18.12: Occurrence, Preparation, and Properties of Halogens
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Learning Objectives
By the end of this section, you will be able to:
- Describe the preparation, properties, and uses of halogens
- Describe the properties, preparation, and uses of halogen compounds
The elements in group 17 are the halogens. These are the elements fluorine, chlorine, bromine, iodine, and astatine. These elements are too reactive to occur freely in nature, but their compounds are widely distributed. Chlorides are the most abundant; although fluorides, bromides, and iodides are less common, they are reasonably available. In this section, we will examine the occurrence, preparation, and properties of halogens. Next, we will examine halogen compounds with the representative metals followed by an examination of the interhalogens. This section will conclude with some applications of halogens.
Occurrence and Preparation
All of the halogens occur in seawater as halide ions. The concentration of the chloride ion is 0.54 M ; that of the other halides is less than 10 –4 M . Fluoride also occurs in minerals such as CaF 2 , Ca(PO 4 ) 3 F, and Na 3 AlF 6 . Chloride also occurs in the Great Salt Lake and the Dead Sea, and in extensive salt beds that contain NaCl, KCl, or MgCl 2 . Part of the chlorine in your body is present as hydrochloric acid, which is a component of stomach acid. Bromine compounds occur in the Dead Sea and underground brines. Iodine compounds are found in small quantities in Chile saltpeter, underground brines, and sea kelp. Iodine is essential to the function of the thyroid gland.
The best sources of halogens (except iodine) are halide salts. It is possible to oxidize the halide ions to free diatomic halogen molecules by various methods, depending on the ease of oxidation of the halide ion. Fluoride is the most difficult to oxidize, whereas iodide is the easiest.
The major method for preparing fluorine is electrolytic oxidation. The most common electrolysis procedure is to use a molten mixture of potassium hydrogen fluoride, KHF 2 , and anhydrous hydrogen fluoride. Electrolysis causes HF to decompose, forming fluorine gas at the anode and hydrogen at the cathode. It is necessary to keep the two gases separated to prevent their explosive recombination to reform hydrogen fluoride.
Most commercial chlorine comes from the electrolysis of the chloride ion in aqueous solutions of sodium chloride; this is the chlor-alkali process discussed previously. Chlorine is also a product of the electrolytic production of metals such as sodium, calcium, and magnesium from their fused chlorides. It is also possible to prepare chlorine by the chemical oxidation of the chloride ion in acid solution with strong oxidizing agents such as manganese dioxide (MnO 2 ) or sodium dichromate (Na 2 Cr 2 O 7 ). The reaction with manganese dioxide is:
\[\ce{MnO_2(s) + 2 Cl^{-}(aq) + 4 H3O^{+}(aq) \longrightarrow Mn^{2+}(aq) + Cl_2(g) + 6 H2O(l)} \nonumber \]
The commercial preparation of bromine involves the oxidation of bromide ion by chlorine:
\[\ce{2 Br^{-}(aq) + Cl_2(g) \longrightarrow Br_2(l) + 2 Cl^{-}(aq)} \nonumber \]
Chlorine is a stronger oxidizing agent than bromine. This method is important for the production of essentially all domestic bromine.
Some iodine comes from the oxidation of iodine chloride, ICl, or iodic acid, HlO 3 . The commercial preparation of iodine utilizes the reduction of sodium iodate, NaIO 3 , an impurity in deposits of Chile saltpeter, with sodium hydrogen sulfite:
\[\ce{2 IO_3^{-}(aq) + 5 HSO_3^{-}(aq) \longrightarrow 3 HSO_4^{-}(aq) + 2 SO_4^{2-}(aq) + H2O(l) + I_2(s)} \nonumber \]
Properties of the Halogens
Fluorine is a pale yellow gas, chlorine is a greenish-yellow gas, bromine is a deep reddish-brown liquid, and iodine is a grayish-black crystalline solid. Liquid bromine has a high vapor pressure, and the reddish vapor is readily visible in Figure \(\PageIndex{1}\). Iodine crystals have a noticeable vapor pressure. When gently heated, these crystals sublime and form a beautiful deep violet vapor.
Bromine is only slightly soluble in water, but it is miscible in all proportions in less polar (or nonpolar) solvents such as chloroform, carbon tetrachloride, and carbon disulfide, forming solutions that vary from yellow to reddish-brown, depending on the concentration.
Iodine is soluble in chloroform, carbon tetrachloride, carbon disulfide, and many hydrocarbons, giving violet solutions of I 2 molecules. Iodine dissolves only slightly in water, giving brown solutions. It is quite soluble in aqueous solutions of iodides, with which it forms brown solutions. These brown solutions result because iodine molecules have empty valence d orbitals and can act as weak Lewis acids towards the iodide ion. The equation for the reversible reaction of iodine (Lewis acid) with the iodide ion (Lewis base) to form triiodide ion, is:
\[\ce{I_2(s) + I^{-}(aq) \longrightarrow I_3^{-}(aq)} \nonumber \]
The easier it is to oxidize the halide ion, the more difficult it is for the halogen to act as an oxidizing agent. Fluorine generally oxidizes an element to its highest oxidation state, whereas the heavier halogens may not. For example, when excess fluorine reacts with sulfur, SF 6 forms. Chlorine gives SCl 2 and bromine, S 2 Br 2 . Iodine does not react with sulfur.
Fluorine is the most powerful oxidizing agent of the known elements. It spontaneously oxidizes most other elements; therefore, the reverse reaction, the oxidation of fluorides, is very difficult to accomplish. Fluorine reacts directly and forms binary fluorides with all of the elements except the lighter noble gases (He, Ne, and Ar). Fluorine is such a strong oxidizing agent that many substances ignite on contact with it. Drops of water inflame in fluorine and form O 2 , OF 2 , H 2 O 2 , O 3 , and HF. Wood and asbestos ignite and burn in fluorine gas. Most hot metals burn vigorously in fluorine. However, it is possible to handle fluorine in copper, iron, or nickel containers because an adherent film of the fluoride salt passivates their surfaces. Fluorine is the only element that reacts directly with the noble gas xenon.
Although it is a strong oxidizing agent, chlorine is less active than fluorine. Mixing chlorine and hydrogen in the dark makes the reaction between them to be imperceptibly slow. Exposure of the mixture to light causes the two to react explosively. Chlorine is also less active towards metals than fluorine, and oxidation reactions usually require higher temperatures. Molten sodium ignites in chlorine. Chlorine attacks most nonmetals (C, N 2 , and O 2 are notable exceptions), forming covalent molecular compounds. Chlorine generally reacts with compounds that contain only carbon and hydrogen (hydrocarbons) by adding to multiple bonds or by substitution.
In cold water, chlorine undergoes a disproportionation reaction:
\[\ce{Cl_2(aq) + 2 H2O(l) \longrightarrow HOCl(aq) + H3O^{+}(aq) + Cl^{-}(aq)} \nonumber \]
Half the chlorine atoms oxidize to the 1+ oxidation state (hypochlorous acid), and the other half reduce to the 1− oxidation state (chloride ion). This disproportionation is incomplete, so chlorine water is an equilibrium mixture of chlorine molecules, hypochlorous acid molecules, hydronium ions, and chloride ions. When exposed to light, this solution undergoes a photochemical decomposition:
\[\ce{2 HOCl(aq) + 2 H2O(l) ->[\text{sunlight}] 2 H3O^{+}(aq) + 2 Cl^{-}(aq) + O2(g)} \nonumber \]
The nonmetal chlorine is more electronegative than any other element except fluorine, oxygen, and nitrogen. In general, very electronegative elements are good oxidizing agents; therefore, we would expect elemental chlorine to oxidize all of the other elements except for these three (and the nonreactive noble gases). Its oxidizing property, in fact, is responsible for its principal use. For example, phosphorus(V) chloride, an important intermediate in the preparation of insecticides and chemical weapons, is manufactured by oxidizing the phosphorus with chlorine:
\[\ce{P_4(s) + 10 Cl_2(g) \longrightarrow 4 PCl_5(l)} \nonumber \]
A great deal of chlorine is also used to oxidize, and thus to destroy, organic or biological materials in water purification and in bleaching.
The chemical properties of bromine are similar to those of chlorine, although bromine is the weaker oxidizing agent and its reactivity is less than that of chlorine.
Iodine is the least reactive of the halogens. It is the weakest oxidizing agent, and the iodide ion is the most easily oxidized halide ion. Iodine reacts with metals, but heating is often required. It does not oxidize other halide ions.
Compared with the other halogens, iodine reacts only slightly with water. Traces of iodine in water react with a mixture of starch and iodide ion, forming a deep blue color. This reaction is a very sensitive test for the presence of iodine in water.
Halides of the Representative Metals
Thousands of salts of the representative metals have been prepared. The binary halides are an important subclass of salts. A salt is an ionic compound composed of cations and anions, other than hydroxide or oxide ions. In general, it is possible to prepare these salts from the metals or from oxides, hydroxides, or carbonates. We will illustrate the general types of reactions for preparing salts through reactions used to prepare binary halides.
The binary compounds of a metal with the halogens are the halides . Most binary halides are ionic. However, mercury, the elements of group 13 with oxidation states of 3+, tin(IV), and lead(IV) form covalent binary halides.
The direct reaction of a metal and a halogen produce the halide of the metal. Examples of these oxidation-reduction reactions include:
\[\begin{align*}
\ce{Cd(s) + Cl_2(g) & \longrightarrow CdCl_2(s)} \\[4pt][4pt]
\ce{2 Ga(l) + 3 Br_2(l) & \longrightarrow 2 GaBr_3(s)}
\end{align*} \]
Link to Learning
Reactions of the alkali metals with elemental halogens are very exothermic and often quite violent. Under controlled conditions, they provide exciting demonstrations for budding students of chemistry. You can view the initial heating of the sodium that removes the coating of sodium hydroxide, sodium peroxide, and residual mineral oil to expose the reactive surface. The reaction with chlorine gas then proceeds very nicely.
If a metal can exhibit two oxidation states, it may be necessary to control the stoichiometry in order to obtain the halide with the lower oxidation state. For example, preparation of tin(II) chloride requires a 1:1 ratio of Sn to Cl 2 , whereas preparation of tin(IV) chloride requires a 1:2 ratio:
\[\begin{align*}
\ce{Sn(s) + Cl_2(g) &\longrightarrow SnCl_2(s) }\\[4pt][4pt]
\ce{Sn(s) + 2 Cl_2(g) &\longrightarrow SnCl_4(l)}
\end{align*} \]
The active representative metals—those that are easier to oxidize than hydrogen—react with gaseous hydrogen halides to produce metal halides and hydrogen. The reaction of zinc with hydrogen fluoride is:
\[\ce{Zn(s) + 2 HF(g) \longrightarrow ZnF_2(s) + H_2(g)} \nonumber \]
The active representative metals also react with solutions of hydrogen halides to form hydrogen and solutions of the corresponding halides. Examples of such reactions include:
\[\begin{align*}
\ce{Cd(s) + 2 HBr(aq) &\longrightarrow CdBr_2(aq) + H_2(g)} \\[4pt][4pt]
\ce{Sn(s) + 2 HI(aq) &\longrightarrow SnI_2(aq) + H_2(g)}
\end{align*} \]
Hydroxides, carbonates, and some oxides react with solutions of the hydrogen halides to form solutions of halide salts. It is possible to prepare additional salts by the reaction of these hydroxides, carbonates, and oxides with aqueous solution of other acids:
\[\begin{align*}
\ce{CaCo_3(s) + 2 HCl(aq) &\longrightarrow CaCl_2(aq) + CO_2(g) + H2O(l)} \\[4pt][4pt]
\ce{TlOH(aq) + HF(aq) &\longrightarrow TlF(aq) + H2O(l)}
\end{align*} \]
A few halides and many of the other salts of the representative metals are insoluble. It is possible to prepare these soluble salts by metathesis reactions that occur when solutions of soluble salts are mixed (see Figure \(\PageIndex{2}\)). Metathesis reactions are examined in the chapter on the stoichiometry of chemical reactions.
Several halides occur in large quantities in nature. The ocean and underground brines contain many halides. For example, magnesium chloride in the ocean is the source of magnesium ions used in the production of magnesium. Large underground deposits of sodium chloride, like the salt mine shown in Figure \(\PageIndex{3}\), occur in many parts of the world. These deposits serve as the source of sodium and chlorine in almost all other compounds containing these elements. The chlor-alkali process is one example.
Interhalogens
Compounds formed from two or more different halogens are interhalogens . Interhalogen molecules consist of one atom of the heavier halogen bonded by single bonds to an odd number of atoms of the lighter halogen. The structures of IF 3 , IF 5 , and IF 7 are illustrated in Figure \(\PageIndex{4}\). Formulas for other interhalogens, each of which comes from the reaction of the respective halogens, are in Table \(\PageIndex{1}\).
Note from Table \(\PageIndex{1}\) that fluorine is able to oxidize iodine to its maximum oxidation state, 7+, whereas bromine and chlorine, which are more difficult to oxidize, achieve only the 5+-oxidation state. A 7+-oxidation state is the limit for the halogens. Because smaller halogens are grouped about a larger one, the maximum number of smaller atoms possible increases as the radius of the larger atom increases. Many of these compounds are unstable, and most are extremely reactive. The interhalogens react like their component halides; halogen fluorides, for example, are stronger oxidizing agents than are halogen chlorides.
The ionic polyhalides of the alkali metals, such as KI 3 , KICl 2 , KICl 4 , CsIBr 2 , and CsBrCl 2 , which contain an anion composed of at least three halogen atoms, are closely related to the interhalogens. As seen previously, the formation of the polyhalide \(\ce{I3^{-}}\) anion is responsible for the solubility of iodine in aqueous solutions containing an iodide ion.
| YX | YX 3 | YX 5 | YX 7 |
|---|---|---|---|
| ClF( g ) | ClF 3 ( g ) | ClF 5 ( g ) | |
| BrF( g ) | BrF 3 ( l ) | BrF 5 ( l ) | |
| BrCl( g ) | |||
| IF( s ) | IF 3 ( s ) | IF 5 ( l ) | IF 7 ( g ) |
| ICl( l ) | ICl 3 ( s ) | ||
| IBr( s ) |
Applications
The fluoride ion and fluorine compounds have many important uses. Compounds of carbon, hydrogen, and fluorine are replacing Freons (compounds of carbon, chlorine, and fluorine) as refrigerants. Teflon is a polymer composed of –CF 2 CF 2 – units. Fluoride ion is added to water supplies and to some toothpastes as SnF 2 or NaF to fight tooth decay. Fluoride partially converts teeth from Ca 5 (PO 4 ) 3 (OH) into Ca 5 (PO 4 ) 3 F.
Chlorine is important to bleach wood pulp and cotton cloth. The chlorine reacts with water to form hypochlorous acid, which oxidizes colored substances to colorless ones. Large quantities of chlorine are important in chlorinating hydrocarbons (replacing hydrogen with chlorine) to produce compounds such as tetrachloride (CCl 4 ), chloroform (CHCl 3 ), and ethyl chloride (C 2 H 5 Cl), and in the production of polyvinyl chloride (PVC) and other polymers. Chlorine is also important to kill the bacteria in community water supplies.
Bromine is important in the production of certain dyes, and sodium and potassium bromides are used as sedatives. At one time, light-sensitive silver bromide was a component of photographic film.
Iodine in alcohol solution with potassium iodide is an antiseptic (tincture of iodine). Iodide salts are essential for the proper functioning of the thyroid gland; an iodine deficiency may lead to the development of a goiter. Iodized table salt contains 0.023% potassium iodide. Silver iodide is useful in the seeding of clouds to induce rain; it was important in the production of photographic film and iodoform, CHI 3 , is an antiseptic.


1.2: Olmec (1500 BCE – 400 BCE)
As with most other civilizations, the Olmec civilization began where there was water, establishing their location on the alluvial fan of the Coatzacoalcos River basin. The Olmec’s erected three large sites around 900 BCE, La Venta, the largest and most prominent. La Venta became the center of Olmec culture, and they developed a government, traded with other locations and established religion, and became one of the first significant cultures in Mesoamerica.
The grand earthen truncated mound (4.33) was the most massive structure on the Mesoamerican peninsula, rising over 34 meters from the natural level countryside and the center of the city. Researchers initially believed the pyramid was built rounded to reflect the local mountains; however, using modern research tools, the pyramid was rectangular with stepped sides and eroded by time. There are several other pyramid-shaped mounds situated in clusters for over one mile. In the same area, archaeologists found multiple elaborate tombs and the ornate, oversized mosaics (4.34) made from large blocks of serpentine rock, buried under several feet of soil.
The Olmecs were the first people in Mesoamerica to create the massive stone monuments found on Mexico’s southern Gulf Coast. Eighty stone monuments found at La Venta, including seventeen of the famous monumental carved stone heads. These giant heads (4.35) carved from the large basalt boulders with facial features resembling the people of the community. The heads all have helmets or ball caps and may represent the idolization of the ball game the Olmec played. The heads are roughly 2.80 meters high and 2.15 meters wide and carved from basalt. The quarry for basalt rock was in the mountains over eighty kilometers from La Venta, and it is still unknown how the Olmec moved the massive stones and then carved them with small hand tools. The Olmec also carved smaller figures, believed to be for ritual ceremonies, either from granite or jadeite, a blue-green colored and highly valued stone.
Seven altars made from basalt found at La Venta, are approximately 2 meters high and 4 meters wide in size. Altar 4 (4.36) has a person or deity located just inside a cave-like structure holding a large rope wrapped entirely around the base. The altar has carved fans, eyes, and shows a person sitting in the mouth of a creature. La Venta was the capital of the Olmec people based on the sheer number of artifacts uncovered at the complex. It was a system of control by the hierarchy of a king or priest. No known written language exists from the Olmec; however, there are some glyphs arranged in 21 columns on a stone excavated from a river bed, which gave researchers clues into their culture.


4.3: Public Policies on Including Children with Special Needs
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- Gina Peterson and Emily Elam
- College of the Canyons
Public Policies on Including Children with Special Needs
Throughout the past 40 years there have been some significant changes in both state and federal laws, as well as with public policy and social attitudes towards integrating children with special needs and learning disabilities into typical classroom settings. Stigmas from the past have dissipated and more inclusive practices are in place. In addition to Federal laws such as the Individuals with Disabilities Act (IDEA) and the Americans with Disabilities Act (ADA), there are national associations such as the Division for Early Childhood (DEC) and the National Association for the Education of Young Children (NAEYC) who rally to protect the rights of children with disabilities or other special needs. As stated in their joint position on inclusion, the DEC and NAEYC believe:
Early childhood inclusion embodies the values, policies, and practices that support the right of every infant and young child and his or her family, regardless of ability, to participate in a broad range of activities and contexts as full members of families, communities, and society. The desired results of inclusive experiences for children with and without disabilities and their families include a sense of belonging and membership, positive social relationships and friendships, and development and learning to reach their full potential. The defining features of inclusion that can be used to identify high quality early childhood programs and services are access, participation, and supports. (p. 141; DEC and NAEYC 2009, 1)
When early caregivers and preschool teachers practice monitoring as part of their regular routines, they demonstrate accountability and responsive caregiving. Nearly 65% of children are identified as having a special need, disability, delay or impairment, and will require some special services or intervention. As early educators our role is twofold:
- Provide an environment where children feel safe, secure and cared for
- Help children develop coping skills to decrease stress and promote learning and development
Individualized Education Plan?
Some children may need more individualized support and might benefit from specialized services or individualized accommodations. Children who are over the age of 3 who qualify for special education must have an individualized education program (IEP) in place. As required by both federal and state laws, IEPs must have clearly identified goals and objectives that can be regularly monitored. IEPs are designed by a TEAM that usually includes the child’s parents or guardians, the preschool teacher, special education professionals (e.g. behaviorists, speech pathologists, occupational therapists). Together the team plans appropriately accommodations, modifications and makes recommendations that will help the child meet their developmental goals.
While everyone on the team has a role, the teacher’s role is to integrate approaches that can best support the child while in class. For example, if the IEP notes that the child needs support with language development, the teacher would consider finding someone in class who could provide peer to peer scaffolding. The teacher would want to find someone who has strong language skills, and who is cooperative and kind to others. She would then partner the two children up throughout the day so that the typical child could model ideal language skills to the child with the IEP. The teacher would also provide regular updates to parents, continue observing and monitoring the child’s development, and would provide access to alternative resources and materials as much as possible. [47]
Creating Inclusive Learning Environments
To ensure that all children feel safe, secure and nurtured, teachers must strive to create a climate of cooperation, mutual respect and tolerance. To support healthy development, teachers must offer multiple opportunities for children to absorb learning experiences, as well as process information, at their own pace. While one child may be comfortable with simple verbal instructions to complete a particular task, another child may benefit from a more direct approach such as watching another child or adult complete the requested task first. Teachers who are devoted to observing their children are motivated to provide experiences that children will enjoy and be challenged by. The classroom is not a stagnant environment - it is ever-changing. In order to maintain a high-quality classroom setting, it is essential to utilize your daily observations of children and the environment to monitor the experiences and interactions to ensure there is a good fit. [48]


1.8: States Shifting Focus from Incarceration to Rehabilitation
As the prison populations continued to climb through the decades, more and more states are looking for ways to ease the population. The current direction many states are taking is to release “non-violent” offenders and provide rehabilitation services. In this section we review the practice and policy of offender rehabilitation. Rehabilitation programs are nothing new, this idea, once called the medical model dates back to the 1940’s and seeks to treat criminal behavior through treatment as opposed to punishment and incarceration. It lost favor in the 1970’s when correctional professionals determined rehabilitation didn’t work. However, significant research into criminal behavior and new assessment tools have led to a renewal of interest in this method of dealing with crime.
Rehabilitation Programs
Rehabilitation programs are nothing new to the criminal justice system. For many decades we have been providing substance abuse treatment programs, drug diversion programs, domestic violence and DUI treatment programs to deal with illegal behavior with varying success. However, as states have tried to address the overcrowding in jails and prisons, they have tried to apply more treatment programs to what they call “non-violent” offenders. Often this “non-violent” classification addresses drug offenders and offenders convicted of property offenses.
As previously indicated, The State of California passed legislation - AB 109 Realignment - that transferred the incarceration and supervision of these offenders out of state control (prison/parole) to local (jail/probation) control. The theory behind this transition was that local government could provide better treatment options to this non-violent offender and maintain public safety. The State awards local governments funding based on their treatment options and success in reducing recidivism. However, the State also required that the programs met specific goals and the agencies had to adopt “evidence-based” practices to be compliant with to receive funding.
Evidence-Base Practices
According to the National Institute of Corrections, the definition of evidence-based practices is as following:
Evidence-based practice (EBP) is the objective, balanced, and responsible use of current research and the best available data to guide policy and practice decisions, such that outcomes for consumers are improved. Used originally in the health care and social science fields, evidence-based practice focuses on approaches demonstrated to be effective through empirical research rather than through anecdote or professional experience alone.
An evidence-based approach involves an ongoing, critical review of research literature to determine what information is credible, and what policies and practices would be most effective given the best available evidence. It also involves rigorous quality assurance and evaluation to ensure that evidence-based practices are replicated with fidelity, and that new practices are evaluated to determine their effectiveness.
In contrast to the terms "best practices" and "what works," evidence-based practice implies that 1) there is a definable outcome(s); 2) it is measurable; and 3) it is defined according to practical realities (recidivism, victim satisfaction, etc.). Thus, while these three terms are often used interchangeably, EBP is more appropriate for outcome-focused human service disciplines.
This shift in theory drastically changed the way in which correctional facilities and community correction officers managed the treatment of offenders. These agencies were now required to not only state they were making an impact through statistical date, but also needed to provide programs which could also show positive influence on offender behavior. New ways of assessing offenders’ risk to reoffend and determination of criminogenic needs were needed. These tools allow officers to not only use their “professional judgement,” but a validated tool that could provide scientific support to the likelihood and offender would reoffend. These tools also allowed officers to identify those offenders who were at the highest risk to reoffend. Officers could then focus attention (supervision/public safety) and support towards those offenders while allowing moderate and low risk offenders to be placed in more appropriate treatment.
Risk Assessments Tools and Criminogenic Needs
The ability to predict the likelihood to reoffend and determine an offender’s criminogenic needs is important to provide officers and offenders with the appropriate treatment plan. By identifying the offenders who need the most intensive supervision, agencies can allocate the resources to those high-risk individuals. This means officer can provide a higher level of supervision to the right classification of offender. It also allows means officers with these high-risk offenders have lower caseloads. Research indicates that officers who supervise high risk offenders should be in the range of 30-50 offenders. The next step in the process is to conduct detail comprehensive interviews with the offender to identify the specific criminogenic needs of the offender and prepare a case plan. This case plan is shared with the offender, so he become part of his/her rehabilitation. Offenders are not always willing to participate with treatment and this can cause delay in treatment and may require to be returned to custody.
Another important aspect of this approach is that by identify each offender’s risk to reoffend we avoid mixing the population of offenders. For example, high-risk offenders are generally more criminally sophisticated the low or moderate offenders. If we integrate all offenders in similar treatment programs we run the risk of affecting or influencing low/moderate offender with higher risk offenders thereby increasing their risk to reoffend. The higher-risk offenders could negatively influence low/moderate risk offenders when they interact. Significant amount of research indicate low/moderate risk will often complete community supervision with limited contact with supervision officers.


12.0: Introduction
In this chapter, you will learn the fundamental skills needed to work with graphs used in an area of mathematics known as graph theory. You can think of these graphs as a kind of map. Maps have served many purposes over the course of history. You probably use GPS maps to navigate to various destinations. A scientist from ancient Greece named Ptolemy wanted an accurate map of the world to make more accurate astrological predications. In recent years, neurobiologists have mapped the cerebral cortex to better understand the human brain. Social network analysts map online interactions to assist advertisers in reaching target audiences. Like other maps, the graphs you will study in this chapter can serve many purposes, but they do not have a lot of the details you might expect in a map such as size, shape, and distance between objects. All of that is stripped away so that we can focus on one element of maps, the connections between objects.


15.8G: Pathogenic Escherichia coli
- Distinguish between the different types of pathogenic E. coli in regards to classification and mode of transmission
Escherichia coli (E. coli) is a Gram-negative, rod-shaped bacterium that is commonly found in the lower intestine of warm-blooded organisms (endotherms). Most E. coli strains are harmless, but some serotypes are pathogenic and can cause serious food poisoning in humans and other species. The harmless strains are part of the normal flora of the gut, and can benefit their hosts by producing vitamin K2, and by preventing the establishment of pathogenic bacteria within the intestine.
Pathogenic E. coli
Pathogenic E. coli strains can be categorized based on elements that can elicit an immune response in animals, namely: O antigen, K antigen, H antigen, and F antigen in the lipopolysaccharide (LPS) molecules found in the outer membrane of the E. coli cell. The O antigen is a polymer of immunogenic repeating oligosaccharides which is used for serotyping E.coli. It should be noted though that antibodies towards several O antigens cross-react with other O antigens and partially to K antigens not only from E. coli, but also from other Escherichia species and Enterobacteriaceae species. There are two separate groups of K-antigen groups, named group I and group II (while a small in-between subset (K3, K10, and K54/K96) has been classified as group III). Group I consists of 100 kDa (large) capsular polysaccharides, while those in Group II, associated with extraintestinal diseases, are under 50 kDa in size.
In humans and in domestic animals, virulent strains of E. coli can cause various diseases. In humans, gastroenteritis, urinary tract infections, and neonatal meningitis can occur. In rarer cases, virulent strains are also responsible for haemolytic-uremic syndrome, peritonitis, mastitis, septicemia, and Gram-negative pneumonia. Certain strains of E. coli produce potentially lethal toxins. Food poisoning caused by E. coli can result from eating unwashed vegetables or undercooked meat. If E. coli bacteria escape the intestinal tract through a perforation (for example from an ulcer, a ruptured appendix, or due to a surgical error) and enter the abdomen, they usually cause peritonitis that can be fatal without prompt treatment.
Transmission of pathogenic E. coli often occurs via fecal–oral transmission. Common routes of transmission include unhygienic food preparation, farm contamination due to manure fertilization, irrigation of crops with contaminated greywater or raw sewage, feral pigs on cropland, or direct consumption of sewage-contaminated water. According to the U.S. Food and Drug Administration, the fecal-oral cycle of transmission can be disrupted by cooking food properly, preventing cross-contamination, instituting barriers such as gloves for food workers, instituting health care policies so food industry employees seek treatment when they are ill, pasteurization of juice or dairy products and proper hand washing requirements.
Uropathogenic E. coli
Uropathogenic E. coli (UPEC) is responsible for approximately 90% of urinary tract infections (UTI) seen in individuals with ordinary anatomy. In ascending infections, fecal bacteria colonize the urethra and spread up the urinary tract to the bladder, as well as to the kidneys (causing pyelonephritis), or the prostate in males. Because women have a shorter urethra than men, they are 14 times more likely to suffer from an ascending UTI. Uropathogenic E. coli use P fimbriae (pyelonephritis-associated pili) to bind urinary tract endothelial cells and colonize the bladder. UPEC can evade the body’s innate immune defences (e.g. the complement system) by invading superficial umbrella cells to form intracellular bacterial communities (IBCs). They also have the ability to form K antigen, capsular polysaccharides that contribute to biofilm formation. Descending infections in turn, though relatively rare, occur when E. coli cells enter the upper urinary tract organs (kidneys, bladder or ureters) from the blood stream.
E. coli and Meningitis
Neonatal meningitis is produced by a serotype of E. coli that contains a capsular antigen called K1. The colonization of the newborn’s intestines with these stems, that are present in the mother’s vagina, lead to bacteraemia, which leads to meningitis. Severe meningitis in the neonates are caused because of the absence of the IgM antibodies from the mother (these do not cross the placenta because FcRn only mediates the transfer of IgG), plus the fact that the body recognizes as self the K1 antigen, as it resembles the cerebral glicopeptides. In stool samples, microscopy will show Gram-negative rods, with no particular cell arrangement.
Treating E. coli
Bacterial infections are usually treated with antibiotics. However, the antibiotic sensitivities of different strains of E. coli vary widely. As Gram-negative organisms, E. coli are resistant to many antibiotics that are effective against Gram-positive organisms. Antibiotics which may be used to treat E. coli infection include amoxicillin, as well as other semisynthetic penicillins, many cephalosporins, carbapenems, aztreonam, trimethoprim-sulfamethoxazole, ciprofloxacin, nitrofurantoin, and the aminoglycosides. Researchers have actively been working to develop safe, effective vaccines to lower the worldwide incidence of E. coli infection.
Key Points
- Pathogenic E. coli strains can be categorized based on elements that can elicit an immune response in animals. The different categories are: O antigen, K antigen, H antigen, and F antigen in the lipopolysaccharide.
- In humans and in domestic animals, virulent strains of E. coli can cause gastroenteritis, urinary tract infections, and neonatal meningitis.
- Bacterial infections are usually treated with antibiotics.
Key Terms
- bacteraemia : The medical condition of having bacteria in the bloodstream.
- lipopolysaccharide : any of a large class of lipids conjugated with polysaccharides
- flora : the microorganisms that inhabit some part of the body, such as intestinal flora
- enterohemorrhagic E. coli : strains of the bacterium Escherichia coli that, when infecting humans, have been linked with the severe complication hemolytic-uremic syndrome


10.4: §71. The Perfect Participle Base suffix -IO as Abstract Noun
Of all ways to create abstract nouns from Latin verbs, the overwhelming favourite was the addition of the suffix -io to the perfect participle base (or less commonly to the present infinitive base). For example, from dicere , dictus (“speak”), Latin could create an abstract noun dict-io , dict-ionis , which meant “speech” (or “the act of speech,” “the process of speaking,” etc.). Notice that this is a perfectly regular 3rd declension noun, whose base is diction- . Here, then, is the explanation for all those -ion derivatives that we noticed in the last chapter. Historically, English forms in -ion can be traced back through Old French to medieval accusative forms like dictionem , which were prevalent in vulgar Latin at a time when the nominative forms had all but disappeared. For practical purposes, however, we can equate the English -ion spelling with the BASE form of Latin nouns in -io , -ionis. [1] This is a valid historical approach, because the majority of the -ion forms came into Modern English after the Renaissance, drawn directly from Latin nouns on the analogy of the older -ion derivatives. New examples are still being coined today.
To the student of English vocabulary, this circumstance is nothing less than a godsend. Although you may never have stopped to think how many -ion nouns there are in our language, you can be sure that there are enough to keep you counting for hours on end. Almost without exception ( ex-cept-io ), they will have a Latin derivation ( de-rivat-io ), and that knowledge should be reason [2] for great satisfaction ( satis-fact-io )—perhaps even be an occasion ( oc-cas-io ) for exultation ( ex-sultat-io ). There can be few aspects of English etymology that are more dependable: virtually every -ion noun that you meet can now send you scurrying in search of a Latin perfect participle, whose meaning is almost guaranteed to unlock the semantic secrets of that English noun.
If you want to test that assertion ( ad-sert-io ), you can take another quick tour of the Latin verbs on Tables 9.1 , 9.2 , 9.3 , and 9.4 , applying the -ion test to the perfect participles. What you will now be uncovering is a series of Latin 3rd declension abstract nouns in -io , -ionis , probably the largest single category of Latin derivatives in English.
-
This
-ion
noun base may be further extended in Latin forms like
diction-arium
, E
dictionary
, “a place for words.” (There was also a medieval Latin expression,
liber dictionarius
, “word-book.”) ↵
-
Reason
is a word which has lost its
-ion
in the French
transmission
(<
trans-missio
, “a sending across”). The doublets
reason
and
ration
are both derived from
ratio
, a noun formed from the past participle of
reri
,
ratus
(“think”). Similar doublets are
fashion
(Fr.
façon
) and
faction
, both from
factio
. ↵


4.2: Estimating Rates using Independent Contrasts
The information required to estimate evolutionary rates is efficiently summarized in the early (but still useful) phylogenetic comparative method of independent contrasts (Felsenstein 1985) . Independent contrasts summarize the amount of character change across each node in the tree, and can be used to estimate the rate of character change across a phylogeny. There is also a simple mathematical relationship between contrasts and maximum-likelihood rate estimates that I will discuss below.
We can understand the basic idea behind independent contrasts if we think about the branches in the phylogenetic tree as the historical “pathways” of evolution. Each branch on the tree represents a lineage that was alive at some time in the history of the Earth, and during that time experienced some amount of evolutionary change. We can imagine trying to measure that change initially by comparing sister taxa. We can compare the trait values of the two sister taxa by finding the difference in their trait values, and then compare that to the total amount of time they have had to evolve that difference. By doing this for all sister taxa in the tree, we will get an estimate of the average rate of character evolution ( 4.1A). But what about deeper nodes in the tree? We could use other non-sister species pairs, but then we would be counting some branches in the tree of life more than once (Figure 4.1B). Instead, we use a “pruning algorithm,” (Felsenstein 1985, Felsenstein (2004) ) chopping off pairs of sister taxa to create a smaller tree (Figure 4.1C). Eventually, all of the nodes in the tree will be trimmed off – and the algorithm will finish. Independent contrasts provides a way to generalize the approach of comparing sister taxa so that we can quantify the rate of evolution throughout the whole tree.
A more precise algorithm describing how Phylogenetic Independent Contrasts (PICs) are calculated is provided in Box 4.2, below (from Felsenstein 1985) . Each contrast can be described as an estimate of the direction and amount of evolutionary change across the nodes in the tree. PICs are calculated from the tips of the tree towards the root, as differences between trait values at the tips of the tree and/or calculated average values at internal nodes. The differences themselves are sometimes called “raw contrasts” (Felsenstein 1985) . These raw contrasts will all be statistically independent of each other under a wide range of evolutionary models. In fact, as long as each lineage in a phylogenetic tree evolves independently of every other lineage, regardless of the evolutionary model, the raw contrasts will be independent of each other. However, people almost never use raw contrasts because they are not identically distributed; each raw contrast has a different expected distribution that depends on the model of evolution and the branch lengths of the tree. In particular, under Brownian motion we expect more change on longer branches of the tree. Felsenstein (1985) divided the raw contrasts by their expected standard deviation under a Brownian motion model, resulting in standardized contrasts. These standardized contrasts are, under a BM model, both independent and identically distributed, and can be used in a variety of statistical tests. Note that we must assume a Brownian motion model in order to standardize the contrasts; results derived from the contrasts, then, depend on this Brownian motion assumption.
Box 4.2: Algorithm for Phylogenetic Independent Contrasts
One can calculate PICs using the algorithm from Felsenstein (1985) . I reproduce this algorithm below. Keep in mind that this is an iterative algorithm – you repeat the five steps below once for each contrast, or n − 1 times over the whole tree (see Figure 4.1C as an example).
-
Find two tips on the phylogeny that are adjacent (say nodes
i
and
j
) and have a common ancestor, say node
k
. Note that the choice of which node is
i
and which is
j
is arbitrary. As you will see, we will have to account for this “arbitrary direction” property of PICs in any analyses where we use them to do certian analyses!
- Compute the raw contrast, the difference between their two tip values:\[c_{ij} = x_i − x_j \label{4.1}\]
- Under a Brownian motion model, c i j has expectation zero and variance proportional to v i + v j .
- Calculate the standardized contrast by dividing the raw contrast by its variance \[ s_{ij} = \frac {c_{ij}}{v_i + v_j} = \ frac {x_i - x_j}{v_i + v_j} \label{4.2} \[
- Under a Brownian motion model, this contrast follows a normal distribution with mean zero and variance equal to the Brownian motion rate parameter σ 2 .
-
Remove the two tips from the tree, leaving behind only the ancestor k, which now becomes a tip. Assign it the character value: \[ x_k = \frac
{(1/v_i)x_i+(1/v_j)x_j}{1/v_1+1/v_j} \label{4.3}
\[
- It is worth noting that x k is a weighted average of x i and x j , but does not represent an ancestral state reconstruction, since the value is only influenced by species that descend directly from that node and not other relatives.
- Lengthen the branch below node k by increasing its length from v k to v k + v i v j /( v i + v j ). This accounts for the uncertainty in assigning a value to x k .
As mentioned above, we can apply the algorithm of independent contrasts to learn something about rates of body size evolution in mammals. We have a phylogenetic tree with branch lengths as well as body mass estimates for 49 species (Figure 4.2). If we ln-transform mass and then apply the method above to our data on mammal body size, we obtain a set of 48 standardized contrasts. A histogram of these contrasts is shown as Figure 4.2 (data from from Garland 1992) .
Figure 4.2. Histogram of PICs for ln-transformed mammal body mass on a phylogenetic tree with branch lengths in millions of years (data from Garland 1992) . Image by the author, can be reused under a CC-BY-4.0 license.
Note that each contrast is an amount of change, x i − x j , divided by a branch length, v i + v j , which is a measure of time. Thus, PICs from a single trait can be used to estimate σ 2 , the rate of evolution under a Brownian model. The PIC estimate of the evolutionary rate is:
\[ \hat{\sigma}_{PIC}^2 = \frac{\sum{s_{ij}^2}}{n-1} \label{4.4}\]
That is, the PIC estimate of the evolutionary rate is the average of the n − 1 squared contrasts. This sum is taken over all s i j , the standardized independent contrast across all ( i , j ) pairs of sister branches in the phylogenetic tree. For a fully bifurcating tree with n tips, there are exactly n − 1 such pairs. If you are statistically savvy, you might note that this formula looks a bit like a variance. In fact, if we state that the contrasts have a mean of 0 (which they must because Brownian motion has no overall trends), then this is a formula to estimate the variance of the contrasts.
If we calculate the mean sum of squared contrasts for the mammal body mass data, we obtain a rate estimate of $\hat{\sigma}_{PIC}^2$ = 0.09. We can put this into words: if we simulated mammalian body mass evolution under this model, we would expect the variance across replicated runs to increase by 0.09 per million years. Or, in more concrete terms, if we think about two lineages diverging from one another for a million years, we can draw changes in ln-body mass for both of them from a normal distribution with a variance of 0.09. Their difference, then, which is the amount of expected divergence, will be normal with a variance of 2 ⋅ 0.09 = 0.18. Thus, with 95% confidence, we can expect the two species to differ maximally by two standard deviations of this distribution, $2 \cdot \sqrt{0.18} = 0.85$. Since we are on a log scale, this amount of change corresponds to a factor of e 2.68 = 2.3, meaning that one species will commonly be about twice as large (or small) as the other after just one million years.


2.6: Overview of the Criminal Procedure
Every state and the federal government also has its own criminal procedural rules. The Federal Rules of Criminal Procedure are written by judicial advisory committees and promulgated by the Supreme Court, subject to amendment by Congress. State criminal procedural rules are usually defined by the state legislatures. Of the 23 separate rights noted in the first eight amendments to the Constitution, 12 concern criminal procedure. Before World War II, these rights were held only to protect the individual against the federal government. Since World War II, practically all of these rights have been incorporated through the Fourteenth Amendment’s due process clause and applied to state law enforcement as well. The federal Constitution sets a floor, not a ceiling, on the rights of the citizenry against police, prosecutors, courts, and prison officials. The states may grant more rights to criminal defendants. For example, states such as New York are substantially more protective of the rights of criminal suspects and criminal defendants than is the U.S. Supreme Court.
In American legal parlance, criminal procedure refers to the constitutional, statutory, and administrative limitations on police investigations—searches of persons, places, and things; seizures and interrogations—as well as to the formal steps of the criminal process. Both the Fourth and Fifth Amendments protect the citizenry, not just criminals and criminal suspects, from over-reaching police activity.
Due Process
The Fifth Amendment's due process clause, among other rights, guarantees a presumption of innocence. The government must prove guilt beyond a reasonable doubt. Fifth Amendment “due process,” confers on defendants a broad array of protections and rights. The amendment also protects defendants against double jeopardy (being tried more than once for the same crime by the same authority), and against being required to testify against themselves in criminal cases.
Right to Counsel
The Sixth Amendment guarantees defendants a “speedy and public trial by an impartial jury of the state and district wherein the crime shall have been committed.” It also entitles defendants to be confronted by (and to cross-examine) the witnesses against them and to have the “assistance of counsel” for their defense. The right to counsel begins when the suspect becomes the accused, that is at the initiation of judicial proceedings. If the accused is indigent, the judge assigns him/her a defense counsel at the first court appearance. A U.S. Supreme Court decision—Gideon v. Wainwright (1963) —held that the government must appoint defense lawyers for indigents accused of felonies. Later cases extended that ruling to cover all cases where the defendant could be sent to jail or prison.
Watch this video to learn more about the importance of the Supreme Court decision in this landmark case: Gideon v. Wainwright .
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Bail and Pre-Trial Detention
If the accused pleads not guilty, the judge must decide on pre-trial release and, if so, whether bail or other conditions ought to be imposed. Historically, the courts have held that a defendant ought to be released unless he presents a risk of flight. Typically, despite the supposed link between bail and assuring appearance at trial, judges set a high bail for individuals arrested for serious offenses because they are concerned about public safety, i.e., the defendant committing more crimes if released. Federal law permits pre-trial detention without bail in certain situations where the court finds that the defendant poses a serious threat of future danger to the community and that no combination of release conditions can reasonably assure community safety.
Formal Accusation and the Grand Jury - Indictment
American prosecutors have extensive discretion over whether to charge, what to charge and how many charges to bring against an arrestee. However, most prosecutors dismiss charges against a substantial percentage of arrestees at an early point in the process because:
- the arrestee’s conduct did not constitute a crime;
- while there was a crime, it was too insignificant to prosecute;
- while there was a crime, it is not provable against this person at this point; and
- while there was a crime, the prosecutor believes that pre-trial diversion to a treatment or other program is the most appropriate disposition.
Until the trial begins, the prosecutor may voluntarily dismiss the charges against the accused without prejudice, and thus can bring the same charges at a later date. The Sixth Amendment provides that there shall be no criminal prosecution except upon indictment by a grand jury. A grand jury is an investigative body that determines whether there is sufficient evidence to indict. However, the Supreme Court has held that this is one of the few rights included in the Bill of Rights that is not binding on the states. Thus, each state can decide for itself whether to use a grand jury to initiate the formal criminal proceeding.
The accused must be arraigned and formally charged within a short period of time. At the arraignment, the judge reads the formal charges and with respect to each charge, asks the defendant to plead guilty, not guilty, or not guilty by reason of insanity. Most states also permit a plea of nolo contendere (no contest) which, for practical purposes, is equivalent to a guilty plea. A plea of not guilty can subsequently be changed to a plea of guilty. Only in limited circumstances can a guilty plea be withdrawn.
Preliminary Hearing – Information
While the grand jury is a way to formally charge and determine if enough evidence exist to proceed to trial, the more common method is called a preliminary hearing. Also known as a preliminary examination, preliminary inquiry, evidentiary hearing, or probable cause hearing is a formal hearing after the district attorney has filed a complaint outlining the charges against the defendant. In a preliminary hearing, like the grand jury hearing, the district attorney must present enough evidence to a judge and demonstrate probable cause the crime was committed by the defendant.
At a preliminary hearing, two key questions must be shown by the district attorney.
- There is probable cause the crime occurred, and it is within the court’s jurisdiction.
- There is probable cause to believe the defendant charged with the crime committed the crime.
If the judge determines the district attorney has proven probable cause to both questions, the defendant is “held to answer” the charges proven in the preliminary hearing. It is important to understand, that all the charges outlined in the complaint must be found true. If the district attorney fails to prove probable cause, the case will cease. Additionally, if the district attorney only proves certain charges, those charges that were not proven cannot proceed to trial. At the end of the preliminary creates a new charging document called the information which identifies the charges that were proven and will proceed to trial.
Grand Jury Indictment v. Preliminary Hearing
The district attorney decides whether they will take the case to the Grand Jury or Preliminary hearing. So how or why does the district attorney chose one process or another? There are key differences to each process. The district attorney often uses the process appropriate to the specific issues of the case. The Grand Jury process is held outside of the public view. The defendant and his counsel are not present for the presentation of the evidence. However, the district attorney must prove their case to a panel of grand jurors. This is not an adversarial process, and the district is the only one presenting evidence. However, the district attorney is required to present exculpatory evidence (evidence that suggests the defendant may not be guilty). In contrast, the preliminary hearing is a public hearing and both the defendant, and his attorney are present for the evidentiary hearing. It is an adversarial process, and the defense counsel may cross-examine the district attorney’s witnesses. It also gives the defense counsel an opportunity to preview the state’s case against the defendant. The district attorney only must prove probable cause to the judge as opposed to a jury panel.
The district attorney with examine all these procedural requirements to determine how to best manage their case. For example, in high profile cases, the district attorney may not want all the crime details available to the public before the actual trial, or they may want to protect the accused from damaging information if no charges are filed, or it may be used to protect the witnesses and allow them to feel more comfortable to testify more freely and truthfully. Of course, the secrecy of the grand jury process has some significant issues. Some critics indicate the grand jury process is a “rubber stamp” for the prosecution and they do not evaluate the evidence as critically as a judge would making it easier for an indictment.
Pre-Trial Motions
The rules of criminal procedure provide that the defendant and his or her attorney have a certain number of days to make pre-trial motions challenging the legal sufficiency of the indictment or information or seeking the suppression of evidence. In addition, the defendant may move for the limited discovery of certain evidence held by the prosecutor. Under most states’ rules, the defense, if it makes the request, has a right to a copy of any statements made by the accused, copies of scientific tests, and a list of the prosecution’s witnesses. In some jurisdictions, the defendant must notify the prosecution in advance of its intent to rely on certain defenses such as an alibi or insanity.
Plea Bargaining
The American practice of “plea bargaining” is often misunderstood. The practice might more accurately be referred to as a system of guilty plea “discounts.” More than 90 percent of convictions are the result of guilty pleas. For most defendants who plead guilty, there has been no “bargaining.” Rather, the defendant has accepted the prosecutor’s offer to drop some charges in exchange for the defendant’s plea of guilty to one or more remaining charges. At the federal level, there is a tradition of “charge bargaining,” that is, the prosecutor drops the most serious charge, and the defendant pleads guilty to a lesser one. In some counties and cities, the judge explicitly offers sentencing discounts. For example, the defendant is promised a 3-year minimum, 5-year maximum prison term if he/she pleads guilty before the trial takes place; however, he/she will face a5–10-year minimum, 15-year maximum prison term if found guilty at trial.
Right to Trial
The defendant has a right to a public trial. Thus, American courtrooms are open to the public, including journalists. Indeed, the Supreme Court has held that the defendant cannot waive the right to a public trial because the citizenry also shares this right; nor can a judge prohibit the press from reporting on criminal trials. However, this does not mean that television cameras must be allowed in the courtroom. Some states, like California, permit live television coverage of criminal trials. Supporters argue that television coverage provides legal education for a public that otherwise would never see a criminal trial. Critics contend that TV cameras in the courtroom distort the conduct of the lawyers, judge, and jurors, and alter the courtroom atmosphere. There are no cameras in federal courtrooms.
Under the Sixth Amendment, the criminal defendant has a constitutional right to a speedy trial. Statutes of limitation, not the speedy trial right, govern the delay between the commission of a crime and the filing of charges. The Constitution dictates that there must not be an undue delay between indictment and trial. The Supreme Court, however, has never specified a definite period of time, which, if exceeded, violates this right. Every case has to be assessed individually. Every state has a speedy trial law that establishes time constraints within which the prosecution and the courts must bring the defendant to trial.
The Sixth Amendment also guarantees a criminal defendant the right to a jury trial. However, like most rights, the jury trial right may be waived. The defendant may elect a bench trial before a single judge or plead guilty. Usually, defendants have a better chance of acquittal by a jury. One-fourth to one-third of jury trials end in acquittals. But some defendants prefer a judge to a jury: because they believe a judge would be more likely to see the gaps in the prosecution’s case; the judge would sentence more leniently after a “bench” trial; or that the nature of the crime would inflame the jury against the defendant.
Although not constitutionally required, in the federal system and practically every state, the jury must reach a unanimous verdict. A jury that cannot agree is called a “hung jury.” In the event of a hung jury, a mistrial is declared, and the prosecution must decide whether to try the defendant again. There is no limit on how many times a defendant can be retried, but very few defendants are tried more than three times.
The Trial
Only 10 percent or less of American criminal cases are resolved by trials. The criminal trial is based upon the adversary system. The defense lawyer vigorously represents his/her client, whether or not he believes him guilty. The prosecutor represents the state and the people but also bears an ethical responsibility to act as a minister of justice.
Learn more about the differences between adversarial and inquisitional systems in this video: adversarial vs. inquisitional systems .
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According to the Supreme Court, the Constitution requires that, in order to find the defendant guilty, the factfinder, whether jury or judge, must determine that the prosecution has proven every element of the offense beyond a reasonable doubt. This is the meaning of the oft-quoted maxim that the “defendant is presumed innocent.”
Both sides have the right to call their own witnesses and to subpoena witnesses who will not appear voluntarily. The lawyers subject their own witnesses to direct examination and their adversary’s witnesses to cross-examination. The judge, but not the jurors, may ask the witnesses questions, but in practice, the lawyers ask practically all the questions and the judge acts as an impartial umpire. A witness may refuse on Fifth Amendment grounds to testify if he/she has a well-founded belief that the testimony could incriminate him/her. The prosecution may grant the witness immunity and then may compel the witness to answer every question. (The defense has no such power.) Immunity extends to any crime the witness admits to, as well as to any crime that investigators uncover as a result of the witness's immunized testimony.
Sentencing
The legislatures, courts, probation departments, parole boards, and, in some jurisdictions, sentencing commissions all play a role in the sentencing process. In the first instance, criminal sentences, or at least the maximum permissible sentence for each offense, are prescribed by legislatures. State sentencing statutes vary considerably and sometimes the same state has different types of sentencing statutes for different crimes. The sentence is imposed by the judge after a sentencing hearing at which the prosecutor and defense attorney argue for the sentence each thinks is appropriate. The defendant is usually given an opportunity to address the court prior to the sentence. In some jurisdictions, the victim or the victim’s representatives may address the court as well. The defense lawyer is likely to emphasize the defendant’s remorse, family responsibilities, good job prospects, and amenability to out-patient treatment (if necessary) in the community; the prosecution is likely to emphasize the defendant’s prior criminal record, injuries to the victim, and the victim’s family, and the need to deter other would-be offenders.
The judge is advised by the probation department, which independently investigates the defendant’s background, prior criminal record, circumstances of the offense, and other factors. The judge does not have to make formal factual findings and need not write an opinion explaining or justifying the sentence. As long as the sentence is within the statutory range, it cannot be appealed.
The Eighth Amendment rules out “excessive bail” for defendants and prohibits “cruel and unusual punishments.” This last prohibition has been interpreted by the courts to limit the kinds of punishments that can be inflicted. In 1972, the death penalty statutes of 38 states were effectively voided based on this constitutional provision. Some 40 states then passed new death penalty statutes in uniformity with the Supreme Court’s decisions. Neither Congress nor the states can pass laws that violate the Constitution.
Sanctions
Probation is the most common sentence meted out by American criminal court judges. In effect, the defendant avoids prison as long as he/she keeps out of trouble and adheres to the probation department’s rules, regulations, and reporting requirements. The judge determines how long the probationary term will last; several years is not uncommon. The judge may also impose special conditions, like participating in a drug treatment program, maintaining employment or staying in school, if the offender is a juvenile.
Imprisonment is a very widely used sentence; in 2004, on any given day there were more than 2 million persons in U.S. prisons and jails. Each state and the federal government has its own prison system. The prison department classifies (according to danger risk, escape risk, age, etc.) offenders and assigns them to an appropriate maximum-, medium-, or minimum-security penal institution.
Forfeiture of property has increased dramatically as a criminal sentence in recent years, especially in drug and organized crime cases. Typically, forfeiture laws provide that, as part of the criminal sentence, the judge may order the defendant to forfeit any property used in the crime (including car, boat, plane, and even house) and/or the proceeds of his/her criminal activity (business, bank accounts, securities, etc.).
Fines are less frequently imposed by U.S. courts. When they are imposed, it is usually in addition to other sanctions. Historically, the size of fines has been low, indeed, much lower than the fee a private criminal lawyer charges. Recently, however, maximum fines have increased dramatically. When fines are imposed, the Supreme Court has held that a defendant cannot be imprisoned for failure to pay the fine, unless the failure is willful.
Appeal and Post-Conviction Remedies
The Constitution does not guarantee a convicted offender a right of appeal, but every jurisdiction allows at least one appeal as a right, and many states have two levels of appellate courts and two levels of appeals. For some second-level appeals, the court has the discretion to hear only those cases that it chooses. Because of the guarantee against double jeopardy, the prosecution may not appeal a not-guilty verdict. Thus, an acquittal stands, even if it was based upon an egregious mistake by the judge in interpreting the law or upon an incomprehensible factual finding by the judge or jury.
After an offender’s state court appeals have been exhausted, he/she may file a habeas corpus petition in federal district court alleging that he/she is being held in state custody in violation of his/her federally guaranteed statutory or constitutional rights. (Federal prisoners may also petition the federal courts for post-conviction relief in the event, for example, that new evidence which could not have been discovered before trial, demonstrates innocence.) The right of habeas corpus is guaranteed by the Constitution and implemented by a federal statute. In some limited circumstances, an offender who was unsuccessful in the first habeas corpus proceeding may bring additional habeas corpus petitions alleging other constitutional violations.
Learn more about Habeas Corpus in this video: habeas corpus .
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Parole, Remission and Commutation
Traditionally, parole boards have played a major role in releasing offenders from prisons. Each state has its own parole board whose members are appointed by the governor. The parole board is usually one component of a large parole agency that supplies post-prison supervision to offenders after they are released from prison. The point at which a prisoner is eligible for parole is a matter of state law, so there is considerable variation among the states.
In a sentencing system in which the judge only specifies a maximum sentence, the prisoner might, for example, become eligible for parole after serving one-third of the sentence. Members of the parole board typically hold brief interviews with the prospective parolees at the prison. The board is generally interested in the prisoner’s adjustment within the prison, but it will invariably consider the facts of the crime and the prisoner’s previous criminal record.
Finally, the governor of each state has the power to pardon or commute the sentences of offenders in that state. The president of the United States has similar authority for federal offenders. Frequently, the law provides for the appointment of a pardon board, which sifts through petitions, conducts investigations, and makes affirmative recommendations to the chief executive. Governors, especially in the most prolific death sentencing states, are frequently called upon to commute death sentences. Unlike in many countries, general amnesties are not a part of American law or tradition.


15.1B: Toxoplasmosis
- Compare and contrast: acute and latent toxoplasmosis and outline the life cycle of the protazoan that causes it
Toxoplasmosis is an infection caused by the parasite Toxoplasma gondii. Toxoplasmosis is found in humans worldwide, but the definitive hosts are cats. Humans may become infected as a result of infected blood transfusions, organ transplants, ingesting contaminated soil, raw or undercooked meat, and most commonly from the careless handling of cat litter, which can lead to accidental ingestion of the parasite. Toxoplasmosis can also be passed from an infected mother to her baby via the placenta (transplacentally). Symptoms that may occur from toxplasmosis include: enlarged lymph nodes, headache, fever, muscle pain, and sore throat. Individuals with immunocompromised or weakened systems display more severe symptoms, such as: confusion, fever, headache, blurred vision and seizures. The three categories of toxoplasmosis include acute, latent, and cutaneous toxoplasmosis.
Symptoms
Acute toxoplasmosis is characterized by swollen lymph nodes found in the neck or under the chin, followed by the axillae, and the groin area. Enlarged lymph nodes will occur at different times after the initial infection. Latent toxoplasmosis is characterized by the formation of cysts in both the nervous and muscle tissue due to the bradyzoite form of the parasite. Often times, individuals infected with latent toxoplasmosis do not present with symptoms, as the infection enters a latent phase. In individuals with cutaneous toxoplasmosis, skin lesions will occur due to the tachyzoite form of the parasite and its presence in the epidermis.
Hosts, Life Cycle
The known definitive hosts for Toxoplasma gondii are members of family Felidae (domestic cats and their relatives). In the life cycle of this parasite, unsporulated oocysts are shed in the cat’s feces. The cat will shed large numbers of these cysts over a short period of time. The oocysts will then take 1-5 days to sporulate in the environment and become infective. The intermediate hosts in nature (including birds and rodents) become infected after ingesting contaminated soil, water, or plant material. The oocysts, upon ingestion, will transform into tachyzoites, which will localize in the neural and muscle tissue. After localizing to these sites, they will develop into tissue cyst bradyzoites. Cats, can become infected after consuming intermediate hosts that are infected with tissue cysts or by ingesting sporulated oocysts.
Key Points
- Cats are the definitive hosts for Toxoplasma gondii and are the primary source of infection to humans.
- Toxoplasmosis can occur in either acute, latent or cutaneous forms.
- Toxoplasmosis is found worldwide and can be transmitted by eating undercooked meat of animals which may contain cysts, ingesting contaminated food or water, transplacentally or from coming in contact with infected cat feces.
Key Terms
- definitive host : a host in which the parasite reaches maturity and, if possible, reproduces sexually
- axillae : The armpit
- transplacental : Through or across the placenta


17.14: Human Resources and Sustainability
- Discuss the role of human resource management in advancing sustainability
Given the business case for sustainability, what can a human resource management do to advance sustainability within their organization?Here are four key actions, derived from the Human Resources chapter of The Business Guide to Sustainability, to move the discussion forward: [1]
- Introduce the topic to senior executives: If senior management isn’t thinking about sustainability, present the business case and related resources or arrange an executive briefing.
- Align HR systems to embed sustainability in the culture: Incorporate sustainability into job descriptions, selection and evaluation criteria, employee orientation and training, evaluation and compensation.
- Model sustainable practices: Assess HR impacts and make changes to practices and procedures—for example, recycling and leveraging technology to minimize paper use and waste—to set an example and get a sense for what’s possible.
- Measure the impact: Incorporate sustainability initiatives in existing measurement systems in order to quantify the benefits and track progress.
Hitchcock and Willard also identify classic change management mistakes to avoid, including:
- Spray and pray training—Providing training without an associated plan and systems for implementation.
- The big black hole—Conducting training and soliciting implementation ideas that are never assessed, acknowledged or acted upon.
- Language hijack—Failure to recognize that terms such as “environmentalist” or “climate change” may evoke different responses, from engagement to resistance.
As is true at an organizational performance level, Human Resource management stands to benefit from a successful implementation.Sustainability positively impacts employee recruitment, engagement and retention. To illustrate, here are 3 key takeaways from a 2016 Cone Communications Millennial Employee Engagement study: [2]
- 64% of Millennials consider a company’s social and environmental commitments when deciding where to work
- 88% of Millennials say their job is more fulfilling when they are provided opportunities to make a positive impact on social and environmental issues and
- 83% of Millennials would be more loyal to a company that helps them contribute to social and environmental issues.
For perspective, millennials currently represent 50% of the workforce and are projected to constitute 75% by 2025. [3]
-
Hitchcock, Darcy and Marsha Willard.
The Business Guide to Sustainability.
Earthscan. 2006 ↵
-
"
2016 Cone Communications Millennial Employee Engagement Study.
" Cone. 2016. Accessed July 18, 2019. ↵
-
Donston-Miller, Debra. "
Workforce 2020: What You Need to Know Now.
" Forbes. May 5, 2016. Accessed July 18, 2019. ↵
Contributors and Attributions
- Untitled. Authored by : Amy Hirschi. Provided by : Unsplash. Located at : https://unsplash.com/photos/uwpo02K55zw . License : CC0: No Rights Reserved . License Terms : Unsplash License


2 .
Why is it important to know the EDD?
3 .
What instruments may be included on a delivery table?
4 .
Why should the delivery team consist of a nurse for the birthing person and a nurse for the newborn?
5 .
What are the three signs of placental separation?
6 .
When assessing a laceration, describe the difference between first-, second-, third- and fourth-degree lacerations.
7 .
What are the benefits of early skin-to-skin contact, and how can the nurse support it?
8 .
As a postpartum nurse, you are responsible for assessing the lochia of a birthing person during the fourth stage of labor. During your assessment, you find that the lochia is bright red and the pad was saturated within 30 minutes. The birthing person has no other signs of distress or abnormal vital signs. What is your immediate nursing action, and what does this finding suggest?


11.3: Two Population Means with Known Standard Deviations
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Even though this situation is not likely (knowing the population standard deviations is not likely), the following example illustrates hypothesis testing for independent means, known population standard deviations. The sampling distribution for the difference between the means is normal and both populations must be normal. The random variable is \(\bar{X}_{1} - \bar{X}_{2}\). The normal distribution has the following format:
Normal distribution is:
\[\bar{X}_{1} - \bar{X}_{2} \sim{N}\left[\mu_{1} - \mu_{2}, \sqrt{\dfrac{(\sigma_{1})^{2}}{n_{1}} + \dfrac{(\sigma_{2})^{2}}{n_{2}}}\right] \label{eq1}\]
The standard deviation is:
\[\sqrt{\dfrac{(\sigma_{1})^{2}}{n_{1}} + \dfrac{(\sigma_{2})^{2}}{n_{2}}}\label{eq2}\]
The test statistic ( z -score) is:
\[z = \dfrac{(\bar{x}_{1} - \bar{x}_{2}) - (\mu_{1} - \mu_{2})}{\sqrt{\dfrac{(\sigma_{1})^{2}}{n_{1}} + \dfrac{(\sigma_{2})^{2}}{n_{2}}}} \label{eq3}\]
Example \(\PageIndex{1}\)
Independent groups, population standard deviations known: The mean lasting time of two competing floor waxes is to be compared. Twenty floors are randomly assigned to test each wax. Both populations have a normal distributions. The data are recorded in Table.
| Wax | Sample Mean Number of Months Floor Wax Lasts | Population Standard Deviation |
|---|---|---|
| 1 | 3 | 0.33 |
| 2 | 2.9 | 0.36 |
Does the data indicate that wax 1 is more effective than wax 2 ? Test at a 5% level of significance.
Answer
This is a test of two independent groups, two population means, population standard deviations known.
Random Variable: \(\bar{X}_{1} - \bar{X}_{2} =\) difference in the mean number of months the competing floor waxes last.
- \(H_{0}: \mu_{1} \leq \mu_{2}\)
- \(H_{a}: \mu_{1} > \mu_{2}\)
The words "is more effective" says that wax 1 lasts longer than wax 2 , on average. "Longer" is a “>” symbol and goes into \(H_{a}\). Therefore, this is a right-tailed test.
Distribution for the test: The population standard deviations are known so the distribution is normal. Using Equation \ref{eq1}, the distribution is:
\[\bar{X}_{1} - \bar{X}_{2} \sim{N} \left(0, \sqrt{\dfrac{0.33^{2}}{20} + \dfrac{0.36^{2}}{20}}\right)\]
Since \(\mu_{1} \leq \mu_{2}\) then \(\mu_{1} - \mu_{2} \leq 0\) and the mean for the normal distribution is zero.
Calculate the \(p\text{-value}\) using the normal distribution: \(p\text{-value} = 0.1799\)
Graph:
Figure 10.3.1.\(\bar{X}_{1} - \bar{X}_{2} = 3 – 2.9 = 0.1\)
Compare \(\alpha\) and the \(p\text{-value}\) : \(\alpha = 0.05\) and \(p\text{-value} = 0.1799\). Therefore, \(\alpha < p\text{-value}\).
Make a decision: Since \(\alpha < p\text{-value}\), do not reject \(H_{0}\).
Conclusion: At the 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the mean time wax 1 lasts is longer (wax 1 is more effective) than the mean time wax 2 lasts.
The Two Independent Samples With Statistics and Known Population Standard Deviations calculator is much more direct. Just enter in:
First Sample Sample Size = 20, First Sample Sample Size = 3, First Sample Population Standard Deviation = 0.33
Second Sample Sample Size = 20, Second Sample Sample Size = 2.9, Second Sample Population Standard Deviation = 0.36
Check ">" and click on Calculate. The \(p\text{-value}\) is \(p = 0.1799\) and the test statistic is 0.9157.
Two Independent Samples with statistics, Population Standard Deviation known Calculator
Enter in the statistics, the tail type and the confidence level and hit Calculate and the test statistic, t, the p-value, p, the confidence interval's lower bound, LB, and the upper bound, UB will be shown. Be sure to enter the confidence level as a decimal, e.g., 95% has a CL of 0.95.
| Sample Size | Sample Mean | Population Standard Deviation | |
| First Sample | |||
| Second Sample |
|
|
| z: | p: | LB: | UB: |
Exercise \(\PageIndex{1}\)
The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5% level of significance.
| Engine | Sample Mean Number of RPM | Population Standard Deviation |
|---|---|---|
| 1 | 1,500 | 50 |
| 2 | 1,600 | 60 |
Answer
The \(p\text{-value}\) is almost 0, so we reject the null hypothesis. There is sufficient evidence to conclude that Engine 2 runs at a higher RPM than Engine 1.
Example \(\PageIndex{2}\): Age of Senators
An interested citizen wanted to know if Democratic U. S. senators are older than Republican U.S. senators, on average. On May 26 2013, the mean age of 30 randomly selected Republican Senators was 61 years 247 days old (61.675 years) with a standard deviation of 10.17 years. The mean age of 30 randomly selected Democratic senators was 61 years 257 days old (61.704 years) with a standard deviation of 9.55 years.
Do the data indicate that Democratic senators are older than Republican senators, on average? Test at a 5% level of significance.
Answer
This is a test of two independent groups, two population means. The population standard deviations are unknown, but the sum of the sample sizes is 30 + 30 = 60, which is greater than 30, so we can use the normal approximation to the Student’s-t distribution. Subscripts: 1: Democratic senators 2: Republican senators
Random variable: \(\bar{X}_{1} - \bar{X}_{2} =\) difference in the mean age of Democratic and Republican U.S. senators.
- \(H_{0}: \mu_{1} \leq \mu_{2} H_{0}: \mu_{1} - \mu_{2} \leq 0\)
- \(H_{a}: \mu_{1} > \mu_{2} H_{a}: \mu_{1} - \mu_{2} > 0\)
The words "older than" translates as a “>” symbol and goes into \(H_{a}\). Therefore, this is a right-tailed test.
Distribution for the test: The distribution is the normal approximation to the Student’s t for means, independent groups. Using the formula, the distribution is: \[\bar{X}_{1} - \bar{X}_{2} \sim N\left[0, \sqrt{\dfrac{(9.55)^{2}}{30} + \dfrac{(10.17)^{2}}{30}}\right]\]
Since \(\mu_{1} \leq \mu_{2}, \mu_{1} - \mu_{2} \leq 0\) and the mean for the normal distribution is zero.
(Calculating the p -value using the normal distribution gives \(p\text{-value} = 0.4040\))
Graph:
Figure 10.3.2.Compare \(\alpha\) and the \(p\text{-value}\) : \(\alpha = 0.05\) and \(p\text{-value} = 0.4040\). Therefore, \(\alpha < p\text{-value}\).
Make a decision: Since \(\alpha < p\text{-value}\), do not reject \(H_{0}\).
Conclusion: At the 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the mean age of Democratic senators is greater than the mean age of the Republican senators.
References
- Data from the United States Census Bureau. Available online at http://www.census.gov/prod/cen2010/b...c2010br-02.pdf
- Hinduja, Sameer. “Sexting Research and Gender Differences.” Cyberbulling Research Center, 2013. Available online at http://cyberbullying.us/blog/sexting...r-differences/ (accessed June 17, 2013).
- “Smart Phone Users, By the Numbers.” Visually, 2013. Available online at http://visual.ly/smart-phone-users-numbers (accessed June 17, 2013).
- Smith, Aaron. “35% of American adults own a Smartphone.” Pew Internet, 2013. Available online at http://www.pewinternet.org/~/media/F...martphones.pdf (accessed June 17, 2013).
- “State-Specific Prevalence of Obesity AmongAduls—Unites States, 2007.” MMWR, CDC. Available online at http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5728a1.htm (accessed June 17, 2013).
- “Texas Crime Rates 1960–1012.” FBI, Uniform Crime Reports, 2013. Available online at: http://www.disastercenter.com/crime/txcrime.htm (accessed June 17, 2013).
Chapter Review
- A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations), will have these characteristics:
- Random variable: \(\bar{X}_{1} - \bar{X}_{2} =\) the difference of the means
- Distribution: normal distribution
Formula Review
Normal Distribution:
\[\bar{X}_{1} - \bar{X}_{2} \sim N\left[\mu_{1} - \mu_{2}, \sqrt{\dfrac{(\sigma_{1})^{2}}{n_{1}} + \dfrac{(\sigma_{2})^{2}}{n_{2}}}\right]\]
Generally \(\mu_{1} - \mu_{2} = 0\).
Test Statistic ( z -score):
\[z = \dfrac{(\bar{x}_{1} - \bar{x}_{2}) - (\mu_{1} - \mu_{2})}{\sqrt{\dfrac{(\sigma_{1})^{2}}{n_{1}} + \dfrac{(\sigma_{2})^{2}}{n_{2}}}}\]
Generally \(\mu_{1} - \mu_{2} = 0\).
where:
\(\sigma_{1}\) and \(\sigma_{2}\) are the known population standard deviations. \(n_{1}\) and \(n_{1}\) are the sample sizes. \(\bar{x}_{1}\) and \(\bar{x}_{2}\) are the sample means. \(\mu_{1}\) and \(\mu_{2}\) are the population means
Contributors and Attributions
-
Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


3.1: Sign of an angle
The positive and negative angles can be visualized as counterclockwise and clockwise directions; formally, they are defined the following way:
- The angle \(AOB\) is called positive if \(0 < \measuredangle AOB < \pi\);
- The angle \(AOB\) is called negative if \(\measuredangle AOB < 0\).
Note that according to the above definitions the straight angle as well as the zero angle are neither positive nor negative.
Exercise \(\PageIndex{1}\)
Shoe that \(\angle AOB\) is positive if and only if \(\angle BOA\) is negative.
- Hint
-
Set \(\alpha = \measuredangle AOB\) and \(\beta = \measuredangle BOA\). Note that \(\alpha = \pi\) if and only if \(\beta = \pi\). Otherwise \(\alpha = -\beta\). Hence the result.
Let \(\angle AOB\) be straight. Then \(\angle AOX\) is positive if and only if \(\angle BOX\) is negative.
- Proof
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Set \(\alpha = \measuredangle AOX\) and \(\beta = \measuredangle BOX\). Since \(\angle AOB\) is straight,
\[\alpha - \beta \equiv \pi.\]
It follows that \(\alpha = \pi \Leftrightarrow \beta = 0\) and \(\alpha = 0 \Leftrightarrow \beta = \pi\). In these two cases the sign of \(\angle AOX\) and \(\angle BOX\) are undefined.
In the remaining cases we have that \(|\alpha| < \pi\) and \(|\beta| < \pi\). If \(\alpha\) and \(\beta\) have the same sign, then \(|\alpha - \beta| < \pi\); the latter contradicts 3.1.1. Hence the statement follows.
Exercise \(\PageIndex{2}\)
Assume that the angles \(ABC\) and \(A'B'C'\) have the same sign and
\(2 \cdot \measuredangle ABC \equiv 2 \cdot \measuredangle A'B'C'.\)
Show that \(\measuredangle ABC = \measuredangle A'B'C'\).
- Hint
-
Set \(\alpha = \measuredangle ABC\), \(\beta = \measuredangle A'B'C'\). Since \(2 \cdot \alpha \equiv 2 \cdot \beta\), Exercise 1.8.1 implies that \(\alpha \equiv \beta\) or \(\alpha \equiv \beta + \pi\). In the latter case the angles have opposite signs which is impossible.
Since \(\alpha, \beta \in (-\pi, \pi]\), equality \(\alpha \equiv \beta\) implies \(\alpha = \beta\).


29.12D: Hypoxia
Hypoxia, or hypoxiation, is inadequate oxygen supply to the body as a whole (generalized hypoxia) or a region of the body (tissue hypoxia).
- Differentiate between hypoxia and hypoxemia
Key Points
- A mismatch between oxygen supply and its demand at the cellular level may result in a hypoxic condition.
- Hypoxia in which there is complete deprivation of oxygen supply is referred to as anoxia.
- Hypoxia occurs in healthy people when they ascend to high altitude, where it causes altitude sickness leading to high altitude pulmonary edema (HAPE) and high altitude cerebral edema (HACE).
- Hypoxia also occurs in healthy individuals when breathing mixtures of gases with a low oxygen content.
- Hypoxia is a serious consequence of preterm birth in the neonate.
- In humans, hypoxia is detected by chemoreceptors in the carotid body, which override the signals from central chemoreceptors in the hypothalamus, increasing pO 2 despite a falling pCO 2 .
Key Terms
- hyperventilation : The state of breathing faster or deeper than necessary.
- hypoxemia : An abnormal deficiency in the concentration of oxygen in the blood, be it the partial pressure of oxygen (mm Hg), the content of oxygen (ml oxygen per dl of blood) or the percent saturation of the blood’s hemoglobin, singly or in combination.
- anoxia : A condition in which tissues are severely or totally deprived of oxygen, severe hypoxia.
Hypoxia, or hypoxiation, is a pathological condition in which the body as a whole (generalized hypoxia) or a region of the body (tissue hypoxia) is deprived of adequate oxygen supply. Variations in arterial oxygen concentrations can be part of the normal physiology, for example, during strenuous physical exercise. A mismatch between oxygen supply and its demand at the cellular level may result in a hypoxic condition. Hypoxia in which there is complete deprivation of oxygen supply is referred to as anoxia.
Hypoxia vs. Hypoxemia
Hypoxia differs from hypoxemia in that in the latter the oxygen concentration within the arterial blood is abnormally low. It is possible to experience hypoxia and have a low oxygen content (e.g., due to anemia) but maintain high oxygen partial pressure (pO 2 ). Incorrect use of these terms can easily lead to confusion, especially as hypoxemia is among the causes of hypoxia (in hypoxemic hypoxia). Generalized hypoxia occurs in healthy people when they ascend to high altitude where it causes altitude sickness leading to potentially fatal complications: high altitude pulmonary edema (HAPE) and high altitude cerebral edema (HACE). Hypoxia also occurs in healthy individuals when breathing mixtures of gases with a low oxygen content, e.g., while diving underwater especially when using closed-circuit rebreather systems that control the amount of oxygen in the supplied air. A mild and non-damaging intermittent hypoxia is used intentionally during altitude trainings to develop an athletic performance adaptation at both the systemic and cellular level.
Hypoxia is also a serious consequence of preterm birth in the neonate. The main cause for this is that the lungs of the human fetus are among the last organs to develop during pregnancy. To assist the lungs to distribute oxygenated blood throughout the body, infants at risk of hypoxia are often placed inside an incubator capable of providing continuous positive airway pressure (also known as a humidicrib). In humans, hypoxia is detected by chemoreceptors in the carotid body. This response does not control ventilation rate at normal pO 2 , but below normal the activity of neurons innervating these receptors increases dramatically, so much so to override the signals from central chemoreceptors in the hypothalamus, increasing pO 2 despite a falling pCO 2 .
Hypoxemic hypoxia is a generalized hypoxia, with an inadequate supply of oxygen to the body as a whole. The term “hypoxemic hypoxia” specifies hypoxia caused by low partial pressure of oxygen in arterial blood. In the other causes of hypoxia that follow, the partial pressure of oxygen in arterial blood is normal. Hypoxemic hypoxia may be due to hypoventilation or inadequate pulmonary minute ventilation (e.g., respiratory arrest or by drugs such as opiates).
Symptoms of Hypoxia
Cyanosis during hypoxia : Cyanosis in the hand of patient suffering from hypoxia.
The symptoms of generalized hypoxia depend on its severity and acceleration of onset. In the case of altitude sickness, where hypoxia develops gradually, the symptoms include headaches, fatigue, shortness of breath, a feeling of euphoria, and nausea. In severe hypoxia, or hypoxia of very rapid onset, changes in levels of consciousness, seizures, coma, priapism, and death occur. Severe hypoxia induces a blue discoloration of the skin, called cyanosis. Because hemoglobin is a darker red when it is not bound to oxygen (deoxyhemoglobin), as opposed to the rich red color that it has when bound to oxygen (oxyhemoglobin), when seen through the skin it has an increased tendency to reflect blue light back to the eye. In cases where the oxygen is displaced by another molecule, such as carbon monoxide, the skin may appear “cherry red” instead of cyanotic.
Body’s Response to Hypoxia
In most tissues of the body, the response to hypoxia is vasodilation. By widening the blood vessels, the tissue allows greater perfusion. By contrast, in the lungs, the response to hypoxia is vasoconstriction. This is known as “Hypoxic pulmonary vasoconstriction” or “HPV.” To counter the effects of high-altitude diseases, the body must return arterial pO 2 toward normal. Acclimatization, the means by which the body adapts to higher altitudes, only partially restores pO 2 to standard levels. Hyperventilation, the body’s most common response to high-altitude conditions, increases alveolar pO 2 by raising the depth and rate of breathing.
However, while pO 2 does improve with hyperventilation, it does not return to normal. Studies of miners and astronomers working at 3,000 meters and above show improved alveolar pO 2 with full acclimatization, yet the pO 2 level remains equal to or even below the threshold for continuous oxygen therapy for patients with chronic obstructive pulmonary disease (COPD). In addition, there are complications involved with acclimatization. Polycythemia, in which the body increases the number of red blood cells in circulation, thickens the blood, raising the danger that the heart can’t pump it.
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