower than the current ratio.
| Ratio Analysis for Delicious Desserts at Year-End 2018 | |||
|---|---|---|---|
| Ratio | Formula | Calculation | Result |
| Liquidity Ratios | |||
| Current ratio | Total current assetsTotal current liabilitiesTotal current assetsTotal current liabilities | $83,200$60,150$83,200$60,150 | 1.4 |
| Acid-test (quick) ratio | Total current assets–inventoryTotal current liabilitiesTotal current assets–inventoryTotal current liabilities | $83,200−$15,000$60,150$83,200−$15,000$60,150 | 1.1 |
| Net working capital | Total current assets–Total current liabilitiesTotal current assets–Total current liabilities | $83,200−$60,150$83,200−$60,150 | $23,050 |
| Profitability Ratios | |||
| Net profit margin | Net profitNet salesNet profitNet sales | $32,175$270,500$32,175$270,500 | 11.9% |
| Return on equity | Net profitTotal owners' equityNet profitTotal owners' equity | $32,175$78,750$32,175$78,750 | 40.9% |
| Earnings per share | Net profitNumber of shares of common stock outstandingNet profitNumber of shares of common stock outstanding | $32,17510,000$32,17510,000 | $3.22 |
| Activity Ratio | |||
| Inventory turnover | Cost of goods soldAverage inventoryCost of goods soldAverage inventory | ||
| Cost of goods sold(Beginning inventory+Ending inventory)/2Cost of goods sold(Beginning inventory+Ending inventory)/2 | $112,500($18,000+$15,000)/2$112,500($18,000+$15,000)/2 | ||
| $112,500$16,500$112,500$16,500 | 6.8 times | ||
| Debt Ratio | |||
| Debt-to-equity ratio | Total liabilitiesOwners' equityTotal liabilitiesOwners' equity | $70,150$78,750$70,150$78,750 | 89.1% |
Table 14.4
Net working capital , though not really a ratio, is often used to measure a firm’s overall liquidity. It is calculated by subtracting total current liabilities from total current assets. Delicious Desserts’ net working capital for 2018 is $23,050. Comparisons of net working capital over time often help in assessing a firm’s liquidity.
Profitability Ratios
To measure profitability, a firm’s profits can be related to its sales, equity, or stock value. Profitability ratios measure how well the firm is using its resources to generate profit and how efficiently it is being managed. The main profitability ratios are net profit margin, return on equity, and earnings per share.
The ratio of net profit to net sales is the net profit margin , also called return on sales. It measures the percentage of each sales dollar remaining after all expenses, including taxes, have been deducted. Higher net profit margins are better than lower ones. The net profit margin is often used to measure the firm’s earning power. “Good” net profit margins differ quite a bit from industry to industry. A grocery store usually has a very low net profit margin, perhaps below 1 percent, whereas a jewelry store’s net profit margin would probably exceed 10 percent. Delicious Desserts’ net profit margin for 2018 is 11.9 percent. In other words, Delicious Desserts is earning 11.9 cents on each dollar of sales.
The ratio of net profit to total owners’ equity is called return on equity (ROE) . It measures the return that owners receive on their investment in the firm, a major reason for investing in a company’s stock. Delicious Desserts has a 40.9 percent ROE for 2018. On the surface, a 40.9 percent ROE seems quite good. But the level of risk in the business and the ROE of other firms in the same industry must also be considered. The higher the risk, the greater the ROE investors look for. A firm’s ROE can also be compared to past values to see how the company is performing over time.
Earnings per share (EPS) is the ratio of net profit to the number of shares of common stock outstanding. It measures the number of dollars earned by each share of stock. EPS values are closely watched by investors and are considered an important sign of success. EPS also indicates a firm’s ability to pay dividends. Note that EPS is the dollar amount earned by each share, not the actual amount given to stockholders in the form of dividends. Some earnings may be put back into the firm. Delicious Desserts’ EPS for 2018 is $3.22.
Activity Ratios
Activity ratios measure how well a firm uses its assets. They reflect the speed with which resources are converted to cash or sales. A frequently used activity ratio is inventory turnover. The inventory turnover ratio measures the speed with which inventory moves through the firm and is turned into sales. It is calculated by dividing cost of goods sold by the average inventory. (Average inventory is estimated by adding the beginning and ending inventories for the year and dividing by 2.) Based on its 2018 financial data, Delicious Desserts’ inventory, on average, is turned into sales 6.8 times each year, or about once every 54 days (365 days ÷ 6.8). The acceptable turnover ratio depends on the line of business. A grocery store would have a high turnover ratio, maybe 20 times a year, whereas the turnover for a heavy equipment manufacturer might be only three times a year.
Debt Ratios
Debt ratios measure the degree and effect of the firm’s use of borrowed funds (debt) to finance its operations. These ratios are especially important to lenders and investors. They want to make sure the firm has a healthy mix of debt and equity. If the firm relies too much on debt, it may have trouble meeting interest payments and repaying loans. The most important debt ratio is the debt-to-equity ratio.
The debt-to-equity ratio measures the relationship between the amount of debt financing (borrowing) and the amount of equity financing (owners’ funds). It is calculated by dividing total liabilities by owners’ equity. In general, the lower the ratio, the better. But it is important to assess the debt-to-equity ratio against both past values and industry averages. Delicious Desserts’ ratio for 2018 is 89.1 percent. The ratio indicates that the company has 89 cents of debt for every dollar the owners have provided. A ratio above 100 percent means the firm has more debt than equity. In such a case, the lenders are providing more financing than the owners.
CONCEPT CHECK
- How can ratio analysis be used to interpret financial statements?
- Name the main liquidity and profitability ratios, and explain what they indicate.
- What kinds of information do activity ratios give? Why are debt ratios of concern to lenders and investors?


6.1: Creating Drawings and Sketches
Freehand sketching is an instrumental skill that can be mastered with practice and by following a few guidelines. The ability to interpret drawings is complemented by the ability to sketch information from a drawing to take to your work location. Sketching is also a valuable tool when no drawing is available and you must communicate job information to someone else.
For freehand sketching, you require a pad of graph paper (8 ½ " × 11" sheets with a 5 mm or ¼" grid), a sharp HB pencil, and an eraser. Do not begin any sketch with a dull pencil.
Sketching technique
Sketching provides a quick and straightforward way to express ideas and communicate an object's shape and general size.
Sketching parallel lines
Start by drawing lines parallel to the paper's edges, such as a border line and title block. Use your finger as a guide when you draw along the grid line on the sketch pad (Figure \(\PageIndex{1}\)). Letting the end of your little finger run down the edge of the paper pad as you draw will steady your hand and make it easier to get a straight line.
Sketching non-parallel lines
When sketching lines that are not parallel to the sides of the paper, turn the paper around so that the line you wish to draw is either straight up and down in front of you or straight across the sheet of paper.
Drawing lines this way rather than at an angle across the sheet is much easier.  This will help you steady your hand (Figure \(\PageIndex{2}\)).
Sketching a rectangle
Locate the corners of the rectangle first. Then place your paper in a comfortable position for sketching and sketch downward for vertical lines and left to right for horizontal lines. Use the grid lines as a guide to help maintain your parallel and at 90 degrees lines to each other (Figure \(\PageIndex{3}\)).
Sketching a circle
First, locate the center of the circle (Figure \(\PageIndex{4}\)), and then very lightly box in the size of the circle (using the diameter as a guide), as in the top right. Sketch in the circle, one quarter at a time, as shown in the bottom row, left to right. You may find it necessary at first to add light points along the projected circumference to help guide you through each quarter. Remember to move your sketch pad to maintain a comfortable sketching position.
Sketching to approximate scale
The full-size square is on the left in Figure \(\PageIndex{5}\). The center square is half size, and the right square is quarter size. Note that the center and right squares are the same shape as the left square, only smaller.
When sketching freehand, your sketches should reflect the actual shapes of objects as much as possible. If you use grid paper, sketching to an approximate scale is not difficult. Assume that the object in Figure \(\PageIndex{6}\) is shown full size. As it is necessary to show all orthographic views on the same sheet of paper, the views must be scaled. Figure \(\PageIndex{7}\) shows the views at approximately one-half the original size.


7.7: Young British Artists (1980-2000)
Introduction
In 1988, a group of young artists in Britain held two pop-up exhibits, Freeze in 1988 and Sensation in 1997. The art was different from the traditional, as artists used unusual materials and sometimes shocking images. The art was distinctive, almost notorious, and the artists earned the name, Young British Artists. The negative coverage by the English press gained them publicity. Many artists attended or graduated from Goldsmiths College of Art in London, including Damien Hirst, one of the most well-known. The school helped develop the movement and cultivated new art forms by abolishing the typical separation of painting, printmaking, sculpture, or other art methods. They encouraged students to combine concepts for new themes in mixed studios and be more entrepreneurial in marketing and showing artwork.
Stylistically, the artists used ideas from Minimalism and Conceptualism; however, they frequently incorporated the darker properties of modern life. Each artist developed a different approach. Some artists used found materials; others employed video, film, printmaking, paint, or photography, and others fashioned extensive installations. The Young British Artists have used appropriated objects, dead animals, furniture from their house, food, cement blocks, cigarettes, or other material. There were no limits or parameters they had to follow; the artists were open to developing a process and selecting objects that may be shocking or challenging. The artists developed a reputation for doing whatever they wanted with whatever material they chose, which was not always an acceptable idea to many in the art world.
Damien Hirst was considered the de facto leader of the inventive artistic concepts, his unusual sculpture of the shark winning him publicity and awards. Most artists were in their twenties and recognized the opportunity to bring change to the stagnant English art market, each with different ideas. The Tate Modern Gallery was also part of the sensational acceptance of the new art forms. London had no modern art public museum, and private donors supported the funds to acquire contemporary modern art and build a gallery. The Young British Artists were a significant part of the move to modernity.
Damien Hirst
Damien Hirst (1965-) was born in England, studied art, and then attended Jacob Kramer College. After employment on building sites for two years, he went to Goldsmiths College. While he was at Goldsmiths, Hirst worked in a mortuary, influencing his future concepts. At the college, he was the main organizer of the student exhibition and the new revolutionary ideas of art. One of the most symbolic representations of the Young British Artists is Hirst's shark. Entitled The Physical Impossibility of Death in the Mind of Someone Living (7.7.1), the shark is suspended in formaldehyde. The shark appears alive, yet everyone knows it is dead. The image was known for its shock value and reaction of a viewer to the symbol of death. The original shark was purchased at a high price by a collector, and when the shark began to deteriorate, the collector paid for a replacement. This led to the argument – was it still the same artwork or something new – upsetting the concept of art conservation.
Away from the Flock (7.7.2) is another sculpture composed of a glass-walled tank and a dead sheep in formaldehyde solution. The sheep is positioned to seem it is still alive. Hirst made different versions of the sculpture with distinctive sheep posed in various positions, all dead but seemingly moving. The sheep and shark were part of Hirst's show, with animals, fish, and insects encased in tanks or boxes.
Hirst has generated a significant amount of criticism for the number of dead animals he has used in his work, including animal rights groups. Artnet News performed a study on Hirst's use of animals and found Hirst used thirty-six different farm animals: sheep, horses, cows, pigs, and even one bear and one zebra. In the category of fish, Hirst used seventeen sharks and 668 other fish. Hirst also added thousands of different insects to his art, including 17,000 butterflies, 45,000 insects from 3,000 species, and five birds. [1]
Hirst made the immense six-meter-tall painted bronze statue, Hymn (7.7.3), created after the anatomical toy he purchased for his son. Hirst loved the way all the body parts fit together; the colors of the parts allowed each distinct element to stand out. However, Hirst made his sculpture precisely like the toy he bought, created for the Young Scientist Anatomy set. Although he did scale the image larger and changed from the toy's plastic to bronze, Hirst was accused of plagiarism and had to pay a settlement to the toy company. The title Hymn is a play on the word 'him.' The statue is reminiscent of the Greek sculptures, arms close to the body with a naked form demonstrating the beauty of the body. The Greeks also favored using bronze and placing lead weights in the feet for stability, just as Hirst used bronze.
Hirst generally used repetition in his work and created a series of any of his themes. Hirst stated,
"People are afraid of change, so you create a kind of belief for them through repetition. It's like breathing. I've always been drawn to series and pairs. A unique thing is quite a frightening object." [2]
He painted over one thousand Spot paintings like Dantrolene (7.7.4) with multicolored spots. Hirst used white backgrounds and painted the spots by hand using shiny house paint. He wanted the spots to look as though a machine applied them; only subtle blemishes reflect the use of an artist's hand. Hirst's Spot series at times appear calming or unnerving, presenting the viewer with a visual dichotomy. Hirst named his Spot series after pharmaceuticals. Dantrolene was a muscle relaxer used to treat muscle spasms or stiffness. Hirst started making a series of Pill Cabinets filled with pharmaceutical and medical bottles and jars. Carefully arranged, most of the bottles had their warning labels exposed.
Pretty Vacant (7.7.5) is one of his cabinets, mounted on the wall and filled with items Hirst bought from stores. The series turns viewers into voyeurs as they appear to be looking into a person's private medicines, our medicines a very personal concept, especially addictive pills. In the series, Hirst examines society's belief in drugs as a cure-all. The success of the different medicine cabinets led to his installation of a complete pharmacy.
Tracey Emin
Tracey Emin (1963-) was born in London. Her father was a Turkish Cypriot, and her mother from Romanian descent. She studied fashion design and printing at different colleges before receiving a master's degree in painting from the Royal College of Art. Unfortunately, Emin was raped when she was only thirteen, something she said was all too familiar in her neighborhood. The tragedy significantly influenced her work, and she is known for her autobiographical and confessional style of art. Emin works in multiple types of media, sculpture, film, paint, photography, and others. One of her first significant exhibitions was about her bed, bringing her major recognition.
For her installation of My Bed (7.7.6), Emin took the bed from her room, along with all the detritus surrounding it, and installed it in the gallery. Emin stated the space was an accurate reconstruction of her room after she became depressed. She spent weeks in bed drinking, smoking, having sexual relationships, or eating, all to deal with her emotional distress. Strewn around the bed, Emin included used condoms, dirty underwear, stained sheets, old Kleenex, and cigarette butts. [3]  The press and critics were in an uproar declaring the installation was not art. Others thought of the bed as a definition of the boundaries of a young woman.
Psyco Slut (7.7.7) was made on a blanket. Emin appliqued different words and phrases on patches of text she wrote by hand. The blanket became a history of Emin's life in intimate detail. She inscribed her childhood abuse and the pain of an abortion. Emin made other blankets from fabrics she felt brought her comfort, including her clothing, the clothes of her parents, and other scraps found around the house. Emin made multiple digital neon art of her poetic thoughts. She wrote about the tensions of relationships and how the interdependencies affect a person's vulnerability or feelings of empowerment.
Fantastic to Feel Beautiful Again (7.7.8) demonstrates her recovery from a poor relationship. All her sayings reflected her open feelings, sometimes playful or other times confrontational and constantly thought-provoking.
Sarah Lucas
Sarah Lucas (1962-) was one of the later members of the Young British Artists recognized in the 1990s for her extraordinary subject matter. Her work was sexual and blurred masculinity and femininity; Lucas declared she liked androgyny. She was born in London and studied art at different colleges before graduating from Goldsmiths College with her degree in Fine Art. Lucas' work was part of the early Freeze exhibition and was considered one of the more shocking members of the group. She experimented with materials and images, including making a toilet with cigarettes. Lucas used found materials she manipulated and altered. She applied some of the odder materials like fruit or vegetables to portray body parts. Lucas' work was based on everyday objects to depict her exploration of sexual ambiguity and how something familiar or strange brings a disorienting tension.
Lucas stuffed nylon stockings to form the body of the soldier in her sculpture, Oh! Soldier (7.7.9). Old used suspenders form the top of the body as the legs are set in army boots, she cast from concrete. Two coat hangers help hold the shapes in place. Automatically, the soldier is perceived to be a male, a reaction to the title of the work and the heavy boots. However, the body is made from tights worn by women, making this sculpture open for sexual interpretation. Titti Doris (7.7.10) is made from tights stuffed with fluff and slouched in a chair. The figure demonstrates and focuses on the objectification of female breasts, a cluster of saggy shapes mounded like a pile of melons—each oversized shape announcing its right to exist.
Anya Gallaccio
Anya Gallaccio (1963-) was born in Scotland, where her father was a TV producer and her mother an actress. Gallaccio attended Goldsmiths College and was part of the Young British Artists Freeze exhibition. She created installations based on organic materials that transform and decay into unpredictable artwork. Because she uses objects like flowers, ice, sugar, trees, or other natural material, the materials may smell good or be exceptionally colorful when first established. The elements may melt, wilt, collapse, or decay from their biological processes as time passes. Gallaccio referred to her artwork as performance because activity occurred, even slowly. One of her installations included assembling a ton of oranges over the floor and watching the natural progression of decay, the performance of nature interacting with the oranges.
In her installation, The Light Pours Out of Me (7.7.11), Gallaccio said, "I would like it to be unsettling for people when they first encounter it. I'd like them to question whether they should enter the gate or not. Then, when they come into the space, it is very formal, quite grandiose but intimate, a quiet place for one or two people." [4] Gallaccio wanted viewers to see the artwork personally and up close. She created a grotto like those found in older English landscapes.
The walls (7.7.12) ripple with amethyst and groups of crystals, all appearing smooth yet dangerously jagged.
At the bottom lays a small pool of water (7.7.13) from black obsidian stone. The installation changes by season, rainfall, vegetation growth, or even as people remove small pieces of stone. Gallaccio imagined the installation would change over geological time instead of human time.
Gallaccio's installation of Red on Green (7.7.14) was composed of 10,000 red roses laid like a carpet across the gallery floor. Initially, the roses were bright red, soft, and emitting the voluptuous aroma of roses. However, the thorns were still on the stems, dangerous to carelessly walk across the floor or pick a handful of blooms. The roses began to decay over a relatively short time (7.7.15) until they turned moldy and dark. The roses transform from beauty and romance to ugly and decayed.
Angus Fairhurst
Born in England, Angus Fairhurst (1966-2008) graduated from Goldsmiths College in Fine Art at the same time as Damien Hirst. Fairhurst and Hirst became friends and collaborated on multiple projects. Fairhurst worked in different media; his work included practical jokes and distorted or exaggerated visuals. He was well-known for his bronze gorilla sculptures in unusual portrayals. Fairhurst was described as brilliant, witty, and intensely intelligent. Sadly, at the age of forty-one, he committed suicide. Damien Hirst said, "He was a great artist and a great friend, he always supported me in fair weather and foul. He shone like the moon and as an artist he had just the right amount of slightly-round-the-bend. I loved him." [5] A Couple of Differences Between Thinking and Feeling I (7.7.16) depicts the odd combination of the oversized gorilla holding a fish under its arm. The giant gorilla appears to be looking into the distance with little emotion. The statue is posed in a full-frontal view.
The immense gorilla in A Couple of Differences Between Thinking and Feeling II (7.7.17) stands on his legs and one arm as it stares at his left arm lying on the floor in front of him. The statues display Fairhurst's practice of working with the thinking and feeling or the sublime and absurd. Fairhurst made multiple drawings of different gorilla statue ideas, playing with the absurd and comic.
Fairhurst's Underdone/Overdone (7.7.18) is composed of a set of thirty paintings. He used black and white photos of the forest. He overlaid the different images and branches with primary colors, crisscrossing each other to create a thicket of trees.
The first image (7.7.19) used a single color with a few branches overlapping. Each image in the line became more abstracted as the layers developed, more branches were added, and the panels at the end of the line became a mass of color. Fairhurst changed the known at the beginning to the unrecognizable at the finale. He explored the boundaries and an antithesis of the formed becoming formless. The subject matter of trees reveals Fairhurst's love of the outdoors as he spent much of his time exploring the Scottish Highlands. Unfortunately, the same woods are where Fairhurst took his life.
Jenny Saville
Born in England, Jenny Saville (1970-) received a degree from Glasgow School of Art and went to the United States to study at the University of Cincinnati. Saville took a women's study class at the university and was exposed to different political and feminist views. While in Ohio, she observed, "You saw lots of big women. Big white flesh in shorts and T-shirts, all of whom had the physicality that I was interested in." [6] Saville also went to New York and watched a plastic surgeon work, helping her understand the anatomical shapes and formations of extreme human bodies. The images and her studies influenced Saville's unashamedly feminist artwork of large or obese women. Her first show in England was successful, and the gallery began to show her work with the other Young British Artists. Saville's paintings were larger than life-sized, and the skin highly marked and distorted. Her paintings illustrate the voluminous body, unable to hide the distorted proportions. Propped (7.7.20) was an early image, the oversized nude woman with her head tossed backward. Her eyes are closed as her hands claw her large thighs as though her thoughts are painful. The woman appears to be repulsed by her image, hiding from the disdain of the male gaze. Saville applied the paint in thick layers, becoming visceral flesh, generating an emotional response.
Saville was a master of the constructs of the body. She demonstrates how flesh flows and rolls upon itself, how excess skin drapes and causes different shadows. Saville paints the body as a complete entity and how its stretches in one place and falls in another. In Strategy (7.7.21), Saville depicts the same women in different positions. She painted the person as viewed from the ground exaggerating the size of her thighs and stomach, the upward angle in the massive painting dwarfing the viewer. The dimpled flesh has overtones of grays portraying the flesh as sickly and bruised. The image is not the idealized person and view generally expected in paintings; instead, the viewer is uncomfortable with the images because it does not meet the standard, flawless feminine body. Saville also painted a series of large-scale works portraying heads.
Rosetta II (7.7.22) and Bleach (7.7.23) are two of the paintings in the series. Both images demand the viewer's gaze, unable to look away. The women do not have smooth, silky skin seen in advertisements, movies, or other media. They carry the marks and scars obtained over years of society's subjective actions against women.  Bleach looks directly back at the viewer, her mouth seeming swollen on the marked face. Saville was interested in how image-conscious people in the country were, these women not meeting the proper image of the plastic surgery population.
Michael Landy
Michael Landy (1963-) was from London and attended Goldsmiths College. He was part of the Freeze exhibition Damien Hirst organized and became one of the Young British Artists. As an artist, Landy frequently focused on consumerism and its effects on society. One of his shows, Break Down , was an exhibit of all the possessions he destroyed. Landy recognized all artists are not successful with everything they make, and he decided to create a mammoth structure in a South London gallery, a container to hold discarded artwork. He planned to have the structure filled with creative failures. The growing discards may have looked like a pile of junk; however, one could still identify parts of well-known artists. Art students and collectors were invited to add to the bin, a popular activity. The Art Bin (7.7.24) demonstrated how much work artists had to create to achieve success; no matter how famous the artist became, they still had failures. Landy stated, "Nobody discards art which has some sort of intrinsic value, so the bin becomes a monument to creative failure." [7]
Landy's exhibition, Saints Alive , was composed of seven different kinetic sculptures that moved according to operations by the visitors. The sculptures were based on old paintings or images of religious saints from the past. Landy made cast statues and combined them with an array of assemblages from recycled materials, including toys, junk, and machinery. In the exhibition, he hung the original inspirational portraits by the statues. Landy wanted the exhibit to be interactive with the viewers while including a critique of the representative saint. One of the first statues in the exhibition was Saint Apollonia (7.7.25), dressed in Renaissance clothing. The space in her torso revealed a congregation of wheels and gears, a set of pincers in her hand. As part of her martyrdom for sainthood, her teeth were all pulled out. In the exhibit, the viewer can press a button and watch the pincers hit her face. Her face became significantly scarred as Landy structured Saint Apollonia to eventually deface herself.
Saint Francis Lucky Dip (7.7.26) was an image of Saint Francis of Assisi, who wore a brown tunic and was barefoot. The statue is headless and hollow. Landy constructed a push-button for the viewer to drop a grabbing claw into the hollow space. Occasionally, the claw grasped a T-shirt printed with 'Poverty-Chasity-Obedience. Landy referred to Saint Francis, who took a vow of poverty and gave away all his worldly possessions.
Chris Ofili
Chris Ofili (1968-) was born in England. His father went back to Nigeria when Ofili was only eleven. Ofili finished his foundation course at one college and then went to London to study at the Chelsea School of Art and the Royal College of Art. When he attended a workshop in Port of Spain, Trinidad, he decided to move there permanently. Ofili also maintains a residence and studio in London and Brooklyn. Some of the Neo-expressionists were very influential on Ofili, especially Jean-Michel Basquiat and Georg Baselitz. Intricate paintings with kaleidoscopic designs were the style Ofili used to create figurative yet abstract images. His work is vibrant, colorful, and multi-layered; the materials he uses are unusual including, glitter, resin, beads, and even elephant dung.
Ofili wanted his work to convey black culture and history while maintaining a feeling of exoticism. No Woman, No Cry (7.7.27) depicts a woman crying oversized tears. The yellow background is patterned with a thin brown line and brown circles. Ofili used phosphorescent paint as a layer for the background, and when the woman was painted, he used oil paint thinned with turpentine to achieve a translucent look. The woman is positioned on top of the background showing through. Her bright blue eye shadow and red lipstick stand out against her dark skin. Her narrow black necklace has a lump of elephant dung for the pendant. Each tear descending from her eyes contains a photograph of a young boy's face, demonstrating her sadness over the boy's loss. The death of a teenage boy influenced Ofili during a racist assault in London. The image in the tears was a photo of the young boy.
Princess of the Posse (7.7.28) was based on the battle to define one's identity, primarily through race and gender. Ofili used a wide variety of materials, built-in multiple layers as he painted and scraped. As in other paintings, he used the background as part of the complete image as the woman's clothing follows the same pattern. Ofili used acrylic paint, resin, bits of paper, map pins, and elephant poop.
He formed the elephant poop into a ball, painted it, and then attached it to the painting as the pendant (7.7.29) on her necklace with map pins.  At the time of the show in the Brooklyn Museum, the city's mayor tried to sue the museum for exhibiting Ofili's work. The mayor declared the work as "horrible and disgusting," [8] The mayor lost and Ofili had a lot of publicity.
Gary Hume
Born in Kent, England, Gary Hume (1962-) graduated from Goldsmiths College, where he attended with the other Young British Artists and was part of the Freeze exhibition. He resides and works in both London and New York. As with the other artists, Hume rejected the standard methods of visual arts to experiment with different types of materials and techniques. He liked to use aluminum panels for much of his work, applying high-gloss paint because it was not traditional. Hume liked to say he was picture-making instead of just painting, developing his sense of autonomy from conventional artists. Most of Hume's early work was based on "door paintings." The paintings appeared to be minimalist images; however, his first ones were based on the doors in British hospitals. In Four Doors I (7.7.30), Hume made four doors of different colors and sizes. Each door is like one found in industrial settings, with small windows in the doors to view who is coming or going through the door as in a restaurant. Hume used high gloss paint to reflect light, the colors changing as the light changes. He focused on the edges, straight and abrupt. He used the concept of high gloss paint on aluminum panels to make other images, always creating absolute boundaries between the colors on the doors. Hume had to lay his panels horizontal when he worked on them to distribute the weight evenly and have the paint stay smoothly in place. When he first started using aluminum instead of other materials, he described the panel as "something absolutely lovely, this big shiny rectangle that you're just about to ruin, rather than a piece of canvas that already says, I'm empty, do something to me. With my first mark the beauty is gone forever." [9] Hume's idea of ruining the surface occurred when he had to roughen the pristine shiny surface to add the glossy paint. To start the door images, Hume drew the specifics on acetate and projected them onto the aluminum. After the outline is ready, he defines the colors to exist in adjacent planes.
Until the early 2000s, Hume only created "door paintings." At first glance, the pieces appear to be minimalist paintings. They are conceptual works, realistic real-size recreations of doors in British hospitals – offering a good illustration of the artist's clever take on mainstream contemporary art trends. Even today, as Hume works with a broader range of subject matter, he continues to blur the boundaries between abstract and figurative, maintaining a critical stance where he remains on the borderline without belonging to either. Though Hume's works may appear abstract, they represent things observed in daily life. In his conceptual paintings, the object exists like an icon – a fixed symbol. When seeking out subjects for his work, Hume draws inspiration from things that evoke conflicting emotions. Hume created the American Tan series, including paintings, sculptures, and prints related to the American pastime of cheerleading. Although Hume was from England, he spent summers visiting upstate New York. Each of the works from the series sent mixed messages, different from each other while based on the same forms. American Tan III (7.7.31) is symbolic, the legs of the cheerleader are carefully formed as the person leaps or does splits or otherwise is posed indiscreetly. Hume used painted bronze for the sculpture, making the pompoms from pieces of sheet metal attached to the end of one of the limbs.
Rachel Whiteread
Rachel Whiteread (1963-) was born in Essex, England, her mother an artist and her father a teacher. Her first art education was at Cyprus College of Art, followed by the Slade School of Art, where she studied sculpture. Whiteread was part of the Young British Artists' second show, Sensation . Most of her works are based on ordinary objects she casts. Whiteread is known to make a cast of an existing chair or table, interested in the line and form the object creates. She constructs sculptures from small elements to entirely cast buildings. One of Whiteread's most famous works is the inside of a Victorian house cast in concrete. The cast objects become a replica of the original, forming ghostly representations. One of her major outdoor works is the Judenplatz Holocaust Memorial (7.7.32) in Vienna, a memorial for the 65,000 Austrians murdered in the Holocaust under the Nazi regime in World War II. On the outside, each row is a set of nameless books representing the people. The pages of the books are facing outwards, the spines of the book are inwards, and the identity of the titles unknown. The doors on the front are permanently closed and inside out without handles, the finality of the lives of the people killed. Incised on the broad concrete base are the names of the different concentration death camps where the people were sent for execution. There was some controversy about the appearance of the monument-it was not beautiful. At the unveiling, Simon Wiesenthal stated, "This monument shouldn't be beautiful; it must hurt." [10]
Embankment (7.7.33) was constructed from 14,000 translucent, white polyethylene boxes stacked in multiple formations. Some think they might be icebergs, with others believe they are stacked sugar cube villages. Whiteread became fascinated with boxes when she was cleaning out her mother's belongings. She filled different boxes with plaster for the installation and then stripped the actual box off, leaving the cast plaster box. Each box was unique with scars, torn sections, or even staples; all the blemishes showed in the plaster and remained. Next, she re-made the boxes with translucent polyethylene, a process she followed for thousands of boxes. The actual installation projected different and unusual feelings of space and scale. Some of the box stacks were exceptionally high; a dizzyingly view, other stacks allowed the viewer to touch them. Whiteread was also known for her casts of furniture.
Untitled (100 Spaces) (7.7.34) is an exhibition composed of 100 resin casts of the undersides of different chairs. They are arranged in twenty rows, with five objects in each row. The pieces form a grid, the colors translucent. Art critic Craig Berry stated, "the sculpture oscillates between abstraction and reference. It shifts from being an accumulation of mute cubic forms to a shimmering index of everyday life." [11]
England was ready for a new art style when the Young British Artists held their first show, their work startling, provocative, and unusual, developing a new audience and an atmosphere for modern art. The success of their artwork led to the development of the Tate Modern and the Turner Prize. Today the Tate is an exceptionally successful modern art gallery, and the artists have continued to push the meaning of art.
[1] Retrieved from https://news.artnet.com/art-world/da...ur-beef-916097
[2] Retrieved from https://gagosian.com/artists/damien-hirst/
[3] Retrieved from https://www.theartstory.org/movement...itish-artists/
[4] Retrieved from https://www.jupiterartland.org/art/a...urs-out-of-me/
[5] Retrieved from https://www.theguardian.com/artandde...08/mar/31/art2
[6] Retrieved from https://www.theguardian.com/artandde...igallery.art10
[7] Retrieved from https://www.theguardian.com/artandde...-landy-art-bin
[8] Retrieved from https://www.sartle.com/artwork/princ...se-chris-ofili
[9] Retrieved from https://www.tate.org.uk/research/pub...ings-gary-hume
[10] Retrieved from https://www.theguardian.com/world/20...6/kateconnolly
[11] Retrieved from https://craigberry93.medium.com/rach...n-135c9482f024


16.10: Sage
Rings are very important in your study of abstract algebra, and similarly, they are very important in the design and use of Sage. There is a lot of material in this chapter, and there are many corresponding commands in Sage.
Creating Rings
Here is a list of various rings, domains and fields you can construct simply.
-
Integers()
,ZZ
: the integral domain of positive and negative integers, \({\mathbb Z}\text{.}\) -
Integers(n)
: the integers mod \(n\text{,}\) \({\mathbb Z_n}\text{.}\) A field when \(n\) is prime, but just a ring for composite \(n\text{.}\) -
QQ
: the field of rational numbers, \({\mathbb Q}\text{.}\) -
RR
,CC
: the field of real numbers and the field of complex numbers, \({\mathbb R}\text{,}\) \({\mathbb C}\text{.}\) It is impossible to create every real number inside a computer, so technically these sets do not behave as fields, but only give a good imitiation of the real thing. We say they are inexact rings to make this point. -
QuadraticField(n)
: the field formed by combining the rationals with a solution to the polynomial equation \(x^2-n=0\text{.}\) The notation in the text is \({\mathbb Q}[\sqrt{n}]\text{.}\) A functional equivalent can be made with the syntaxQQ[sqrt(n)]
. Note thatn
can be negative. -
CyclotomicField(n)
: the field formed by combining the rationals with the solutions to the polynomial equation \(x^n-1=0\text{.}\) -
QQbar
: the field formed by combining the rationals with the solutions to every polynomial equation with integer coefficients. This is known as a the field of algebraic numbers, denoted as \(\overline(click for details)\text{.}\)Callstack: at (Bookshelves/Abstract_and_Geometric_Algebra/Abstract_Algebra:_Theory_and_Applications_(Judson)/16:_Rings/16.10:_Sage), /content/body/div[1]/ol[1]/li[7]/span, line 1, column 1
-
FiniteField(p)
: for a prime \(p\text{,}\) the field of integers \({\mathbb Z_p}\text{.}\)
If you print a description of some of the above rings, you will sometimes see a new symbol introduced. Consider the following example:
Here
Number Field
describes an object generally formed by combining the rationals with another number (here \(\sqrt{7}\)). “a” is a new symbol which behaves as a root of the polynomial \(x^2-7\text{.}\) We do not say which root, \(\sqrt{7}\) or \(-\sqrt{7}\text{,}\) and as we understand the theory better we will see that this does not really matter.
We can obtain this root as a generator of the number field, and then manipulate it. First squaring
root
yields 7. Notice that
root
prints as
a
. Notice, too, that computations with
root
behave as if it was
either
root of \(x^2-7\text{,}\) and results print using
a
.
This can get a bit confusing, inputing computations with
root
and getting output in terms of
a
. Fortunately, there is a better way. Consider the following example:
With the syntax
F.<b>
we can create the field
F
along with specifying a generator
b
using a name of our choosing. Then computations can use
b
in both input and output as a root of \(x^2-7\text{.}\)
Here are three new rings that are best created using this new syntax.
-
F.<a> = FiniteField(p^n)
: We will later have a theorem that tells us that finite fields only exist with orders equal to to a power of a prime. When the power is larger than 1, then we need a generator, here given asa
. -
P.<x>=R[]
: the ring of all polynomials in the variablex
, with coefficients from the ringR
. Notice thatR
can be any ring, so this is a very general construction that uses one ring to form another. See an example below. -
Q.<r,s,t> = QuaternionAlgebra(n, m)
: the rationals combined with indeterminatesr
,s
andt
such that \(r^2=n\text{,}\) \(s^2=m\) and \(t = rs = -sr\text{.}\) This is a generalization of the quaternions described in this chapter, though over the rationals rather than the reals, so it is an exact ring. Notice that this is one of the few noncommutative rings in Sage. The “usual” quaternions would be constructed withQ.<I,J,K> = QuaternionAlgebra(-1, -1)
. (Notice that usingI
here is not a good choice, because it will then clobber the symbolI
used for complex numbers.)
Syntax specifying names for generators can be used for many of the above rings as well, such as demonstrated above for quadratic fields and below for cyclotomic fields.
Properties of Rings
The examples below demonstrate how to query certain properties of rings. If you are playing along, be sure to execute the first compute cell to define the various rings involved in the examples.
Exact versus inexact.
Finite versus infinite.
Integral domain?
Field?
Commutative?
Characteristic.
Additive and multiplicative identities print like you would expect, but notice that while they may print identically, they could be different because of the ring they live in.
There is some support for subrings. For example,
Q
and
S
are extensions of the rationals, while
F
is totally distinct from the rationals.
Not every element of a ring may have a multiplicative inverse, in other words, not every element has to be a unit (unless the ring is a field). It would now be good practice to check if an element is a unit before you try computing its inverse.
Quotient Structure
Ideals are the normal subgroups of rings and allow us to build “quotients” — basically new rings defined on equivalence classes of elements of the original ring. Sage support for ideals is variable. When they can be created, there is not always a lot you can do with them. But they work well in certain very important cases.
The integers, \({\mathbb Z}\text{,}\) have ideals that are just multiples of a single integer. We can create them with the
.ideal()
method or just by wrting a scalar multiple of
ZZ
. And then the quotient is isomorphic to a well-understood ring. (Notice that
I
is a bad name for an ideal if we want to work with complex numbers later.)
We might normally be more careful about the last statement. The quotient is a set of equivalence classes, each infinite, and certainly not a single integer. But the quotient is isomorphic to \({\mathbb Z}_4\text{,}\) so Sage just makes this identification.
Notice that the construction of the quotient ring has created a new generator, converting
y
(\(y\)) to
ybar
(\(\overline{y}\)). We can override this as before with the syntax demonstrated below.
So from a quotient of an infinite ring and an ideal (which is also a ring), we create a field, which is finite. Understanding this construction will be an important theme in the next few chapters. To see how remarkable it is, consider what happens with just one little change.
There are a few methods available which will give us properties of ideals. In particular, we can check for prime and maximal ideals in rings of polynomials. Examine the results above and below in the context of Theorem 16.35.
The fact that
M
is a prime ideal is verification of Corollary \(16.40\).
Ring Homomorphisms
When Sage is presented with
3 + 4/3
, how does it know that 3 is meant to be an integer? And then to add it to a rational, how does it know that we really want to view the computation as 3/1 + 4/3? This is really easy for you and me, but devilishly hard for a program, and you can imagine it getting ever more complicated with the many possible rings in Sage, subrings, matrices, etc. Part of the answer is that Sage uses ring homomorphisms to “translate” objects (numbers) between rings.
We will give an example below, but not pursue the topic much further. For the curious, reading the Sage documentation and experimenting would be a good exercise.
So
phi
is a homomorphism (“morphism”) that converts integers (the domain is
ZZ
) into rationals (the codomain is
QQ
), whose parent is a set of homomorphisms that Sage calls a “homset.” Even though
a
and
b
both print as
3
, which is indistinguishable to our eyes, the parents of
a
and
b
are different. Yet the numerical value of the two objects has not changed.


2: Introduction to 2D Art Making
From the beginning of our species, humans have been object makers. The first things made were items for survival (tools, weapons, and clothing) or for spiritual use (representations of animals or gods). As human cultures evolved, the kinds of objects also evolved to serve a vast range of purposes and functions. We are on that evolutionary makers continuum as we make things that are relevant to contemporary culture.
This course deals with the construction of 2D objects. One major difference between this way of creating artwork is that it takes place on a flat plane and only gives the illusion of physical depth and material texture. It tries to create the illusion of space. The objects illustrated do not take up 3D space with the viewer and often only see limited sides or points of view.
At its core, art and design are about communication. The goal is to communicate with the viewer or user. There are three components to any work that can be examined to see how well it communicates to the viewer. They are:
- Subject : [What] this is what is being presented. Is the object meant to be representational of something, non-representational but an abstraction of something, or conceptual (where the idea becomes the subject)?
- Form : [How] this is the overall arrangement or organization of the work. This uses the elements (building blocks/words) and principles (organizing elements into relationships/sentences) of art to build the work.
- Context : [Why] this is the emotional I intellectual message of the work. The context is the artist's intention and the message they are trying to get to the viewer.
The challenge of making interesting 2d subjects and ideas is a complex and rewarding process. Breaking down the basics and building up an effective art making process will be discussed in the rest of the studio handbook.


16: Misinformation and Biases Infect Social Media, Both Intentionally and Accidentally (Ciampaglia and Filippo Menczer)
Giovanni Luca Ciampaglia and Filippo Menczer
#argument, #causalargument, #cognitivebias, #ethos, #logos, #sharedvalues, #reportinginformation
Social media are among the primary sources of news in the U.S. and across the world. Yet users are exposed to content of questionable accuracy, including conspiracy theories , clickbait , hyperpartisan content , pseudo science and even fabricated “fake news” reports .
It’s not surprising that there’s so much disinformation published: Spam and online fraud are lucrative for criminals , and government and political propaganda yield both partisan and financial benefits . But the fact that low-credibility content spreads so quickly and easily suggests that people and the algorithms behind social media platforms are vulnerable to manipulation.
Explaining the tools developed at the Observatory on Social Media.
Our research has identified three types of bias that make the social media ecosystem vulnerable to both intentional and accidental misinformation. That is why our Observatory on Social Media at Indiana University is building tools to help people become aware of these biases and protect themselves from outside influences designed to exploit them.
 The brain can deal with only a finite amount of information, and too many incoming stimuli can cause information overload . That in itself has serious implications for the quality of information on social media. We have found that steep competition for users’ limited attention means that some ideas go viral despite their low quality – even when people prefer to share high-quality content .
To avoid getting overwhelmed, the brain uses a number of tricks . These methods are usually effective, but may also become biases when applied in the wrong contexts.
One cognitive shortcut happens when a person is deciding whether to share a story that appears on their social media feed. People are very affected by the emotional connotations of a headline , even though that’s not a good indicator of an article’s accuracy. Much more important is who wrote the piece.
To counter this bias, and help people pay more attention to the source of a claim before sharing it, we developed Fakey , a mobile news literacy game (free on Android and iOS ) simulating a typical social media news feed, with a mix of news articles from mainstream and low-credibility sources. Players get more points for sharing news from reliable sources and flagging suspicious content for fact-checking. In the process, they learn to recognize signals of source credibility, such as hyperpartisan claims and emotionally charged headlines.
Bias in society
Another source of bias comes from society. When people connect directly with their peers, the social biases that guide their selection of friends come to influence the information they see.
In fact, in our research we have found that it is possible to determine the political leanings of a Twitter user by simply looking at the partisan preferences of their friends. Our analysis of the structure of these partisan communication networks found social networks are particularly efficient at disseminating information – accurate or not – when they are closely tied together and disconnected from other parts of society .
The tendency to evaluate information more favorably if it comes from within their own social circles creates “ echo chambers ” that are ripe for manipulation, either consciously or unintentionally. This helps explain why so many online conversations devolve into “us versus them” confrontations .
To study how the structure of online social networks makes users vulnerable to disinformation, we built Hoaxy , a system that tracks and visualizes the spread of content from low-credibility sources, and how it competes with fact-checking content. Our analysis of the data collected by Hoaxy during the 2016 U.S. presidential elections shows that Twitter accounts that shared misinformation were almost completely cut off from the corrections made by the fact-checkers.
When we drilled down on the misinformation-spreading accounts, we found a very dense core group of accounts retweeting each other almost exclusively – including several bots. The only times that fact-checking organizations were ever quoted or mentioned by the users in the misinformed group were when questioning their legitimacy or claiming the opposite of what they wrote.
Bias in the machine
The third group of biases arises directly from the algorithms used to determine what people see online. Both social media platforms and search engines employ them. These personalization technologies are designed to select only the most engaging and relevant content for each individual user. But in doing so, it may end up reinforcing the cognitive and social biases of users, thus making them even more vulnerable to manipulation.
For instance, the detailed advertising tools built into many social media platforms let disinformation campaigners exploit confirmation bias by tailoring messages to people who are already inclined to believe them.
Also, if a user often clicks on Facebook links from a particular news source, Facebook will tend to show that person more of that site’s content . This so-called “ filter bubble ” effect may isolate people from diverse perspectives, strengthening confirmation bias.
Our own research shows that social media platforms expose users to a less diverse set of sources than do non-social media sites like Wikipedia. Because this is at the level of a whole platform, not of a single user, we call this the homogeneity bias .
Another important ingredient of social media is information that is trending on the platform, according to what is getting the most clicks. We call this popularity bias , because we have found that an algorithm designed to promote popular content may negatively affect the overall quality of information on the platform. This also feeds into existing cognitive bias, reinforcing what appears to be popular irrespective of its quality.
All these algorithmic biases can be manipulated by social bots , computer programs that interact with humans through social media accounts. Most social bots, like Twitter’s Big Ben , are harmless. However, some conceal their real nature and are used for malicious intents, such as boosting disinformation or falsely creating the appearance of a grassroots movement , also called “astroturfing.” We found evidence of this type of manipulation in the run-up to the 2010 U.S. midterm election.
To study these manipulation strategies, we developed a tool to detect social bots called Botometer . Botometer uses machine learning to detect bot accounts, by inspecting thousands of different features of Twitter accounts, like the times of its posts, how often it tweets, and the accounts it follows and retweets. It is not perfect, but it has revealed that as many as 15 percent of Twitter accounts show signs of being bots .
Using Botometer in conjunction with Hoaxy, we analyzed the core of the misinformation network during the 2016 U.S. presidential campaign. We found many bots exploiting both the cognitive, confirmation and popularity biases of their victims and Twitter’s algorithmic biases.
These bots are able to construct filter bubbles around vulnerable users, feeding them false claims and misinformation. First, they can attract the attention of human users who support a particular candidate by tweeting that candidate’s hashtags or by mentioning and retweeting the person. Then the bots can amplify false claims smearing opponents by retweeting articles from low-credibility sources that match certain keywords. This activity also makes the algorithm highlight for other users false stories that are being shared widely.
Understanding complex vulnerabilities
Even as our research, and others’, shows how individuals, institutions and even entire societies can be manipulated on social media, there are many questions left to answer. It’s especially important to discover how these different biases interact with each other, potentially creating more complex vulnerabilities.
Tools like ours offer internet users more information about disinformation, and therefore some degree of protection from its harms. The solutions will not likely be only technological , though there will probably be some technical aspects to them. But they must take into account the cognitive and social aspects of the problem.
Editor’s note: This article was updated on Jan. 10, 2019, to replace a link to a study that had been retracted. The text of the article is still accurate, and remains unchanged.
____________________
Giovanni Luca Ciampaglia
is an Assistant Professor, Department of Computer Science and Engineering, University of South Florida.
Filippo Menczer
is a
Professor of Computer Science and Informatics and the Director of the Center for Complex Networks and Systems Research at Indiana University. This article originally appeared in
The Conversation
.
Misinformation and Biases Infect Social Media, Both Intentionally and Accidentally by Giovanni Luca Ciampaglia and Filippo Menczer is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License .


6.1: Problem Set
EXERCISE \(\PageIndex{1}\)
Consider the \(C^{r}\), \(r \ge 1\), autonomous vector field on \(\mathbb{R}^2\):
\(\dot{x} = f(x)\),
with flow
\(\phi_{t}(\cdot)\),
and let \(x = \bar{x}\) denote a hyperbolic saddle type equilibrium point for this vector field. We denote the local stable and unstable manifolds of this equilibrium point by:
\(W_{loc}^{s}(\bar{x})\), \(W_{loc}^{u}(\bar{x})\),
respectively. The global stable and unstable manifolds of \(\bar{x}\) are defined by:
\(W^{s}(\bar{x}) \equiv \cup_{t \le 0} \phi_{t} (W_{loc}^{s}(\bar{x}))\),
\(W^{u}(\bar{x}) \equiv \cup_{t \ge 0} \phi_{t} (W_{loc}^{s}(\bar{x}))\),
(a) Show that \(W^{s}(\bar{x})\) and \(W^{u}(\bar{x})\) are invariant set.
(b) Suppose that \(p \in W^{s}(\bar{x})\), show that \(\phi_{t}(p) \rightarrow \bar{x}\) at an exponential rate as \(t \rightarrow \infty\).
(c) Suppose that \(p \in W^{u}(\bar{x})\), show that \(\phi_{t}(p) \rightarrow \bar{x}\) at an exponential rate as \(t \rightarrow -\infty\).
EXERCISE \(\PageIndex{2}\)
Consider the \(C^{r}, r \ge 1\), autonomous vector field on \(\mathbb{R}^2\) having a hyperbolic saddle point. Can its stable and unstable manifolds intersect at an isolated point (which is not a fixed point of the vector field) as shown in figure 2?
EXERCISE \(\PageIndex{3}\)
Consider the following autonomous vector field on the plane:
\(\dot{x} = \alpha x\),
\[\dot{y} = \beta y + \gamma x^{n+1}, \label{6.42}\]
where \(\alpha < 0\), \(\beta > 0\), \(\gamma\) is a real number, and n is a positive integer.
- Show that the origin is a hyperbolic saddle point.
- Compute and sketch the stable and unstable subspaces of the origin.
- Show that the stable and unstable subspaces are invariant under the linearized dynamics.
-
Show the the flow generated by this vector field is given by:
\(x(t, x_{0}) = x_{0}e^{\alpha t}\),
\(y(t, x_{0}, y_{0}) = e^{\beta t}(y_{0} - \frac{\gamma x_{0}^{n+1}}{\alpha (n+1) - \beta}) + (\frac{\gamma x_{0}^{n+1}}{\alpha (n+1) - \beta}) e^{\alpha (n+1)t}\)
- Compute the global stable and unstable manifolds of the origin from the flow.
- Show that the global stable and unstable manifolds that you have computed are invariant.
- Sketch the global stable and unstable manifolds and discuss how they depend on g and n.
EXERCISE \(\PageIndex{4}\)
Suppose \(\dot{x} = f(x), x \in \mathbb{R}^n\) is a \(C^r\) vector field having a hyperbolic fixed point, \(x = x_{0}\), with a homoclinic orbit. Describe the homoclinic orbit in terms of the stable and unstable manifolds of \(x_{0}\).
EXERCISE \(\PageIndex{5}\)
Suppose \(\dot{x} = f(x), x \in \mathbb{R}^n\) is a \(C^r\) vector field having hyperbolic fixed points, \(x = x_{0}\) and \(x_{1}\), with a heteroclinic orbit connecting \(x_{0}\) and \(x_{1}\). Describe the heteroclinic orbit in terms of the stable and unstable manifolds of \(x_{0}\) and \(x_{1}\).


8.1: Heat Capacity as A Function of Temperature
-
- Last updated
- Save as PDF
It is relatively easy to measure heat capacities as a function of temperature. If we measure the constant-pressure heat capacity of a pure substance over a wide temperature range, we typically observe a curve like that in Figure 1. The heat capacity is a smooth, continuous function of temperature except for a small number of discontinuities. These occur at temperatures where the substance undergoes phase changes. These can be changes from one solid phase to another, melting to convert a solid phase to the liquid, or vaporization to convert the liquid to the gas. The details of the curve are pressure dependent; for example, at a low pressure, we might observe sublimation of the material from a solid phase directly into its gas phase.
Another general feature of these curves is that the heat capacity of the solid substance decreases to zero as the absolute temperature decreases to zero; the curve meets the abscissa at the zero of temperature and does so asymptotically. That this is true for all substances seems like an odd sort of coincidence. Why should all solid substances exhibit essentially the same heat capacity (zero) at one temperature (absolute zero)?
As it turns out, this result has a straightforward molecular interpretation in the theory of statistical thermodynamics. In Section 22.6 , we consider a theory of low-temperature heat capacity developed by Einstein. Einstein’s theory explains all of the qualitative features that are observed when we measure heat capacities at low temperatures, but its predictions are not quantitatively exact. Debye extended the Einstein model and developed a theory that gives generally excellent quantitative predictions. The Debye theory predicts that, at temperatures near absolute zero, the heat capacity varies as the cube of temperature: \(C_P=AT^3\), where \(A\) is a constant. If we have heat capacity data down to a temperature near absolute zero, we can estimate the value of \(A\) from the value of \(C_P\) at the lowest available temperature.
Anticipating results that we develop in Chapter 22 , we can characterize the statistical interpretation as follows: When a system of molecules gives up heat to its surroundings, some of the molecules move from higher energy levels to lower ones. Statistical thermodynamics posits that the fraction of the molecules that are in the lowest energy level approaches one as the temperature goes to zero. If nearly all of the molecules are already in the lowest energy level, decreasing the temperature still further has a negligible effect on the energy and enthalpy of the system.
Given such heat capacity data, we can find the enthalpy or entropy change that occurs as we change the temperature of a quantity of the substance from some reference temperature to any other value. When we use pressure and temperature as the independent variables, we have
\[dH=C_PdT+\left[V-T{\left(\frac{\partial V}{\partial T}\right)}_P\right]dP \nonumber \]
and
\[dS=\frac{C_P}{T}dT-{\left(\frac{\partial V}{\partial T}\right)}_PdP \nonumber \]
At constant pressure, we have
\[\left(dH\right)_P=C_PdT \nonumber \]
so that
\[H\left(T\right)-H\left(T_{ref}\right)=\int^T_{T_{ref}}{C_PdT} \nonumber \]
and
\[{\left(dS\right)}_P=\frac{C_P}{T}dT \nonumber \] so that \[S\left(T\right)-S\left(T_{ref}\right)=\int^T_{T_{ref}}{\frac{C_P}{T}dT} \nonumber \]
If phase transitions occur as the temperature goes from the reference temperature to the temperature of interest, these integrations must be carried out in steps. Also, we must include the enthalpy and entropy changes that occur during these phase changes.


10.2: Juvenile Justice
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- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
The contemporary juvenile justice system operates under the premise that juveniles are different than adults and require special attention and treatment. The juvenile justice system believes that juveniles are malleable and can be rehabilitated. The juvenile court is based on the premise that public safety is best served by emphasizing the rehabilitation, rather than incapacitation and punishment of juveniles. [1] Unfortunately, sensationalized media exposure of violent youth has led to exaggerated public fear of juvenile crime, get tough legislation, and a perceived need to “do something” about juvenile crime. [2] This punitive position is nothing new. Before the inception of the juvenile justice system a mere 100 years ago, youth were treated the same as adults. They were considered culpable for their actions and housed alongside adult offenders in jails and prisons. Recent research has utilized neuroscience to support the need to treat juveniles differently because they are different. The sections of the brain that govern characteristics associated with moral culpability do not stop maturing until the early 20s. Therefore, it is assumed that someone under age 20, such as a juvenile delinquent, has an underdeveloped brain.
When addressing juvenile delinquency in America, the pendulum swings from punitive policies to rehabilitative policies and then back again depending on media, politics, and the current climate. There is no magic bullet approach to preventing juvenile delinquency, but as the court evolves, changes, and utilizes best practices, it gets closer.
Ted Talks : Stephen Case The youth crime ‘problem’ is examined as a social construction and moral panic created by institutions in Western societies. The talk traces the evolution of youth crime into a phenomenon persistently misrepresented as an escalating social epidemic. The developmental life stages of ‘childhood’ and ‘adolescence’ as inventions are explored, highlighting differences between young people and adults. In this way, ‘youth crime’ can be identified as a social problem requiring distinct responses. A running theme is a child as a source of adult anxiety and fear, motivating societies to create structures, processes, theories, and images of youth crime that punish lawbreakers. The ‘solution’ is the ‘positive youth justice’ model. Children should not be punished as if they are adults but their criminal behavior should be seen as a normal part of growing up. Instead, they should be worked with to meet their needs, to embrace their human rights and to promote their life chances. https://www.youtube.com/watch?v=QYWPyiZIpV8


28.4: Lesson Plan for Walt Whitman’s Song of Myself (Group Anthology Contribution 2019)
Anthology Contribution – Lesson Plan
Materials
- Text (Walt Whitman’s Song of Myself)
- Notebook
- Pencil/pen/laptop
Procedure:
Opening Move:
Print out certain sections of the poem and randomly pass them out to the class. Have students look for themes. They get roughly five minutes to look for themes and write them down.
Main Lesson:
The students get into groups based on the passage that they received, and they pick the theme they liked the most . The instructor writes those themes on the board, then the instructor writes the themes that they themselves found on the board.
Have the students connect the passage to the theme that the instructor gives them ( randomly assign everyone a theme from the class list of themes ). If there is any time left over when a group is done, they pick a theme from the instructor’s list , and try to connect it to that theme .
- Have each group share what themes they found.
- Have class discuss overarching themes of the poem, allowing them to freely discuss as a class.
Through the discussion the instructor takes notes of important ideas and topics that were presented in the class’ discussions, connecting them to show what the students came up with and how it all connects together.
Extra Time?
If we have extra time at the end, pick sections of the poem to talk about, or have them write an English summary of the passage they read.
Section:
Section 2: Existence, romanticism, nature, personhood, identity
Section 3: Humanity, time, sexuality
Section 6: Life, birth, innocence, age, time, death
Section 13: Humanity, understanding, curiosity, sexuality
Section 14: Nature, love, purpose
Section 16: Growth, diversity, peace
Section 17: Uncanny, transcendentalism, purpose
Section 18: Juxtaposition, Death, Success, Failure
Section 19: Equality, humanity, utopia, uncanny
Section 20: Existence, identity
Overarching themes: Crescendo, Purpose, Self, Transcendentalism, Romanticism
Discussion Questions (for end of lesson):
- How does passage 10 relate to the previous texts and topics we have worked with?
- After so much discussion on themes, are there any major overarching themes throughout the entire poem?
- What is the point of the poem? What is Whitman trying to say/tell us?


6.0: Sir Gawain and the Green Knight- Background
Sir Gawain and the Green Knight (Middle English: Sir Gawayn and þe Grene Knyȝt ) is a late 14th-century Middle English chivalric romance. It is one of the best known Arthurian stories, and is of a type known as the “beheading game.” The Green Knight is interpreted by some as a representation of the Green Man of folklore and by others as an allusion to Christ. Written in stanzas of alliterative verse, each of which ends in a rhyming bob and wheel, it draws on Welsh, Irish and English stories, as well as the French chivalric tradition. It is an important poem in the romance genre, which typically involves a hero who goes on a quest which tests his prowess, and it remains popular to this day in modern English renderings from J. R. R. Tolkien, Simon Armitage and others, as well as through film and stage adaptations.
It describes how Sir Gawain, a knight of King Arthur’s Round Table, accepts a challenge from a mysterious “Green Knight” who challenges any knight to strike him with his axe if he will take a return blow in a year and a day.  In his struggles to keep his bargain Gawain demonstrates chivalry and loyalty until his honour is called into question by a test involving Lady Bertilak, the lady of the Green Knight’s castle.
The poem survives in a single manuscript, the Cotton Nero A.x. , which also includes three religious narrative poems: Pearl , Purity and Patience . All are thought to have been written by the same unknown author, possibly Cameron of Sutherland, dubbed the “Pearl Poet” or “Gawain Poet,” since all four are written in a North West Midland dialect of Middle English.
Additional information on Sir Gawain and the Green Knight can be found here.
- Sir Gawain and the Green Knight. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Sir_Gawain_and_the_Green_Knight . License : CC BY-SA: Attribution-ShareAlike
- Image of Sir Gawain and the Green Knight. Located at : https://commons.wikimedia.org/wiki/File:Sir_Gawain_first_page_670x990.jpg . License : Public Domain: No Known Copyright


14.9.1: Review Questions
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Review Questions
1 .
What is Lamaze International Childbirth Education based on?
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breathing techniques
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comprehensive evidence-based childbirth teachings
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empowerment of the nursing staff
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positions to promote breast-feeding
2 .
What does the nurse say about labor beginning to the laboring person who has studied Lamaze?
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“We should walk in the hallways to get your labor started.”
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“Let’s turn the lights down and get you into a comfortable position with your partner next to you.”
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“I bet you are ready for the Pitocin to get started to get your baby here.”
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“Early labor is the best time for you to come to the hospital.”
3 .
How would a patient who has taken Lamaze education respond when the health-care provider recommends breaking the bag of waters in early labor?
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“As long as it will speed up my labor, that is fine.”
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“I trust whatever intervention you think is right.”
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“What are the risks and benefits of breaking my water right now?”
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“Will I be able to get an epidural after you break my water?”
4 .
What statement by a health-care provider is an example of shared decision making between a health-care provider and a patient?
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“I’m going to start this medication because it is best for your baby.”
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“Can you agree with me because I am your health-care provider?”
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“I understand how the hospital works, and it will be easier for you to just do what is easy for the nurses.”
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“Do you feel ready to make a decision after we talked about this medication?”
5 .
The nurse is attempting to explain physiologic birth. What do they say?
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“Physiologic birth involves interventions that do not harm the baby.”
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“Physiologic birth occurs only in birth centers.”
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“If your partner and I give you support, you can have a birth without medical intervention.”
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“If you want to have a cesarean birth, we can ask your health-care provider to schedule it.”
6 .
Why was the Bradley Method originally introduced?
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as a novel approach to pregnancy where low-intervention, medication-free births were the goal
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as an education program that supported use of twilight birth
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as a system of supporting families wanting community birth
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as a program of education that focused on the importance of using a doula instead of a partner as a birth support
7 .
Nutrition is an integral part of the Bradley Method. What important nutrition advice is taught in this method?
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Only eat low-fat foods.
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Increase protein to 100 g per day.
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Do not eat dairy because it causes food allergies.
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Eat a low-protein diet.
8 .
In what way is the Mongan Method of childbirth education beneficial to birthing people?
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It helps people push with great effort in second stage labor.
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Birthing people feel confident about the use of an epidural to relax the body.
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People are taught how to release fear to decrease pain.
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HypnoBirthing is proven to be 100 percent effective in relieving pain in labor.
9 .
Who created the Mongan Method?
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physician
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midwife
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hypnotherapist
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organization
10 .
What is the theory that supports HypnoBirthing?
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the fear-tension-pain theory
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the theory that pain is productive in labor
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the idea that self-hypnosis always works if you try hard enough
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the theory that when hypnotized during labor, the environment does not matter because the person is not aware of the surroundings
11 .
What technique is used for visualization and deepening in HypnoBirthing?
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counting contractions
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the “on-off” switch
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visualizing the instruments used to assist with birth
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deepening into hypnosis to help push harder
12 .
What does HypnoBirthing teach about the emotional and physical changes in pregnancy?
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Fear of childbirth provides a healthy incentive to learn.
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Physical changes in pregnancy make relaxation harder.
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Physical and emotional changes are normal.
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Emotional changes cause anxiety that is difficult to let go of.
13 .
F. M. Alexander was an actor who developed a medical technique. What was the basis for this technique?
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Relaxing his throat helped his voice return to normal.
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Relaxing his back helped him overcome chronic back pain.
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Sitting upright allowed him to breathe better.
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Better posture controlled his movements.
14 .
Relaxation of muscles in labor provides many benefits. What is one benefit of this technique in labor?
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Relaxation will prevent a cesarean section.
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Relaxation of the pelvic floor helps in pushing the fetus in the second stage.
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Relaxation of the abdomen ensures an unmedicated birth.
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Relaxation causes the contractions to decrease in strength.
15 .
What can self-awareness with postural adjustments lead to?
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tension formation
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tension release
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suboptimal posture
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back pain
16 .
What is one characteristic of the Alexander Technique the nurse can explain to a patient?
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taught only in person
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focused on unmedicated birth
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taught by a person who will assess the muscles and posture
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only useful for pregnancy but not birth
17 .
What is the purpose of a birth plan?
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dream about birth
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learn about birth options and determine personal preferences
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list all things not wanted for the birth
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ensure an unmedicated birth
18 .
The laboring person asks the nurse to review the birth plan. What item is on a typical birth plan?
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where the patient will be staying after birth
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who will be watching their other children
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what position they want to birth in
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how they will time contractions


7: Alpha, Beta, and Gamma Diversity
Whittaker (1972) described three terms for measuring biodiversity over spatial scales: alpha, beta, and gamma diversity. Alpha diversity refers to the diversity within a particular area or ecosystem, and is usually expressed by the number of species (i.e., species richness ) in that ecosystem. For example, if we are monitoring the effect that British farming practices have on the diversity of native birds in a particular region of the country, then we might want to compare species diversity within different ecosystems, such as an undisturbed deciduous wood, a well-established hedgerow bordering a small pasture, and a large arable field. We can walk a transect in each of these three ecosystems and count the number of species we see; this gives us the alpha diversity for each ecosystem; see Table (this example is based on the hypothetical example given by Meffe et al., 2002; Table 6.1).
If we examine the change in species diversity between these ecosystems then we are measuring the beta diversity. We are counting the total number of species that are unique to each of the ecosystems being compared. For example, the beta diversity between the woodland and the hedgerow habitats is 7 (representing the 5 species found in the woodland but not the hedgerow, plus the 2 species found in the hedgerow but not the woodland). Thus, beta diversity allows us to compare diversity between ecosystems.
Gamma diversity is a measure of the overall diversity for the different ecosystems within a region. Hunter (2002: 448) defines gamma diversity as "geographic-scale species diversity". In the example in Table, the total number of species for the three ecosystems 14, which represent the gamma diversity.
| Hypothetical species | Woodland habitat | Hedgerow habitat | Open field habitat |
|---|---|---|---|
| A | X | ||
| B | X | ||
| C | X | ||
| D | X | ||
| E | X | ||
| F | X | X | |
| G | X | X | |
| H | X | X | |
| I | X | X | |
| J | X | X | |
| K | X | ||
| L | X | X | |
| M | X | ||
| N | X | ||
| Alpha diversity | 10 | 7 | 3 |
| Beta diversity | Woodland vs. hedgerow: 7 | Hedgerow vs. open field: 8 | Woodland vs. open field: 13 |
| Gamma diversity | 14 |
Table \(\PageIndex{1}\) Alpha, beta and gamma diversity for hypothetical species of birds in three different ecosystems
Glossary
- Ecosystem
- a community plus the physical environment that it occupies at a given time
Alpha diversity
- the diversity within a particular area or ecosystem; usually expressed by the number of species (i.e., species richness) in that ecosystem
- Beta diversity
- a comparison of of diversity between ecosystems, usually measured as the amount of species change between the ecosystems
- Gamma diversity
- a measure of the overall diversity within a large region. Geographic-scale species diversity according to Hunter (2002: 448)


7.6: Direct and Step-Down Methods
Learning Outcomes
- Discuss how to allocate service costs as operations costs using the direct and step-down methods
In process costing, all of the processing departments are classified as operating departments. Other departments, called service departments are needed for the business to operate, but do not directly engage in operating processes. Service departments include accounting, human resources and purchasing. These departments all provide services to each of the operating departments.
So with our Ultimate Planner business, the product itself is produced in the production/manufacturing department, but in order for that department to run, payroll needs to be prepared, employees need to be hired and product needs to be purchased. There are two main ways to allocate these service costs to the operating departments to make sure we are including all of the costs when we price our products.
The first method is the direct method. This is the simplest and most commonly used method of allocation.
In this method, we will be ignoring the fact that one service department may offer services to another service department. For example, the HR department will offer services to the accounting department by hiring staff and providing training. Instead, we will allocate ALL of the services of each of these departments to the operating departments.
We can allocate using a couple of different methods of allocation. Some costs may be allocated based on employee hours. Administration costs are a good example here. So the hours incurred by administrative departments such as payroll, purchasing, accounting and HR, would be allocated, based on the number of hours worked in each of the operating departments and allocated accordingly. Here, if process 1 of manufacturing our Ultimate Planner takes 5,000 hours per period, while packaging (process 3) only takes 1,000 hours per period, then allocation based on employee hours would be the most effective way to allocate service costs.
Custodial services on the other hand, may be better allocated based on the square footage of each of the operating departments. If the press area (process 1) of the Ultimate Planner business occupies 10,000 square feet, while the packaging area only occupies 2,000 square feet, it probably takes more custodial effort in the press area! So allocation on space would work best.
The second method is called the step-down method. This method is more complicated than the direct method, as it also takes into account the services that one service department offers another.
Note in this method, the human resources costs are allocated between custodial and all of the operational processes, while in the direct method, human resources and custodial are directly allocated to the operational processes.
So if the custodial department cleans the HR department, some costs from the custodial department should be allocated to the HR department, right? Also, the HR department provides services to the custodial department, by hiring and training the employees, so some of the HR costs should be allocated to the custodial department.
There are many reasons companies may use each of these allocation methods. HERE is another explanation of this concept if you would like further clarification.
Practice Questions


16.2: Quantum Mechanics is Bizarre
The development of quantum mechanics is a great intellectual achievement, but at the same time, it is bizarre. The reason is that quantum mechanics is quite different from classical physics. The development of quantum mechanics is likened to watching two players having a game of chess, but the watchers have not a clue as to what the rules of the game are. By observations, and conjectures, finally the rules of the game are outlined. Often, equations are conjectured like conjurors pulling tricks out of a hat to match experimental observations. It is the interpretations of these equations that can be quite bizarre. Quantum mechanics equations were postulated to explain experimental observations, but the deeper meanings of the equations often confused even the most gifted. Even though Einstein received the Nobel prize for his work on the photo-electric effect that confirmed that light energy is quantized, he himself was not totally at ease with the development of quantum mechanics as charted by the younger physicists. He was never comfortable with the probabilistic interpretation of quantum mechanics by Born and the Heisenberg uncertainty principle: “God doesn’t play dice,” was his statement assailing the probabilistic interpretation. He proposed “hidden variables” to explain the random nature of many experimental observations. He was thought of as the “old fool” by the younger physicists during his time. Schrödinger came up with the bizarre “Schrödinger cat paradox” that showed the struggle that physicists had with quantum mechanics’s interpretation. But with today’s understanding of quantum mechanics, the paradox is a thing of yesteryear. The latest twist to the interpretation in quantum mechanics is the parallel universe view that explains the multitude of outcomes of the prediction of quantum mechanics. All outcomes are possible, but with each outcome occurring in different universes that exist in parallel with respect to each other.\(^1\)
The development of quantum mechanics was initially motivated by two observations which demonstrated the inadeqacy of classical physics. These are the “ultraviolet catastrophe” and the photoelectric effect.
- This section was adapted in part from Prof. Weng Cho CHEW’s Quantum Mechanics Made Simple Lecture Notes available here .


10.7: Academic Search Tools
Scholarly Content Online
There are some specialized search tools on the internet that target academic audiences. Perhaps the most popular one is Google Scholar , which looks for academic, scholarly content. Another tool is Microsoft Academic Search . There are also a few subject-specific search tools that you might want to become familiar with, such as PubMed (for the biomedical field) or ERIC (for the education field).
Paywalls
Typically, you would find scholarly content using a library database, but the tools described above can also help connect you to scholarly content that your college subscribes to. The problem—especially for community college students—is that these tools also find a lot of resources that your college might not subscribe to.
For this reason, a lot of the content these search tools will find is behind something called a paywall. A paywall is a barrier you may encounter online, when you have to pay before you can access a resource. Scholarly journal articles you find online come with a price, which can range anywhere from $25 per article up to well over $100 per article!
In our scenario, you have to find 10 resources. That means, for this class assignment, it might cost you anywhere from $250 to over $1000 to complete. At this point, you might be thinking that these academic search tools are not worth using, and we wouldn’t blame you. But these tools don’t always lead you to a paywall, and a paywall is not always a dead end. These tools can help you identify resources that might also be available for free in library databases your college subscribes to, and these tools will often connect you to open access resources.


3.5: Multivariate Brownian motion
The Brownian motion model we described above was for a single character. However, we often want to consider more than one character at once. This requires the use of multivariate models. The situation is more complex than the univariate case – but not much! In this section I will derive the expectation for a set of (potentially correlated) traits evolving together under a multivariate Brownian motion model.
Character values across species can covary because of phylogenetic relationships, because different characters tend to evolve together, or both. Fortunately, we can generalize the model described above to deal with both of these types of covariation. To do this, we must combine two variance-covariance matrices. The first one, C , we have already seen; it describes the variances and covariances across species for single traits due to shared evolutionary history along the branches of a phylogentic tree. The second variance-covariance matrix, which we can call R , describes the variances and covariances across traits due to their tendencies to evolve together. For example, if a species of lizard gets larger due to the action of natural selection, then many of its other traits, like head and limb size, will get larger too due to allometry. The diagonal entries of the matrix R will provide our estimates of σ i 2 , the net rate of evolution, for each trait, while off-diagonal elements, σ i j , represent evolutionary covariances between pairs of traits. We will denote number of species as n and the number of traits as m , so that C is n × n and R is m × m .
Our multivariate model of evolution has parameters that can be described by an m × 1 vector, a , containing the starting values for each trait – $\bar{z}_1(0)$, $\bar{z}_2(0)$, and so on, up to $\bar{z}_m(0)$, and an m × m matrix, R , described above. This model has m parameters for a and m ⋅ ( m + 1)/2 parameters for R , for a total of m ⋅ ( m + 3)/2 parameters.
Under our multivariate Brownian motion model, the joint distribution of all traits across all species still follows a multivariate normal distribution. We find the variance-covariance matrix that describes all characters across all species by combining the two matrices R and C into a single large matrix using the Kroeneker product :
\[\textbf{V} = \textbf{R} ⊗ \textbf{C} \label{3.23}\]
This matrix V is n ⋅ m × n ⋅ m , and describes the variances and covariances of all traits across all species.
We can return to our example of evolution along a single branch (Figure 3.4a). Imagine that we have two characters that are evolving under a multivariate Brownian motion model. We state the parameters of the model as:
\[ \begin{array}{lcr} \mathbf{a} = \begin{bmatrix} \bar{z}_1(0) \\ \bar{z}_2(0) \\ \end{bmatrix} \\ \mathbf{R} = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{12} & \sigma_2^2 \\ \end{bmatrix} \\ \end{array} \label{3.24}\]
For a single branch, C = [ t 1 ], so:
\[ \mathbf{V} = \mathbf{R} \otimes \mathbf{C} = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{12} & \sigma_2^2 \\ \end{bmatrix} \otimes [t_1] = \begin{bmatrix} \sigma_1^2 t_1 & \sigma_{12} t_1 \\ \sigma_{12} t_1 & \sigma_2^2 t_1 \\ \end{bmatrix} \label{3.25}\]
The two traits follow a multivariate normal distribution with mean a and variance-covariance matrix V .
For the simple tree in figure 3.4b,
\[ \begin{align} \mathbf{V} &= \mathbf{R} \otimes \mathbf{C} \\[5pt] &= \begin{bmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{12} & \sigma_2^2 \\ \end{bmatrix} \otimes \begin{bmatrix} t_1+t_2 & t_1 \\ t_1 & t_1+t_3 \\ \end{bmatrix} \\[5pt] &= \begin{bmatrix} \sigma_1^2 (t_1+t_2) & \sigma_{12} (t_1+t_2) & \sigma_1^2 t_1 & \sigma_{12} t_1 \\ \sigma_{12} (t_1+t_2) & \sigma_2^2 (t_1+t_2) & \sigma_{12} t_1 & \sigma_2^2 t_1 \\ \sigma_1^2 t_1 & \sigma_{12} t_1 & \sigma_1^2 (t_1+t_3) & \sigma_{12} (t_1+t_3) \\ \sigma_{12} t_1 & \sigma_2^2 t_1 & \sigma_{12} (t_1+t_3) & \sigma_2^2 (t_1+t_3) \\ \end{bmatrix} \\ \end{align} \label{3.26}\]
Thus, the four trait values (two traits for two species) are drawn from a multivariate normal distribution with mean
\[a=[\bar{z}_1(0), \bar{z}_1(0), \bar{z}_2(0), \bar{z}_2(0)]\]
and the variance-covariance matrix shown above.
Both univariate and multivariate Brownian motion models result in traits that follow multivariate normal distributions. This is statistically convenient, and in part explains the popularity of Brownian models in comparative biology.