3.3: Isomorphic Groups
One of the key ideas we've discussed in determining whether binary structures are essentially “the same” or “different.” We approach this rigorously using the concept of isomorphic groups.
Definition: Isomorphic and Nonisomorphic
We say that two groups \(G\) and \(G'\) (or binary structures \(S\) and \(S'\)) are isomorphic (or \(G\) is isomorphic to \(G'\)), and write \(G\simeq G'\text{,}\) if there exists an isomorphism from \(G\) to \(G'\text{.}\) We say that \(G\) is isomorphic to \(G'\) via \(\phi\) if \(\phi\) is an isomorphism from \(G\) to \(G'\text{.}\) If there exists no isomorphism from \(G\) and \(G'\text{,}\) then we say that \(G\) and \(G'\) are nonisomorphic (or \(G\) is not isomorphic to \(G'\)), and write \(G\not\simeq G'\text{.}\)
Note
Just because a particular map (even an “obvious” one) from group \(G\) to group \(G'\) is not an isomorphism, we do not know that \(G\) and \(G'\) are not isomorphic! For instance, the map \(\phi: \mathbb{Z}\to \mathbb{Z}\) defined by \(\phi(x)=2x\) for all \(x\) is not an isomorphism (since it's not onto), but \(\mathbb{Z}\) is isomorphic to itself, as we will see in Part 1 of Theorem \(3.3.1\).
Isomorphic groups have the same structure as far as algebraists are concerned. Again, picture two houses that are identical except for the colors they are painted. Though they differ in some ways (one house is red while the other is green), they are structurally identical. Isomorphic groups have identical structures, though the elements of one group may differ greatly from those of the other. Returning to the house analogy: if two houses are structurally identical, we can learn many things about one house by looking at the other (e.g., how many bathrooms it has, whether it has a basement, etc.). Similarly, suppose we know a great deal about group \(G\) and are given a new group, \(G'\text{.}\) If we prove that \(G'\) is isomorphic to \(G\text{,}\) then we can likely deduce information about \(G'\) from the information we know about \(G\text{.}\)
Theorem \(\PageIndex{1}\)
Let \(\langle G,\cdot\rangle\text{,}\) \(\langle G',\cdot'\rangle\text{,}\) and \(\langle G'',\cdot''\rangle\) be groups.
- Group \(G\) is isomorphic to itself.
- If \(\phi\) is an isomorphism from \(G\) to group \(G'\text{,}\) then there exists an isomorphism from \(G'\) to \(G\text{.}\) Hence, \(G\simeq G'\) if and only if \(G'\simeq G\text{.}\)
- If \(G\simeq G'\) and \(G'\simeq G''\text{,}\) then \(G\simeq G''\text{.}\)
- Proof
-
For Part 1: The identity map \(1_G:G→G\) defined by \(1_G(a)=a\) for all \(a∈G\) is clearly an isomorphism.
For Part 2: Since \(ϕ\) is an isomorphism, it's a bijection, hence has inverse \(ϕ^{−1}\). From Theorem \(1.2.1\), we know that \(ϕ^{−1}\) must also be a bijection (in this case, from \(G′\) to \(G\)). So it suffices to show that \(ϕ^{−1}\) is a homomorphism. Let \(a,b∈G′\). We want to show that \(ϕ^{−1}(a \cdot′b)=ϕ^{−1}(a) \cdot ϕ^{−1}(b)\). Since \(ϕ\) is 1-1, it suffices to show that
\(ϕ(ϕ^{−1}(a \cdot ′b))=ϕ(ϕ^{−1}(a) \cdot ϕ^{−1}(b))\).
Notice, we have \(ϕ(ϕ^{−1}(a \cdot ′b))=a \cdot ′b\); further, we have
\(ϕ(ϕ^{−1}(a) \cdot ϕ^{−1}(b))=ϕ(ϕ^{−1}(a)) \cdot ′ϕ(ϕ^{−1}(b))=a \cdot ′b\).
This shows that \(ϕ^{−1}(a \cdot ′b)=ϕ^{−1}(a) \cdot ϕ^{−1}(b)\), as desired.
For Part 3: Since \(G \simeq G′\) and \(G′ \simeq G′′\), there exist isomorphisms \(ϕ:G→G′\) and \(ψ:G′→G′′\). Define \(θ:G→G″\) by \(θ=ψ \circ ϕ\). Since \(ϕ\) and \(ψ\) are both bijections, \(θ\) is a bijection (Theorem \(1.2.3\)). Next, let \(a,b∈G\). The
\(\begin{array} &θ(a⋅b)&=ψ(ϕ(a⋅b)) &(\text{by definition of \(θ\)}) \\ &=ψ(ϕ(a) \cdot ′ϕ(b)) &(\text{since \(ϕ\) is a homomorphism}) \\ &=ψ(ϕ(a)) \cdot ′′ψ(ϕ(b)) &(\text{since \(ψ\) is a homomorphism})\\ &=θ(a) \cdot ′′θ(b) (\text{by definition of } θ). \end{array}\)
Thus, \(θ\) is a homomorphism, and hence, since it is also a bijection, an isomorphism.
Remark
To show that given groups \(G\) and \(G'\) are isomorphic, we must do three things:
- Define a function \(\phi\) from \(G\) to \(G'\) (or from \(G'\) to \(G\text{,}\) as we have Theorem \(3.3.1\)).
- Prove that \(\phi\) is a homomorphism.
- Prove that \(\phi\) is a bijection.
Note
Remember, you can show that \(\phi\) is a bijection by proving that it's one-to-one and onto, or by showing that it has an inverse.
Note
Do NOT try to prove that a function \(\phi\) is an isomorphism WITHOUT DEFINING \(\phi\text{!}\)
We know provide some terminology that will be helpful for our study of the structures of groups.
Definition: Unique Group
Given a certain property (or properties), we say there is a unique group with that property (or properties) up to isomorphism if any two groups sharing that property (or properties) are isomorphic to one another.
This may seem a little abstruse at the moment, but seeing examples will help illuminate the concept.
Example \(\PageIndex{1}\)
- If \(G\) and \(G'\)are groups with \(|G|=|G'|=1\text{,}\) then \(G\simeq G'\text{,}\) since the map from \(G\) to \(G'\) sending \(G\)'s identity (and sole) element to \(G'\)'s identity (and sole) element is clearly an isomorphism. This is why we can mildly abuse terminology and call any group of order 1 the trivial group instead of a trivial group: \(G\) and \(G'\) may technically be different groups, but structurally they are identical, so we can consider them to be more or less “the same.” Thus, there is a unique group of order 1, up to isomorphism.
- Let \(G\) be a group with \(|G|=2\text{.}\) Then \(G\) must consist of an identity element \(e\) and a nonidentity element \(a\text{,}\) and have the following group table. Compare the respective group tables for \(G\) and for the specific two-element group \(\mathbb{Z}_2\text{.}\)
| \(*\) | \(e\) | \(a\) |
|---|---|---|
| \(e\) | \(e\) | \(a\) |
| \(a\) | \(a\) | \(e\) |
| \(+\) | \(0\) | \(1\) |
|---|---|---|
| \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) |
Note that the first table looks exactly like the second table if we replace \(*\) with \(+\text{,}\) each \(e\) with \(0\text{,}\) and each \(a\) with \(1\text{.}\) This shows that groups \(G\) and \(\mathbb{Z}_2\) have identical structures; more precisely, it shows that the function \(\phi\) from \(G\) to \(\mathbb{Z}_2\) defined by \(\phi(e)=0\) and \(\phi(a)=1\) is an isomorphism. Since any group of order \(2\) is isomorphic to \(\mathbb{Z}_2\text{,}\) using Theorem \(3.3.1\) we see that there is a unique group of order \(2\), up to isomorphism.
-
A similar argument shows that there is a unique group of order \(3\) up to isomorphism: specifically, any group of order \(3\) is isomorphic to \(\mathbb{Z}_3\text{.}\)
-
We will see later, in Example \(3.3.6\), that there is not a unique group of order \(4\) up to isomorphism: that is, there are two nonisomorphic groups of order \(4\).
Theorem \(\PageIndex{2}\)
The groups \(\langle \mathbb{R},+\rangle\) and \(\langle \mathbb{R}^+, \cdot\rangle\) are isomorphic.
- Proof
-
Define \(ϕ:\mathbb{R}→\mathbb{R}^+\) by \(ϕ(x)=e^x\). Our map \(ϕ\) is a homomorphism since for every \(x,y∈\mathbb{R}\), we have
\(ϕ(x+y)=e^{x+y}=e^xe^y=ϕ(x)ϕ(y)\).
Moreover, \( ϕ\) is a bijection, since it has inverse function \(\ ln x : \mathbb{R}^+→\mathbb{R}\). Hence, \(\mathbb{R}≃\mathbb{R}^+\) via isomorphism \(ϕ\).
Example \(\PageIndex{2}\)
Let \(n\in \mathbb{Z}^+\text{.}\) Then the groups \(\langle n\mathbb{Z},+\rangle\) and \(\langle \mathbb{Z},+\rangle\) are isomorphic. The proof of this is left as an exercise for the reader.
We have now seen examples in which we have proved that two groups are isomorphic. How, though, do we prove that two groups are not isomorphic? It is usually wildly impractical, if not impossible, to check that no function from one group to the other is an isomorphism. For instance, it turns out that \(\mathbb{R}^*\) is not isomorphic to \(GL(2,\mathbb{R})\) (see Example \(3.3.3\)), but there are infinitely many bijections from \(\mathbb{R}^*\) to \(GL(2,\mathbb{R})\)—it is impossible to check that each one is not an isomorphism. Instead, we use group invariants .
Definition: Group Invariant
A group property is called a group invariant if it is preserved under isomorphism.
Group invariants are structural properties . Some examples of group invariants are:
- Cardinality (since any isomorphism between groups is a bijection);
- Abelianness (the proof that this is a group invariant is left as an exercise for the reader);
- Number of elements which are their own inverses (proven by an argument similar to that in Example \(3.3.6\)).
A nonexample of a group invariant is the property of being a subset of \(\mathbb{R}\text{.}\)
Example \(\PageIndex{3}\)
The group \(\mathbb{R}\) cannot be isomorphic to the group \(GL(2,\mathbb{R})\) since the former group is abelian and the latter nonabelian.
Example \(\PageIndex{4}\)
The groups \(\mathbb{R}\) and \(\mathbb{Q}\) cannot be isomorphic since the former group is uncountable and the latter countable.
Sometimes we must resort to trickier methods in order to decide whether or not two groups are isomorphic.
Example \(\PageIndex{5}\)
The groups \(\mathbb{Z}\) and \(\mathbb{Q}\) are not isomorphic. We use contradiction to prove this. Suppose that \(\mathbb{Z}\) and \(\mathbb{Q}\) are isomorphic via isomorphism \(\phi :\mathbb{Q} \to \mathbb{Z}\text{.}\) Let \(a\in \mathbb{Q}\text{.}\) Then \(\dfrac{a}{2} \in \mathbb{Q}\) with \(\dfrac{a}{2} + \dfrac{a}{2} =a\text{.}\) Then
\begin{equation*} \phi \left(\dfrac{a}{2} \right)+\phi \left(\dfrac{a}{2} \right)=\phi \left(\dfrac{a}{2}+\dfrac{a}{2}\right)=\phi(a); \end{equation*}
since \(\phi \left( \dfrac{a}{2} \right)\) is in \(\mathbb{Z}\text{,}\) \(\phi(a)\) must be evenly divisible by \(2\). But \(a\) was arbitrary in \(\mathbb{Q}\) and \(\phi\) is onto, so this means every element of \(\mathbb{Z}\) must be evenly divisible by \(2\), which is clearly false. Thus, \(\mathbb{Z}\not\simeq \mathbb{Q}\text{.}\)
Example \(\PageIndex{6}\)
The groups \(\mathbb{Z}_4\) and \(V=\mathbb{Z}_2^2\) are not isomorphic. Why? Well, they are both abelian of order \(4\), so we cannot use cardinality or commutativity to prove they are nonisomorphic. The gist of our argument will be to note that every element in \(V\) is its own inverse; so if \(V\) and \(\mathbb{Z}_4\) are isomorphic (hence structurally identical) we must have that every element of \(\mathbb{Z}_4\) is also its own inverse, which doesn't hold (e.g., in \(\mathbb{Z}_4\text{,}\) \(3+3=2\text{,}\) not \(0\)).
A rigorous proof of the fact that \(V\) and \(\mathbb{Z}_4\) are not isomorphic is as follows: For now, denote the usual operation on \(V\) by \(*\text{.}\) Suppose that \(V\) and \(\mathbb{Z}_4\) are isomorphic, via isomorphism \(\phi\) from \(V\) to \(\mathbb{Z}_4\text{.}\) Then since \(\phi\) is onto, there exists an element \(a\in V\) such that \(\phi(a)=3\text{.}\) Then
\(\begin{array} &3+3& =\phi(a)+\phi(a)& \text{ (by definition of \(a\)) }\\ & =\phi(a*a) & \text{ (since \(\phi\) is a homomorphism) }\\ & =\phi((0,0)) & \text{ (since every element of \(V\) is its own inverse) }\\ & =0, & \end{array}\)
since \(\phi\) is a homomorphism, so sends identity element to identity element. But this is a contradiction, since \(3+3=2\neq 0\) in \(\mathbb{Z}_4\text{.}\) Thus, \(V\not\simeq \mathbb{Z}_4\text{.}\)


3.1: Introduction
Proteins are the workhorses of cells, responsible for just about all aspects of life (look at oxytocin in the cartoon)! Comprised of one or more polypeptides , they:
- are the catalysts that make biochemical reactions possible.
- are membrane components that selectively let substances in and out of the cell.
- allow cell-cell communication and cell’s response to environmental change .
- form the internal structure of cells ( cytoskeleton ) and nuclei ( nucleoskeleton ).
- enable the motility of cells and things inside cells.
- are in fact responsible for other cell functions too numerous to summarize here!
We owe much of what we know about biomolecular structure to the development of X-ray crystallography. In fact an early determination of the structure of insulin (as well as penicillin and vitamin B12) using X-ray crystallography earned Dorothy Hodgkins the 1964 Nobel Prize in Chemistry. In this chapter, we look at the different levels of protein structure…, in fact what it takes to be a functional protein.
The primary structure ( 1 o structure ) of a polypeptide is its amino acid sequence. Interactions between amino acids near each other in the sequence cause the polypeptide to fold into secondary (2 o) structures, including a helix and b-, or pleated sheet conformations. Tertiary ( 3 o ) structures form when non-covalent interactions between amino acid side-chains at some distance from one another in the primary sequence cause the polypeptide further folds into more a complex 3-dimensional structure. Other proteins (called chaperones !) facilitate the accurate folding of a polypeptide into correct, bioactive, 3-dimensional conformations. Quaternary (4 o) structure refers to proteins made up of two or more polypeptides. Refer to the four levels of structure on the next page as we explore how each level affects the shape and biological/biochemical function of the protein.
Covalent bonds between specific amino acids (e.g., cysteines) that end up near each other after folding may stabilize tertiary and quaternary structures. Many proteins also bind metal ions (e.g., Mg++, Mn++) or small organic molecules (e.g., heme) before they become functionally active. Finally, we look beyond these orders of structure at their domains and motifs that have evolved to perform one or another specific protein functions.
Clearly, in trying to understand molecular (especially macromolecular) function, a recurring theme emerges: the function of a protein depends on its conformation . In turn, protein conformation is based on the location and physical and chemical properties of critical functional groups , usually amino acid side chains. Watch for this theme as we look at enzyme catalysis, the movement of molecules in and out of cells, the response of cells their environment, the ability of cells and organelles to move, how DNA replicates, how gene transcription and protein synthesis are regulated…, just about everything a cell does! We will conclude this chapter with a look at some techniques for studying protein structure.
Learning Objectives
When you have mastered the information in this chapter, you should be able to:
1. define and distinguish between the orders of protein structure.
2. differentiate between beta sheet, alpha helix and random coil structure based on the atomic interactions involved on each.
3. trace the path to the formation of a polypeptide; define its primary structure and how it is determined by ‘protein sequencing’.
4. describe how globular proteins arise from the hydrophobic and hydrophilic interactions that drive protein folding and how changes in protein shape can cause disease.
5. formulate an hypothesis (or look one up) to explain why the amino acid glycine is a disruptor of alpha helical polypeptide structure.
6. compare and contrast motif and domain structure of proteins and polypeptides, and their contribution to protein function.
describe different techniques for studying proteins and the physical/chemical differences between proteins that make each technique possible.


As Robert Gagné described, the instructional events (gaining attention, informing the learner of the learning outcome, stimulating recall of prerequisites, presenting the material, providing learning guidance, eliciting the performance, providing feedback, assessing performance, and enhancing retention and transfer) represent what should be done to ensure that learning occurs. If you address each instructional event, you will have a solid foundation for creating effective instructional materials. You will need to determine what will be done for each instructional event for each learning outcome.
Gaining Attention
Gain attention by getting the students involved and motivated. Ideas for gaining attention were presented earlier within the ARCS model of motivation above.
Consider using an interesting animation or video on the title page and first screen of each lesson. This is called an attract sequence. Note that video tends to be more effective than still images in gaining attention.
Remember that you also have to keep the learners attentive throughout the entire lesson. You can maintain attention by using different media, leading lively discussions, asking questions, providing different learning activities, etc.
Informing the Student of the Learning Outcome
Help students focus their efforts in this event. You can do this with simple statements or thought-provoking questions. If possible, also make the students feel that they need to learn the knowledge and skills.
You can let the learner know about the learning outcome in an introduction or overview. This can be a good use for video, since some students skim over text as they find it boring.
Stimulating Recall of Prerequisites
Prepare students for what is to come in this event. One strategy you can use is simply stating the needed prerequisite skills. Alternatively, pre-tests can remind learners of the prerequisites and also help to determine a student’s current skill level. You should advise students who do not have the prerequisite skills to learn the skills before continuing. Stimulating recall of prerequisites should be done before major learning occurs. This is often done in an introduction or overview.
The learner analysis should have previously determined the relevant knowledge and experiences that typical students will bring into the learning situation.
Presenting the Material
When presenting material to the students in this event, in general, you should sequence the material in increasing difficulty and in small incremental steps. This helps ensure success and increases learner confidence.
A variety of methods can inspire interest. No single approach can be used to teach all learning outcomes, but the activities you choose must effectively address the learning outcomes and different learning styles. As much as possible, the activities learners do online should match what will be done in the real world. Learning by doing is very powerful. As the Buddha said, “Teach you? I cannot teach you. Go, experience for yourself.”
Note
Use a variety of methods to teach.
Where appropriate, the instructional activities you create should include fun ways to learn. However, remember that some learning is simply hard work. Every instructional activity can have strengths and weaknesses, depending on the learning outcome being taught. Incorporating a variety of creative instructional approaches can help maintain student interest and motivation as well as ensure that each student occasionally has a match between their learning style and the teaching style. Many effective lessons include more than one type of instructional activity.
Note
Try to make learning fun.
Remember to provide examples that are meaningful, relevant, and realistic. Base some of the content on the potential for making mistakes. Get this information by asking subject-matter experts about typical mistakes students make after they are taught the content in the traditional way. If you only teach what is correct, the learner may never learn what can go wrong. For example, teaching what can go wrong is important in teaching physicians how to make an accurate diagnosis.
Note
Consider teaching both the correct material and what can go wrong.
Base the total amount of material presented in a lesson on the learners’ age and assumed attention span, the material’s complexity, the activities needed, and the time needed for all of the instructional events. A rough estimate of the proportional amount of effort needed to cover a learning outcome should be based on the learning outcome’s frequency, importance, and difficulty.
-
Frequency—How often is the behaviour needed?
-
Importance—How significant is the behaviour to job performance?
-
Difficulty—How hard is the behaviour to master?
For each learning outcome, give a rating (e.g., a number out of five) for the frequency, importance, and difficulty and then add the total. Base the estimated amount of content (e.g., a percentage of the number of screens) proportionally for each learning outcome. Table \(\PageIndex{1}\) shows an example.
You can gain ideas for presenting the material through brainstorming with all team members, other instructors, resource personnel, and even target audience learners. You can also review existing materials for ideas. You should not be responsible for generating all of the creative ideas yourself. When thinking about ideas, remember that people are social. Collaboration and discussions can be powerful in enhancing learning and can easily be done through computers and the Internet. In groups, students can discuss, debate, and explore many things. Imagine how much can be learned if students discuss issues or explain concepts to each other. As Giambattista Vico said, “One only knows something if one can explain it”. Also through computers, it is possible to tap into real data or tools such as those used by scientists. Wouldn’t students enjoy learning about climate, for example, if they could use real data and models to predict the weather?
Table \(\PageIndex{1}\):
|
Objective
|
Frequency
|
Importance
|
Difficulty
|
Total
|
Percent
|
|
Number 1
|
2
|
1
|
1
|
4
|
10%
|
|
Number 2
|
4
|
3
|
5
|
12
|
30%
|
|
Number 3
|
2
|
3
|
3
|
8
|
20%
|
|
Number 4
|
3
|
1
|
2
|
6
|
15%
|
|
Number 5
|
1
|
5
|
4
|
10
|
25%
|
|
Total
|
|
|
|
40
|
100%
|
Depending on the learning outcome, you may need to teach some of them or support them through computer-based resources when the more common online strategies will not suffice. Computer-based resources include drill and practice, tutorials, simulations, online labs, educational games, intelligent tutoring systems, and virtual reality. These are described in Chapter 22, Computer-Based Resources for Learning. Some drill and practice activities can be effectively provided within Learning Management Systems. However, depending on the learning domain, thinking level required, complexity of the problem presentation, and feedback that needs to be provided, some drill and practice activities will need to be created with specialized tools such as Macromedia Flash.
Providing Learning Guidance
In helping students to learn the material, you can provide ways to categorize materials, provide memory devices, and link new knowledge to previously learned knowledge. You can also emphasize differences between related skills. As an example, you might explain that adding two digit numbers is similar to adding single digit numbers, except that a value may have to be “carried”. You can also provide students with strategies for recalling information and encourage them to create their own memory recall techniques. Providing guidance is particularly important because many students have not learned how to learn effectively.
Remember that learning is minimal if you simply provide information. As Paulo Freire said, “To teach is not to transfer knowledge but to create the possibilities for the production or construction of knowledge”.
This event is usually integrated with “presenting the material”.
Eliciting the Performance
Learners must know how well they are progressing. You can do this by asking questions or providing opportunities to practise the skill being taught and then giving feedback. This event is also usually integrated with “presenting the material”.
It is better to provide a little bit of practice often as compared to a lot of practice given seldom. Allow for practice as learners logically need it after each concept of a lesson has been presented, rather than at a fixed interval such as at the end of each lesson after many concepts have been presented. This is even more important when learners need to practise sub-skills before proceeding to higher-level skills. In other words, help learners learn the material as the content is taught. Learning effectiveness can be compromised if you wait too long.
Make the difficulty level of the practice proportional to the difficulty of the task. Practice should not be so easy that it is trivial nor so difficult that it is frustrating. Remember to also check whether the learner makes expected mistakes.
Metacognition is an important step in eliciting the performance. Metacognition can be defined as your knowledge and understanding about your own mental processes, as well as how you actively control and monitor your memory, comprehension, and other thinking processes involved in planning to learn, learning, and assessing your learning. In simple terms, metacognition is a self-questioning strategy that entails “thinking about thinking”.
To address metacognition, learners can be prompted to answer questions such as:
-
“How do I learn best?”
-
Answers to this question relate to the individual’s learning style. For example, the learner may study best in a quiet area.
-
“How does the nature of the task affect my decisions regarding learning the material?”
-
The learner needs to think about issues such as the difficulty of the task. This can impact the time needed for learning the material.
-
The type of task is also a factor. A common situation is that learning material needed for answering multiple-choice questions is different from studying for long-answer questions.
-
“Do I have the time needed to do the task?”
-
“For this type of task, what strategies work best for me?”
-
“Am I motivated to do the task? If not, what needs to change?”
-
“What related skills do I already know how to do or need to learn?”
-
“How do I know that I have learned the concept?”
-
“What did I learn from making that error?”
-
“How well am I progressing?”
-
“What do I still need to learn?”
-
“How well is my plan and learning strategy working?”
-
“Should I change my plan and learning strategy?”
-
“What could I have done differently?”
-
“What should I have done differently?”
-
“How can the mental processes I used work for learning other content?”
Providing Feedback
Your feedback should be positive, constructive, and immediate. It should provide complete information as to why their answer and other possibilities are right or wrong, and/or guide students towards attaining the learning outcome. Detailed feedback is important to ensure understanding, especially if the learner’s answer was simply a guess or if the learner’s answer was correct but the reasoning was wrong. This event is coordinated with eliciting the performance.
Assessing Performance
Students are tested in this event. This step is basically more formal than the “elicit the performance” event. As much as possible, the tests you create should approximate real situations. Test all learning outcomes and only the learning outcomes. Tests should be criterion-referenced (that is, performance based on achieving the specified learning outcomes).
You should provide the students with their test results as soon as possible. The feedback you provide should pinpoint areas in which the student had difficulties.
Enhancing Retention and Transfer
In this event, ensure students retain the information and that the information can be transferred beyond the specific ideas presented in the lesson. More exposure leads to more retention. You can increase retention through questioning, giving reviews, paraphrasing, and providing summaries. Retention activities should occur at spaced intervals and occur before more complex skills are learned.
Note
Increase retention by exposing the learner to the material in a variety of ways.
You can facilitate transfer by providing links to related situations, related information, or novel problems and solutions. If possible, transfer should focus on real-world situations.


6: Steady Current and Conductivity
In practice, we deal with two physical mechanisms for current: convection and conduction. The distinction between these types of current is important in electromagnetic analysis. Convection current consists of charged particles moving in response to mechanical forces, as opposed to being guided by the electric field (Sections 2.2 and/or 5.1). An example of a convection current is a cloud bearing free electrons that moves through the atmosphere driven by wind. Conduction current consists of charged particles moving in response to the electric field and not merely being carried by motion of the surrounding material. In some materials, the electric field is also able to dislodge weakly-bound electrons from atoms, which then subsequently travel some distance before reassociating with other atoms. For this reason, the individual electrons in a conduction current do not necessarily travel the full distance over which the current is perceived to exist. The distinction between convection and conduction is important because Ohm’s Law (Section 6.3) – which specifies the relationship between electric field intensity and current – applies only to conduction current.
-
- 6.2: Current Distributions
- The convention in electrical engineering defines positive current as the flow of positive charge into the positive voltage terminal of a passive device such as a resistor, capacitor, or inductor. For an active device such as a battery, positive current corresponds to the flow of positive charge out of the positive voltage terminal.
-
- 6.6: Power Dissipation in Conducting Media
- The displacement of charge in response to the force exerted by an electric field constitutes a reduction in the potential energy of the system. If the charge is part of a steady current, there must be an associated loss of energy that occurs at a steady rate. Since power is energy per unit time, the loss of energy associated with current is expressible as power dissipation. Here. we address two questions: (1) How much power is dissipated in this manner, and (2) What happens to the lost energy?
Contributors and Attributions
-
Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 Licensed with CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0 . Report adoption of this book here . If you are a professor reviewing, adopting, or adapting this textbook please help us understand a little more about your use by filling out this form.


1.2: History of Home Care
In 1813, the Ladies Benevolent Society, (LBS), a group of women volunteers in Charleston, South Carolina, began the first efforts at providing home care services (Buhler-Wilkerson, 2001). These untrained women were the first to provide direct care services within people’s homes. The LBS visited the sick poor in their homes, helped them to obtain medicines, food, and supplies such as soap, bed linens, and blankets. They also helped to supply them with nurses, although these nurses were untrained.
According to Buhler-Wilkerson (2001), in the North, women from wealthy families volunteered with the sick poor to establish “friendships” in which to help the sick overcome disease and poverty. These women quickly realized that trained nurses were needed to help the sick poor, as establishing friendships alone could not help prevent or cure disease (Buhler-Wilkerson). They began to hire trained nurses, who they called “visiting nurses.” This idea came about based on the “district nurse” model which was established in England (Buhler-Wilkerson).
The National Nursing Association for Providing Trained Nurses for the Sick Poor was created in England in 1875 (Buhler-Wilkerson, 2001). This organization trained, organized, and created standardized practices for district nurses who worked within people’s homes. In addition to attending to the physical needs of their patients, these visiting nurses worked to teach the sick poor about how disease is spread and how to maintain a clean home in order to prevent the spread of infection.
Based on this model, Visiting Nurse Societies were established in major cities throughout the Northern United States (Buhler-Wilkerson, 2001). By 1890, there were 21 home care visiting nursing associations (Buhler-Wilkerson). The need for nursing care within the home continued to grow. This need grew to not only caring for the sick poor, but also to provide preventative services to babies, children, mothers, and to care for patients with infectious diseases such as tuberculosis. Although the death rate for infectious diseases had declined, there was a growing concern for prevention and good hygiene. By 1909, the Metropolitan Life Insurance Company began to send nurses into their policyholders’ homes to provide nursing services (Buhler-Wilkerson). Their hope was that providing home nursing care would reduce the amount of death benefits claimed. They were the first organization to provide reimbursement for home care nursing services.
Lillian Wald, a nurse, is credited for establishing the Henry Street Settlement and with defining the term “public health nursing”. The nurses who worked at the Henry Street Settlement visited the sick in their homes, and also provided social services for people throughout the city. In addition to the Henry Street Settlement house, the organization grew to include numerous nursing houses throughout the city to meet the growing need for nurses within communities. These nurses also held classes for their neighbors to teach carpentry, sewing, cooking, English, and home nursing (Buhler-Wilkerson, 2001). They established kindergartens and various social clubs to meet the needs of their neighborhoods. By the time of Lillian Wald’s retirement, her nurses were making 550,000 home visits to 100,000 patients (Buhler-Wilkerson).
In the late 1920s, many of the home care agencies closed due to the poor economy and the nursing shortage during World War II (Buhler-Wilkerson, 2001). The establishment of hospitals resulted in a model where patients moved from receiving care in the homes to into hospitals. Despite experiments by The Health Insurance Plan of Greater New York and Blue Cross to include home care services, coverage for visiting home care was not universally provided at that time (Buhler-Wilkerson). By the late 1950s and early 1960s, however, it became clear that there was again a growing need for home care services. People with chronic illnesses did not necessarily need to be hospitalized. The cost of hospitalizations began to be apparent, and the long-term effects on lengthy institutionalizations began to be studied (Buhler-Wilkerson).
In the U.S., it was not until 1965, when Medicare was established for people over 65 years of age, that home care services were once again covered by insurance (Buhler-Wilkerson, 2001). Medicare is a federal health insurance program. Medicare now also pays for patients with kidney failure and certain disabilities. According to the U.S. Department of Health & Human Services, Centers for Medicare & Medicaid Services (2010), patients who receive home services through Medicare must be under the care of a physician who certifies the need for skilled nursing care, physical therapy, speech-language pathology services, or occupational therapy. Patients must also be certified to be home-bound by their doctors. This means that it is either unsafe for the patients to leave their home or they have a condition that makes leaving the home difficult. Medicare provides “intermittent” home care, meaning home care is not needed on a full-time basis. While Medicare will often pay the full cost of most covered home health services, they do not pay for 24 hour a day care. Medicare may also cover up to 80% of special equipment the patient needs, such as a wheelchair or walker (U.S. Department of Health & Human Services, Centers for Medicare & Medicaid Services).
Medicaid is a joint state and federal health insurance program. Coverage for patients will vary from state to state, and states may call it different names, such as “Medi-Cal” or “Medical Assistance” (U.S. Department of Health & Human Services, Centers for Medicare & Medicaid Services, 2010). Medicaid provides coverage for low-income patients and families. Eligibility for this program depends on income, number of people in a household, and other circumstances. It is important to remember that not everyone is eligible to receive Medicare or Medicaid, and home care services may not be covered in full. Agencies who receive reimbursement through Medicare or Medicaid must meet certain guidelines, including the requirement that HHAs receive formal training and pass certification exams. Due to the growing need for home care services, and in an effort to reduce costs to insurance programs such as Medicare, the need for home health aides (HHAs) and personal care aides (PCAs) continues to increase.


16.2: Sudden Food Shortages and the Disenfranchised Citizen
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In 2007/8, and again in 2011, the world market prices of cereals, meat and dairy products, vegetable oils and sugar all began to increase rapidly. This was blamed on a variety of causes. These ranged from poor harvests in agricultural producing countries like Australia and Russia; policies in the United States and Brazil that encouraged food crops to be replaced by biofuel; rising gas prices that pushed up the cost of fertilisers; and financial speculation leading to volatile prices. Commentators spoke of a ‘global food crisis’ as the effects were felt in every country, albeit to differing degrees. In the United Kingdom (UK) the average cost of a loaf of bread doubled from £0.63 in January 2005 to £1.26 just four years later; an increase way ahead of inflation and an unwanted burden for those on lower incomes. In states with greater dependency on food imports and higher levels of poverty, though, the impact was felt even more deeply. These states could mainly be found in the Middle East and Africa, and in city after city riots broke out as people found it difficult to access basic staples at prices they could afford.
One of these cities was Algiers, the capital of Algeria. As elsewhere, people took to the streets not simply because food was hard to get hold of but also because of the injustice they perceived in the way their country had been run.
Demands for affordable food ran alongside calls for jobs, political freedoms and an end to government corruption. Banners were written saying things like ‘Give us back our Algeria’ and ‘No to the police state’. At first the Algerian government responded to these events with repression. The police fired tear gas and water cannons at youths who had angrily taken to the streets and set up roadblocks. Football matches were suspended as it was thought the crowds might turn political and become a threat to public order. However, aware of the Arab Spring revolutions and fearful that the uprisings seen in Egypt and Tunisia would be repeated in Algeria, the government soon relented. Import taxes on sugar and cooking oil were slashed and prices capped for flour and vegetables. The government also renounced the 19-year-old State of Emergency law that had prohibited peaceful protest in the country. The forcible removal of long-standing president Abdelaziz Bouteflika was thus averted, although widespread disapproval of his autocratic regime continued to simmer.
What effect did these food riots have on international relations? First of all they created the sense that there was a ‘global food crisis’ to resolve. It is important to note here that if a food crisis were to be simply defined as the existence of widespread hunger, then the situation would have been nothing new. Throughout the 1990s and 2000s there were consistently between 800 million and 1 billion people in the world who were chronically undernourished. Living largely in rural areas in Asia and Africa, these people suffered away from the spotlight. However, based on the position of the disenfranchised citizen, the food riots that broke out in volatile urban areas directly challenged the legitimacy of political leaders and forced a response (Bush 2010). This kind of hunger could not be ignored.
Attempting to manage the food crisis, world leaders gathered at the United Nations’ High-Level Conference on World Food Security. They produced a declaration to provide more emergency aid, prevent international agricultural trade from being disrupted, and increase global agricultural production. Critics saw this as a conservative response that did not address the root causes of the crisis. Instead of ensuring people had decent incomes and accountable leaders, reflecting the demands of the protestors, the focus was simply on bringing down world market prices. This also reproduced the misleading idea that hunger is best dealt with by growing more food rather than changing existing power relations. Oxfam, a confederation of charitable organisations, made this point when they said that there was already enough food to feed everyone. For Oxfam the problem unveiled by the riots was not so much lack of supply but unequal distribution (Oxfam 2009). During 2008, the height of the food crisis, there was a global average of 2,826 calories produced, per person, per day according to official United Nations data. The recommended intake for an adult is between 2,000–2,500 calories. So, if the data is taken at face value, there was no actual shortage of food. Rather, political decisions had created a situation where some people could acquire food more easily than others.


16.5G: Fibrinolysis
Fibrinolysis is a process of breaking down clots in order to prevent them from growing and becoming problematic.
- Describe the process of fibrinolysis
Key Points
- Fibrinolysis is the breakdown of a fibrin clot.
- Plasmin is the enzyme that breaks down fibrin. It is activated from inactive plasminogen by tissue plasminogen activator (t-PA) and urokinase.
- Tissue plasminogen activator (t-PA) and urokinase are inhibited by plasminogen activator inhibitor-1 and plasminogen activator inhibitor-2 (PAI-1 and PAI-2).
- Many drugs have fibrinolytic properties that can be used to treat uncontrolled clotting and embolism, including streptokinase, synthetic t-PA, aspirin, heparin, warfarin, and citrates.
- Patients suspected to be having a blood clot-induced stroke should be screened for hemorrhage and aneurysm first, since fibrinolytic treatment would help with a stroke but make bleeding conditions much more dangerous.
Key Terms
- fibrin : An elastic, insoluble, whitish protein produced by the action of thrombin on fibrinogen and forming an interlacing fibrous network in the coagulation of blood.
- protease : An enzyme that cuts or cleaves proteins.
- Plasmin : A protease that breaks down plasmin. It is cleaved from inactive plasminogen.
Fibrinolysis is a process that removes clots following hemostasis and clot retraction, preventing uncontrolled thrombosis and embolism. There are two types of fibrinolysis: primary fibrinolysis and secondary fibrinolysis. Primary fibrinolysis is a normal body process, whereas secondary fibrinolysis is the breakdown of clots due to a medication, medical disorder, or other cause.
Mechanisms of Primary Fibrinolysis
Primary fibrinolysis normally occurs following clot retraction, in which the clot has already condensed considerably in size. The main enzyme in primary fibrinolysis is plasmin, a proteolytic enzyme that degrades fibrin mesh. Plasmin cleaves fibrin at various places, leading to the production of circulating fragments that are cleared by other proteases or by the kidneys and liver.
Plasmin is produced in an inactive form, plasminogen, in the liver. Plasminogen cannot cleave fibrin and circulates in the bloodstream. Instead, it is incorporated into the clot when it is formed and then activated into plasmin later. Plasminogen is activated to plasmin by tissue plasminogen activator (t-PA) and urokinase, an enzyme found in the urine.
Fibrinolysis : Blue arrows denote stimulation and red arrows inhibition.
T-PA is released into the blood very slowly by the damaged endothelium of the blood vessels. T-PA and urokinase are themselves inhibited by plasminogen activator inhibitor-1 and plasminogen activator inhibitor-2 (PAI-1 and PAI-2). In contrast, plasmin further stimulates plasmin generation by producing more active forms of both tissue plasminogen activator (tPA) and urokinase. Following fibrin degradation by plasmin, old activated platelets from the platelet plug are phagocytized and destroyed by macrophages.
Alpha 2-antiplasmin and alpha 2-macroglobulin inactivate plasmin. Plasmin activity is also reduced by thrombin -activatable fibrinolysis inhibitor (TAFI), which modifies fibrin to make it more resistant to the tPA-mediated plasminogen. Plasmin operates on a negative feedback process because it is reduced when the fibrin clot is fully degraded.
Mechanisms of Secondary Fibrinolysis
Secondary fibrinolysis generally refers to treatment of pathological thromboembolism. If blood clots embolize to different parts of the body, they can cause tissue death by blocking off blood flow to those tissues. This is a common cause of heart attacks, pulmonary embolism, and strokes. Several medications exist to help treat and prevent these conditions.
Fibrinolytic drugs include synthesized tissue plasminogen activator and streptokinase, a bacterial enzyme that has degrades fibrin directly. Clots may also be prevented or kept from worsening through the use of blood thinners ( anticoagulants ). Aspirin has anticoagulant properties because it inhibits cyoclo-oxygenase dependent pathways of platelet activation, which can prevent clotting from worsening. Heparin is a fast-acting anticoagulant produced by the body and used as a drug which inhibits the activity of thrombin. Warfarin inhibits vitamin K cofactor activation during the coagulation cascade, and citrates chelate calcium to prevent prothrombin activation into thrombin.
All of these treatments have been shown to have tremendous therapeutic benefit in treating those with thromboembolic diseases; however, they can make injury much more difficult to treat by disrupting the clotting process. For example, patients thought to be suffering from a stroke (obstructed artery in the brain ) must be screened through imaging before given aspirin or a fibrinolytic drug, because if they have an aneurysm or hemorrhage (burst blood vessel or bleeding in the brain), administering fibrinolytic treatment would make their condition worse and possibly fatal by inhibiting the clotting that could save their lives.
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14.3: Checking Model Assumptions using Graphs
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Multiple regression methods using the model
\[\hat {y} = \beta _0 + \beta _1x_1 + \beta _2x_2 + \dots + \beta _kx_k\]
generally depend on the following four assumptions:
- the residuals of the model are nearly normal,
- the variability of the residuals is nearly constant,
- the residuals are independent, and
- each variable is linearly related to the outcome.
Simple and effective plots can be used to check each of these assumptions. We will consider the model for the auction data that uses the game condition and number of wheels as predictors.
Normal probability plot . A normal probability plot of the residuals is shown in Figure \(\PageIndex{1}\). While the plot exhibits some minor irregularities, there are no outliers that might be cause for concern. In a normal probability plot for residuals, we tend to be most worried about residuals that appear to be outliers, since these indicate long tails in the distribution of residuals.
Absolute values of residuals against fitted values . A plot of the absolute value of the residuals against their corresponding fitted values (\(\hat {y}_i\)) is shown in Figure \(\PageIndex{2}\). This plot is helpful to check the condition that the variance of the residuals is approximately constant. We do not see any obvious deviations from constant variance in this example.
Residuals in order of their data collection . A plot of the residuals in the order their corresponding auctions were observed is shown in Figure \(\PageIndex{3}\). Such a plot is helpful in identifying any connection between cases that are close to one another, e.g. we could look for declining prices over time or if there was a time of the day when auctions tended to fetch a higher price. Here we see no structure that indicates a problem. 12
Residuals against each predictor variable . We consider a plot of the residuals against the cond_new variable and the residuals against the wheels variable. These plots are shown in Figure \(\PageIndex{4}\). For the two-level condition variable, we are guaranteed not to see any remaining trend, and instead we are checking that the variability does not fluctuate across groups. In this example, when we consider the residuals against the wheels variable, we see some possible structure. There appears to be curvature in the residuals, indicating the relationship is probably not linear.
12 An especially rigorous check would use time series methods. For instance, we could check whether consecutive residuals are correlated. Doing so with these residuals yields no statistically significant correlations.
It is necessary to summarize diagnostics for any model fit. If the diagnostics support the model assumptions, this would improve credibility in the ndings. If the diagnostic assessment shows remaining underlying structure in the residuals, we should try to adjust the model to account for that structure. If we are unable to do so, we may still report the model but must also note its shortcomings. In the case of the auction data, we report that there may be a nonlinear relationship between the total price and the number of wheels included for an auction. This information would be important to buyers and sellers; omitting this information could be a setback to the very people who the model might assist.
"All models are wrong, but some are useful" -George E.P. Box
The truth is that no model is perfect. However, even imperfect models can be useful. Reporting a awed model can be reasonable so long as we are clear and report the model's shortcomings.
Caution: do not report results when assumptions are grossly violated
While there is a little leeway in model assumptions, do not go too far. If model assumptions are very clearly violated, consider a new model, even if it means learning more statistical methods or hiring someone who can help.
TIP: Confidence intervals in multiple regression
Confidence intervals for coefficients in multiple regression can be computed using the same formula as in the single predictor model:
\[b_i \pm t^*_{df} SE_{b_i}\]
where \(t^*_{df}\) is the appropriate t value corresponding to the confidence level and model degrees of freedom, \(df = n - k - 1\).


12: Sources of Magnetic Fields
In this chapter, we examine how magnetic fields are created by arbitrary distributions of electric current, using the Biot-Savart law. Then we look at how current-carrying wires create magnetic fields and deduce the forces that arise between two current-carrying wires due to these magnetic fields. We also study the torques produced by the magnetic fields of current loops. We then generalize these results to an important law of electromagnetism, called Ampère’s law.
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- 12.1: Prelude to Sources of Magnetic Fields
- In the preceding chapter, we saw that a moving charged particle produces a magnetic field. This connection between electricity and magnetism is exploited in electromagnetic devices, such as a computer hard drive. In fact, it is the underlying principle behind most of the technology in modern society, including telephones, television, computers, and the internet.
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- 12.2: The Biot-Savart Law
- We have seen that mass produces a gravitational field and also interacts with that field. Charge produces an electric field and also interacts with that field. Since moving charge (that is, current) interacts with a magnetic field, we might expect that it also creates that field—and it does.
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- 12.3: Magnetic Field due to a Thin Straight Wire
- How does the shape of wires carrying current affect the shape of the magnetic field created? We know that a current loop created a magnetic field similar to that of a bar magnet, but what about a straight wire? We can use the Biot-Savart law to answer all of these questions, including determining the magnetic field of a long straight wire.
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- 12.4: Magnetic Force between Two Parallel Currents
- You might expect that two current-carrying wires generate significant forces between them, since ordinary currents produce magnetic fields and these fields exert significant forces on ordinary currents. But you might not expect that the force between wires is used to define the ampere. It might also surprise you to learn that this force has something to do with why large circuit breakers burn up when they attempt to interrupt large currents.
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- 12.5: Magnetic Field of a Current Loop
- We can use the Biot-Savart law to find the magnetic field due to a current. We first consider arbitrary segments on opposite sides of the loop to qualitatively show by the vector results that the net magnetic field direction is along the central axis from the loop. From there, we can use the Biot-Savart law to derive the expression for magnetic field.
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- 12.6: Ampère’s Law
- A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral B and is known as Ampère’s law.
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- 12.8: Magnetism in Matter
- Why are certain materials magnetic and others not? And why do certain substances become magnetized by a field, whereas others are unaffected? To answer such questions, we need an understanding of magnetism on a microscopic level. Within an atom, every electron travels in an orbit and spins on an internal axis. Both types of motion produce current loops and therefore magnetic dipoles. For a particular atom, the net magnetic dipole moment is the vector sum of the magnetic dipole moments.


4.10: Illustration
- Describe techniques for illustrating a point
Illustration is a rhetorical style that uses examples to support the thesis or main idea of a paragraph or essay. Don’t confuse illustration with the use of pictures, although we will be discussing later how visual images can be used effectively in multimedia writing. Illustration is most often used at the paragraph level to help illustrate or support a point, but you may also encounter illustration essays of various types in your college courses.
In an illustration essay or a paragraph that employs illustration, your focus is on using examples that are relevant and strong to your argument and appropriate for your audience.
The point of any illustration assignment is for the writer to assert an overall observation and back up that assertion with evidence-based examples. Like other rhetorical modes, it can be simply informative—providing a neutral presentation of information for readers to use to draw their own conclusions, or it can be argumentative—providing a stance or point of view on the topic. The key to organizing the overall essay is to decide on categories of main ideas that are needed to provide a comprehensive overview of the topic.
An Illustrative Thesis
The thesis statement for an illustration essay should convey the main point and suggest why further clarification or development of a deeper understanding of the topic is necessary or important.
Examples:
- The over-reliance on social media and texting has created an environment where people feel comfortable sharing critical feelings they would have previously kept to themselves.
- Many of today’s popular movies rely on excessive gore and violence to entertain audiences which could explain why book adaptations are more violent than the original text.
- If money is no object, then a vacation to the Kanaapali Shores Beach Resort will satisfy a tourist’s paradise dream.
Using scientific studies, experts in a particular field, statistics, historical events, current events, analogies, and personal anecdotes are all ways in which a writer can illustrate a thesis. Ultimately, you want the evidence to help the reader “see” your point, as one would see a good illustration in a magazine or on a website. The stronger your evidence is, the more clearly the reader will consider your point.
Using evidence effectively can be challenging, though. The evidence you choose will usually depend on your subject and who your reader is (your audience). When writing an illustration essay, keep in mind the following:
- Use evidence that is appropriate to your topic as well as appropriate for your audience.
- Assess how much evidence you need to adequately explain your point depending on the complexity of the subject and the knowledge of your audience regarding that subject.
For example, if you are writing about a new communication software and your audience is a group of English-major undergrads, you might want to use an analogy or a personal story to illustrate how the software works. However, if you are writing about the same subject and your audience members are information technology (IT) specialists, your personal experience is less likely to be an effective illustration. Instead, you need to use more technical evidence because your audience has more familiarity with and greater knowledge of the subject.
Keeping your subject matter in mind in relation to your audience will increase your chances of effectively illustrating your point. Be careful not to overexplain simple concepts that your readers are already familiar with—you don’t want to insult their intelligence! Instead of more explanation, consider using an example.
Organizing an Illustration
The organization of an illustration essay depends on the purpose of the essay and requires a clear rationale for why the examples apply as an illustration of a concept. When pulling in examples, you may rely on words or phrases such as: for example, for instance, in particular, to illustrate, or specifically.
Typically in a single supporting paragraph, a writer uses a topic sentence to designate the main idea followed by primary and secondary support structure. In a full essay devoted to illustration, primary supports are the main ideas to support a topic sentence, and secondary supports are the examples and details to provide the concrete information to complete the writer’s point.
Introduction and Thesis:
- Purpose of Illustration: To demonstrate how a vacation at the Kanaapali Shores Beach Club Resort is enjoyable and affordable.
Primary support 1: The hotel amenities
- Secondary supporting details: the room, the bed, the bathroom, the kitchenette, the view, the concierge services
Primary support 2: The restaurants
- Secondary supporting details: the variety of food, the quality of food, the service, the ambiance
Primary support 3: The beach and activities
- Secondary supporting details: the beauty of the sand, sky, and water; sunbathing, snorkeling, windsurfing
Primary support 4: The cost
- Secondary supporting details: the price of the room per night, the prices of meals, the price of activities/entertainment
Conclusion
Now that you have had the chance to learn about illustration essays, it’s time to see one in practice. Here you’ll see a traditional or typical sample illustration essay from a beginning writing class. In this assignment, the student was asked to write an essay using illustration to make his points, to follow APA guidelines, and to use at least two sources.
Contributors and Attributions
- Organizing an Illustration. Authored by : Marianne Botos, Lynn McClelland, Stephanie Polliard, Pamela Osback . Located at : https://pvccenglish.files.wordpress.com/2010/09/eng-101-inside-pages-proof2-no-pro.pdf . Project : Horse of a Different Color: English Composition and Rhetoric . License : CC BY: Attribution
- Illustration Essay. Provided by : Excelsior College Online Writing Lab. Located at : https://owl.excelsior.edu/rhetorical-styles/illustration-essay/ . License : CC BY: Attribution


<IP_ADDRESS>: The Ability to Use Motility and Other Means to Contact Host Cells
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Learning Objectives
- State why it might be of an advantage for a bacterium trying to colonize the bladder or the intestines to be motile.
- Describe specifically how certain bacteria are able to use motility to contact host cells and state how this can promote colonization.
- Briefly describe why being extremely thin and being motile by means of axial filaments may be an advantage to pathogenic spirochetes.
- Give one example of how a nonmotile bacterium may be able to better disseminate within a host.
- Give a brief description of how a bacterium may use toxins to better disseminate from one host to another.
Highlighted Bacterium
- Read the description of Helicobacter pylori and match the bacterium with the description of the organism and the infection it causes.
The mucosal surfaces of the respiratory tract, the intestinal tract, and the genitourinary tract constantly flush bacteria away in order to prevent colonization of host mucous membranes. Motile bacteria can use their motility and chemotaxis to swim through mucus towards mucosal epithelial cells. Many bacteria that can colonize the mucous membranes of the bladder and the intestines, in fact, are motile. Motility probably helps these bacteria move through the mucus between the mucin strands or in places where the mucus is less viscous. Examples of motile opportunists and pathogens include Helicobacter pylori, Salmonella species, Escherichia coli, Pseudomonas aeruginosa , and Vibrio cholerae . Once bacteria contact host cells they can subsequently attach, and colonize. (Attachment will be discussed in the next section. )
- Movie of motile Escherichia coli with fluorescent labelled-flagella #1 Courtesy of Dr. Howard C. Berg from the Roland Institute at Harvard.
- Movie of motile Pseudomonas from YouTube.
For example, Helicobacter pylori , the bacterium that causes most gastric and duodenal ulcers, produces urease, an enzyme that breaks down urea into ammonia and carbon dioxide. The ammonia neutralizes the hydrochloric acid in the stomach. In addition, the urease is thought to alter the proteins in the mucus changing it from a solid gel to a thinner fluid that the bacteria are able to swim through by way of their flagella, and subsequently use adhesins to adhere to the epithelial cells of the mucous membranes. To further help protect the bacterium from the acid, H. pylori produces an acid-inhibitory protein that blocks acid secretion by surrounding parietal cells in the stomach. Bacterial toxins then lead to excessive production of cytokines and chemokines , as well as mucinase and phospholipase that damage the gastric mucosa. The cytokines and chemokines, in turn, result in a massive inflammatory response. Neutrophils leave the capillaries, accumulate at the area of infection, and discharge their lysosomes for extracellular killing. This not only kills the bacteria, it also destroys the mucus-secreting mucous membranes of the stomach. Without this protective layer, gastric acid causes ulceration of the stomach. This, in turn, leads to either gastritis or gastric and duodenal ulcers.
YouTube movie of a video endoscopy exam showing duodenal ulcers caused by Helicobacter pylori.
Click on this link, read the description of Helicobacter pylori , and be able to match the bacterium with its description on an exam.
Planktonic Pseudomonas aeruginosa uses its polar flagellum to move through water or mucus and make contact with a solid surface such as the body's mucous membranes (Figure \(\PageIndex{5}\).1.1). It then can use pili and cell wall adhesins to attach to the epithelial cells of the mucous membrane. Attachment activates signaling and quorum sensing genes to eventually enable the population of P. aeruginosa to start synthesizing a polysaccharide biofilm composed of alginate. As the biofilm grows, the bacteria lose their flagella to become nonmotile and secrete a variety of enzymes that enable the population to obtain nutrients from the host cells. Eventually the biofilm mushrooms up and develops water channels to deliver water and nutrients to all the bacteria within the biofilm. As the biofilm begins to get too crowded with bacteria, quorum sensing enables some of the Pseudomonas to again produce flagella, escape the biofilm, and colonize a new location.
Because of their thinness, their internal flagella (axial filaments), their corkscrew shape, and their motility (Figure \(\PageIndex{5}\).1.2), spirochetes are more readily able to penetrate host mucous membranes, skin abrasions, etc., and enter the body. Motility and penetration may also enable the spirochetes to penetrate deeper in tissue and enter the lymphatics and bloodstream and disseminate to other body sites. Spirochetes that infect humans include Treponema pallidum , Leptospira , and Borrelia burgdorferi ) .
- Movie of motile Borrelia bergdorferi , the spirochete that causes Lyme disease. From You Tube, courtesy of CytoViva.
- Movie of motile Borrelia bergdorferi , the spirochete that causes Lyme disease.
Along a different line, many bacteria produce enzymes such as elastases and proteases that degrade the extracellular matrix proteins that surround cells and tissues and make it easier for those bacteria to disseminate within the body. For example, Streptococcus pyogenes produces streptokinase that lyses the fibrin clots produced by the body in order to localize the infection. It also produces DNase that degrades cell-free DNA found in pus and reduces the viscosity of the pus. Both of these enzymes facilitate spread of the bacterium from the localized site to new tissue.
Staphylococcus aureus , on the other hand, produces surface adhesins that bind to extracellular matrix proteins and polysaccharides surrounding host cell tissue, including fibronectin, collagen, laminin, hyaluronic acid, and elastin. S. aureus proteases and hyaluronidase then dissolve these components of the extracellular matrix providing food for the bacteria and enabling the bacteria to spread.
Finally, as will be seen later in this unit under toxins, some bacteria produce toxins that induce diarrhea in the host. Diarrhea is also a part of our innate immunity to flush harmful microbes and toxins out of the intestines. On one hand, diarrhea is an advantage to the body because it flushes out harmful microbes and toxins. On the other hand, it is beneficial for the bacterium inducing the diarrhea because it also flushes out a good deal of the normal flora of the intestines and this reduces the competition for nutrients between normal flora and pathogens. In addition, diarrhea enables the pathogen to more readily leave one host and enter new hosts through the fecal-oral route.
Summary
Bacteria have to make physical contact with host cells before they can adhere to those cells and resist being flushed out of the body. Motile bacteria can use their flagella and chemotaxis to swim through mucus towards mucosal epithelial cells. Because of their thinness, their internal flagella (axial filaments), their corkscrew shape, and their motility, certain spirochetes are more readily able enter lymph vessels and blood vessels and spread to other body sites. Many bacteria produce enzymes that degrade the extracellular matrix proteins that surround cells and tissues and help to localize infection, making it easier for those bacteria to spread within the body. Some bacteria produce toxins that induce diarrhea in the host enabling the pathogen to more readily leave one host and enter new hosts through the fecal-oral route.


1.36: Meter in Music
The concept of meter is very important to us in this class, as the ability to recognize the meter of a piece of music is a very handy tool in identifying a particular piece.
What is Meter?
The meter of a piece of music is the arrangment of its rhythms in a repetitive pattern of strong and weak beats. This does not necessarily mean that the rhythms themselves are repetitive, but they do strongly suggest a repeated pattern of pulses. It is on these pulses, the beat of the music, that you tap your foot, clap your hands, dance, etc.
Some music does not have a meter. Ancient music, such as Gregorian chants; new music, such as some experimental twentieth-century art music; and Non-Western music, such as some native American flute music, may not have a strong, repetitive pattern of beats. Other types of music, such as traditional Western African drumming, may have very complex meters that can be difficult for the beginner to identify.
But most Western music has simple, repetitive patterns of beats. This makes meter a very useful way to organize the music. Common notation, for example, divides the written music into small groups of beats called measures, or bars. The lines dividing each measure from the next help the musician reading the music to keep track of the rhythms. A piece (or section of the piece) is assigned a time signature that tells the performer how many beats to expect in each measure, and what type of note should get one beat.
Conducting also depends on the meter of the piece; conductors use different conducting patterns for the different meters. These patterns emphasize the differences between the stronger and weaker beats to help the performers keep track of where they are in the music.
But the conducting patterns depend only on the pattern of strong and weak beats. In other words, they only depend on “how many beats there are in a measure”, not “what type of note gets a beat”. So even though the time signature is often called the “meter” of a piece, one can talk about meter without worrying about the time signature or even being able to read music. (Note that this means that children can be introduced to the concept of meter long before they are reading music.)
Classifying Meters
Meters can be classified by counting the number of beats from one strong beat to the next. For example, if the meter of the music feels like “strong-weak-strong-weak”, it is in duplemeter. “strong-weak-weak-strong-weak-weak” is triple meter, and “strong-weak-weak-weak” is quadruple. (Most people don’t bother classifying the more unusual meters, such as those with five beats in a measure.)
Meters can also be classified as either simple or compound. In a simple meter, each beat is basically divided into halves. In compound meters, each beat is divided into thirds.
A borrowed division occurs whenever the basic meter of a piece is interrupted by some beats that sound like they are “borrowed” from a different meter. One of the most common examples of this is the use of triplets to add some compound meter to a piece that is mostly in a simple meter.
Recognizing Meters
To learn to recognize meter, remember that (in most Western music) the beats and the subdivisions of beats are all equal and even. So you are basically listening for a running, even pulse underlying the rhythms of the music. For example, if it makes sense to count along with the music “ONE-and-Two-and-ONE-and-Two-and” (with all the syllables very evenly spaced) then you probably have a simple duple meter. But if it’s more comfortable to count “ONE-and-a-Two-and-a-ONE-and-a-Two-and-a”, it’s probably compound duple meter. (Make sure numbers always come on a pulse, and “one” always on the strongest pulse.)
This may take some practice if you’re not used to it, but it can be useful practice for anyone who is learning about music. To help you get started, the figure below sums up the most-used meters. To help give you an idea of what each meter should feel like, here are some animations (with sound) of duple simple , duple compound , triple simple , triple compound , quadruple simple , and quadruple compound meters. You may also want to listen to some examples of music that is in simple duple , simple triple , simple quadruple , compound duple , and compound triple meters.
Contributors and Attributions
- Authored by : Elliott Jones. Provided by : Santa Ana College. Located at : http://www.sac.edu . License : CC BY: Attribution
- Meter in Music. Authored by : Catherine Schmidt-Jones. Provided by : OpenStax. Located at : http://cnx.org/contents/bf5a39f8-1c52-41f4-910e-b82a8079e5e6@12/Meter_in_Music . License : CC BY: Attribution


5.1: Connection and Love Preview Questions
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As you read this chapter, consider the following questions:
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How are community and connection important to individuals? What theory best helps you understand this idea?
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How are kinship and family similar? Different?
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What are the factors contribute to Union Formation? Which ones have influenced you the most personally?
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In what ways does the government influence partnership, marriage, and break ups?
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How does societal stigma influence union formations?
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What are the issues related to equity when it comes to partnerships including marriage?
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If you were writing the laws and regulations around taxes and benefits related to union formations and kinship groups, what would they look like?


3.3: The Sources of Law
The primary function of substantive criminal law is to define crimes, including the associated punishment. The procedural criminal law sets the procedures for arrests, searches and seizures, and interrogations. In addition, it establishes the rules for conducting trials. Where does criminal law come from? In this module, we examine the foundations of law and focus on the rights of the accused.
Learn more about the sources of law in the US: sources of law .
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Common Law
The term common law can be disturbingly vague for the student. That is because different sources use it in several different ways with subtle differences in meaning. The best way to get a grasp on the term’s meaning is to understand a little of the history of the American legal system. Common law, which some sources refer to as judge-made law , first appeared when judges decided cases based on the legal customs of medieval England at the time. It may be hard for us to imagine today, but in the early days of English common law, the law was a matter of oral tradition. That is, the definitions of crimes and associated punishments were not written down in a way that gave them binding authority.
By the end of the medieval period, some of these cases were recorded in written form. Over a period, imported judicial decisions became recorded on a regular basis and collected into books called reporters. The English-speaking world is forever indebted to Sir William Blackstone, an English legal scholar, for collecting much of the common law tradition of England and committing it to paper in an organized way. His four-volume set, Commentaries on the Laws of England , was taken to the colonies by the founding fathers. The founding fathers incorporated the common law of England into the laws of the Colonies, and ultimately into the laws of the United States.
In modern America, most crimes are defined by statute. These statutory definitions use ideas and terms that come from the common law tradition. When judges take on the task of interpreting a statute, they still use common law principles for guidance. The definitions of many crimes, such as murder and arson, have not deviated much from their common law origin. Other crimes, such as rape, have seen sweeping changes.
One of the primary characteristics of the common law tradition is the importance of precedent. Known by the legal Latin phrase stare decisis , the doctrine of precedence means that once a court makes a decision on a particular matter, they are bound to rule the same way in future cases that have the same legal issue. This is important because a consistent ruling in identical factual situations means that everyone gets the same treatment by the courts. In other words, the doctrine of stare decisis ensures equal treatment under the law.
Constitution*
(*We will go into greater depth on the Constitutional Rights of the accused in Section 3.4)
When the founding fathers signed the Constitution, they all agreed that it would be the supreme law of the land; the Framers stated this profoundly important agreement in Article VI. After the landmark case of Marbury v. Madison (1803), the Supreme Court has had the power to strike down any law or any government action that violates constitutional principles. This precedent means that any law made by the Congress of the United States or the legislative assembly of any state that does not meet constitutional standards is subject to nullification by the Supreme Court of the United States.
Every state adopted this idea of constitutional supremacy when creating its constitutions. All state laws are subject to review by the high courts of those states. If state law or government practice (e.g., police, courts, or corrections) violates the constitutional law of that state, then it will be struck down by that state’s high court. Local laws are subject to similar scrutiny.
Statutory Law
Statutes are written laws passed by legislative assemblies. Modern criminal laws tend to be a matter of statutory law. In other words, most states and the federal government have moved away from the common-law definitions of crimes and established their own versions through the legislative process. Thus, most of the criminal law today is made by state legislatures, with the federal criminal law being made by Congress. Legislative assemblies tend to consider legislation as it is presented, not in subject order. This chronological ordering makes finding the law concerning a particular matter very difficult. To simplify finding the law, almost all statutes are organized by subject in a set of books called a code. The body of statutes that comprises the criminal law is often referred to as the criminal code, or less commonly as the penal code.
Administrative Law
The clear distinction between the executive, legislative, and judicial branches of government becomes blurry when U.S. government agencies and commissions are considered. These types of bureaucratic organizations can be referred to as semi-legislative and semi-judicial in character. These organizations have the power to make rules that have the force of law, the power to investigate violations of those laws, and the power to impose sanctions on those deemed to be in violation. Examples of such agencies are the Federal Trade Commission (FTC), the Internal Revenue Service (IRS), and the Environmental Protection Agency (EPA). When these agencies make rules that have the force of law, the rules are collectively referred to as administrative law.
Court Cases
When the appellate courts decide a legal issue, the doctrine of precedence means that future cases must follow that decision. This means that the holding in an appellate court case has the force of law. Such laws are often referred to as case law. The entire criminal justice community depends on the appellate courts, especially the Supreme Court, to evaluate and clarify both statutory laws and government practices against the requirements of the Constitution. These legal rules are all set down in court cases.
Learn more about what case law is and the processes of researching case law in this video: how to research case law .
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