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Necessity and sufficiency
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This article is about the formal terminology in logic. For causal meanings of the terms, see Causality. For the concepts in statistics, see Sufficient statistic.
In logic, necessity and sufficiency are implicational relationships between statements.
The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true or simultaneously false.[1][2][3]
In ordinary English, "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. Being a male sibling is a necessary and sufficient condition for being a brother.
Contents
[hide]
1 Definitions
2 Necessity
3 Sufficiency
4 Relationship between necessity and sufficiency
5 Simultaneous necessity and sufficiency
6 See also
6.1 Argument forms involving necessary and sufficient conditions
6.1.1 Valid forms of argument
6.1.2 Invalid forms of argument (i.e., fallacies)
7 References
8 External links
Definitions[edit]
In the conditional statement, "if S, then N", the expression represented by S is called the antecedent and the expression represented by N is called the consequent. This conditional statement may be written in many equivalent ways, for instance, "N if S", "S implies N", "S only if N", "N is implied by S", S ⇒ N, or "N whenever S".[4]
In the above situation, we also say that N is a necessary condition for S. In common language this is saying that if the conditional statement is a true statement, then the consequent N must be true if S may at all be true (see "truth table" immediately below). Phrased differently, the antecedent S can not be true without N being true. For example, in order for someone to be called Socrates, it is necessary for that someone to be Named.
We also say that S is a sufficient condition for N. Consider the truth table again. If the conditional statement is true, then if S is true, N must be true. In common terms, "S guarantees N". Continuing the example, knowing that someone is called Socrates is sufficient to know that that someone has a Name.
A necessary and sufficient condition requires that both of the implications S ⇒ {\displaystyle \Rightarrow } N and N ⇒ {\displaystyle \Rightarrow } S (which can also be written as S ⇐ {\displaystyle \Leftarrow } N) hold. From the first of these we see that S is a sufficient condition for N, and from the second that S is a necessary condition for N. This is expressed as "S is necessary and sufficient for N ", "S if and only if N ", or S ⇔ {\displaystyle \Leftrightarrow } N.
Truth table
S
N
S ⇒ {\displaystyle \Rightarrow } N
S ⇐ {\displaystyle \Leftarrow } N
S ⇔ {\displaystyle \Leftrightarrow } N
T T T T T
T F F T F
F T T F F
F F T T T
Necessity[edit]
The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition, as something else may be casting a shadow, e.g., the moon in the case of an eclipse.
The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between them is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q). It may also be expressed as any of "P only if Q", "Q, if P", "Q whenever P", and "Q when P". One often finds, in mathematical prose for instance, several necessary conditions that, taken together, constitute a sufficient condition, as shown in Example 5.
Example 1
For it to be true that "John is a bachelor", it is necessary that it be also true that he is
unmarried,
male,
adult,
since to state "John is a bachelor" implies John has each of those three additional predicates.
Example 2
For the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime.
Example 3
Consider thunder, the sound caused by lightning. We say that thunder is necessary for lightning, since lightning never occurs without thunder. Whenever there's lightning, there's thunder. The thunder does not cause the lightning (since lightning causes thunder), but because lightning always comes with thunder, we say that thunder is necessary for lightning. (That is, in its formal sense, necessity doesn't imply causality.)
Example 4
Being at least 30 years old is necessary for serving in the U.S. Senate. If you are under 30 years old, then it is impossible for you to be a senator. That is, if you are a senator, it follows that you are at least 30 years old.
Example 5
In algebra, for some set S together with an operation ⋆ {\displaystyle \star } to form a group, it is necessary that ⋆ {\displaystyle \star } be associative. It is also necessary that S include a special element e such that for every x in S it is the case that e ⋆ {\displaystyle \star } x and x ⋆ {\displaystyle \star } e both equal x. It is also necessary that for every x in S there exist a corresponding element x "such that both x ⋆ {\displaystyle \star } x " and x" ⋆ {\displaystyle \star } x equal the special element e. None of these three necessary conditions by itself is sufficient, but the conjunction of the three is.
Sufficiency[edit]
That a train runs on schedule can be a sufficient condition for arriving on time (if one boards the train and it departs on time, then one will arrive on time); but it is not always a necessary condition, since there are other ways to travel (if the train does not run to time, one could still arrive on time through other means of transport).
If P is sufficient for Q, then knowing P to be true is adequate grounds to conclude that Q is true; however, knowing P to be false does not meet a minimal need to conclude that Q is false.
The logical relation is expressed as "if P, then Q" or "P ⇒ Q". This can also be expressed as "P only if Q" or "P implies Q". Several sufficient conditions may, taken together, constitute a single necessary condition, as illustrated in example 5.
Example 1
"John is a king" implies that John is male. So knowing that it is true that John is a king is sufficient to know that he is a male.
Example 2
A number's being divisible by 4 is sufficient (but not necessary) for its being even, but being divisible by 2 is both sufficient and necessary.
Example 3
An occurrence of thunder is a sufficient condition for the occurrence of lightning in the sense that hearing thunder, and unambiguously recognizing it as such, justifies concluding that there has been a lightning bolt.
Example 4
If the U.S. Congress passes a bill, the president's signature of the bill is sufficient to make it law. Note that the case whereby the president did not sign the bill, e.g. through exercising a presidential veto, does not mean that the bill has not become law (it could still have become law through a congressional override).
Example 5
That the center of a playing card should be marked with a single large spade (♠) is sufficient for the card to be an ace. Three other sufficient conditions are that the center of the card be marked with a diamond (♦), heart (♥), or club (♣), respectively. None of these conditions is necessary to the card's being an ace, but their disjunction is, since no card can be an ace without fulfilling at least (in fact, exactly) one of the conditions.
Relationship between necessity and sufficiency[edit]
Being in the purple region is sufficient for being in A, but not necessary. Being in A is necessary for being in the purple region, but not sufficient. Being in A and being in B is necessary and sufficient for being in the purple region.
A condition can be either necessary or sufficient without being the other. For instance, being a mammal (N) is necessary but not sufficient to being human (S), and that a number x {\displaystyle x} is rational (S) is sufficient but not necessary to x {\displaystyle x} being a real number (N) (since there are real numbers that are not rational).
A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant.
Mathematically speaking, necessity and sufficiency are dual to one another. For any statements S and N, the assertion that "N is necessary for S" is equivalent to the assertion that "S is sufficient for N". Another facet of this duality is that, as illustrated above, conjunctions (using "and") of necessary conditions may achieve sufficiency, while disjunctions (using "or") of sufficient conditions may achieve necessity. For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).
Simultaneous necessity and sufficiency[edit]
See also: Material equivalence
To say that P is necessary and sufficient for Q is to say two things:
that P is necessary for Q, P ⇐ Q {\displaystyle P\Leftarrow Q} , and that P is sufficient for Q, P ⇒ Q {\displaystyle P\Rightarrow Q} .
equivalently, it may be understood to say that P and Q is necessary for the other, P ⇒ Q ∧ Q ⇒ P {\displaystyle P\Rightarrow Q\land Q\Rightarrow P} , which can also be stated as
each is sufficient for or implies the other.
One may summarize any, and thus all, of these cases by the statement "P if and only if Q", which is denoted by P ⇔ Q {\displaystyle P\Leftrightarrow Q} , whereas cases tell us that P ⇔ Q {\displaystyle P\Leftrightarrow Q} is identical to P ⇒ Q ∧ Q ⇒ P {\displaystyle P\Rightarrow Q\land Q\Rightarrow P} .
For example, in graph theory a graph G is called bipartite if it is possible to assign to each of its vertices the color black or white in such a way that every edge of G has one endpoint of each color. And for any graph to be bipartite, it is a necessary and sufficient condition that it contain no odd-length cycles. Thus, discovering whether a graph has any odd cycles tells one whether it is bipartite and conversely. A philosopher[5] might characterize this state of affairs thus: "Although the concepts of bipartiteness and absence of odd cycles differ in intension, they have identical extension.[6]
In mathematics, theorems are often stated in the form "P is true if and only if Q is true". Their proofs normally first prove sufficiency, e.g. P ⇒ Q {\displaystyle P\Rightarrow Q} . Secondly, the opposite is proven, Q ⇒ P {\displaystyle Q\Rightarrow P}
either directly, assuming Q is true and demonstrating that the Q circle is located within P, or
contrapositively, that is demonstrating that stepping outside circle of P, we fall out the Q: assuming not P, not Q results.
This proves that the circles for Q and P match on the Venn diagrams above.
Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. P ⇐ Q {\displaystyle P\Leftarrow Q} is equivalent to Q ⇒ P {\displaystyle Q\Rightarrow P} , if P is necessary and sufficient for Q, then Q is necessary and sufficient for P. We can write P ⇔ Q ≡ Q ⇔ P {\displaystyle P\Leftrightarrow Q\equiv Q\Leftrightarrow P} and say that the statements "P is true if and only if Q, is true" and "Q is true if and only if P is true" are equivalent.
See also[edit]
Causality
Material implication (disambiguation)
Wason selection task
Closed concept
Argument forms involving necessary and sufficient conditions[edit]
Valid forms of argument[edit]
Modus ponens
Modus tollens
Invalid forms of argument (i.e., fallacies)[edit]
Affirming the consequent
Denying the antecedent
References[edit]
Jump up ^ Betz, Frederick (2011). Managing Science: Methodology and Organization of Research. New York: Springer. p. 247. ISBN 978-1-4419-7487-7.
Jump up ^ Manktelow, K.I. (1999). Reasoning and Thinking. East Sussex, UK: Psychology Press. ISBN 0-86377-708-2.
Jump up ^ Asnina, Erika; Osis, Janis & Jansone, Asnate (2013). "Formal Specification of Topological Relations". Databases and Information Systems VII: 175. doi:10.3233/978-1-61499-161-8-175.
Jump up ^ Devlin, Keith (2004), Sets, Functions and Logic / An Introduction to Abstract Mathematics (3rd ed.), Chapman & Hall, pp. 22–23, ISBN 978-1-58488-449-1
Jump up ^ Stanford University primer, 2006.
Jump up ^ "Meanings, in this sense, are often called intensions, and things designated, extensions. Contexts in which extension is all that matters are, naturally, called extensional, while contexts in which extension is not enough are intensional. Mathematics is typically extensional throughout." Stanford University primer, 2006.
External links[edit]
Critical thinking web tutorial: Necessary and Sufficient Conditions
Simon Fraser University: Concepts with examples
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List of countries by oil production
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This is a list of countries by oil production, as compiled from the U.S. Energy Information Administration database for calendar year 2016, tabulating all countries on a comparable best-estimate basis. Compared with shorter-term data, the full-year figures are less prone to distortion from periodic maintenance shutdowns and other seasonal cycles. The volumes in the table represent crude oil and lease condensate, the hydrocarbon liquids collected at or near the wellhead. The volumes in the table do not include biofuel. They also do not include the increase in liquid volumes during oil refining ("refinery gain"), or liquids separated from natural gas in gas processing plants (natural gas liquids).[1]
Under this definition, total world oil production in 2016 averaged 80,622,000 barrels per day. Approximately 68% came from the top ten countries, and an overlapping 44% came from the fourteen current OPEC members, highlighted with blue shading in the table below.
For many years, the top three producers have been (alphabetically) Russia, Saudi Arabia, and the United States. Each of these countries experienced major production declines at different times in the past, but since 2014 all three have been producing near their peak rates of 9 to 11 million barrels per day.[2]
Top oil-producing countries (million barrels per day, 1973–2016)[2]
Countries producing oil 2013, bbl/day (CIA World Factbook)
Historical worldwide production of Crude Oil and Natural Gas Plant Liquids (IEA, 1960–2009)
OPEC oil exports and production in 2014, when Indonesia was preparing to rejoin the organization

Country
Oil Production
(bbl/day, 2016)[1]
1 Russia 10,551,497
2 Saudi Arabia (OPEC) 10,460,710
3 United States 8,875,817
4 Iraq (OPEC) 4,451,516
5 Iran (OPEC) 3,990,956
6 China 3,980,650
7 Canada 3,662,694
8 United Arab Emirates (OPEC) 3,106,077
9 Kuwait (OPEC) 2,923,825
10 Brazil 2,515,459
11 Venezuela (OPEC) 2,276,967
12 Mexico 2,186,877
13 Nigeria (OPEC) 1,999,885
14 Angola (OPEC) 1,769,615
15 Norway 1,647,975
16 Kazakhstan 1,595,199
17 Qatar (OPEC) 1,522,902
18 Algeria (OPEC) 1,348,361
19 Oman 1,006,841
20 United Kingdom 939,760
21 Colombia 897,784
22 Indonesia 833,667
23 Azerbaijan 833,538
24 India 734,180
25 Malaysia 661,240
26 Ecuador (OPEC) 548,421
27 Argentina 510,560
28 Egypt 494,325
29 Libya (OPEC) 384,686
30 Congo, Republic of the 308,363
31 Vietnam 301,850
32 Australia 289,749
33 Thailand 257,525
34 Sudan and South Sudan 255,000
35 Turkmenistan 230,779
36 Equatorial Guinea (OPEC) 227,000
37 Gabon (OPEC) 210,820
38 Denmark 140,637
39 Chad 110,156
40 Brunei 109,117
41 Ghana 100,549
42 Cameroon 93,205
43 Pakistan 84,746
44 Romania 77,910
45 Italy 70,675
46 Timor-Leste 60,661
47 Trinidad and Tobago 60,090
48 Bolivia 58,077
49 Papua New Guinea 56,667
50 Uzbekistan 52,913
51.5 Bahrain 50,000
51.5 Cuba 50,000
53 Turkey 49,497
54 Tunisia 48,757
55 Germany 46,839
56 Peru 40,266
57 New Zealand 35,574
58 Ukraine 31,989
59.5 Ivory Coast 30,000
59.5 Syria 30,000
61 Belarus 25,000
62 Mongolia 23,426
63 Albania 22,915
64 Yemen 22,000
65 Poland 20,104
67 Congo, Democratic Republic of the 20,000
67 Philippines 20,000
67 Serbia 20,000
69 Netherlands 18,087
70 Suriname 17,000
71 France 16,418
72 Austria 15,161
73 Myanmar 15,000
74 Hungary 13,833
75 Croatia 13,582
76 Niger 13,000
77 Guatemala 8,977
78 Mauritania 5,000
79 Chile 4,423
80 Bangladesh 4,189
81 Japan 3,918
82 Greece 3,172
83 Spain 2,667
84 Czech Republic 2,333
86 Belize 2,000
86 Lithuania 2,000
86 South Africa 2,000
89 Barbados 1,000
89 Bulgaria 1,000
89 Kyrgyzstan 1,000
91 Georgia 400
92 Israel 390
93 Slovakia 200
94 Taiwan 196
95 Tajikistan 180
96 Morocco 160
97 Jordan 22
98 Slovenia 5
References[edit]
^ Jump up to: a b "Production of Crude Oil including Lease Condensate 2016" (CVS download). U.S. Energy Information Administration. Retrieved 27 May 2017.
^ Jump up to: a b "Monthly Energy Review" (PDF). U.S. Energy Information Administration. 25 May 2017. Figure 11.1a. Retrieved 28 May 2017.
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List of family members and friends in ER
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This partial list of fictional characters in the medical drama ER encompasses the notable family members and friends of the main characters of the series.
Contents
[hide]
1 Family and friends of Peter Benton
1.1 Jackie Robbins
2 Family and friends of Susan Lewis
2.1 Chloe Lewis
3 Family and friends of Abby Lockhart
3.1 Maggie Wyczenski
4 References
Family and friends of Peter Benton[edit]
Jackie Robbins[edit]
Jackie Robbins
First appearance
January 5, 1995 (Season 1: "Happy New Year")
Last appearance
December 13, 2001 (Season 8: "I'll Be Home for Christmas")
Portrayed by
Khandi Alexander
Information
Gender
Female
Spouse(s)
Walt Robbins
Children
Joanie Robbins
Steven Robbins
Jesse Robbins
Relatives
Peter Benton (brother)
Cleo Finch (sister-in-law)
Reese Benton (nephew)
Mae Benton (mother)
Jackie Robbins (née Benton), portrayed by Khandi Alexander, is the daughter of Mae Benton. Her husband Walt Robbins (portrayed by Ving Rhames) is a mechanic.
In Season 1, Jackie and Peter are shown to have a good relationship but also to be deeply at odds over how to treat Mae, who is no longer able to take care of herself and needs constant care; Jackie insists Mae should be in a nursing home, and Peter finally agrees to this after she is badly injured while he's supposed to be watching her (he had fallen asleep after working a double shift at the hospital). In season 3, Peter reunites with his old girlfriend, Carla Reese, at a barbecue at Jackie's house. Their ill-fated relationship leads to the birth of Reese Benton. Jackie is often seen over the next several seasons as helping her brother look after Reese and in supporting him in his various conflicts with Carla, going from pushing him to take responsibility for his child to being furiously on his side when Carla tells them that Peter may not even be Reese's biological father (it's later proven that Carla, by then deceased, did conceive Reese with an unidentified stranger). In the season 7 episode "Benton Backwards", Jackie's son Jesse gets in a fight and is brought in by her to the ER. He is having problems at school and at home which causes Jackie to ask Peter to talk to him. Jessie, however, continues to be involved with the wrong crowd and ultimately gets shot and brought into the ER where he dies. Peter hears Malucci refer to his late nephew as a "banger" and Benton beats him up. Jackie falls into a long depression over Jesse's death and only comes out this around the same time Peter left the ER to work at another hospital. She was not seen again after Season 8.
Family and friends of Susan Lewis[edit]
Chloe Lewis[edit]
Chloe Lewis
First appearance
October 20, 1994 (Season 1: "Chicago Heat")
Last appearance
April 25, 2002 (Season 8: "Brothers and Sisters")
Portrayed by
Kathleen Wilhoite
Information
Gender
Female
Family
Henry Lewis (father)
Cookie Lewis (mother)
Susan Lewis (younger sister)
Spouse(s)
Joe (fiance)
Children
Susan Lewis (a.k.a. "Little Suzy"; named after her aunt)
Chloe Lewis, portrayed by Kathleen Wilhoite, is the older sister of ER physician Susan Lewis. She first appears in Episode 6 where it is revealed that she has had consistent personal problems over a number of years with substance abuse, inappropriate relationships with men, and the inability to maintain a steady job or support herself. Broke and homeless, Chloe is invited to stay with Susan at her apartment with great reluctance. Later, Susan is not surprised to find Chloe gone and her TV and VCR stolen when she returns home.
In the following episode, "Another Perfect Day", Chloe makes another unexpected entrance into Susan's life by showing up at the ER drunk on her birthday with a bunch of her wild friends. The sisters get into an argument which results in Chloe injuring herself when she smashes her hand and arm through a glass window. This ruins Susan's dinner plans with her boyfriend, psychiatrist Dr. Div Cvetic. Div, with some reluctance, evaluates Chloe per Susan's request.
In Episode 9, "ER Confidential", Susan, exasperated with her sister but also compassionate, tries to outreach to Chloe by inviting her and her boyfriend to Thanksgiving dinner at her apartment. Div, who is suffering from depression, skips out on the meal which leaves Susan alone with Chloe and her boyfriend. To make matters worse, Chloe has undercooked the turkey.
In Episode 11, "The Gift" Chloe announces to Susan that she is pregnant. Susan is understandably highly skeptical about Chloe's ability to look after a child and urges her to have an abortion. Chloe, however, is convinced that she can not only be a great mother but that having the child will be a strong motivation for her to get her life together. In the following episode, Chloe informs Susan that she is moving to Texas with her boyfriend. Susan, urges her to stay, but Chloe leaves after Susan gives her some money and her winter coat. Susan later admits to Mark Greene that she thinks Chloe left because she urged her to have an abortion.
Chloe once again pops back into Susan's life at the end of Episode 19 "House of Cards", looking like she has been homeless and is in the late stages of pregnancy. Susan lets her in only after Chloe promises to do what Susan tells her to this time. In the following episode, Susan is seen taking over all the responsibilities of preparing for the coming baby, including making sure Chloe and the baby are healthy. Chloe sees an OB, Dr. Janet Coburn, and we learn that the baby is going to be a girl. She tells Chloe that she needs to watch her diet and Susan tells her that she needs to quit smoking. Chloe tells Susan that she knew she was going to have a girl and that she is going to name her Susan. Susan buys lots of supplies and even contacts her mother, Cookie Lewis, about helping out financially.
In Episode 23 "Love Among the Ruins", Susan catches Chloe smoking in her apartment after she had promised she would quit. Angry that Chloe is not holding up to her end of the bargain and that she could do something that she knows can hurt the baby, Susan tells Chloe that she is going to have to move out. Chloe doesn't know where she can go and Susan reluctantly lets her stay.
In Episode 24 "Motherhood" Chloe wakes Susan up and tells her that it is time for the baby; her contractions are only 2 minutes apart. Chloe wants Susan to put on "Blackbird" while she is in labor. It is 4:30 am and Susan calls Dr. Colburn to come, but Susan ends up delivering the baby herself. A nurse named Chuny Marquez assists her. Chloe names the baby Suzy after Susan. Cookie, Susan and Chloe's mom, arrives to see the baby. Susan had initially assumed that her mother would help Chloe raise her niece, but Cookie tells Susan that she has already raised her girls and does not want to raise another one. Susan now realizes that she is going to have to take care of Chloe and little Suzy herself.
At the beginning of Season 2 Chloe and the baby are living with Susan. Susan is intent on getting Chloe to get a steady job to help with finances. Things appear to be going well when Chloe starts attending school; although Chloe's school schedule now requires that Susan look after the baby herself more. Fortunately, County General's day care allows Suzy to join. Later, Chloe leaves her daughter with Susan at the apartment because she is running late for class; throwing a kink in Susan's own work day. Susan later finds out that Chloe has been skipping classes and has dropped out. This causes further friction between the sisters. In Episode 028 "Do One, Teach One, Kill One", Chloe, evidently high again with a strange man, informs Susan that she is leaving to go out of state to work at a flea market. Susan begs her not to leave her with the baby, but Chloe drives off. Susan wants to take care of Suzy herself but after Cookie's usual passive-aggressive bullshit (she is shocked that Susan would give up her niece for adoption but provides no better ideas or support) she strongly considers giving Suzy up, later reconsidering and being pleasantly surprised by her family for once when her dad defies Cookie and shows up at her house, saying he will watch Suzy on nights when Susan has to work because he feels "it's about time" he did something unselfish for his daughter.
After not hearing anything from Chloe in several months, Susan receives a money package of thirty 100 dollar bills from her. At this point Susan is in the midst of attempting to adopt Little Suzy as her own child. A few months later, in Episode 041 "The Healers", Chloe returns greatly altered. Over the next few episodes it is revealed that she has been clean of drugs for five months, has maintained a great job for several months, and has a fiance, Joe, a cop and excellent man whom she met while she was in rehab. It appears that Chloe has finally gotten her life together. Chloe informs Susan that she wants to be a mother to her daughter. Susan, still skeptical and in love with little Suzy, tells her that is too bad. Chloe contests Susan's adoption plan, and the court-appointed mediator tells her that if she pursues custody she will lose because Chloe has turned her life around and is now stable and would not lose custody as the biological parent. Chloe, Joe and Little Suzy move away to Arizona. Susan eventually moves there as well in Season 3.
In the Season 8 episode 176 "Brothers and Sisters", Susan receives a frightening phone message from Suzy in which she says that her mom is really sick and she can't get her to wake up. Suzy says that they are in a hotel but doesn't say where. Susan calls the police and learns that Suzy's call came from a cell phone in New York City. Susan catches an 11:30 flight out to New York intent on finding them. Chloe is found, strung out on drugs, with the help of the Third Watch officers. Suzy is unharmed, but Susan is concerned for her safety if she continues to live with Chloe. As it turns out, Joe had wanted to leave Chloe, who discovered he was having an affair. Chloe's reaction led to her relapse and little Suzy's kidnap by a man posing as a member of neighborhood watch. After she's found by the NYPD, Chloe takes Suzie and leaves the hospital without saying anything but a post-note goodbye to Susan via a clerk, and she was never seen again.
In the episode after,The Letter, it was explained by Susan that Chloe and Suzy were staying in a hotel in uptown New York having learned the information from Joe because he was charged with the bill for the hotel room suggesting that Chloe has his credit card in her possession. Later in the episode Susan receives a call from Chloe revealing that Joe took her back and that she is in an out patient program for drug addiction and Suzy will stay with Joe in the meantime.
Family and friends of Abby Lockhart[edit]
Maggie Wyczenski[edit]
Maggie Wyczenski
First appearance
November 16, 2000 (Episode: The Visit)
Last appearance
September 28, 2006 (Episode: Graduation Day)
Portrayed by
Sally Field
Information
Gender
Female
Occupation
Doctor
Spouse(s)
Eddie Wyczenski
(ex-husband)
Children
Abby Lockhart,
Eric Wyczenski
Relatives
Luka Kovač (son-in-law)
Josip "Joe" Kovac (grandson)
Maggie Wyczenski is the mother of Dr Abby Lockhart. Maggie suffers from bipolar disorder, and her uncontrolled mental illness had a negative impact on her ability to parent Abby and her younger brother, Eric, who is also bipolar. Abby did much of the parenting of her brother and has also taken care of Maggie herself-she recalled one incident where Maggie went into a rage and chased her through the house with a knife. Because of this, Abby is extremely cynical towards all efforts to rein in or improve her mother's condition, as she believes Maggie will inevitably suffer a breakdown, leave and eventually return. Abby had an abortion while married to Richard because she feared that the baby would inherit Maggie's disease; she hid this from everyone until she told Maggie about it in the 7th season and cited it as the point her and Richard's marriage began to disintegrate because they hid everything and began lying constantly to each other. When Abby became pregnant a second time after resuming her relationship with Dr Luka Kovač, she considered abortion again, but decided to keep the baby with Luka and eventually informed her mother when she was about three months along.
Maggie made her first appearance during the sixth episode of season 7. She is first found in the doctors' lounge by Kerry Weaver, who told her that patients are not allowed in the lounge. Maggie replied that she was not a patient, but that a member of the staff is her daughter. After realizing that her mother had unexpectedly arrived to the County General Hospital, Abby first denied that Maggie was her mother, thus Kerry told Frank to call psych. When Kerry told Maggie that Abby said she was not her mother, Maggie became extremely agitated and began shouting for Abby all around the ER until Abby herself appeared and calmed Maggie down. During a long time, Maggie had not been taking her medication and Kim Legaspi told her to take some new medications and Maggie finally agrees. Later, Abby gave Maggie some money so that she could go home but Maggie told her she had no place to go as Eric did not want to see her again. Maggie applied for a job interview in a store but did not last long and the owner wanted Maggie to be arrested after causing an accident. Back in the ER, Maggie argues again with Abby and is threatened with an injection of Haldol. After being examined by Dr Legaspi again, Maggie ran away. Maggie returned to cause more problems for Abby and left her daughter in tears over her insane actions.
Several months later, Richard told Abby that Maggie was holed up in a motel room in Oklahoma (he found out because a credit card still had an account in both their names that they hadn't cancelled post-divorce and he received statements showing where Maggie was) and gave Abby a phone number to call her. Abby and Carter looked for Maggie and found her in a bad state. Abby gave her a bath and some food, and returned with her to Chicago. During the way back to Chicago, Maggie takes an entire box of sleeping pills and falls unconscious; she is rushed to the ER barely breathing and is treated by Luka, Carter and Abby. She seizes on the trauma table and a devastated Abby is forced to watch. For attempting to kill herself with the pills, which she stole from a gas station, Maggie was due in court for a competency hearing, but in the end made her way out of being committed. But after Abby tearfully recounts how she was sure she was watching her own mother die, and later stating that Maggie had power over her to constantly put her through this before sobbing out "I love you, Mom", Maggie for the first time seems aware that her selfish actions are devastating Abby and looks ashamed (she had also blatantly lied to get out of being committed and gotten away with it). Towards the end of the season, Maggie had had some sessions with Dr Lesgaspi and appeared to be better off. Finally, Maggie decided to return to her original home in Minnesota. Abby had a more heart-to-heart conversation with Maggie before her departure, with Maggie encouraging her to embrace her own life and stop coming to Maggie's rescue; she was going to try harder to make it on her own.
In recent years, Maggie's illness was better controlled with medication. Maggie and Abby found in each other some support after Eric's crisis during Season 9, after Abby was initially angry and jealous that Eric turned to Maggie instead of her for help, before Maggie explained that Eric reached out to be her BECAUSE of her mental condition to try and make sense of it. After Abby informed her mother she was pregnant in Season 12, Maggie sent her a Bible given to her by her own mother with a message on the inside cover: "Dear Abby, you will love your child like nothing else. Love, Maggie" At the start of Season 13, she was also responsible for saving the life of Abby and Luka's premature baby Joe, as she took control of the situation while Luka and Abby were struggling with their own problems after the rampage. Maggie, knitting beside her grandson's isolette, demanded that the neonatal nurse summon a doctor when monitors began to beep. Abby thought that Joe would not make it, but it was Maggie's support that made her change her mind. When it came time for Joe to leave the hospital with his parents, for once Abby was reluctant to see her mother go home- indicating that she has forgiven Maggie.
Sally Field has portrayed Maggie in several guest appearances. In 2000, Field was nominated for Outstanding Actress in the Screen Actors Guild awards.
References[edit]
[hide]
v
t
e
ER
Characters
Main
John Carter
Kerry Weaver
Abby Lockhart
Luka Kovač
Mark Greene
Peter Benton
Elizabeth Corday
Susan Lewis
Greg Pratt
Carol Hathaway
Neela Rasgotra
Samantha Taggart
Jing-Mei Chen
Archie Morris
Doug Ross
Jeanie Boulet
Tony Gates
Cleo Finch
Dave Malucci
Lucy Knight
Anna Del Amico
Catherine Banfield
Supporting
Doctors
Nurses
Non-medical staff
Family members and friends
Seasons
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Episodes
"Love's Labor Lost"
"On the Beach"
"The Show Must Go On"
"Strange Bedfellows"
"No Place to Hide"
"There Are No Angels Here"
"The Gallant Hero and the Tragic Victor"
"Twenty-One Guns"
"And in the End..."
Related
Cast
Awards and nominations
Retrieved from "https://en.wikipedia.org/w/index.php?title=List_of_family_members_and_friends_in_ER&oldid=822336685"
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text:
IEEE 802.1X
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (September 2010) (Learn how and when to remove this template message)
IEEE 802.1X is an IEEE Standard for port-based Network Access Control (PNAC). It is part of the IEEE 802.1 group of networking protocols. It provides an authentication mechanism to devices wishing to attach to a LAN or WLAN.
IEEE 802.1X defines the encapsulation of the Extensible Authentication Protocol (EAP) over IEEE 802,[1][2] which is known as "EAP over LAN" or EAPOL.[3] EAPOL was originally designed for IEEE 802.3 Ethernet in 802.1X-2001, but was clarified to suit other IEEE 802 LAN technologies such as IEEE 802.11 wireless and Fiber Distributed Data Interface (ISO 9314-2) in 802.1X-2004.[4] The EAPOL protocol was also modified for use with IEEE 802.1AE (“MACsec”) and IEEE 802.1AR (Secure Device Identity, DevID) in 802.1X-2010[5][6] to support service identification and optional point to point encryption over the local LAN segment.
Contents
[hide]
1 Overview
2 Protocol operation
2.1 Port entities
2.2 Typical authentication progression
3 Implementations
3.1 Supplicants
3.1.1 Windows
3.1.2 Windows XP
3.1.3 Windows Vista
3.1.4 Windows 7
3.1.5 Windows PE
3.1.6 OS X Yosemite[22]
3.1.7 GNU/Linux
3.2 Federations
4 Proprietary extensions
4.1 MAB (MAC Authentication Bypass)
5 Vulnerabilities in 802.1X-2001 and 802.1X-2004
5.1 Shared media
6 Alternatives
7 See also
8 References
9 External links
Overview[edit]
EAP data is first encapsulated in EAPOL frames between the Supplicant and Authenticator, then re-encapsulated between the Authenticator and the Authentication server using RADIUS or Diameter.
802.1X authentication involves three parties: a supplicant, an authenticator, and an authentication server. The supplicant is a client device (such as a laptop) that wishes to attach to the LAN/WLAN. The term 'supplicant' is also used interchangeably to refer to the software running on the client that provides credentials to the authenticator. The authenticator is a network device, such as an Ethernet switch or wireless access point; and the authentication server is typically a host running software supporting the RADIUS and EAP protocols. In some cases, the authentication server software may be running on the authenticator hardware.
The authenticator acts like a security guard to a protected network. The supplicant (i.e., client device) is not allowed access through the authenticator to the protected side of the network until the supplicant’s identity has been validated and authorized. With 802.1X port-based authentication, the supplicant provides credentials, such as user name/password or digital certificate, to the authenticator, and the authenticator forwards the credentials to the authentication server for verification. If the authentication server determines the credentials are valid, the supplicant (client device) is allowed to access resources located on the protected side of the network.[7]
Protocol operation[edit]
EAPOL operates at the network layer on top of the data link layer, and in Ethernet II framing protocol has an EtherType value of 0x888E.
Port entities[edit]
802.1X-2001 defines two logical port entities for an authenticated port—the "controlled port" and the "uncontrolled port". The controlled port is manipulated by the 802.1X PAE (Port Access Entity) to allow (in the authorized state) or prevent (in the unauthorized state) network traffic ingressing and egressing to/from the controlled port. The uncontrolled port is used by the 802.1X PAE to transmit and receive EAPOL frames.
802.1X-2004 defines the equivalent port entities for the supplicant; so a supplicant implementing 802.1X-2004 may prevent higher level protocols being used if it is not content that authentication has successfully completed. This is particularly useful when an EAP method providing mutual authentication is used, as the supplicant can prevent data leakage when connected to an unauthorized network.
Typical authentication progression[edit]
The typical authentication procedure consists of:
Sequence diagram of the 802.1X progression
Initialization On detection of a new supplicant, the port on the switch (authenticator) is enabled and set to the "unauthorized" state. In this state, only 802.1X traffic is allowed; other traffic, such as the Internet Protocol (and with that TCP and UDP), is dropped.
Initiation To initiate authentication the authenticator will periodically transmit EAP-Request Identity frames to a special Layer 2 address (01:80:C2:00:00:03) on the local network segment. The supplicant listens on this address, and on receipt of the EAP-Request Identity frame it responds with an EAP-Response Identity frame containing an identifier for the supplicant such as a User ID. The authenticator then encapsulates this Identity response in a RADIUS Access-Request packet and forwards it on to the authentication server. The supplicant may also initiate or restart authentication by sending an EAPOL-Start frame to the authenticator, which will then reply with an EAP-Request Identity frame.
Negotiation (Technically EAP negotiation) The authentication server sends a reply (encapsulated in a RADIUS Access-Challenge packet) to the authenticator, containing an EAP Request specifying the EAP Method (The type of EAP based authentication it wishes the supplicant to perform). The authenticator encapsulates the EAP Request in an EAPOL frame and transmits it to the supplicant. At this point the supplicant can start using the requested EAP Method, or do an NAK ("Negative Acknowledgement") and respond with the EAP Methods it is willing to perform.
Authentication If the authentication server and supplicant agree on an EAP Method, EAP Requests and Responses are sent between the supplicant and the authentication server (translated by the authenticator) until the authentication server responds with either an EAP-Success message (encapsulated in a RADIUS Access-Accept packet), or an EAP-Failure message (encapsulated in a RADIUS Access-Reject packet). If authentication is successful, the authenticator sets the port to the "authorized" state and normal traffic is allowed, if it is unsuccessful the port remains in the "unauthorized" state. When the supplicant logs off, it sends an EAPOL-logoff message to the authenticator, the authenticator then sets the port to the "unauthorized" state, once again blocking all non-EAP traffic.
Implementations[edit]
Supplicants[edit]
Main article: Supplicant (computer)
Windows XP, Windows Vista and Windows 7 support 802.1X for all network connections by default. Windows 2000 has support in the latest service pack (SP4) for wired connections. Windows Mobile 2003 and later operating systems also come with a native 802.1X client.
An open source project known as Open1X produces a client, Xsupplicant. This client is currently available for both Linux and Windows. The main drawbacks of the Open1X client are that it does not provide comprehensible and extensive user documentation and the fact that most Linux vendors do not provide a package for it. The more general wpa_supplicant can be used for 802.11 wireless networks and wired networks. Both support a very wide range of EAP types.[8]
The iPhone and iPod Touch support 802.1X as of the release of iOS 2.0. Android has support for 802.1X since the release of 1.6 Donut. Chrome OS has supported 802.1X since mid-2011.[9]
Mac OS X has offered native support since 10.3.[10]
Avenda Systems provides a supplicant for Windows, Linux and Mac OS X. They also have a plugin for the Microsoft NAP framework.[11] Avenda also offers health checking agents.
Windows[edit]
Windows defaults to not responding to 802.1X authentication requests for 20 minutes after a failed authentication. This can cause significant disruption to clients.
The block period can be configured using the BlockTime value in the registry. A hotfix is required for Windows XP SP3 and Windows Vista SP2 to make the period configurable.[12]
Wildcard server certificates are not supported by EAPHost, the Windows component that provides EAP support in the operating system.[13] The implication of this is that when using a commercial certification authority, individual certificates must be purchased.
Windows XP[edit]
Windows XP has major issues with its handling of IP address changes that result from user-based 802.1X authentication that changes the VLAN and thus subnet of clients.[14] Microsoft has stated that it will not back port the SSO feature from Vista that resolves these issues.[15]
If users are not logging in with roaming profiles, a hotfix must be downloaded and installed if authenticating via PEAP with PEAP-MSCHAPv2.[16]
Windows Vista[edit]
Windows Vista based computers that are connected via an IP phone may not authenticate as expected and, as a result, the client can be placed into the wrong VLAN. A hotfix is available to correct this.[17]
Windows 7[edit]
Windows 7 based computers that are connected via an IP phone may not authenticate as expected and, as a result, the client can be placed into the wrong VLAN. A hotfix is available to correct this.[17]
Windows 7 does not respond to 802.1X authentication requests after initial 802.1X authentication fails. This can cause significant disruption to clients. A hotfix is available to correct this.[18]
Windows PE[edit]
For most enterprises deploying and rolling out operating systems remotely, it is worth noting that Windows PE does not have native support for 802.1X. However, support can be added to WinPE 2.1[19] and WinPE 3.0[20] through hotfixes that are available from Microsoft. Although full documentation is not yet available, preliminary documentation for the use of these hotfixes is available via a Microsoft blog.[21]
OS X Yosemite[22][edit]
GNU/Linux[edit]
Most Linux distributions support 802.1x via wpa_supplicant and desktop integration like NetworkManager.
Federations[edit]
eduroam (the international roaming service), mandates the use of 802.1X authentication when providing network access to guests visiting from other eduroam enabled institutions.[23]
BT (British Telecom, PLC) employs Identity Federation for authentication in services delivered to a wide variety of industries and governments.[24]
Proprietary extensions[edit]
MAB (MAC Authentication Bypass)[edit]
Not all devices support 802.1X authentication. Examples include network printers, Ethernet-based electronics like environmental sensors, cameras, and wireless phones. For those devices to be used in a protected network environment, alternative mechanisms must be provided to authenticate them.
One option would be to disable 802.1X on that port, but that leaves that port unprotected and open for abuse. Another, slightly more reliable option is to use the MAB option. When MAB is configured on a port, that port will first try to check if the connected device is 802.1X compliant, and if no reaction is received from the connected device, it will try to authenticate with the AAA server using the connected device's MAC address as username and password. The network administrator then must make provisions on the RADIUS server to authenticate those MAC-addresses, either by adding them as regular users, or implementing additional logic to resolve them in a network inventory database.
Many managed Ethernet switches[25][26] offer options for this.
Vulnerabilities in 802.1X-2001 and 802.1X-2004[edit]
Shared media[edit]
In the summer of 2005, Microsoft's Steve Riley posted an article detailing a serious vulnerability in the 802.1X protocol, involving a man in the middle attack. In summary, the flaw stems from the fact that 802.1X authenticates only at the beginning of the connection, but after that authentication, it's possible for an attacker to use the authenticated port if he has the ability to physically insert himself (perhaps using a workgroup hub) between the authenticated computer and the port. Riley suggests that for wired networks the use of IPsec or a combination of IPsec and 802.1X would be more secure.[27]
EAPOL-Logoff frames transmitted by the 802.1X supplicant are sent in the clear and contain no data derived from the credential exchange that initially authenticated the client.[28] They are therefore trivially easy to spoof on shared media, and can be used as part of a targeted DoS on both wired and wireless LANs. In an EAPOL-Logoff attack a malicious third party with access to the medium the authenticator is attached to, repeatedly sends forged EAPOL-Logoff frames from the target device's MAC Address. The authenticator (believing that the targeted device wishes to end its authentication session) closes the target's authentication session, blocking traffic ingressing from the target, denying it access to the network.
The 802.1X-2010 specification, which began as 802.1af, addresses vulnerabilities in previous 802.1X specifications, by using MACSec IEEE 802.1AE to encrypt data between logical ports (running on top of a physical port) and IEEE 802.1AR (Secure Device Identity / DevID) authenticated devices.[5][6][29][30]
As a stopgap until these enhancements are widely implemented, some vendors have extended the 802.1X-2001 and 802.1X-2004 protocol, allowing multiple concurrent authentication sessions to occur on a single port. While this prevents traffic from devices with unauthenticated MAC addresses ingressing on an 802.1X authenticated port, it will not stop a malicious device snooping on traffic from an authenticated device and provides no protection against MAC spoofing, or EAPOL-Logoff attacks.
Alternatives[edit]
The IETF-backed alternative is the Protocol for Carrying Authentication for Network Access (PANA), which also carries EAP, although it works at layer 3, using UDP, thus not being tied to the 802 infrastructure.[31]
See also[edit]
AEGIS SecureConnect
EAP
IEEE 802.11i-2004
RADIUS
References[edit]
Jump up ^ RFC 3748, § 3.3
Jump up ^ RFC 3748, § 7.12
Jump up ^ IEEE 802.1X-2001, § 7
Jump up ^ IEEE 802.1X-2004, § 3.2.2
^ Jump up to: a b IEEE 802.1X-2010, page iv
^ Jump up to: a b IEEE 802.1X-2010, § 5
Jump up ^ "802.1X Port-Based Authentication Concepts". Retrieved 2008-07-30.
Jump up ^ "eap_testing.txt from wpa_supplicant". Retrieved 2010-02-10.
Jump up ^ "The computer that keeps getting better". Retrieved 2013-11-27.
Jump up ^ "Apple — iPhone — Enterprise". Retrieved 2008-07-31.
Jump up ^ "NAP clients for Linux and Macintosh are available". 2008-12-16.
Jump up ^ "A Windows XP-based, Windows Vista-based or Windows Server 2008-based computer does not respond to 802.1X authentication requests for 20 minutes after a failed authentication". Support.microsoft.com. 2009-09-17. Retrieved 2010-03-23.
Jump up ^ "EAPHost in Windows Vista and Longhorn (January 18, 2006)". Technet.microsoft.com. 2007-01-18. Retrieved 2010-03-24.
Jump up ^ "Problems when obtaining Group Policy objects, roaming profiles and logon scripts from a Windows Server 2003-based domain controller". Support.microsoft.com. 2007-09-14. Retrieved 2010-02-10.
Jump up ^ "802.1X with dynamic VLAN switching — Problems with Roaming Profiles". Forums.technet.microsoft.com. Retrieved 2010-02-10.
Jump up ^ "A Windows XP Service Pack 3-based client computer cannot use the IEEE 802.1X authentication when you use PEAP with PEAP-MSCHAPv2 in a domain". Support.microsoft.com. 2009-04-23. Retrieved 2010-03-23.
^ Jump up to: a b "A computer that is connected to an IEEE 802.1X authenticated network through a VOIP phone does not connect to the correct network after you resume it from Hibernate mode or Sleep mode". Support.microsoft.com. 2010-02-08. Retrieved 2010-03-23.
Jump up ^ "Windows 7 or Windows Server 2008 R2 does not respond to 802.1X authentication requests after the authentication fails". Support.microsoft.com. 2010-03-08. Retrieved 2010-03-23.
Jump up ^ "Windows PE 2.1 does not support the IEEE 802.1X authentication protocol". Support.microsoft.com. 2009-12-08. Retrieved 2010-02-10.
Jump up ^ "The IEEE 802.1X authentication protocol is not supported in Windows Preinstall Environment (PE) 3.0". Support.microsoft.com. 2009-12-08. Retrieved 2010-02-10.
Jump up ^ "Adding Support for 802.1X to WinPE". Blogs.technet.com. 2010-03-02. Retrieved 2010-03-03.
Jump up ^ "OS X Yosemite: Connect to a network that requires 802.1X authentication". support.apple.com. Retrieved 2017-03-10.
Jump up ^ "Eduroam — About". Retrieved 2009-11-29.
Jump up ^ "BT Identity and Access Management" (PDF). Retrieved 2010-08-17.
Jump up ^ MAC Authentication Bypass Deployment Guide, May 2011. Retrieved: 26 January, 2012
Jump up ^ Dell PowerConnect 6200 series CLI Guide Archived 2012-11-18 at the Wayback Machine., page: 622, Revision: A06-March 2011. Retrieved: 26 Januari, 2013
Jump up ^ "Steve Riley's article on the 802.1X vulnerabilities". Microsoft.com. 2005-08-09. Retrieved 2010-02-10.
Jump up ^ IEEE 802.1X-2001, § 7.1
Jump up ^ "2 February 2010 Early Consideration Approvals". Standards.ieee.org. Retrieved 2010-02-10.
Jump up ^ "IEEE 802.1: 802.1X-2010 - Revision of 802.1X-2004". Ieee802.org. 2010-01-21. Retrieved 2010-02-10.
Jump up ^ Philip Golden; Hervé Dedieu; Krista S. Jacobsen (2007). Implementation and Applications of DSL Technology. Taylor & Francis. pp. 483–484. ISBN 978-1-4200-1307-8.
External links[edit]
IEEE page on 802.1X
GetIEEE802 Download 802.1X-2010
GetIEEE802 Download 802.1X-2004
GetIEEE802 Download 802.1X-2001
Ultimate wireless security guide: Self-signed certificates for your RADIUS server
WIRE1x
Wired Networking with 802.1X Authentication on Microsoft TechNet
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