21.14: Verbs
In a sentence, a verb expresses an action, an occurrence, or a state of being.
Subject-Verb Agreement
In many sentences, making the verb agree with the subject is straightforward: I run every day. My sister runs every other day. Sometimes our brother joins us, and all of us run together . However, subject-verb agreement gets tricky in the following circumstances. (See Editing Focus: Subject-Verb Agreement for more on subject-verb agreement.)
Agreement with Compound Subjects
Two or more subjects joined by and take a plural verb in most sentences:
Yoga and meditation are effective activities for relieving stress.
However, when the parts of the subject form a single idea or unit, the verb is singular:
Macaroni and cheese is my favorite meal.
When compound subjects are joined by or or nor , the verb agrees with the word closest to it:
Either your aunts or your mother remembers where your great-grandmother’s grave is located.
Neither the image nor the words convey the message of the advertisement clearly.
Agreement When Words Come between Subject and Verb
The verb must agree with the subject even when words and phrases come between them:
The cost of the flights is prohibitive.
A box of invitations with stamps and return addresses was on the desk.
Agreement When the Verb Comes Before the Subject
The verb must agree with the subject, even when it comes before the subject:
Are James and Tamara at the front of the line?
There were three people ahead of us in line.
Under the table are a newspaper and a magazine .
Agreement with Everyone and Other Indefinite Pronouns
An indefinite pronoun is general; it does not refer to a specific person, place, or thing. Most indefinite pronouns take a singular verb, but not all. Those that take a singular verb include anybody, anyone, anything, each, everybody, everyone, everything, nobody, no one, nothing, one, somebody, someone, and something .
Everyone in the class has prepared a research proposal.
Nobody among the accused suspects admits to the crime.
The following indefinite pronouns take a plural verb: both, few many, others , and several .
Several of the students in the class have proposed researching hurricanes.
Both of the suspects deny committing the crime.
Several indefinite pronouns take a singular or plural verb depending on whether the word they refer to is singular or plural. These include all, any, enough, more, most, neither, none , and some .
Most of the class has proposed researching a topic related to climate change. ( Most refers to class .)
Most of the students in the class have proposed researching a topic related to climate change. ( Most refers to students .)
Neither the students nor the teachers have proposed a field trip. ( Neither/nor refers to students and teachers .)
Agreement with Collective Nouns
Collective nouns such as audience, band, class, crowd, family, group , or team can take a singular or a plural verb depending on the context. When the group acts as a single unit, which is the most common construction, use a singular verb:
The band rehearses every day.
When the group acts individually, use a plural verb, or to avoid confusion, add the word members and use a plural verb.
The jury do not agree on a verdict.
The jury members do not agree on a verdict.
Agreement with Words Such as News and Statistics
Some nouns that end in -s , such as athletics, economics, measles, news, physics, politics , and statistics seem plural but are usually regarded as singular in meaning. In most situations, these words take a singular verb:
Day after day, the news was bad.
Statistics fulfills a math requirement for many college majors.
When a word like economics, politics , or statistics refers to a specific situation, use a plural verb:
The economics of the situation are hard to comprehend.
Agreement with Titles and Words Used as Words
Whether singular or plural in form, titles and words used as words take singular verbs:
Directed by Spike Lee, Da 5 Bloods centers around four veterans returning to Vietnam to find the remains of their squad leader and the fortune they hid together.
Children is the plural form of child .
Verb Tense
Tense expresses the time of a verb’s action—the past, present, or future. Tense comes naturally in speech, but it can be tricky to control in writing. The following guidelines will help you choose the appropriate tense for your writing and use it consistently. (See Editing Focus: Verb Tense Consistency for a related discussion of consistent verb tense.)
Verb Tense in Narrative Writing
Personal experience stories, such as literacy narratives, memoirs, personal essays, or profiles, can be written in either the past or the present tense. Although the most natural way to tell a story about a past experience is to write in the past tense, the present tense can draw readers into the story and give the illusion that the experience is happening as they are reading it. In the following examples, the writer describes driving with her Native American grandfather to a tribal conference. Notice the difference between the past and present tense.
Narrative Writing Using Past Tense I sat silently next to Grandfather and watched him slowly tear the thin white paper from the tip of the cigarette. He gathered the tobacco in one hand and drove the van with the other. I memorized his every move as he went through the motions of the prayer, which ended when he blew the tobacco out the window and into the wind.
Narrative Writing Using Present Tense I sit silently next to Grandfather and watch him slowly tear the thin white paper from the tip of the cigarette. He gathers the tobacco in one hand and drives the van with the other. I memorize his every move as he goes through the motions of the prayer, which ends when he blows the tobacco out the window and into the wind.
Verb Tense in Academic Writing
Academic disciplines differ in their tense preferences for signal phrases used in formal essays and reports to introduce and discuss evidence. A signal phrase is a verb that tells readers the words or ideas that follow come from another source. Signal phrases include words such as argues, asserts, claims, comments, denies, discusses, implies, proposes, says, shows, states , and suggests . (For more discussion and a more extensive list of signal phrases, see Editing Focus: Integrating Sources and Quotations .)
| acknowledges | declares | observes |
| admits | endorses | poses |
| agrees | explains | positis |
| argues | finds | proposes |
| asserts | grants | reports |
| believes | illustrates | reveals |
| claims | implies | says |
| comments | insists | shows |
| concedes | maintains | states |
| concludes | notes | suggests |
| thinks | writes |
If you are writing for a course in English, a foreign language, or a related discipline and using MLA documentation style, you generally will use the present tense or the present perfect tense in signal phrases.
Present Tense The film critic Manohla Dargis claims that . . .
Present Perfect Tense The film critic Manohla Dargis has claimed that . . .
When you are analyzing a work of literature, common practice is to use the literary present tense in discussing both the work of the author and the action that occurs in the work:
Being cool is key to the lives of the speakers in “We Real Cool,” a poem by Gwendolyn Brooks. Brooks uses short lines and stanzas in which speakers list what it means to be cool: dropping out of school, staying out late, playing pool, drinking, carousing, and so on. Being cool unites the speakers, and they celebrate their lifestyle, even as they acknowledge in the final line of the poem that their coolness may cause them to die young.
(For more on literary present tense, see Editing Focus: Literary Works Live in the Present .)
If you are writing for a course in history, art history, philosophy, religion, or a related discipline in the humanities, you generally will use the present tense or the present perfect tense in signal phrases.
Present Tense The historian Eduardo Galeano argues that . . .
Present Perfect Tense The historian Eduardo Galeano has argued that . . .
On the other hand, if you are writing for a course in the social sciences, such as psychology, political science, or economics; a course in the natural sciences, such as biology, chemistry, or physics; or a technical field such as engineering, you will generally use past tense or present perfect tense for most signal phrases.

Verb Tense Consistency
Whichever tense you choose, be consistent throughout a piece of writing. You may need to shift tenses to indicate actual changes in time, but the governing tense should remain constant. (See Editing Focus: Verb Tense Consistency for a related discussion of consistent verb tense.)
 It is 2003, and I was headed to active duty in Iraq with the National Guard. I hug my spouse, my mom, my dad, my brothers, and my grandma. Then I turn and climbed on the bus that takes me to a future that, in all honesty, was terrifying to me.
Consistent Blinking back tears, I clutched my two-year-old son to my chest, kissed his forehead, and gathered my things. It was 2003, and I was headed to active duty in Iraq with the National Guard. I hugged my spouse, my mom, my dad, my brothers, and my grandma. Then I turned and climbed on the bus that would take me to a future that, in all honesty, was terrifying to me.
Irregular Verbs
Most verbs are regular and form the past tense and past participle forms by adding -d or -ed .
- I bake/I baked/I have baked
- She discovers/she discovered/she has discovered
- They shovel/they shoveled/they have shoveled
Some verbs, however, are irregular and form the past tense and participle in another way. Below are a few of the approximately 200 irregular verbs in English. For a comprehensive list of irregular verbs, see this list ( https://openstax.org/r/this_list ).
- begin/began/begun
- bring/brought/brought
- buy/bought/bought
- do/did/done
- drive/drove/driven
- fall/fell/fallen
- go/went/gone
- have/had/had
- is/was/been
- lead/led/led
- hide/hid/hidden
- ring/rang/rung
- run/ran/run
- see/saw/seen
- sing/sang/sung
- sit/sat/sat
- shake/shook/shaken
- speak/spoke/spoken
- take/took/taken
- wear/wore/worn
- write/wrote/written
Verb Mood
Verbs have three moods: indicative, imperative, and subjunctive. Mood can be said to indicate a speaker’s attitude or intention.
Indicative Mood
Use the indicative mood to state a fact or an opinion or to ask a question:
Thousands of women currently serve in the military.
I think college tuition is expensive.
The weather was awful for much of the winter but will improve soon.

Imperative Mood
Use the imperative mood to give instructions and commands. The subject, you , is often implied but not stated:
(You) Use the online form to request time off.
(You) Submit your request for time off by Friday.
You must submit your request on time.
Subjunctive Mood
Use the subjunctive mood to express wishes, suggestions, or requirements or to state hypothetical or unlikely conditions:
The rules state that every member be present for the vote.
I wish you were here to see the exhibition.
The governing board could be more effective if all members were active.
Students who failed the class would have passed had they completed all assignments.


32.9: Pollination and Fertilization - Development of Fruit and Fruit Types
- Describe the development of a fruit in a flowering plant
After fertilization, the ovary of the flower usually develops into the fruit. Fruits are generally associated with having a sweet taste; however, not all fruits are sweet. The term “fruit” is used for a ripened ovary. In most cases, flowers in which fertilization has taken place will develop into fruits, while unfertilized flowers will not. The fruit encloses the seeds and the developing embryo, thereby providing it with protection. Fruits are diverse in their origin and texture. The sweet tissue of the blackberry, the red flesh of the tomato, the shell of the peanut, and the hull of corn (the tough, thin part that gets stuck in your teeth when you eat popcorn) are all fruits. As the fruit matures, the seeds also mature.
Fruits may be classified as simple, aggregate, multiple, or accessory, depending on their origin. If the fruit develops from a single carpel or fused carpels of a single ovary, it is known as a simple fruit, as seen in nuts and beans. An aggregate fruit is one that develops from numerous carpels that are all in the same flower; the mature carpels fuse together to form the entire fruit, as seen in the raspberry. A multiple fruit develops from an inflorescence or a cluster of flowers. An example is the pineapple where the flowers fuse together to form the fruit. Accessory fruits (sometimes called false fruits) are not derived from the ovary, but from another part of the flower, such as the receptacle (strawberry) or the hypanthium (apples and pears).
Fruits generally have three parts: the exocarp (the outermost skin or covering), the mesocarp (middle part of the fruit), and the endocarp (the inner part of the fruit). Together, all three are known as the pericarp. The mesocarp is usually the fleshy, edible part of the fruit; however, in some fruits, such as the almond, the seed is the edible part (the pit in this case is the endocarp). In many fruits, two, or all three of the layers are fused, and are indistinguishable at maturity. Fruits can be dry or fleshy. Furthermore, fruits can be divided into dehiscent or indehiscent types. Dehiscent fruits, such as peas, readily release their seeds, while indehiscent fruits, like peaches, rely on decay to release their seeds.
Key Points
- Fruits can be classified as simple, aggregate, multiple, or accessory.
- Simple fruits develop from a single carpel or fused carpels of a single ovary, while aggregate fruits develop from more than one carpel found on the same flower.
- Multiple fruits develop from a cluster of flowers, while accessory fruits do not develop from an ovary, but from other parts of a plant.
- The main parts of a fruit include the exocarp (skin), the mesocarp (middle part), and the endocarp (inner part); these three parts make up the pericarp.
- Dehiscent fruits promptly release their seeds, while indehiscent fruits rely on decay to release their seeds.
Key Terms
- exocarp : the outermost covering of the pericarp of fruits; the skin
- simple fruit : fruit that develops from a single carpel or fused carpels of a single ovary
- endocarp : the inner part of the fruit
- mesocarp : middle part of the fruit
- accessory fruit : a fruit not derived from the ovary but from another part of the flower


9.6: Summary of Learning Outcomes
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9.1 Work Groups: Basic Considerations
1. How do you manage group and intergroup processes effectively?
A group is a collection of individuals who share a common set of norms, who generally have differentiated roles among themselves, and who interact with one another in the joint pursuit of common goals. Groups may be divided into permanent and temporary groups and formal and informal groups. Formal groups include command and task groups, whereas informal groups include friendship and interest groups.
9.2 Work Group Structure
2. How do group norms, roles, and status systems affect employee behavior and performance?
People join groups because they offer security, meet social needs, enhance self-esteem, fulfill economic interests, introduce them to people with mutual interests, and, sometimes, because they are in close physical proximity. Groups typically develop through several distinct stages, including forming, storming, norming, and performing. A role may be defined as an expected behavior pattern assigned or attributed to a particular position in the organization. Roles may be oriented toward the task, social relations, or the self.
9.3 Managing Effective Work Groups
3. How do managers develop group cohesiveness, which facilitates organizational goal attainment?
Social loafing is a tendency for individual members of a group to reduce their task effort in the belief that other members will cover for them. A norm is a standard that is shared by group members and that regulates member behavior within an organization. Norms facilitate group survival, simplify expected behaviors, help members avoid embarrassing situations, and help identify group members. Asch’s experiment in group pressure and individual judgment demonstrated that individuals will discount their own perceptions of a situation and follow the will of a group. Status systems serve to differentiate individuals on the basis of some criterion or set of criteria. Status incongruence occurs when one individual holds a position in the status hierarchy that is inconsistent with the conventional criteria for that position. Group cohesiveness is the extent to which individual members of a group are motivated to remain in the group. Work group effectiveness is defined by three criteria: group productivity, personal need satisfaction of the members, and the group’s capacity for future cooperation.
9.4 Intergroup Behavior and Performance
4. What are barriers to intergroup cooperation, and how do you take action to minimize such impediments and understand how to get the most out of the collective actions of groups in organizations in order to enhance industrial competitiveness?
Intergroup performance is influenced by three interaction requirements. These include the requirements for interdependence, information, and integration. A linking role is a position or unit within the organization that is charged with overseeing and coordinating the activities of two or more groups. A task force consists of members from several departments or units who are brought together on a temporary basis to solve a specific and immediate problem. Decoupling refers to the practice of physically or administratively separating groups that are not able to work together effectively.


Fuels and Enthalpy
Skills to Develop
- Perform enthalpy calculations and describe the process and results
What is Fuel?
One of the most important applications of chemistry is the study of fuels . Fuel basically means a chemical that can provide energy. We use fuel to do nearly everything. Food provides fuel to our bodies. Gasoline provides fuel for our cars. Many different chemicals, from coal and gas to uranium, provide fuel for the power plants that make electric power. When we use a fuel, it becomes a reactant in some type of reaction. Most often, fuels are burned in air to provide heat, and the heat is converted to work. For this reason, we often want to know how much heat we can get out of a chemical reaction.
Enthalpy
When our systems includes chemicals that participate in a reaction, the system may gain or lose heat because of the reaction, and the system may also do work, or work may be done on the system. How would the system do work? Suppose you burn some propane (C 3 H 8 ). Write a balanced equation for this reaction, and convince yourself that there are more moles of gas present in the products than the reactants. Also, you know that burning propane raises the temperature. If you burn some propane, the system will increase in volume, because there is more gas, and it is hotter. (If you burn the propane in a very strong container, then the volume will stay the same and the pressure will increase.) When the volume of the system increases in an open container, it will push on the surroundings, like the atmosphere, and do pV work. We might be able to use this work (in an internal combustion engine like in a car, for instance) but only if we control the volume. If we do the reaction open to the atmosphere, at constant pressure (atmospheric pressure), then we won't be able to use the work done by the reaction.
In chemistry, because reactions are often done at atmospheric pressure, we often want to know how much heat is available from a reaction that occurs at constant pressure. To make this convenient, we can define a new quantity, related to internal energy, which is called enthalpy , abbreviated H:
\[H=E+pV\]
Here's why this definition is useful. The work done by a reaction at constant pressure is
\[w=-p \Delta V\]
where p is the pressure, and ΔV is the change in volume of the reaction system, and the sign of w is negative because the system is doing work. The change in enthalpy for a reaction is
\[\Delta H=\Delta (E+pV) = \Delta E + p\Delta V (at\; constant\; p)\]
Since ΔE = q + w,
\[\Delta H = (q + w) + p\Delta V = (q + w) − w = q\]
Thus, the enthalpy change in a reaction tells us exactly how much heat the reaction can provide if it runs at constant pressure. We don't need to worry about calculating the work done by the reaction pushing back the atmosphere because it is already removed from the definition of enthalpy. Enthalpy is a state function because E, p and V are all state functions. Enthalpy doesn't have a molecular meaning like internal energy, but usually pV is small, so enthalpy is similar to internal energy.
When ΔH is positive, then heat has entered the system, and the process is called endothermic . Endothermic reactions feel cold to the touch because they pull heat from your hand into the reaction system. Evaporation is endothermic, which is why sweat helps us cool off. When ΔH is negative, heat leaves the system, and the process is called exothermic . Exothermic processes feel hot. This is why flames will burn you.


23.3: Objects and Classes
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Overview
Object-oriented programming (OOP) is a programming paradigm based on the concept of “objects”, which may contain data, in the form of fields, often known as attributes; and code, in the form of procedures, often known as methods. A feature of objects is that an object’s procedures can access and often modify the data fields of the object with which they are associated (objects have a notion of “this” or “self”). There is significant diversity of OOP languages, but the most popular ones are class-based, meaning that objects are instances of classes, which typically also determine their type. [1]
Discussion
Thus far, we have focused on procedural programming. Based on structured programming, procedures (routines, subroutines, or functions) contain a series of computational steps to be carried out. Any given procedure might be called at any point during a program’s execution, including by other procedures or itself. The focus of procedural programming is to break down a programming task into a collection of variables, data structures, and subroutines. [2] Small programs and scripts tend to be easier to develop using a simple procedural approach.
Object-oriented programming instead breaks down a programming task into objects that expose behavior (methods) and data (members or attributes) using interfaces. The most important distinction is that while procedural programming uses procedures to operate on separate data structures, object-oriented programming bundles the two together, so an “object”, which is an instance of a class, operates on its “own” data structure. [3] Larger programs benefit from better code and data isolation and reuse provided by an object-oriented approach.
Objects and classes are often designed to represent real-world objects. Consider a door as an example of a real-world object. Most doors have limited functionality. They may be opened and closed, and locked and unlocked. In procedural programming, we might design functions to open, close, lock, and unlock a door, such as:
Procedural Programming - Functions OpenDoor(door) CloseDoor(door) LockDoor(door) UnlockDoor(door)
Object-oriented programming combines code and data, so that, rather than having separate functions act on doors, we design doors that have methods that can act on themselves. Methods represent something the object can do, and are typically defined using verbs. Object-oriented door pseudocode might look like:
Object-Oriented Programming - Methods door.Open() door.Close() door.Lock() door.Unlock()
Objects may also have attributes, something the object is or has, and are typically defined using nouns or adjectives. Door attributes might include:
Object-Oriented Programming - Attributes door.Height door.Width door.Color door.Closed door.Locked
When we write code to define a generic door, we would create a door class. The door class would contain all of the methods a door can perform and all of the attributes a door might have. We would then create instances of the class (objects) to represent specific doors, such as a front door, back door, or room door on a house, or a left door and right door on a car.
Key Terms
- attribute
- A specification that defines a property of an object. [4]
- class
- An extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). [5]
- instance
- :A concrete occurrence of an object. [6]
- method
- A specification that defines a procedure or behavior of an object. [7]
- object
- A particular instance of a class where the object can be a combination of variables, functions, and data structures. [8]
- this, self, or Me
- Keywords used in some computer programming languages to refer to the object, class, or other entity that the currently running code is part of. [9]
References
- Wikibooks: Object-Oriented Programming
- Wikipedia: Object-oriented programming
- Wikiversity: Computer Programming
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9.2: PROPAGANDA, PERSUASION, POLITICS, AND POWER
The word propaganda has gotten a bad reputation. The Latin origin of the word propaganda is propagare , meaning “to spread or disseminate.” As it is used today, the word mainly refers to promoting information often biased or misleading, sometimes hidden in order to influence views, beliefs, or behavior. Originally, the word was not associated with politics, as it is generally today, nor did it imply lies or bad faith; propaganda was simply a means of publicly communicating ideas, instruction, and the like. In such a case, we now are more likely to use the word persuasion , which has a more neutral connotation and suggests convincing rather than coercing. For example, advertising tries to persuade or entice the consumer to make a choice or purchase. To many, however, there is a fine line between propaganda and persuasion. They are separated more by purpose and intention good, bad, or neutral than how they are carried out. Garth Jowett and Victoria O’Donnell describe the fine but crucial differences between the two words:
Propaganda is the deliberate, systematic attempt to shape perceptions, manipulate cognitions, and direct behavior to achieve a response that furthers the desired intent of the propagandist. Persuasion is interactive and attempts to satisfy the needs of both persuader and persuadee. 1
King Darius I (r. 522-486 BCE) had both persuasion and propaganda in mind when he built the Apadana at Persepolis, today Iran. (Figure 9.1) Darius I was the first king of the Achaemenid Empire (c. 550-330 BCE) to have royal structures erected on the site, but construction would continue under succeeding Persian kings for approximately one hundred years. The Apadana was begun in 515 BCE and completed thirty years later by Darius I’s son, Xerxes I. Apadana means hypostyle hall, a stone building with a roof supported by columns. It originally had seventy-two columns thirteen still stand each sixty-two feet tall in a grand hall that was 200 x 200 feet, or 4,000 square feet. Needless to say, a building of such monumental proportions was an over- whelming sight for those who approached it. Brightly painted in many colors and raised on a plat- form with the Kuhe Rahmat or Mountain of Mercy rising behind it, the towering structure could be seen for miles from the sparsely vegetated plain to the east.
For King Darius I, the Apadana and Persepolis the city of Persians as a whole was a statement of propaganda. The hypostyle hall and the city were awe inspiring and intimidating; they in no uncertain terms let the viewer know the King had formidable power and tremendous resources. Upon entering the King’s hall, the viewer was surrounded by his strength in the form of columns the height of a modern six-story building, holding up a ceiling of incalculable weight. How small and powerless the visitor was in the midst of such force. But Darius I, whose empire stretched from Egypt in the west to the Indus Valley, today Pakistan, to the east, knew that he could not effectively rule through domination and fear. So, he had elements of persuasion included at Persepolis, as well.
In addition to the building’s resplendent majesty, it was adorned with sumptuous and masterful frescoes, glazed brickwork, and relief sculpture. Two staircases led up to the platform on which the Apadana was built, on the north and east sides, but only the north staircase was completed during Darius’s lifetime. That staircase and the platform walls to either side are covered with reliefs: figures in even, orderly rows as they approach the Persian King’s hall. (Figure 9.2) They are representatives of the twenty-three countries within the Achaemenid Empire, coming to pay homage to the King during festivals for the New Year, carrying gifts. Accompanying them are Persian dignitaries, followed by soldiers with their weaponry, horses, and chariots.
The native Persian and foreign-born delegates are shown together in these friezes , or rows, of relief sculpture. (Figure 9.3) They have facial features that correspond with their ethnicity, and hair, clothing, and accessories that indicate what region they are from. Even the gifts are objects and animals from their own countries. Rather than showing the foreigners as subservient to the Persians, they mingle with one another and at times appear to be in conversation.
The staircase reliefs, as opposed to the magnificent building as a whole, can be seen as a form of persuasion. It was in the king’s better interests to win over his subjects, to gain their trust, allegiance, and cooperation, than to bend themto his will through force and subjugation. Having already demonstrated from a distance that he had the power to de-feat his enemies, Darius I could, as the delegates ascended the stairs to his great hall, literally show them the respect with which he treated his loyal subjects.
In more recent history, Jacques-Louis David (1748-1825, France) painted five versions of Napoleon Crossing the Alps between 1801 and 1805. (Figure 9.4) David was born and raised in Paris and entered the École des Beaux-Arts in 1866at the age of eighteen. After eight years of mixed success in his studies there, David won the Prix de Rome in 1774, a prestigious government scholarship that also included travel to Italy. He lived in Rome from 1775 to 1780, studying the art of great masters from the classical past, through the Renaissance, and to the present. But, he was most impressed with the philosophical and artistic ideals of some of his contemporaries, the Neoclassical thinkers and painters he met in Italy.
When he returned to France, he soon began exhibiting work in this new style; with their somber, moral tones, stories of family loyalty and patriotic duty, fine detail, and sharp focus, works in the Neoclassical style (c. 1765-1830) were in stark contrast to the frivolous, sentimental subjects and delicate, pastel hues of the prevailing Rococo style (c. 1700-1770s). Over the course of the 1780s, as social disconnect and political upheaval were building toward the French Revolution of 1789, the self-sacrificing, stoic heroes from classical and contemporary history David painted increasingly reflected the public de- sire for liberté , egalité , fraternité , or liberty, equality, and fraternity (universal brotherhood).
In the aftermath of the revolution, during the mercurial times of the 1790s, David was first a powerful figure in the short-lived Republic and then a jailed outcast. When Napoleon Bonaparte, named First Consul in 1799, commissioned David to paint his portrait in 1800, however, David’s return to official favor was complete.
The commission came about this way: in the spring of 1800, Napoleon led troops south to support French troops already in Genoa, Italy, in an effort to take back land captured by the Austrians. He did so on June 9th at the Battle of Marengo. The victory led to France and Spain reestablishing diplomatic relations eleven years after the French Revolution and, as part of the formal exchange of gifts to mark the occasion, King Charles IV of Spain requested a portrait of Napoleon to hang in the Royal Palace of Madrid. Learning of this, Napoleon requested three more versions from David (and the painter independently created a fifth, which remained in his possession until his death.)
It was to be an equestrian portrait, Napoleon specified, that is, depicting him on horseback, crossing the Great St. Bernard Pass in the Alps, leading the Reserve Army south to Italy. David was to show Napoleon on a spirited, rearing horse as a calm and decisive leader, much like his heroes Hannibal and Charlemagne, who crossed the Alps before Napoleon and whose names are inscribed with his on rocks in the left foreground of the painting. In actuality, however, it did not happen that way at all: Napoleon crossed on the Alps on the back of a mule, in good weather, a few days after the soldiers went through the pass.
What Napoleon was asking David to paint was a piece of propaganda. And, the artist succeeded admirably. With the wind whipping his cloak around him, assuredly holding the reins of his wild-eyed horse in one hand while gesturing the way up and over the peaks with the other, and holding the viewer’s gaze with his look of complete composure, David has shown Napoleon as a leader who guides his people to victory and who will be remembered as a hero throughout the ages. That was the story Napoleon wanted told: the timeless ideal of the great man, not the transitory pettiness of his physical likeness. For, as Napoleon is attributed with claiming, “History is the version of past events that people have decided to agree upon.”
- Garth Jowett and Victoria O’Donnell, Propaganda and Persuasion, 6 th ed. (California: Sage Publications, 2014), 7


3.3F: Electron Microscopy
- Describe the technique employed for electron microscopy, distinguishing between different types
Electron microscopy uses a beam of electrons as an energy source. An electron beam has an exceptionally short wavelength and can hit most objects in its path, increasing the resolution of the final image captured. The electron beam is designed to travel in a vacuum to limit interference by air molecules. Magnets are used to focus the electrons on the object viewed.
There are two types of electron microscopes. The more traditional form is the transmission electron microscope (TEM). To use this instrument, ultra-thin slices of microorganisms or viruses are placed on a wire grid and then stained with gold or palladium before viewing, to create contrast. The densely coated parts of the specimen deflect the electron beam and both dark and light areas show up on the image. TEM can project images in a much higher resolution—up to the atomic level of thinner objects.
The second and most contemporary form is the scanning electron microscope (SEM). It allows the visualization of microorganisms in three dimensions as the electrons are reflected when passed over the specimen. The same gold or palladium staining is employed.
Electron microscopy has multiple applications. It is ideal to:
- explore the in vivo molecular mechanisms of disease;
- visualize the three dimensional architecture of tissues and cells;
- determine the conformation of flexible protein structures and complexes;
- observe individual viruses and macromolecular complexes in their natural biological context.
Sample preparation can be critical to generate a successful image because the choice of reagents and methods used to process a sample largely depends on the nature of the sample and the analysis required.
Key Points
- A beam of electrons, instead of light, is used with an electron microscope.
- Electron microscopes have a greater magnification because the wavelengths of electrons are much smaller than those of visible light (0.005nm as opposed to 500nm respectively–one hundred thousand times smaller).
- There are two types of electron microscopes, scanning and transmission.
- The best compound light microscopes can magnify 2000x, electron microscopes can magnify up to 100,000x.
Key Terms
- electron beam : a stream of electrons observed in vacuum tubes.


3: The Origin and Structure of Earth
After reading this chapter you should be able to:
- know the age of the universe, the solar system, and Earth
- explain the processes responsible for the early formation of Earth
- know the various layers of the Earth, including their composition
- know the differences between oceanic and continental crust
- explain the difference between lithosphere and asthenosphere
- explain the concept of isostasy
- explain how indirect methods can be used to investigate the interior of Earth
To understand the geological processes occurring in the ocean, it is important to recognize some of the phenomena that led to the formation and structure of the Earth. In this chapter we will start at the very beginning, with a discussion of the Big Bang and the origin of the universe and our solar system. From there, we will investigate the formation of the Earth, and the reasons behind its interior and exterior structure. Finally, we will end the chapter by attempting to answer the question of how we can know what is happening deep within the Earth’s interior.


3.2: Building Remixing Maps
Before using the OER Remixer, it is important to construct a Remixing Map. This can take many forms and does not need to be constructed online. In essence it is a table of contents for your remix and a good place to start would be the ToC of a textbook that you like.
Two words of warning before you get started
- The largest book that the LibreTexts online bookstore can provide a hard copy of is 800 pages.
- Some people have tried to build books which were piles of books. This can be done, but at some point the system chokes and no pdfs can be provided at all.
In both cases the solution may be to remix several books.
To access the Remixer for your project, from your Project in Conductor, then use the More Tools menu to open the Remixer.
Book Structure
It is best to have a flat structure
and not something with sub sub sub pages which can get lost if moved in re-remixing and other bad things, besides looking ugly on a table of contents.
Remixing maps are best assembled in a spreadsheet, for example
or
Lubbock Christian University created an excellent excel sheet to help out in this procedure for their general chemistry course and an image of this excel sheet is shown below. The gist of this map is to identify the content in the libraries (green) that will map into the organization of the new remix (yellow). This requires faculty/instructional designers to explicitly peruse the Bookshelves of Source texts and of other Course Remixes to identify desired content.
Once remixed, these pages can be then edited at the sub-page level (e.g., sub-sections, paragraph, pages etc). The Remixing Map reflects only the initial organization of a custom remix. Notice the customized organization; there is no limit other than imagination and the size/makeup of the LibreTexts libraries. While the Remixing Map below does not demonstrate it, it is possible to make placeholder pages in the Remixer if a gap exists in the libraries. New custom content can be added to these pages once the text is created or new open material brought into LibreTexts.
While it is easy to remix content that already is on LibreTexts, the LibreTexts team will bring in open material for you, although this may take some time, depending on the format of the materials and the amount of work that has to be done for such things as equations, images, accessibility issues, etc. Priority is given to materials for institutions that are members of the Libretexts Network. Requests can be made at https://harvest.libretexts.org .


4.2: Evaluations
Students are evaluated by their Site Work Supervisor, Practicum Instructor, and through self- evaluations. A Site supervisor appraises the student’s field work while the Practicum Instructor evaluates the student’s classroom work. Throughout the semester students assess their accomplishments and need for skill development via the Educational Plan and Weekly Report. The Practicum Instructor is responsible for the final grade in the practicum.
The Site Supervisor evaluates what the student has achieved at the practicum site, noting the objectives as stated in the Educational Plan. The Practicum Instructor evaluates written assignments submitted by a student in the classroom seminar and the degree of integration and understanding between classroom learning and direct practice.
The Evaluation of the student must be shared with the student and the student must have an opportunity to provide feedback and sign the final evaluation. A confirmation of hours the student has worked is requested in the supervisor's evaluation. A time log will be provided for students to track hours.
The purpose of supervision is to help the student not only learn to perform the tasks in an agency, but to become a competent Human Services Professional. This means a relationship should develop between the Site Supervisor and the student where the student can be open and share concerns about becoming an effective helper. The student must be able to accept constructive criticism and grow.
The Practicum Instructor considers the Site Supervisor's evaluation of a student and the student's self-assessment before arriving at a final grade for the student. If discrepancies exist about the student’s evaluation between the Practicum Instructor and the Site Supervisor, the Practicum Instructor discusses the issues with the Field Work Supervisor before submitting a final grade for the student.


1.5.3: Sex, Gender, and Sexuality
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When filling out official documents, you are often asked to provide your name, birthdate, and sex or gender. But have you ever been asked to provide your sex and your gender? It may not have occurred to you that sex and gender are not the same. However, sociologists and most other social scientists view sex and gender as conceptually distinct. Sex denotes biological characteristics and exists along a spectrum from male to female. Gender, on the other hand, denotes social and cultural characteristics that are assigned to different sexes. Sex and gender are not always synchronous, meaning they do not always line up in an easy-to-categorize way.
Sex
“Sex” refers to physiological differences found among male, female, and various intersex bodies. Sex includes both primary sex characteristics (those related to the reproductive system) and secondary sex characteristics (those that are not directly related to the reproductive system, such as breasts and facial hair). In humans, the biological sex of a child is determined at birth based on several factors, including chromosomes, gonads, hormones, internal reproductive anatomy, and genitalia. Biological sex has traditionally been conceptualized as binary in Western medicine, typically divided into male and female. However, anywhere from 1.0 to 1.7% of children are born intersex, having a variation in sex characteristics (including chromosomes, gonads, or genitals) that do not allow them to be distinctly identified as male or female. Due to the existence of multiple forms of intersex conditions (which are more prevalent than researchers once thought), many view sex as existing along a spectrum, rather than simply two mutually exclusive categories.
Gender
A person’s sex, as determined by his or her biology, does not always correspond with their gender; therefore, the terms “sex” and “gender” are not interchangeable. “Gender” is a term that refers to social or cultural distinctions associated with being male, female, or intersex.  Because our society operates in a binary system when it comes to gender (in other words, seeing gender as only having two options), many children who are born intersex are forcibly assigned as either a boy or a girl and even surgically “corrected” to fit a particular gender. Scholars generally regard gender as a social construct—meaning that it does not exist naturally, but is instead a concept that is created by cultural and societal norms.
Gender Identity: Cisgender versus Transgender
Gender identity is a person’s sense of self as a member of a particular gender. Individuals who identify with a role that corresponds to the sex assigned to them at birth (for example, they were born with male sex characteristics, were assigned as a boy, and identify today as a boy or man) are cisgender. Those who identify with a role that is different from their biological sex (for example, they were born with male sex characteristics, were assigned as a boy, but identify today as a girl, woman, or some other gender altogether) are often referred to as transgender. The term “transgender” encompasses a wide range of possible identities, including agender, genderfluid, genderqueer, two-spirit (for many indigenous people), androgynous, and many others. The prefix “trans-” comes from Latin, meaning “across from” or “on the other side of”. In contrast, the prefix “cis-” means “on this side of”.
Cultural Variations of Gender
Since the term “sex” refers to biological or physical distinctions, characteristics of sex will not vary significantly between different human societies. For example, persons of the female sex, in general, regardless of culture, will eventually menstruate and develop breasts that can lactate. Characteristics of gender, on the other hand, may vary greatly between different societies. For example, in American culture, it is considered feminine (or a trait of the female gender) to wear a dress or skirt. However, in many Middle Eastern, Asian, and African cultures, dresses or skirts (often referred to as sarongs, robes, or gowns) can be considered masculine. Similarly, the kilt worn by a Scottish male does not make him appear feminine in his culture.
  Sexuality may be experienced and expressed in a variety of ways, including thoughts, fantasies, desires, beliefs, attitudes, values, behaviors, practices, roles, and relationships. These may manifest themselves in biological, physical, emotional, social, or spiritual aspects. The biological and physical aspects of sexuality largely concern the human reproductive functions, including the human sexual-response cycle and the basic biological drive that exists in all species. Emotional aspects of sexuality include bonds between individuals that are expressed through profound feelings or physical manifestations of love, trust, and care. Social aspects deal with the effects of human society on one’s sexuality, while spirituality concerns an individual’s spiritual connection with others through sexuality.
LGBTQ+ Health
People who are lesbian, gay, bisexual, transgender, queer, and/or questioning (LGBTQ+) are members of every community. They are diverse, come from all walks of life, and include people of all races and ethnicities, all ages, all socioeconomic statuses, and from all parts of the United States and world. The perspectives and needs of LGBTQ+ people should be routinely considered in public health efforts to improve the overall health of every person and eliminate health disparities.
In addition to considering the needs of LGBTQ+ people in programs designed to improve the health of entire communities, there is also a need for culturally competent medical care and prevention services that are specific to this population. Social inequality is often associated with poorer health status, and sexual orientation has been associated with multiple health threats. Members of the LGBTQ+ community are at increased risk for a number of health threats when compared to their heterosexual peers. Differences in sexual behavior account for some of these disparities, but others are associated with social and structural inequities, such as the stigma and discrimination that LGBTQ+ populations still experience.
LGBTQ+ sexual health and well-being is affected by numerous social and cultural challenges across the life course, contributing to negative health outcomes and posing barriers to attain such protective health indicators as marriage and family formation, community support, and inclusion in faith communities. The incidence of hate crimes and discrimination promulgated through the denial of equal rights contribute to the perpetuation of homophobia as a structural norm.
As a result of cultural and societal discrimination, many LGBTQ+ people suffer an added burden of stress and experience health disparities, such as:
- Potential difficulties in getting or keeping health insurance, and possible employment instability.
- Limited access to high quality health care that is responsive to LGBTQ+ health issues.

- Challenges or difficulties with being open about one’s sexual orientation, which can increase stress, limit social support, and negatively affect overall health.
- The effects of homophobia, stigma and discrimination can be especially hard on adolescents and young adults. In addition to an increased risk of being bullied at school, they are also at risk of being rejected by their families and, as a result, are at increased risk of homelessness.
Whether you are gay or straight, you can help reduce homophobia, stigma, and discrimination in your community and decrease the associated negative health effects. Even small things can make a difference, such as accepting and supporting a family member, friend, or co-worker.


17: Alcohols and Phenols
When you have completed Chapter 17, you should be able to
- fulfill all of the detailed objectives listed under each individual section.
- design a multi‑step synthesis using any of the reactions introduced in this chapter, together with any number of the reactions discussed in Chemistry 350 .
- solve “road‑map” problems that require a knowledge of the chemistry of alcohols and phenols, in addition to the chemistry of the other classes of compounds discussed in Chemistry 350 .
- define, and use in context, the key terms introduced in this chapter.
In this chapter, we examine the chemistry of the alcohol family of compounds. Alcohols can undergo a wide variety of reactions, and because of this reactivity and because they can be prepared in a number of different ways, alcohols occupy an important position in organic chemistry.
The discussion begins with an outline of the nomenclature of alcohols and phenols. We review the physical properties of these compounds, and discuss methods used to obtain the lower members of the series on an industrial scale. A detailed discussion of the laboratory preparation of alcohols follows, with particular emphasis on those methods that involve either the reduction of a carbonyl compound or the use of a Grignard reagent.
Certain reactions of alcohols were discussed in previous chapters. In this chapter, we concentrate on the oxidation of alcohols to carbonyl compounds. We also introduce the concept of protecting a sensitive functional group during an organic synthesis. The discussion then turns to the uses of phenols, their preparation and their chemical reactivity.
Infrared, nuclear magnetic resonance and mass spectroscopy each can provide valuable information about alcohols and phenols, and we illustrate the application of these techniques to the identification of unknown alcohols and phenols with a number of examples.


11.7: The Beta-Bernoulli Process
An interesting thing to do in almost any parametric probability model is to
randomize
one or more of the parameters. Done in a clever way, this often leads to interesting new models and unexpected connections between models. In this section we will randomize the success parameter in the Bernoulli trials process. This leads to interesting and surprising connections with Pólya's urn process.
Basic Theory
Definitions
First, recall that the beta distribution with left parameter \(a \in (0, \infty)\) and right parameter \(b \in (0, \infty)\) is a continuous distribution on the interval \( (0, 1) \) with probability density function \(g\) given by \[ g(p) = \frac{1}{B(a, b)} p^{a-1} (1 - p)^{b-1}, \quad p \in (0, 1) \] where \(B\) is the beta function . So \(B(a, b)\) is simply the normalizing constant for the function \(p \mapsto p^{a-1} (1 - p)^{b-1}\) on the interval \((0, 1)\). Here is our main definition:
Suppose that \(P\) has the beta distribution with left parameter \( a \in (0, \infty) \) and right parameter \( b \in (0, \infty) \). Next suppose that \(\bs{X} = (X_1, X_2, \ldots)\) is a sequence of indicator random variables with the property that given \( P = p \in (0, 1) \), \(\bs{X}\) is a conditionally independent sequence with \[ \P(X_i = 1 \mid P = p) = p, \quad i \in \N_+ \] Then \(\bs{X}\) is the beta-Bernoulli process with parameters \(a\) and \(b\).
In short, given \(P = p\), the sequence \(\bs{X}\) is a Bernoulli trials sequence with success parameter \(p\). In the usual language of reliability, \(X_i\) is the outcome of trial \(i\), where 1 denotes success and 0 denotes failure. For a specific application, suppose that we select a random probability of heads according to the beta distribution with with parameters \( a \) and \( b \), and then toss a coin with this probability of heads repeatedly.
Outcome Variables
What's our first step? Well, of course we need to compute the finite dimensional distributions of \(\bs{X}\). Recall that for \( r \in \R \) and \( j \in \N \), \( r^{[j]} \) denotes the ascending power \( r (r + 1) \cdots [r + (j - 1)] \). By convention, a product over an empty index set is 1, so \( r^{[0]} = 1 \).
Suppose that \( n \in \N_+ \) and \((x_1, x_2, \ldots, x_n) \in \{0, 1\}^n\). Let \(k = x_1 + x_2 + \cdots + x_n\). Then \[ \P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n) = \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} \]
Proof
First, note that \(\P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n \mid P = p) = p^k (1 - p)^{n-k}\) by the conditional independence. Thus, conditioning on \(P\) gives \begin{align} \P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n) & = \E[\P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n \mid P)] \\ & = \int_0^1 p^k (1 - p)^{n-k} \frac{1}{B(a, b)} p^{a-1} (1 - p)^{b-1} \, dp \\ & = \frac{B[a + k, b + (n -k)]}{B(a, b)} = \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} \end{align} The last step uses a property of the beta function.
From this result, it follows that Pólya's urn process with parameters \(a, \, b, \, c \in \N_+\) is equivalent to the beta-Bernoulli process with parameters \( a / c \) and \( b / c \), quite an interesting result. Note that since the joint distribution above depends only on \( x_1 + x_2 + \cdots + x_n \), the sequence \( \bs{X} \) is exchangeable. Finally, it's interesting to note that the beta-Bernoulli process with parameters \( a \) and \( b \) could simply be defined as the sequence with the finite-dimensional distributions above, without reference to the beta distribution! It turns out that every exchangeable sequence of indicator random variables can be obtained by randomizing the success parameter in a sequence of Bernoulli trials. This is de Finetti's theorem , named for Bruno de Finetti, which is studied in the section on backwards martingales.
For each \(i \in \N_+\)
- \(\E(X_i) = \frac{a}{a + b}\)
- \(\var(X_i) = \frac{a}{a + b} \frac{b}{a + b}\)
Proof
Since the sequence is exchangeable, \(X_i\) has the same distribution as \(X_1\), so \(\P(X_i = 1) = \frac{a}{a + b}\). The mean and variance now follow from standard results for indicator variables.
Thus \(\bs{X}\) is a sequence of identically distributed variables, quite surprising at first but of course inevitable for any exchangeable sequence. Compare the joint distribution with the marginal distributions . Clearly the variables are dependent, so let's compute the covariance and correlation of a pair of outcome variables.
Suppose that \(i, \; j \in \N_+\) are distinct. Then
- \(\cov(X_i, X_j) = \frac{a \, b}{(a + b)^2 (a + b + 1)}\)
- \(\cor(X_i, X_j) = \frac{1}{a + b + 1}\)
Proof
Since the variables are exchangeable, \(\P(X_i = 1, X_j = 1) = \P(X_1 = 1, X_2 = 1) = \frac{a}{a + b} \frac{a + 1}{a + b + 1}\). The results now follow from standard formulas for covariance and correlation.
Thus, the variables are positively correlated. It turns out that in any infinite sequence of exchangeable variables, the the variables must be nonnegatively correlated. Here is another result that explores how the variables are related.
Suppose that \( n \in \N_+ \) and \( (x_1, x_2, \ldots, x_n) \in \{0, 1\}^n \). Let \( k = \sum_{i=1}^n x_i \). Then \[ \P(X_{n+1} = 1 \mid X_1 = x_1, X_2 = x_2, \ldots X_n = x_n) = \frac{a + k}{a + b + n} \]
Proof
Using the joint distribution , \begin{align*} \P(X_{n+1} = 1 \mid X_1 = x_1, X_2 = x_2, \ldots X_n = x_n) & = \frac{\P( X_1 = x_1, X_2 = x_2, \ldots X_n = x_n, X_{n+1} = 1)}{\P(X_1 = x_1, X_2 = x_2, \ldots X_n = x_n)} \\ & = \frac{a^{[k+1]} b^{[n-k]}}{(a + b)^{[n + 1]}} \frac{(a + b)^{[n]}}{a^{[k]} b^{[n-k]}} = \frac{a + k}{a + b + n} \end{align*}
The beta-Bernoulli model starts with the conditional distribution of \( \bs X \) given \( P \). Let's find the conditional distribution in the other direction.
Suppose that \( n \in \N_+ \) and \( (x_1, x_2, \ldots, x_n) \in \{0, 1\}^n \). Let \( k = \sum_{i=1}^n x_i \). Then the conditional distribution of \(P\) given \((X_1 = x_1, X_2, = x_2, \ldots, X_n = x_n)\) is beta with left parameter \(a + k\) and right parameter \(b + (n - k)\). Hence \[ \E(P \mid X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n) = \frac{a + k}{a + b + k} \]
Proof
This follows from Bayes' theorem. The conditional PDF \( g(\cdot \mid x_1, x_2, \ldots, x_n) \) is given by \[ g(p \mid X_1, x_2, \ldots, x_n) = \frac{g(p) \P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n) \mid P = p)}{\int_0^1 g(t) \P(X_1 = x_1, X_2 = x_2, \ldots, X_n = x_n \mid P = t) dt}, \quad p \in (0, 1) \] The numerator is \[ \frac{1}{B(a, b)} p^{a-1} (1 - p)^{b-1} p^k (1 - p)^{n-k} = \frac{1}{B(a, b)} p^{a + k - 1} (1 - p)^{b + n - k - 1} \] The denominator is simply the normalizing constant for the expression, as a function of \( p \) and is \( B(a + k, b + n - k) / B(a, b) \). Hence \[ g(p \mid k) = \frac{1}{B(a + k, b + n - k)} p^{a + k - 1} (1 - p)^{b + n - k - 1}, \quad p \in (0, 1) \] The last result follows since the mean of the beta distribution is the left parameter divided by the sum of the parameters.
Thus, the left parameter increases by the number of successes while the right parameter increases by the number of failures. In the language of Bayesian statistics, the original distribution of \(P\) is the prior distribution , and the conditional distribution of \(P\) given the data \( (x_1, x_2, \ldots, x_n) \) is the posterior distribution . The fact that the posterior distribution is beta whenever the prior distribution is beta means that the beta distributions is conjugate to the Bernoulli distribution. The conditional expected value in the last theorem is the Bayesian estimate of \( p \) when \( p \) is modeled by the random variable \( P \). These concepts are studied in more generality in the section on Bayes Estimators in the chapter on Point Estimation. It's also interesting to note that the expected values in the last two theorems are the same: If \( n \in \N \), \( (x_1, x_2, \ldots, x_n) \in \{0, 1\}^n \) and \( k = \sum_{i=1}^n x_i \) then \[ \E(X_{n+1} \mid X_1 = x_1, \ldots, X_n = x_n) = \E(P \mid X_1 = x_1, \ldots, X_n = x_n) = \frac{a + k}{a + b + n} \]
Run the simulation of the beta coin experiment for various values of the parameter. Note how the posterior probability density function changes from the prior probability density function, given the number of heads.
The Number of Successes
It's already clear that the number of successes in a given number of trials plays an important role, so let's study these variables. For \( n \in \N_+ \), let \[ Y_n = \sum_{i=1}^n X_i \] denote the number of successes in the first \(n\) trials. Of course, \( \bs{Y} = (Y_0, Y_1, \ldots) \) is the partial sum process associated with \( \bs{X} = (X_1, X_2, \ldots) \).
\(Y_n\) has probability density function given by \[ \P(Y_n = k) = \binom{n}{k} \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}}, \quad k \in \{0, 1, \ldots, n\} \]
Proof
Every bit string of length \( n \) with 1 occurring exactly \( k \) times has the probability given in the joint distribution above. There are \( \binom{n}{k} \) such bit strings.
The distribution of \(Y_n\) is known as the beta-binomial distribution with parameters \(n\), \(a\), and \(b\).
In the simulation of the beta-binomial experiment, vary the parameters and note how the shape of the probability density function of \( Y_n \) (discrete) parallels the shape of the probability density function of \( P \) (continuous). For various values of the parameters, run the simulation 1000 times and compare the empirical density function to the probability density function.
The case where the parameters are both 1 is interesting.
If \( a = b = 1 \), so that \( P \) is uniformly distributed on \( (0, 1) \), then \( Y_n \) is uniformly distributed on \( \{0, 1, \ldots, n\} \).
Proof
Note that \( 1^{[j]} = j! \) and \( 2^{[j]} = (j + 1)! \) for \( j \in \N \). Hence, from the general PDF \( Y_n \) above \[ \P(Y_n = k) = \frac{n!}{k! (n - k)!} \frac{k! (n - k)!}{(n + 1)!} = \frac{1}{n + 1}, \quad k \in \{0, 1, \ldots, n\} \]
Next, let's compute the mean and variance of \( Y_n \).
The mean and variance of \( Y_n \) are
- \( \E(Y_n) = n \frac{a}{a + b} \)
- \( \var(Y_n) = n \frac{a b}{(a + b)^2} \left[1 + (n - 1) \frac{1}{a + b + 1} \right] \)
Proof
These results follow from the mean and covariance results given above: \begin{align} \E(Y_n) & = \sum_{i=a}^n \E(X_i) = n \frac{a}{a + b} \\ \var(Y_n) & = \sum_{i=1}^n \sum_{j=1}^n \cov(X_i, X_j) = n \frac{a \, b}{(a + b)^2} + n (n - 1) \frac{a \, b}{(a + b)^2 (a + b + 1)} \end{align}
In the simulation of the beta-binomial experiment, vary the parameters and note the location and size of the mean-standard deviation bar. For various values of the parameters, run the simulation 1000 times and compare the empirical moments to the true moments.
We can restate the conditional distributions in the last subsection more elegantly in terms of \( Y_n \).
Let \( n \in \N \).
- The conditional distribution of \( X_{n+1} \) given \( Y_n \) is \[\P(X_{n+1} = 1 \mid Y_n) = \E(X_{n+1} \mid Y_n) = \frac{a + Y_n}{a + b + n} \]
- The conditional distribution of \(P\) given \(Y_n\) is beta with left parameter \(a + Y_n\) and right parameter \(b + (n - Y_n)\). In particular \[ \E(P \mid Y_n) = \frac{a + Y_n}{a + b + n} \]
Proof
The proof is easy using the nesting property of conditional expected value and the fact that the conditional distributions given \( (X_1, X_2, \ldots, X_n) \) depend only on \( Y_n = \sum_{i=1}^n X_i \).
- Note that \begin{align} \E(X_{n+1} \mid Y_n) & = \E[\E(X_{n+1} \mid Y_n) \mid X_1, X_2, \ldots, X_n] \\ & = \E[E(X_{n+1} \mid X_1, X_2, \ldots, X_n) \mid Y_n] = \E\left(\frac{a + Y_n}{a + b + n} \biggm| Y_n\right) = \frac{a + Y_n}{a + b + n} \end{align}
- Similarly, if \( A \subseteq (0, 1) \) is measurable then \( \P(P \in A \mid X_1, X_2, \ldots, X_n) \) depends only on \( Y_n \) and so \begin{align} \P(P \in A \mid Y_n) & = \E[\P(P \in A \mid Y_n) \mid X_1, X_2, \ldots, X_n] \\ & = \E[\P(P \in A \mid X_1, X_2, \ldots, X_n) \mid Y_n] = \P(P \in A \mid Y_n) \end{align}
Once again, the conditional expected value \( \E(P \mid Y_n) \) is the Bayesian estimator of \( p \). In particular, if \(a = b = 1\), so that \( P \) has the uniform distribution on \( (0, 1) \), then \(\P(X_{n+1} = 1 \mid Y_n = n) = \frac{n + 1}{n + 2}\). This is Laplace's rule of succession , another interesting connection. The rule is named for Pierre Simon Laplace, and is studied from a different point of view in the section on Independence.
The Proportion of Successes
For \( n \in \N_+ \), let \[ M_n = \frac{Y_n}{n} = \frac{1}{n} \sum_{i=1}^n X_i\] so that \( M_n \) is the sample mean of \( (X_1, X_2, \ldots, X_n) \), or equivalently the proportion of successes in the first \( n \) trials. Properties of \( M_n \) follow easily from the corresponding properties of \( Y_n \). In particular, \( \P(M_n = k / n) = \P(Y_n = k) \) for \( k \in \{0, 1, \ldots, n\} \) as given above , so let's move on to the mean and variance.
For \( n \in \N_+ \), the mean and variance of \( M_n \) are
- \( \E(M_n) = \frac{a}{a + b} \)
- \( \var(M_n) = \frac{1}{n} \frac{a b}{(a + b)^2} + \frac{n-1}{n} \frac{a b}{(a + b)^2 (a + b + 1)} \)
Proof
These results follow from the mean and variance of \( Y_n \) above and properties of expected value and variance:
- \( \E(M_n) = \frac{1}{n} \E(Y_n) \)
- \( \var(M_n) = \frac{1}{n^2} \var(Y_n) \)
So \( \E(M_n) \) is constant in \( n \in \N_+ \) while \( \var(M_n) \to a b / (a + b)^2 (a + b + 1) \) as \( n \to \infty \). These results suggest that perhaps \( M_n \) has a limit, in some sense, as \( n \to \infty \). For an ordinary sequence of Bernoulli trials with success parameter \( p \in (0, 1) \), we know from the law of large numbers that \( M_n \to p \) as \( n \to \infty \) with probability 1 and in mean (and hence also in distribution). What happens here when the success probability \( P \) has been randomized with the beta distribution? The answer is what we might hope.
\( M_n \to P \) as \( n \to \infty \) with probability 1 and in mean square, and hence also in in distribution.
Proof
Let \( g \) denote the PDF of \( P \). For convergence with probability 1, we condition on \( P \) \begin{align} \P(M_n \to P \text{ as } n \to \infty) & = \E[\P(M_n \to P \text{ as } n \to \infty) \mid P] \\ & = \int_0^1 \P(M_n \to p \text{ as } n \to \infty \mid P = p) g(p) dp = \int_0^1 g(p) dp = 1 \end{align} For convergence in mean square, once again we condition on \( P \). Note that \[ \E[(M_n - P)^2 \mid P = p] = \E[(M_n - p)^2 \mid P = p] = \frac{p (1 - p)}{n} \to 0\ \text{ as } n \to \infty \] Hence by the dominated convergence theorem, \[ \E[(M_n - P)^2] = \int_0^1 \frac{p (1 - p)}{n} g(p) dp \to 0 \text{ as } n \to \infty \]
Proof of convergence in distribution
Convergence with probability 1 implies convergence in distribution, but it's interesting to gove a direct proof. For \( x \in (0, 1) \), note that \[ \P(M_n \le x) = \P(Y_n \le n x) = \sum_{k=0}^{\lfloor nx \rfloor} \binom{n}{k} \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} \] where \( \lfloor \cdot \rfloor \) is the floor function. But recall that \[ \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} = \frac{B(a + k, b + n - k)}{B(a, b)} = \frac{1}{B(a, b)} \int_0^1 p^{a + k - 1} (1 - p)^{b + n - k - 1} dp \] Substituting and doing some algebra we get \[ \P(M_n \le x) = \frac{1}{B(a, b)} \int_0^1 \left[\sum_{k=0}^{\lfloor nx \rfloor} \binom{n}{k} p^k (1 - p)^{n-k}\right] p^{a - 1}(1 - p)^{b - 1} dp \] The sum in the square brackets is \( \P(W_n \le n x) = \P(W_n / n \le x) \) where \( W_n \) has the ordinary binomial distribution with parameters \( n \) and \( p \). But \( W_n / n \) converges (in every sense) to \( p \) as \( n \to \infty \) so \( \P(W_n / n \le x) \to \bs{1}(p \le x) \) as \( n \to \infty \). So by the dominated convergence theorem, \[ \P(M_n \le x) \to \frac{1}{B(a, b)} \int_0^x p^{a - 1} (1 - p)^{b - 1} dp = \P(P \le x)\]
Recall again that the Bayesian estimator of \( p \) based on \( (X_1, X_2, \ldots, X_n) \) is \[ \E(P \mid Y_n) = \frac{a + Y_n}{a + b + n} = \frac{a / n + M_n}{a / n + b / n + 1} \] It follows from the last theorem that \( \E(P \mid Y_n) \to P \) with probability 1, in mean square, and in distribution. The stochastic process \( \bs Z = \{Z_n = (a + Y_n) / (a + b + n): n \in \N\} \) that we have seen several times now is of fundamental importance, and turns out to be a martingale. The theory of martingales provides powerful tools for studying convergence in the beta-Bernoulli process.
The Trial Number of a Success
For \( k \in \N_+ \), let \( V_k \) denote the trial number of the \( k \)th success. As we have seen before in similar circumstances, the process \( \bs{V} = (V_1, V_2, \ldots) \) can be defined in terms of the process \( \bs{Y} \): \[ V_k = \min\{n \in \N_+: Y_n = k\}, \quad k \in \N_+ \] Note that \(V_k\) takes values in \(\{k, k + 1, \ldots\}\). The random processes \(\bs{V} = (V_1, V_2, \ldots)\) and \(\bs{Y} = (Y_0, Y_1, \ldots)\) are inverses of each other in a sense.
For \(k \in \N \) and \(n \in \N_+\) with \(k \le n\),
- \(V_k \le n\) if and only if \(Y_n \ge k\)
- \(V_k = n\) if and only if \(Y_{n-1} = k - 1\) and \(X_n = 1\)
The probability denisty function of \(V_k\) is given by \[ \P(V_k = n) = \binom{n - 1}{k - 1} \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}}, \quad n \in \{k, k + 1, \ldots\} \]
Proof 1
As usual, we can condition on \( P \) and use known results for ordinary Bernoulli trials. Given \( P = p \), random variable \( V_k \) has the negative binomial distribution with parameters \( k \) and \( p \). Hence \begin{align*} \P(V_k = n) & = \int_0^1 \P(V_k = n \mid P = p) g(p) dp = \int_0^1 \binom{n - 1}{k - 1} p^k (1 - p)^{n-k} \frac{1}{B(a, b)} p^{a-1} (1 - p)^{b - 1} dp \\ & = \binom{n - 1}{k - 1} \frac{1}{B(a, b)} \int_0^1 p^{a + k - 1} (1 - p)^{b + n - k - 1} dp \\ & = \binom{n - 1}{k - 1} \frac{B(a + k, b + n - k)}{B(a, b)} = \binom{n - 1}{k - 1} \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} \end{align*}
Proof 2
In this proof, we condition on \( Y_{n-1} \). Using the PDF of \( Y_{n-1} \) and the result above , \begin{align*} \P(V_k = n) & = \P(Y_{n-1} = k - 1, X_n = 1) = \P(Y_{n-1} = k - 1) \P(X_n = 1 \mid Y_{n-1} = k - 1) \\ & = \binom{n - 1}{k - 1} \frac{a^{[k - 1]} b^{[(n - 1) - (k - 1)]}}{(a + b)^{[n-1]}} \frac{a + k - 1}{a + b + (n - 1)} = \binom{n - 1}{k - 1} \frac{a^{[k]} b^{[n-k]}}{(a + b)^{[n]}} \end{align*}
The distribution of \( V_k \) is known as the beta-negative binomial distribution with parameters \( k \), \( a \), and \( b \).
If \(a = b = 1\) so that \( P \) is uniformly distributed on \( (0, 1) \), then \[ \P(V_k = n) = \frac{k}{n (n + 1)}, \quad n \in \{k, k + 1, k + 2, \ldots\} \]
Proof
Recall again that \( 1^{[j]} = j! \) and \( 2^{[j]} = (j + 1)! \) for \( j \in \N \). Hence from the previous result, \[ \P(V_k = n) = \frac{(n - 1)!}{(k - 1)! (n - k)!} \frac{k! (n - k)!}{(n + 1)!} = \frac{k}{n (n + 1)}, \quad n \in \{k, k + 1, \ldots\} \]
In the simulation of the beta-negative binomial experiment, vary the parameters and note the shape of the probability density function. For various values of the parameters, run the simulation 1000 times and compare the empirical density function to the probability density function.
The mean and variance of \( V_k \) are
- \( \E(V_k) = k \frac{a + b - 1}{a - 1} \) if \( a \gt 1 \).
- \( \var(V_k) = k \frac{a + b - 1}{(a - 1)(a - 2)} [b + k (a + b - 2)] - k^2 \left(\frac{a + b - 1}{a - 1}\right)^2 \)
Proof
From our work with the negative binomial distribution we know that \( \E(V_k | P = p) = k \frac{1}{p} \) and \( \E(V_k^2 | P = p) = k \frac{1 - p}{p^2} + \frac{k^2}{p^2} \). Thus, conditioning on \( P \) we have \[ \E(V_k) = \E[\E(V_k | P)] = \int_0^1 \frac{k}{p} \frac{p^{a-1} (1 - p)^{b - 1}}{B(a, b)} = k \frac{B(a - 1, b)}{B(a, b)} = k \frac{a + b - 1}{a - 1}\] which gives part (a). Similarly \begin{align} \E(V_k^2) & = \E[\E(V_k^2 | P)] = \int_0^1 \left(k \frac{1 - p}{p^2} + \frac{k^2}{p^2}\right) \frac{p^{a - 1} (1 - p)^{b - 1}}{B(a, b)}\\ & = k \frac{B(a - 2, b + 1)}{B(a, b)} + k^2 \frac{B(a - 2, b)}{B(a, b)} = k \frac{b (a + b - 2)}{(a - 1)(a - 2)} + k^2 \frac{(a + b - 1)(a + b - 2)}{(a - 1)(a - 2)} \end{align} Simplifying and using part (a) gives part (b).
In the simulation of the beta-negative binomial experiment, vary the parameters and note the location and size of the mean\(\pm\)standard deviation bar. For various values of the parameters, run the simulation 1000 times and compare the empirical moments to the true moments.


10: Categorical Data Analysis
Now that we’ve got the basic theory behind hypothesis testing, it’s time to start looking at specific tests that are commonly used in psychology. So where should we start? Not every textbook agrees on where to start, but I’m going to start with “χ 2 tests” (this chapter) and “t-tests” (Chapter 13). Both of these tools are very frequently used in scientific practice, and while they’re not as powerful as “analysis of variance” (Chapter 14) and “regression” (Chapter 15) they’re much easier to understand.
The term “categorical data” is just another name for “nominal scale data”. It’s nothing that we haven’t already discussed, it’s just that in the context of data analysis people tend to use the term “categorical data” rather than “nominal scale data”. I don’t know why. In any case, categorical data analysis refers to a collection of tools that you can use when your data are nominal scale. However, there are a lot of different tools that can be used for categorical data analysis, and this chapter only covers a few of the more common ones.


4.4: Key Terms and Concepts for Part III
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15.23A: Functions of the Lymphatic System
- Describe the roles of the lymphatic system
The lymphatic system is the site of many key immune system functions. It is important to distinguish that immune system functions can happen almost anywhere in the body, while the lymphatic system is its own system where many immune system functions take place. Besides immune system function, the lymphatic system has many functions of its own. It is responsible for the removal and filtration of interstitial fluid from tissues, absorbs and transports fatty acids and fats as chyle from the digestive system, and transports many of the cells involved in immune system function via lymph.
Removal of Fluid
Interstitial fluid accumulates in the tissues, generally as a result of the pressure exerted from capillaries (hydrostatic and osmotic pressure) or from protein leakage into the tissues (which occurs during inflammation). These conditions force fluid from the capillaries into the tissues. One of the main functions of the lymphatic system is to drain the excess interstitial fluid that accumulates.
The lymphatic system is a blunt-ended linear flow system, in which tissue fluids, cells, and large extracellular molecules, collectively called lymph, are drained into the initial lymphatic capillary vessels that begin at the interstitial spaces of tissues and organs. They are then transported to thicker collecting lymphatics, which are embedded with multiple lymph nodes, and are eventually returned to the blood circulation through the left and right subclavian veins and into the vena cava. They drain into venous circulation because there is lower blood pressure in veins, which minimizes the impact of lymph cycling on blood pressure. Lymph nodes located at junctions between the lymph vessels also filter the lymph fluid to remove pathogens and other abnormalities.
Fluid removal from tissues prevents the development of edema. Edema is any type of tissue swelling from increased flow of interstitial fluid into tissues relative to fluid drainage. While edema is a normal component of the inflammation process, in some cases it can be very harmful. Cerebral and pulmonary edema are especially problematic, which is why lymph drainage is so important. Abnormal edema can still occur if the drainage components of the lymph vessels are obstructed.
Fatty Acid Transport
The lymphatic system also facilitates fatty acid absorption from the digestive system. During fat digestion, fatty acids are digested, emulsified, and converted within intestinal cells into a lipoprotein called chylomicrons. Lymph drainage vessels that line the intestine, called lacteals, absorb the chylomicrons into lymph fluid. The lymph vessels then take the chylomicrons into blood circulation, where they react with HDL cholesterols and are then broken down in the liver.
Immune Cell Transport
In addition to tissue fluid homeostasis, the lymphatic system serves as a conduit for transport of cells involved in immune system function. Most notably, highly-specialized white blood cells called lymphocytes and antigen -presenting cells are transported to regional lymph nodes, where the immune system encounters pathogens, microbes, and other immune elicitors that are filtered from the lymph fluid. Much of the adaptive immune system response, which is mediated by dendritic cells, takes place in the lymph nodes. Lymphatic vessels, which uptake various antigens from peripheral tissues, are positively regulated by chemokines/cytokines secreted by various immune cells during inflammation. This allows antigens to enter lymph nodes, where dendritic cells can present them to lymphocytes to trigger an adaptive immune response.
While the lymphatic system is important for transporting immune cells, its transport capabilities can also provide a pathway for the spread of cancer. Lymph circulation is one of the main ways that tumors can spread to distant parts of the body, which is difficult to prevent.
Key Points
- The lymphatic system is a linear network of lymphatic vessels and secondary lymphoid organs. It is the site of many immune system functions as well as its own functions.
- It is responsible for the removal of interstitial fluid from tissues into lymph fluid, which is filtered and brought back into the bloodstream through the subclavian veins near the heart.
- Edema accumulates in tissues during inflammation or when lymph drainage is impaired.
- It absorbs and transports fatty acids and fats as chylomicrons from the digestive system.
- It transports white blood cells and dendritic cells to lymph nodes where adaptive immune responses are often triggered.
- Tumors can spread through lymphatic transport.
Key Terms
- lacteal : A lymphatic capillary that absorbs dietary fats in the villi of the small intestine.
- interstitial fluid : Also called tissue fluid, a solution that bathes and surrounds the cells of multicellular animals.
- white blood cell : A type of blood cell involved with an immune response. Many white blood cells (primarily lymphocytes) are transported by the lymphatic system.


12.10: Reading- Effects of Mining
Environmental Effects
Environmental issues can include erosion, formation of sinkholes, loss of biodiversity, and contamination of soil, groundwater and surface water by chemicals from mining processes. In some cases, additional forest logging is done in the vicinity of mines to create space for the storage of the created debris and soil. Contamination resulting from leakage of chemicals can also affect the health of the local population if not properly controlled. Extreme examples of pollution from mining activities include coal fires, which can last for years or even decades, producing massive amounts of environmental damage.
Mining companies in most countries are required to follow stringent environmental and rehabilitation codes in order to minimize environmental impact and avoid impacting human health. These codes and regulations all require the common steps of environmental impact assessment, development of environmental management plans, mine closure planning (which must be done before the start of mining operations), and environmental monitoring during operation and after closure. However, in some areas, particularly in the developing world, government regulations may not be well enforced.
Waste
Ore mills generate large amounts of waste, called tailings. For example, 99 tons of waste are generated per ton of copper, with even higher ratios in gold mining. These tailings can be toxic. Tailings, which are usually produced as a slurry, are most commonly dumped into ponds made from naturally existing valleys. These ponds are secured by impoundments (dams or embankment dams). In 2000 it was estimated that 3,500 tailings impoundments existed, and that every year, 2 to 5 major failures and 35 minor failures occurred; for example, in the Marcopper mining disaster at least 2 million tons of tailings were released into a local river. Subaqueous tailings disposal is another option. The mining industry has argued that submarine tailings disposal (STD), which disposes of tailings in the sea, is ideal because it avoids the risks of tailings ponds; although the practice is illegal in the United States and Canada, it is used in the developing world.
The waste is classified as either sterile or mineralised, with acid generating potential, and the movement and storage of this material forms a major part of the mine planning process. When the mineralised package is determined by an economic cut-off, the near-grade mineralised waste is usually dumped separately with view to later treatment should market conditions change and it becomes economically viable. Civil engineering design parameters are used in the design of the waste dumps, and special conditions apply to high-rainfall areas and to seismically active areas. Waste dump designs must meet all regulatory requirements of the country in whose jurisdiction the mine is located. It is also common practice to rehabilitate dumps to an internationally acceptable standard, which in some cases means that higher standards than the local regulatory standard are applied.
Open-Pit Mining
After mining finishes, the mine area must undergo rehabilitation. Waste dumps are contoured to flatten them out, to further stabilise them. If the ore contains sulfides it is usually covered with a layer of clay to prevent access of rain and oxygen from the air, which can oxidise the sulfides to produce sulfuric acid, a phenomenon known as acid mine drainage. This is then generally covered with soil, and vegetation is planted to help consolidate the material. Eventually this layer will erode, but it is generally hoped that the rate of leaching or acid will be slowed by the cover such that the environment can handle the load of acid and associated heavy metals. There are no long term studies on the success of these covers due to the relatively short time in which large scale open pit mining has existed. It may take hundreds to thousands of years for some waste dumps to become “acid neutral” and stop leaching to the environment. The dumps are usually fenced off to prevent livestock denuding them of vegetation. The open pit is then surrounded with afence, to prevent access, and it generally eventually fills up with ground water. In arid areas it may not fill due to deep groundwater levels.
Metal Reserves and Recycling
During the twentieth century, the variety of metals used in society grew rapidly. Today, the development of major nations such as China and India and advances in technologies are fueling an ever greater demand. The result is that metal mining activities are expanding and more and more of the world’s metal stocks are above ground in use rather than below ground as unused reserves. An example is the in-use stock of copper. Between 1932 and 1999, copper in use in the USA rose from 73 kilograms (161 lb) to 238 kilograms (525 lb) per person.
95% of the energy used to make aluminum from bauxite ore is saved by using recycled material. However, levels of metals recycling are generally low. In 2010, the International Resource Panel, hosted by the United Nations Environment Programme (UNEP), published reports on metal stocks that exist within society and their recycling rates.
The report’s authors observed that the metal stocks in society can serve as huge mines above ground. However, they warned that the recycling rates of some rare metals used in applications such as mobile phones, battery packs for hybrid cars, and fuel cells are so low that unless future end-of-life recycling rates are dramatically stepped up these critical metals will become unavailable for use in modern technology.
Contributors and Attributions
- Revision and Adaptation. Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- Open-pit mining. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Open-pit_mining . License : CC BY-SA: Attribution-ShareAlike
- Mining. Provided by : Wikipedia. Located at : http://en.Wikipedia.org/wiki/Mining . License : CC BY-SA: Attribution-ShareAlike