Friday, March 28, 2008

Blodwyn Pig
Blodwyn Pig were a British blues-rock group founded by Mick Abrahams after he left Jethro Tull in 1968. Abrahams had earlier had a major falling out with Tull leader Ian Anderson.
Blodwyn Pig consisted of Abrahams (guitar and vocals), Jack Lancaster (saxophone), Andy Pyle (bass guitar), and Ron Berg (drums), Peter Banks also was a member.
The band recorded two albums, Ahead Rings Out in 1969 and Getting To This in 1970. Both reached the lower half of the British top ten. On the first album they played a heavy blues-rock rooted in the British 60's r'n'b scene from which sprang groups like the Yardbirds, Free and eventually Led Zeppelin, but Blodwyn Pig had a different twist on the genre thanks to Lancaster's sax being so prominent in the mix which led them to more creative sixties underground jazz-influenced music on the second. The single Summer Day from Ahead Rings Out failed to chart.
The band reformed in the 1990s for two more albums.

Thursday, March 27, 2008

Diasystem
In linguistics, in the field of structural dialectology, a diasystem is a single genetic language which has two or more standard forms. Some dialects are often divided into separate languages due to different historical and cultural development. Other possible differences between languages include vocabulary, such as Occitan being affected by French and Catalan by Spanish words, and writing systems, such as Hindi in Devanagari and Urdu in the Arabic script, despite being mutually intelligible. Some languages are officially recognized as distinct despite having no barriers in speech, writing or lexicon, but are distinguished by legal and political factors, such as the Catalan with Valencian, and Romanian with Moldovan. Examples include:

Bulgarian-Macedonian-Torlakian
Czech-Slovak (Czech-Slovak-Pannonian Rusyn)
Danish-Bokmål Norwegian-Nynorsk Norwegian
Filipino-Tagalog
Hindustani (Hindi-Urdu)
Irish-Scottish Gaelic
Lao-Isan
Malay (Malaysian-Indonesian)
Mandarin Chinese-Dungan
Occitano-Romance languages (Occitan-Catalan-Valencian)
Persian-Tajik-Dari
Portuguese-Galician (Portuguese-Galician)
Romanian-Moldovan
Central South Slavic (Bosnian-Croatian-Montenegrin-Serbian)
Spanish-Ladino
Tatar-Bashkir
Tuscan (Italian-Corsican)
Ukrainian-Rusyn
Uyghur-Uzbek

Wednesday, March 26, 2008

Boston campaign
The Boston campaign was part of the American Revolutionary War. It included the Battles of Lexington and Concord, the Siege of Boston, and the Battle of Bunker Hill. It ended with Evacuation Day on March 17, 1776.

Background

Main articles: Powder Alarm and Battles of Lexington and Concord War begins

Main articles: Siege of Boston and Battle of Bunker Hill Siege of Boston
The British regular soldier in Boston was often hated equally by the local civilians and by their own commanders. The winter of 1774-75 had been long and hard, and shortages of food led General Thomas Gage to put his men on salt rations. Some of their supplies of fresh water went bad that winter and stank. Many died of diseases, most likely typhus and diphtheria. The one cheap commodity in Boston that winter was rum. Several regulars suffered alcohol-related deaths. Several more sold their muskets for rum, under the penalty of 500 lashes if caught. Desertion was fairly common, but much less common than might be expected considering the hardships endured by these men. Gage doubled the guards around the city, more to keep his own men in than to prevent the movements of Whigs. Whig leaders promised 300 acres (1.2 km²) in New Hampshire to any deserting soldier, but nearly all the regulars remained loyal to their fellow comrades-in-arms while hating both their commanders and the Bostonians.

Tuesday, March 25, 2008

Hibiscus rosa-sinensis
The Chinese hibiscus (Hibiscus rosa-sinensis, family Malvaceae) is an evergreen shrub native to East Asia. It is also known as China rose and shoe flower. It is widely grown as an ornamental plant throughout the tropics and subtropics. The flowers are large, red, firm, but lack any scent. Numerous cultivars, varieties, and hybrids have been created, with flower colors ranging from white through yellow and orange to scarlet and shades of pink, with both single and double sets of petals.
Hibiscus rosa-sinensis is the national flower of Malaysia, called the Bunga Raya in Malay and "Sembaruthi" in Tamil and mamdaram in Telugu (మందారం). The flowers are used to shine shoes in parts of India, as well as for the worship of Devi. Hibiscus flowers are also used for hair care.

Monday, March 24, 2008


Deprogramming refers to actions to persuade or force a person to abandon allegiance to a religious or political group.
Deprogramming is normally commissioned by concerned relatives of the follower, often parents of adult children, and is taken against his/her will, which has led to controversies over freedom of religion and civil rights.
Supporters of deprogramming portray the practice as an antidote to deceptive religious conversion practices by what they consider to be cults, such as mind control, brainwashing, thought reform, or coercive persuasion. They.

Deprogramming and kidnapping
The deprogramming accounts vary a lot regarding the use of force, with the most dramatic accounts coming from deprogrammees who returned to the group.
The deprogramming case observed by Dubrow-Eichel did not include any violence.
Sociologist Eileen Barker wrote in Watching for Violence:
"Although deprogramming has become less violent in the course of time ... Numerous testimonies by those who were subjected to a deprogramming describe how they were threatened with a gun, beaten, denied sleep and food and/or sexually assaulted. But one does not have to rely on the victims for stories of violence: Ted Patrick, one of the most notorious deprogrammers used by CAGs (who has spent several terms in prison for his exploits) openly boasts about some of the violence he employed; in November 1987, Cyril Vosper, a Committee member of the British cult-awareness group, FAIR, was convicted in Munich of "causing bodily harm" in the course of one of his many deprogramming attempts; and a number of similar convictions are on record for prominent members of CAGs elsewhere."
In Colombrito vs. Kelly, the Court accepted the definition of deprogramming by J. Le Moult published in 1978 in the Fordham Law Review:
"Deprogrammers are people who, at the request of a parent or other close relative, will have a member of a religious sect seized, then hold him against his will and subject him to mental, emotional, and even physical pressures until he renounces his religious beliefs. Deprogrammers usually work for a fee, which may easily run as high as $25,000. The deprogramming process begins with abduction. Often strong men muscle the subject into a car and take him to a place where he is cut from everyone but his captors. He may be held against his will for upward of three weeks. Frequently, however, the initial deprogramming only last a few days. The subject's sleep is limited and he is told that he will not be released until his beliefs meet his captors' approval. Members of the deprogramming group, as well as members of the family, come into the room where the victim is held and barrage him with questions and denunciations until he recants his newly found religion "
Exit counselor Carol Giambalvo writes in From Deprogramming to Thought Reform Consultation
"It was believed that the hold of the brainwashing over the cognitive processes of a cult member needed to be broken – or "snapped" as some termed it – by means that would shock or frighten the cultist into thinking again. For that reason in some cases cult leader's pictures were burned or there were highly confrontational interactions between deprogrammers and cultist. What was often sought was an emotional response to the information, the shock, the fear, and the confrontation. There are horror stories – promoted most vehemently by the cults themselves – about restraint, beatings, and even rape. And we have to admit that we have met former members who have related to us their deprogramming experience – several of handcuffs, weapons wielded and sexual abuse. But thankfully, these are in the minority – and in our minds, never justified. Nevertheless, deprogramming helped to free many individuals held captive to destructive cults at a time when other alternatives did not seem viable. "
Since the success of the deprogramming determined the legality of the endeavor (successful=converted member from his/her beliefs, or unsuccessful=traumatized kidnap victim), progressively extreme measures were taken.

Deprogramming and violence
An American named Ted Patrick was one of the most prominent early proponents of deprogramming. Most of the deprogramming cases took place in the United States, with only sporadic cases in Western Europe In the United States such opinions have been successfully challenged in court and are not supported by the American Psychological Association (APA).[2]

Deprogramming History
One of the points which fired deprogramming controversies was the fact that they were in the majority of cases successful See also Brainwashing controversy in new religious movements.
Deprogrammers claim that the voluntary participation is due to "mind control," a controversial theory that a person's thought processes can be changed by outside forces. They justify this intervention or "therapy" as necessary to bring the person out from under the influence of the group's "mind control." The existence of mind control is widely disputed. Modern behavorist psychology, however, can do much to explain the ability of external forces to control actions even if it has studied little regarding the internal thought processes associated with them (although relational framing and other theoretical constructs hedge into such territory). Present-day psychological principles suggest that traditional deprogramming approaches would almost certainly be inferior to other forms of intervention. Even supposing mind control is possible, it would be extremely difficult to prove to a legal standard that any individual person's mind has been controlled. In light of the legal and psychological issues, less intrusive and more patient-oriented interventions will likely replace this practice completely.
Involuntary deprogramming has fallen into disfavor because of its controversial aspects. A number of prominent anti-cult groups and persons have distanced themselves from the practice, noting that a less intrusive form of intervention called exit counseling has been shown to be more effective, less harmful, and less likely to lead to legal action. Organizations often referred to as cults, such as the Church of Scientology, insist that the practice is still commonplace, and they often make statements that their critics and opponents are "deprogrammers."
The American Civil Liberties Union published a statement in 1977 in which they position deprogramming as a violation of constitutional freedoms:
"ACLU opposes the use of mental incompetency proceedings, temporary conservatorship, or denial of government protection as a method of depriving people of the free exercise of religion, at least with respect to people who have reached the age of majority. Mode of religious proselytizing or persuasion for a continued adherence that do not employ physical coercion or threat of same are protected by the free exercise of religion clause of the First Amendment against action of state laws or by state officials. The claim of free exercise may not be overcome by the contention that 'brainwashing' or 'mind control' has been used, in the absence of evidence that the above standards have been violated."
In the 1980s in the United States, namely in New York (Deprogramming Bill, 1981), Kansas (Deprogramming Bill, 1982), and Nebraska (conservatorship legislation for 1985), lawmakers unsuccessfully attempted to legalize involuntary deprogramming.
Rev. Sun Myung Moon, founder of the Unification Church (many of whose members were targets of deprogramming) issued this statement in 1983:
The methods involved in "deprogramming" are like those used in Communist concentration camps. Using parents and relatives to entrap members, "deprogrammers" commit grown adults to mental hospitals with the supposed "illness" of holding of a minority religious belief. Other typical deprogramming techniques include kidnapping, illegal detention, violence, psychological harassment, sleep deprivation, inducement to use alcohol and drugs, sexual seduction and rape. By such threats, harassment and manipulation professional "deprogrammers" force members to renounce their faith. Many people are injured physically and psychologically because of this criminal activity. [3]

Controversy and related issues
During the 1990s, Rick Ross, a noted "cult" intervention advocate who took part in a number of deprogramming sessions, was sued by Jason Scott, a former member of a group called the Life Tabernacle Church, after an attempt at intervention after an abduction was unsuccessful. The jury awarded Scott $875,000 in compensatory damages and $1,000,000 in punitive damages against the Cult Awareness Network, and $2,500,000 against Ross, which were later settled for $5,000 and 200 hours of services "as an expert consultant and intervention specialist" (Scott vs. Ross, Workman, Simpson, Cult Awareness Network). The judgement was used to force CAN into bankruptcy, and its name and assets were purchased by a representative of the Church of Scientology, which had been frequently criticized by CAN, shortly afterwards. This case was seen as effectively closing the door on the practice of involuntary deprogramming.
Ted Patrick was found guilty of kidnapping Roberta McElfish, a 25-year old woman of Tucson, Ariz., in order to "deprogram" her in 1980 from a group known as the Wesley Thomas Family.
In the case of Kathy Crampton, she went back to the group Love Israel several days after the apparently successful deprogramming. Patrick was charged for kidnapping, but he was acquitted with the reasoning:
"[w]here parents are, as here, of the reasonable and intelligent belief that they were not physically capable of recapturing their daughter from existing, imminent danger, then the defense of necessity transfers or transposes to the constituted agent, the person who acts upon their belief under such conditions. Here that agent is the Defendant [Ted Patrick] ((District Court of the United States 1974: 79; New York Times 1974).
Steve Hassan, author of the book Combatting Cult Mind Control, states that he took part in a number of deprogrammings in the late 1970s, and has spoken out against them since 1980 . Hassan states that he has not participated in any deprogrammings since then, even though page 114 of Combatting, Hassan states that depogrammings can be kept as last resort if all other attempts fail. He is one of the major proponents of exit counseling as a form of intervention therapy, and he refers to his method as "strategic intervention therapy."

People and Places
Deprogramming and exit counseling, sometimes seen as one and the same, are distinct approaches to helping a person to leave a "cult". Some people blur the distinctions on purpose: some practioners do so to avoid criticism; some opponents do so to intensify criticism.
Proponents of the distinction, however, state that deprogramming entails coercion and confinement. In exit counseling the cult member is free to leave at any time. Deprogramming typically costs $10,000 or more, mainly because of the expense of a security team. Exit counseling typically costs $2,000 to $4,000, including expenses, for a three-to-five day intervention, although cases requiring extensive research of little-known groups can cost much more. Deprogramming, especially when it fails, entails considerable legal and psychological risk (e.g., a permanent alienation of the cultist from his or her family). The psychological and legal risks in exit counseling are much smaller. Although deprogrammers prepare families for the process, exit counselors tend to work more closely with families and expect them to contribute more to the process; that is, exit counseling requires that families establish a reasonable and respectful level of communication with their loved one before the exit counseling proper can begin. Because they rely on coercion, which is illegal except in the case of conservatorship and is generally viewed as unethical, deprogrammers' critiques of the unethical practices of cults will tend to have less credibility with cult members than the critiques of exit counselors.[4]

Deprogramming and exit counseling
The section could be improved by integrating relevant items into the main text and removing inappropriate items.
The 70s was a TV miniseries about four friends in the 1970s. One of the friends, played by Amy Smart, suffering a series of failures which damaged her self-esteem. She joins an apparent spiritualist group and changes her name, but does not realize it is under control of Jim Jones. The other friends wish to get her away from what they see as a cult, but express concern that the deprogrammer hired seems militaristic and freaky. Another of the friends, played by Guy Torry does the deprogramming himself, showing her pictures and films of her childhood.
An episode of The Simpsons called Burns' Heir dealt with the family trying to steal Bart away from Mr. Burns, who they believe is taking over Bart's life and upbringing. A deprogrammer who works for Conformco Brain Deprogrammers (which is owned by Mrs. Fields' Cookies) is hired. By mistake, the deprogrammer abducts Hans Moleman and gets him to believe Homer and Marge are his parents.
In the Simpsons episode The Joy of Sect, Homer Simpson is violently kidnapped from a UFO religious facility and then deprogrammed by Groundskeeper Willie, Reverend Lovejoy and Ned Flanders with the help of a baseball bat and beer.

Deprogramming in popular culture

Opposition to cults and new religious movements
Intervention (counseling) See also

Bibliography

Holy Smoke! 1999 movie based on the book with the same name

Sunday, March 23, 2008


In computational complexity theory, big O notation is often used to describe how the size of the input data affects an algorithm's usage of computational resources (usually running time or memory). It is also called Big Oh notation, Landau notation, and asymptotic notation. Big O notation is also used in many other scientific and mathematical fields to provide similar estimations.
The symbol O is used to describe an asymptotic upper bound for the magnitude of a function in terms of another, usually simpler, function. There are also other symbols o, Ω, ω, and Θ for various other upper, lower, and tight bounds. Informally, the O notation is commonly employed to describe an asymptotic tight bound, but tight bounds are more formally and precisely denoted by the Θ (capital theta) symbol as described below. This distiction between upper and tight bounds is useful, and sometimes critical, and most computer scientists would urge distinguishing the usage of O and Θ, but in some other fields the Θ notation is not commonly known.

Usage
In a way to be made precise below, O(f(x)) denotes the collection of functions g(x) – viewed as a function of variable x – that exhibit a growth that is limited to that of f(x) in some respect. The traditional notation for stating that g(x) belongs to this collection is:
g(x) = mathcal{O}(f(x)),.
This is an anomalous and exceptional use of the equals sign in mathematics, as the above statement is not an equation. It is improper to conclude from g(x) = O(f(x)) and h(x) = O(f(x)) that g(x) and h(x) are equal. One way to think of this, is to consider "= O" one symbol here. To avoid the anomalous use, some authors prefer to write instead:
g(x) in mathcal{O}(f(x)),,
without difference in meaning.
The common arithmetic operations are often extended to the class concept. For example, h(x) + O(f(x)) denotes the collection of functions having the growth of h(x) plus a part whose growth is limited to that of f(x). Thus,
g(x) = h(x) + mathcal{O}(f(x)),
expresses the same as
g(x) - h(x) in mathcal{O}(f(x)),.
Another anomaly of the notation, although less exceptional, is that it does not make explicit which variable is the function argument, which may need to be inferred from the context if several variables are involved. The following two right-hand side big O notations have dramatically different meanings:
f(m) = mathcal{O}(m^n),,
g(n),, = mathcal{O}(m^n),.
The first case states that f(m) exhibits polynomial growth, while the second, assuming m > 1, states that g(n) exhibits exponential growth. So as to avoid all possible confusion, some authors use the notation
g in mathcal{O}(f),,
meaning the same as what is denoted by others as
g(x) in mathcal{O}(f(x)),.
A final anomaly is that the notation does not make clear "where" the function growth is to be considered; infinitesimally near some point, or in the neighbourhood of infinity. This is in contrast with the usual notation for limits. A similar notational device as for limits would resolve both this and the preceding anomaly, but is not in use.

Equals or member-of and other notational anomalies
Big O notation is useful when analyzing algorithms for efficiency. For example, the time (or the number of steps) it takes to complete a problem of size n might be found to be T(n) = 4n² - 2n + 2.
As n grows large, the n² term will come to dominate, so that all other terms can be neglected—for instance when n = 500, the term 4n² is 1000 times as large as the 2n term. Ignoring the latter would have negligible effect on the expression's value for most purposes.
Further, the coefficients become irrelevant as well if we compare to any other order of expression, such as an expression containing a term n³ or n². Even if T(n) = 1,000,000n², if U(n) = n³, the latter will always exceed the former once n grows larger than 1,000,000 (T(1,000,000) = 1,000,000³ = U(1,000,000)).
So the big O notation captures what remains: we write
T(n)in mathcal{O}(n^2)
(read as "big o of n squared") and say that the algorithm has order of n² time complexity.

Infinite asymptotics
Big O can also be used to describe the error term in an approximation to a mathematical function. For example,
e^x=1+x+frac{x^2}{2}+mathcal{O}(x^3)qquadhbox{as} xto 0
expresses the fact that the error, the difference e^x - left(1 + x +frac{x^2}{2}right), is smaller in absolute value than some constant times left|x^3right| when x is close enough to 0.

Infinitesimal asymptotics
Suppose f(x) and g(x) are two functions defined on some subset of the real numbers. We say
f(x)mbox{ is }mathcal{O}(g(x))mbox{ as }xtoinfty
if and only if
exists ;x_0,exists ;M>0mbox{ such that } |f(x)| le ; M |g(x)|mbox{ for }x>x_0.
The notation can also be used to describe the behavior of f near some real number a: we say
f(x)mbox{ is }mathcal{O}(g(x))mbox{ as }xto a
if and only if
exists ;delta >0,exists ; M>0mbox{ such that }|f(x)| le ; M |g(x)|mbox{ for }|x - a| < delta.
If g(x) is non-zero for values of x sufficiently close to a, both of these definitions can be unified using the limit superior:
f(x)mbox{ is }mathcal{O}(g(x))mbox{ as }x to a
if and only if
limsup_{xto a} left|frac{f(x)}{g(x)}right| < infty.
In mathematics, both asymptotic behaviours near ∞ and near a are considered. In computational complexity theory, only asymptotics near ∞ are used; furthermore, only positive functions are considered, so the absolute value bars may be left out.

Example
The statement "f(x) is O(g(x))" as defined above is usually written as f(x) = O(g(x)). This is a slight abuse of notation; equality of two functions is not asserted, and it cannot be since the property of being O(g(x)) is not symmetric:
mathcal{O}(x)=mathcal{O}(x^2)mbox{ but }mathcal{O}(x^2)ne mathcal{O}(x).
There is also a second reason why that notation is not precise. The symbol f(x) means the value of the function f for the argument x. Hence the symbol of the function is f and not f(x).
For these reasons, some authors prefer set notation and write f in mathcal{O}(g), thinking of mathcal{O}(g) as the set of all functions dominated by g.
In more complex usage, O( ) can appear in different places in an equation, even several times on each side. For example, the following are true for ntoinfty
(n+1)^2 = n^2 + mathcal{O}(n)
(n+mathcal{O}(n^{1/2}))(n + mathcal{O}(log,n))^2 = n^3 + mathcal{O}(n^{5/2})
n^{mathcal{O}(1)} = mathcal{O}(e^n)
The meaning of such statements is as follows: for any functions which satisfy each O( ) on the left side, there are some functions satisfying each O( ) on the right side, such that substituting all these functions into the equation makes the two sides equal. For example, the third equation above means: "For any function f(n)=O(1), there is some function g(n)=O(e=g(n)." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side.

Big O notation Matters of notation
Here is a list of classes of functions that are commonly encountered when analyzing algorithms. All of these are as n increases to infinity. The slower-growing functions are listed first. c is an arbitrary constant.
Not as common, but even larger growth is possible, such as the single-valued version of the Ackermann function, A(n,n). Conversely, extremely slowly-growing functions such as the inverse of this function, often denoted α(n), are possible. Although unbounded, these functions are often regarded as being constant factors for all practical purposes.

Common orders of functions
If a function f(n) can be written as a finite sum of other functions, then the fastest growing one determines the order of f(n). For example
f(n) = 9 log n + 5 (log n)^3 + 3n^2 + 2n^3 in mathcal{O}(n^3),!.
In particular, if a function may be bounded by a polynomial in n, then as n tends to infinity, one may disregard lower-order terms of the polynomial.
O(n (unless, of course, c=1).

Properties
 f_1 inmathcal{O}(g_1) wedge                              <br />   f_2inmathcal{O}(g_2), implies f_1  f_2inmathcal{O}(g_1  g_2),
fcdot mathcal{O}(g) in mathcal{O}(f g)

Product
 f_1 inmathcal{O}(g_1) wedge                              <br />   f_2inmathcal{O}(g_2), implies f_1 + f_2inmathcal{O}(g_1 + g_2),
f + mathcal{O}(g) in mathcal{O}(f + g)

Sum
mathcal{O}(k g(n)) = mathcal{O}(g(n)),quad k ne 0
f(n)in O(g(n)) Rightarrow kf(n)in O(g(n))<br />

Multiplication by a constant
Big O is the most commonly used asymptotic notation for comparing functions, although in many cases Big O may be replaced with Θ for asymptotically tighter bounds (Theta, see below). Here, we define some related notations in terms of "big O":

Related asymptotic notations
The relation f(x) in  o(g(x)) is read as "f(x) is little-oh of g(x)". Intuitively, it means that g(x) grows much faster than f(x). It assumes that f and g are both functions of one variable. Formally, it states that the limit of f(x) / g(x) is zero, as x approaches infinity.
For example,
Little-o notation is common in mathematics but rarer in computer science. In computer science the variable (and function value) is most often a natural number. In math, the variable and function values are often real numbers. The following properties can be useful:
As with big O notation, the statement "f(x) is o(g(x))" is usually written as f(x) = o(g(x)), which is a slight abuse of notation.

2x  in o(x^2) ,!
2x^2 not in  o(x^2)
o(f) + o(f) subseteq o(f)
o(f)o(g) subseteq o(fg)
o(o(f)) subseteq o(f)
o(f) subset O(f) (and thus the above properties apply with most combinations of o and O). Little-o notation
For more details on other notations go to: Asymptotic Growth of Functions

Other related notations
Big O (and little o, and Ω...) can also be used with multiple variables. For example, the statement
f(n,m) = n^2 + m^3 + hbox{O}(n+m) mbox{ as } n,mtoinfty
asserts that there exist constants C and N such that
forall n, m>N: |g(n,m)| le C(n+m).
where g(n,m) is defined by
f(n,m) = n + g(n,m).
To avoid ambiguity, the running variable should always be specified: the statement
f(n,m) = hbox{O}(n^m) mbox{ as } n,mtoinfty
is quite different from
forall m: f(n,m) = hbox{O}(n^m) mbox{ as } ntoinfty.

Multiple variables
It is often useful to bound the running time of graph algorithms. Unlike most other computational problems, for a graph G = (V, E) there are two relevant parameters describing the size of the input: the number |V| of vertices in the graph and the number |E| of edges in the graph. Inside asymptotic notation (and only there), it is common to use the symbols V and E, when someone really means |V| and |E|. We adopt this convention here to simplify asymptotic functions and make them easily readable. The symbols V and E are never used inside asymptotic notation with their literal meaning, so this abuse of notation does not risk ambiguity. For example O(E + VlogV) means O((E,V) mapsto |E| + |V|cdotlog|V|) for a suitable metric of graphs. Another common convention—referring to the values |V| and |E| by the names n and m, respectively—sidesteps this ambiguity.

Generalizations and related usages

Asymptotic Growth of Functions: Presentation and definition of all notations.
Asymptotic expansion: Approximation of functions generalizing Taylor's formula.
Asymptotically optimal: A phrase frequently used to describe an algorithm that has an upper bound asymptotically within a constant of a lower bound for the problem
Hardy notation: A different asymptotic notation
Limit superior and limit inferior: An explanation of some of the limit notation used in this article
Nachbin's theorem: A precise way of bounding complex analytic functions so that the domain of convergence of integral transforms can be stated.