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Royal Academy of Dance

The Royal Academy of Dance (RAD) is a UK-based examination board specialising in dance education and training, with an emphasis on classical ballet. The RAD was founded in London, England in 1920 as the Association of Teachers of Operatic Dancing, and was granted a Royal Charter in 1935. Queen Camilla is patron of the RAD, and Darcey Bussell was elected to serve as president in 2012, succeeding Antoinette Sibley who served for 21 years.

The RAD was created with the objective to improve the standard of ballet teaching in the UK. In pursuit of improving instruction, a new teaching method and dance technique was devised for the Academy by a group of eminent European dancers. The RAD is one of the largest dance organisations in the world with over 13,000 members in 85 countries, including about 7,500 who hold Registered Teacher Status. There are currently about 1,000 students in full-time or part-time teacher training programmes with the RAD, and each year about 250,000 candidates enter RAD examinations worldwide.

RAD exams are recognised by the national qualifications regulators of all four UK nations (England, Scotland, Wales and Northern Ireland) with selected exams also carrying a UCAS tariff towards university admission. The RAD is also a validated awarding body of the Council for Dance Education and Training. The RAD works in partnership with the International Dance Teachers' Association. Royal Academy of Dance is charity 312826 registered in England and Wales.

1920
On 18 July 1920, Phillip J. S. Richardson, then Editor of Dancing Times magazine, organised a dinner for eminent dance professionals at the former Trocadero Restaurant in Piccadilly. The diners included five special guests, representing the principal methods of ballet training in use at that time.

 * Phyllis Bedells – English Method
 * Lucia Cormani – Italian Method
 * Edouard Espinosa – French Method
 * Adeline Genée – Bournonville Method, Denmark
 * Tamara Karsavina – Imperial Method, Russia

Other guests included Ninette de Valois, the founder of England's Royal Ballet company, and Anton Dolin, the co-founder of English National Ballet. The purpose of the meeting was to discuss the poor quality of dance training in Britain at that time and following further meetings, the Association of Teachers of Operatic Dancing of Great Britain was formed, with Adeline Genée as its first President. The Association would be the predecessor of the RAD.

1921–1928
In 1921, the Association established headquarters at the offices of Dancing Times magazine in London and the first Elementary, Intermediate and Advanced level examinations were held in the years that followed, with the first Children's syllabus being published and then examined in 1923 and 1924. In 1927 a scholarship scheme was introduced for students studying dance with an Association member and in 1928, Queen Mary consented to become Patron of the Association of Teachers of Operatic Dancing.

1930–1934
In November 1930, the first issue of Dance Gazette was published containing a historical review of the Association's first ten years. 'Dance Gazette' is still the official magazine of the RAD, being distributed quarterly to all fully paid members. Since 2011, it is also available to buy in selected branches of WHSmith in the UK. In 1931, the first Genée International Ballet Competition for female dancers was held in London, with awards for male dancers being introduced later in 1939. The competition is the RAD's flagship annual event, named after Dame Adeline Genée DBE. The competition was introduced as an additional incentive for candidates who had passed the Solo Seal examination, and has taken place almost every year since 1931, even during the Second World War. In 1934, the Royal Opera House, Covent Garden agreed to an alliance with the Association and a Grand Council of men & women was formed to act as a governing body to advise the executive committee.

1935–1937
In 1935 King George V approved the granting of a Royal Charter for the Association of Teachers of Operatic Dancing. The charter was eventually affixed with his Great Seal in 1936, and the Association of Teachers of Operatic Dancing officially became the 'Royal Academy of Dancing' (RAD). The following year in 1937, a coat of arms was designed by the College of Arms in London.

Coat of Arms
The RAD coat of arts was granted by the College of Arms in 1937, designed by the Hon. George Bellew, Somerset Herald of Arms and Registrar. The crest at the top of the coat of arms is a figure of Terpsichore, one of the Muses from Greek mythology, representing dance. The supporter at either side of the shield is a winged doe, symbolising lightness and grace of movement. The Escutcheon shows a pentagram symbolising health, with a wavy and zigzag line conveying the movement of dancing. The motto 'Salus et Felicitas' translates to mean health and happiness.

1950–1954
In 1950, founder President of the RAD Adeline Genée was appointed a Dame Commander of the Order of the British Empire in the New Year Honours List. Further honours were awarded to members of the Academy in 1951, with Ninette de Valois being appointed a Dame, Philip Richardson being awarded an Order of the British Empire (OBE) and Margot Fonteyn awarded a Commander of the Order of the British Empire (CBE). Following the death of Queen Mary in 1953, Queen Elizabeth II consented to become the Royal Patron of the Royal Academy of Dancing and Dame Adeline Genée instituted the Queen Elizabeth II Coronation Award to mark the occasion. The award is presented annually in recognition of outstanding services to the art of ballet. The first recipient was Dame Ninette de Valois, founder of The Royal Ballet Company. The following is a list of selected recipients of the award.

 * Phyllis Bedells, the first recognised English ballerina and a founder member of the RAD
 * Tamara Karsavina, Russian ballerina, founder member of the RAD and vice-president for over 30 years
 * Ninette De Valois, dancer, choreographer and director, founder of the Royal Ballet, Birmingham Royal Ballet and *Royal Ballet School
 * Anton Dolin, dancer, choreographer and director, co-founder of the English National Ballet
 * Marie Rambert, founder of the first professional dance company in the UK, which survives today as Rambert Dance Company
 * Alicia Markova, English prima ballerina assoluta and co-founder of English National Ballet
 * Beryl Grey, dancer and director, former RAD vice-president and life president of the Imperial Society of Teachers of Dancing
 * Rudolph Nureyev, Russian dancer, choreographer, director and former artistic director of Paris Opera Ballet
 * Frederick Ashton, founder choreographer and former artistic director of the Royal Ballet
 * Robert Helpmann, Australian dancer, actor, choreographer and director, most famous for playing the Child Catcher in the film Chitty Chitty Bang Bang
 * Gillian Lynne, former ballet dancer, most famous as a choreographer of West End and Broadway musicals including Cats
 * Antoinette Sibley, former ballet dancer who served as President of the RAD from 1991 to 2012.

Dame Adeline Genée retired as President of the RAD in 1954 and Dame Margot Fonteyn was elected as her successor. The leading Principal dancer of the Royal Ballet at that time and considered the greatest Ballerina of her generation, Fonteyn was later appointed Prima Ballerina Assoluta of the Royal Ballet by Queen Elizabeth II.

1963–1968
In 1963, the Academy was granted charitable status. In 1965, the first RAD summer school was held at Elmhurst Ballet School in Camberley, Surrey. Teachers and dancers attended the summer school from the United States, Canada, New Zealand as well as the UK. In 1968, Dame Margot Fonteyn devised a new children's syllabus, which would become the basis for lower graded examinations.

1970–1975
On 23 April 1970, Founder President of the Academy, Dame Adeline Genée died at the age of 92 and in 1972, the RAD moved into its current headquarters in Battersea Square, London. The building was fully refurbished to provide high quality dance facilities and was officially opened by Queen Elizabeth II in 1974. The following year in 1975, the Academy established the Professional Dancer's Teaching Diploma, an intensive course for professional ballet dancers and other dance professionals to gain registered teacher status with the RAD and in 1976, the RAD's teacher training schemes were organised into what is now officially the Faculty of Education of the RAD.

1979
In 1979, a new bursary was founded and named in honour of Phyllis Bedells, a founder member and former vice-president of the RAD. The bursary of £1,000 is held annually, awarded for further training in the academy's method and is awarded to young dancers who are under 17 years of age and have passed RAD Advanced 1 with Distinction but have not entered for the Advanced 2 examination. Past winners have gone on to win medals in very high-profile competitions, such as the Genée International Ballet Competition, and to dance with world-renowned companies including the Australian Ballet, Dutch National Ballet, English National Ballet, London City Ballet, Maurice Béjart and The Royal Ballet. Payment of the Bursary can be offset against existing tuition fees where the winner may be studying, or against material / equipment needed for the winner to continue their training.

1983
In 1983, the RAD opened its first International headquarters in Darlinghurst, New South Wales, Australia. Since that time, the RAD has opened offices worldwide, including Brazil, China, Germany, Greece, Israel, Italy, Jamaica, Japan, Mexico, New Zealand, Singapore, South Africa, Spain, United Arab Emirates and the United States of America,

1990–1992
In 1990, a new studio complex was opened at RAD headquarters. Titled the 'Fonteyn Centre', it was opened by Queen Elizabeth II. The following year in 1991, Dame Margot Fonteyn died on 21 February in Panama City and Antoinette Sibley was elected as the RAD's third President. Also in 1991, the 'Graded Examination Syllabus' was introduced, with Grades 6, 7 and 8 being introduced later in 1992. The three-year teacher training course was also amended in 1992, being replaced by the RAD's first full-time Degree qualification, the BA (Hons) Art & Teaching of Ballet (now the BA in Ballet Education).

1995–1999
The RAD celebrated its 75th anniversary in 1995, the event being marked by events throughout the world. In 1996, RAD President Antoinette Sibley was appointed a Dame in the Queen's New Year Honours List and the Academy's first 12-degree students attended their graduation at Durham Castle. In 1997, the Benesh Institute was incorporated into the RAD and in 1999, The 'Faculty of Education' was established with further teaching qualifications being launched, validated by the University of Durham.

2000
On 20 December 2000, the RAD officially adopted its current title, "Royal Academy of Dance" and in the same year, qualifications were established for students studying 'Benesh Movement Notation'.

2010
In 2010 the RAD became an Accredited Institute of the University of Surrey.

2011
On 4 January 2011 in London and 17 January in Sydney, the RAD launched its new Intermediate Foundation & Intermediate syllabi. RAD Grades 1–8 and the first five levels of the Vocational Grades were accredited by the Office of Qualifications and Examinations Regulation (Ofqual) in England with the RAD as an Awarding Organisation, and the Academy also achieved SQA Accreditation (Scottish Qualifications Authority Accreditation) for RAD exams. UCAS tariff points for Graded and Vocational Graded Examinations in Dance at Level 3 were confirmed in August, meaning those candidates who have achieved a Pass or higher at Grades 6–8, Intermediate or Advanced Foundation can use their exam result as contributing towards their points tariff when applying to a university or Higher Education institution in the UK. The Genée International Ballet Competition 2011 was held for the first time in Cape Town, South Africa, at Artscape Theatre Centre, looking to present the competition in New Zealand in 2012. The first ever Dance Proms took place on Sunday 13 November at the Royal Albert Hall, London, as a partnership project between the International Dance Teachers Association, the Imperial Society of Teachers of Dancing, RAD and the Royal Albert Hall working together in celebration of dance and hosting more than 450 young dancers on the stage. UK and Republic of Ireland members from the three dance organisations were invited to video and submit a short dance piece online, and a variety of acts were then chosen both by an esteemed panel of professionals and through a public vote to perform live at the Royal Albert Hall.

2024
In May 2024, Queen Camilla became patron of the RAD.

Examinations
The RAD offers two examination syllabi, which are suitable for both male and female students and form the basis of the RAD's work in the UK and overseas. Each programme consists of a series of progressively more difficult practical examinations. Grades 1–8 and the first five levels of the Vocational Grades are accredited by the Office of Qualifications and Examinations Regulation (Ofqual) in England, the Qualifications Wales in Wales and the Council for the Curriculum, Examinations & Assessment (CCEA) in Northern Ireland. These organisations are the Government approved qualifications regulators for their respective countries. Candidates who successfully pass an RAD examination are awarded credit on the Qualifications and Credit Framework. The Academy also achieves SQA Accreditation (Scottish Qualifications Authority Accreditation) for RAD exams.
 * Graded Examination Syllabus
 * Vocational Graded Examination Syllabus

In 2009, the RAD launched a new syllabus at Pre-Primary and Primary level in dance. These two new grades replace the existing Pre-Primary and Primary grades in ballet. The Academy has since launched new work for grades 1–5

Graded Syllabus
The Graded Examination Syllabus consists of Pre-Primary, Primary, and numbered Grades 1–8. Each grade incorporates classical ballet, free movement and character dance. The syllabus is devised to progress in difficulty from one grade to the next and a student studying the grades in sequence would be expected to develop a greater degree of dance technique at each level.

 * Classical Ballet is one of the most widespread dance forms in the world. Originating in the Italian royal courts of the Renaissance period, over hundreds of years it has been developed into a highly technical dance form.  Ballet is the foundation of the RAD's work and is the most important part of the Graded Syllabi.
 * Free Movement is the term applied to movement from dance styles such as natural movement, contemporary and Classical Greek dance. Free movement does not have to include codified dance vocabulary and is usually an improvisation based on the students interpretation of a piece of music or stimulus.
 * Character Dance is an integral part of classical ballet repertoire. It is the stylised representation of a traditional folk dance, normally from a European country and uses movements and music which have been adapted for the theatre. The RAD syllabus uses character dances based on Hungarian, Russian and Polish folk dance.

Students who have studied a complete grade from the syllabus will normally take an examination organised by their dance teacher and held at the teachers studio or a suitable venue hired for the occasion. In the examination, the students perform the relevant grade work for an RAD examiner, who assesses the artistic and technical execution of the grade. A successful candidate receives a certificate printed with their name and the grade passed. They also receive a report detailing what marks were awarded and highlighting which aspects of their performance need further improvement. Unsuccessful candidates receive a report and a certificate of participation. The Pre-Primary grade is devised for younger students who are not old enough to enter the Primary examination. There is no examination offered at this level, however students can take part in a Presentation Class.

Presentation Classes were introduced for students who a dance teacher feels may not benefit from, or be suitable for taking the series of examinations. In a Presentation Class, in contrast to an examination, the teacher and a small audience of spectators are present in the room. The students perform for an examiner but are not assessed. They dance a condensed selection of exercises from the appropriate grade and receive a certificate of participation, which is normally presented by the examiner at the end of the class.

As a syllabus devised specifically with children in mind, examinations are not compulsory. The entry level of a new student is decided by the dance teacher based upon the child's age, natural ability for dance or previous examination passes with another dance school or examination board, such as the IDTA or ISTD.

Grades
The Grades are:
 * Pre-Primary – 5 years and over
 * Primary – 6 years and over
 * Grade 1 – 7 years and over
 * Grade 2 – 7 years and over
 * Grade 3 – 7 years and over
 * Grade 4 – 7 years and over
 * Grade 5 – 7 years and over
 * Grade 6 – 11 years and over
 * Grade 7 – 11 years and over
 * Grade 8 – 11 years and over

Vocational Graded Syllabus
The Vocational Graded Syllabus is designed primarily for older children or young adults who are considering a career in professional dance, as a performer, teacher or in another capacity. The vocational syllabus is technically demanding and comprises only Classical Ballet and Pointe Work. Students choosing to study this series of awards are required to be competent in the fundamentals of ballet technique and movement vocabulary.

Unlike the Graded Examination Syllabus, the vocational grades have to be studied in sequence and the student must successfully pass an examination at each level before progressing onto the next. All vocational examinations are organised by RAD headquarters and instead of being held at a dance teachers own venue, they are held in major cities worldwide. In this situation, the session organiser is responsible for timetabling the examinations, and it is normal for students to dance alongside the students of other dance schools in the examination room. As with the graded syllabus, successful candidates receive a certificate personalised with their name and the level passed. They also receive a report, however for this series of examinations, there is a different marking system and assessment criteria.

Students studying the vocational syllabus are expected to achieve a high level of technical and artistic ability in ballet and it can take a great deal of time and commitment to reach the standard required to pass these examinations. Normally, a student will begin studying the Vocational Graded Syllabus after completing Grade 5 in the Graded Examination Syllabus, however some students will continue to study the graded syllabus at the same time. The Intermediate Foundation and Advanced Foundation examinations are the only optional exams in this series of awards. They are devised for students who the teacher feels may need more preparation before studying at the higher level, however they are assessed in the same way, certificates awarded in the same way and credits awarded on the National Qualifications Framework.

The Vocational Grades are:
 * Intermediate Foundation – 11 years and over
 * Intermediate – 12 years and over
 * Advanced Foundation – 13 years and over (non-compulsory)
 * Advanced 1 – 14 years and over (non-compulsory)
 * Advanced 2 – 15 years and over (non-compulsory)
 * Solo Seal- Must hold their Advanced 2 with distinction

LRAD
The Licentiate of the Royal Academy of Dance (LRAD) is a programme to allow students who already have, or are in the process of finishing, qualifications for a dance degree, to specialise in Royal Academy of Dance work. It has no practical placement component, but instead comprises "intensive practical study supported by lectures, presentations, peer teaching and seminars".

Style and technique
The RAD method, is a ballet technique and training system, specially devised by the founders of the RAD, who merged their respective dance methods (Italian, French, Danish and Russian) to create a new style of ballet that is unique to the organisation. The RAD method produces a style of ballet that has become recognised internationally as the English style of ballet.

Training method
The most identifiable aspect of the RAD method is the attention to detail when learning the basic steps, and the progression in difficulty is often very slow. While the difficulty of an exercise may only increase slightly from grade to grade, more importance is placed on whether the student is performing the step with improved technique. For example, plie exercises are employed consistently throughout the lower grades to enable the student to progressively deepen the plie and improve turnout. The principle behind this is that if enough time is spent achieving optimal technique before introducing new vocabulary, the easier it is for the student to learn the harder steps, while exercising basic technique to the maximum at all times.

Associations
From 1 October 2006, the RAD began a new association with the International Dance Teachers Association, a dance organisation based in Brighton, England. A press release issued to members of each organisation stated that "the two organisations would embark on a process of working together for the future of dance and to the mutual benefit of their members in both teacher education and training and examinations".

As a result of this association, both organisations have formally granted teachers of the respective organisation the opportunity to enter candidates for its examinations thereby ensuring that both organisations recognise the right of qualified teachers to enter candidates for examinations of either awarding body. At the RAD these members are called 'teachers recognised by mutual agreement'. Whilst the new association is not a merger, it is intended that it will develop co-operation between the two organisations and mutual recognition of the training and qualifications that they both provide.

Dance Proms is a partnership project between the IDTA, the ISTD, RAD and the Royal Albert Hall working together in celebration of dance. In 2011, Dance Proms hosted more than 450 young dancers on the stage, showcasing a huge range of dance styles and cultural influences. UK and Republic of Ireland members from the three dance organisations are invited to video and submit a short dance piece online, featuring original choreography by themselves or their students in any dance genre, either as a solo, duet, or group performance. Acts are then chosen both by an esteemed panel of professionals and through a public vote to be performed live at the Royal Albert Hall. Dance Proms is designed to showcase the high standards of dance and dance teaching of the organisations and their members, and to raise standards and increase participation in and appreciation of dance in the UK.

Countries
The Royal Academy of Dance is currently active in over 80 countries worldwide. The following is a list of countries, by region, in which the RAD has active members, including the locations of regional administrative offices:

UK & Ireland

 * England – Regional Office, London
 * Ireland
 * Northern Ireland
 * Scotland
 * Wales

Europe

 * Andorra
 * Austria
 * Belgium
 * Cyprus – Regional Office, Limassol
 * Denmark
 * France
 * Germany – Regional Office, Berlin
 * Gibraltar
 * Greece – Regional Office, Athens
 * Italy – Regional Office, Trento
 * Luxembourg – Regional Office, Gonderange
 * Malta – Regional Office, Sliema
 * Netherlands
 * Norway – Regional Office, Trondheim
 * Portugal – Regional Office, Lisbon
 * Serbia
 * Slovenia
 * Spain – Regional Office, Reus
 * Sweden
 * Switzerland
 * Turkey – Regional Office, Istanbul

North America

 * United States – Regional Office, St. Francis
 * Canada – Regional Office, Toronto
 * Mexico – Regional Office, Naucalpan

Caribbean, Central and South America

Mexico
 * Antigua & Barbuda
 * Aruba
 * Bahamas
 * Barbados
 * Bermuda
 * Brazil – Regional Office, Serra Negra
 * Chile
 * Costa Rica
 * Ecuador
 * El Salvador
 * Guadeloupe
 * Guatemala
 * Honduras
 * Jamaica – Regional Office, Kingston
 * Panama
 * Peru
 * St. Lucia
 * Trinidad and Tobago
 * Venezuela

Asia and Pacific

 * Australia – Regional Office, Darlinghurst
 * Brunei
 * China – Regional Office, Shanghai
 * Hong Kong – Regional Office, Kowloon
 * Indonesia – Regional Office, South Jakarta
 * Japan – Regional Office, Tokyo
 * Macau
 * Malaysia – Regional Office, Kuala Lumpur
 * New Zealand – Regional Office, Wellington
 * Papua New Guinea
 * Philippines – Regional Office, Pasig
 * Singapore
 * South Korea – Regional Office, Seoul
 * Taiwan – Regional Office, Taipei
 * Thailand – Regional Office, Chiang Mai

Africa, Middle East and South Asia

 * Bahrain
 * Bangladesh
 * Bhutan
 * Botswana
 * Ghana
 * India
 * Israel – Regional Office, Neve Yamin
 * Jordan
 * Kenya
 * Kuwait
 * Lebanon
 * Lesotho
 * Maldives
 * Mauritius
 * Mozambique
 * Namibia
 * Nepal
 * Oman
 * Pakistan
 * Qatar
 * South Africa – Regional Office, Johannesburg
 * Sri Lanka – Regional Office, Rajagiriya
 * Swaziland
 * United Arab Emirates – Regional Office, Dubai
 * Zimbabwe

Notable alumni

 * Jacqui Chan, Trinidadian actress
 * Mary Day, American dance teacher
 * Ana Paula Höfling, American dance researcher
 * Michelle Yeoh, Malaysian actress
 * Beatriz Luengo, actress, singer and dancer
 * Tara Sutaria, Indian actress and singer.

Ballet Schools & Companies – A number of international ballet schools offer their students the opportunity to take vocational examinations with the RAD. Examples include:

 * Elmhurst Ballet School
 * English National Ballet School
 * National Ballet School of Canada
 * Royal Ballet School

The Royal Academy of Dance is not affiliated to any of these schools.

title: Royal Academy of Dance


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Talk:Strongly connected component

There is also

 * There is also an algorithm called SCC that computes strongly connected components in graphs, by taking the inverse of a graph and working on the transpose G^t (V, E^-1) of G. Would it help if I put the pseudocode algorithm in here? Jontce 11:08, 17 May 2005 (UTC)
 * Isn't this a dictionary definition? At least, it should be linked to something else. m.e. 10:40, 28 May 2004 (UTC)

This page does not render correctly in IE7

Question about the algorithm
In step 1, DFS is called on a specific vertex v.

It needs to visit every vertex in the (weakly) connected component that v belongs to, to compute its finishing time.

In a directed graph, how can we choose the start node v for DFS in such a way as to visit every node in the weakly connected component of v and not add to the total complexity of the algorithm? This does not seem obvious to me. Thanks if you can explain this.

- Panayk (talk) 16:40, 18 January 2008 (UTC)

Nevermind. DSF is called on more than one starting vertices, taking care not to call it on (or revisit during a call) an already visited vertex. Perhaps we should mention that.

- Panayk (talk) 18:16, 18 January 2008 (UTC)

Algorithm
The algorithm section seems to be lifted word-for-word from CLR... —Preceding unsigned comment added by 67.114.158.146 (talk) 08:05, 9 April 2008 (UTC)

Is the image correct?
I see that C and H are not connected, is that correct? —Preceding unsigned comment added by 128.61.23.186 (talk) 19:36, 5 June 2008 (UTC)

 * yes, it is ok. They don't need to be directly connected by edges. --Fioravante Patrone en (talk) 20:08, 21 August 2008 (UTC)

 * I think he's right, since the definition is a PATH between two points. C can get to H and vice versa over a path. It's the fact that you can go both ways that makes that group strongly connected Delvarworld (talk) 08:22, 17 April 2011 (UTC)

Definition
The current definition (and the example) of a strongly connected component subtly avoids the delicate question whether a singleton node without selfloop is strongly connected or not.--94.221.120.119 (talk) 19:46, 22 January 2012 (UTC)
 * It does sort of avoid the question, but I think the only reasonable choice is to count a single node (without selfloop) as strongly connected to itself, by paths of lengths zero. For otherwise, it would not be true that strong connectivity is an equivalence relation and that the strongly connected components form a partition of any graph's vertices. —David Eppstein (talk) 22:30, 22 January 2012 (UTC)

Wrong definition of acyclic graphs
The article says that a graph is acyclic if and only if it has no strongly connected subgraphs with more than one vertex. However, a vertex with a selfloop fulfill this condition but is not acyclic. 141.3.44.192 (talk) 08:27, 13 September 2012 (UTC)

 * Interesting point. Does a node on its own count as 'strongly connected'? I think yes, as there is a path (of length zero) from each node to itself.  Therefore, the only subgraph that is strongly connected, but acyclic, is a single vertex without a self-loop.  Maybe it should be "a graph is acyclic if and only if it has no strongly connected subgraphs with at least one edge." Aaron McDaid (talk - contribs) 09:20, 13 September 2012 (UTC)

Different (graph) condesations?
There are some other possible notions of condensation, where the type of subgraph condensed isn't a strongly connected component. For example McCabe's algorithm for computing the essential complexity of a CFG (iteratively) condenses only the sub-graphs that have a single entry (source) and single exit point (sink), which are of course the structured programming control structures. Perhaps condensation isn't quite the proper term for that (it seems to also involve a sort of fixpoint iteration), but that's the term I found in a textbook (which has something like 3 editions, so it's probably not complete bunk) when I was looking for secondary sources for McCabe's paper:

That book also defines a couple more condensation that like along 2-components, which is for condensing/finding DD-paths. (You can use the google books search function to find them inside.)

In modern compilers, the condensation (although called "reducibility" as McCabe called his stuff in original) is actually done on a different type of sub-graphs called natural loops, defined as "single-entry, multiple-exit loop, with only a single branch back to the entry from within it". (This done so it fits better with languages that have break statements etc. In fact languages like Modula-2 have been designed so they emit natural loops when compiled.) This is standard material in most compiler textbooks; it's in the Dragon Book etc.

I'm not sure if these are worth mentioning here of if Condensation (graph theory) should perhaps be the place. Isn't there some general pattern-matching type of condensation defined somewhere? The above clearly are particularizaitions of a similar template, just with the sub-graphs matched changed. Also, they're all pattern matching just on sub-graphs to condense, there's no other (programming language) notion involved at the CFG level. (Unlike flow charts, CFGs don't have node types or branch labels etc.) 188.27.81.64 (talk) 08:19, 17 July 2014 (UTC)
 * If the word "condensation" is used in compiler graph theory to mean something different than its meaning in more theoretical branches of graph theory, and that meaning is notable enough, then we should probably have a separate article about it. Wikipedia articles are about the meanings, not about the words, so different meanings of the same word shouldn't be packed into the same article. —David Eppstein (talk) 03:03, 18 July 2014 (UTC)
 * After looking at more sources, I think that author (Jorgensen) is using the term condensation (outside of just SCCs) pretty idiosyncratically. I think he means something like modular decomposition, but for directed graphs. I wrote a stub on flow graph with more standard terminology; Jorgensen calls a flow graph a program graph which is an incredibly overloaded term by various other authors, so it took me a while to even find other references talking about the same concept... While the guys writing about flow graphs define a notion of prime flowgraph, it seems to me it's more restrictive than modular decomposition (even ignoring orientation issues) because the decomposition of flow graphs is defined to be limited to certain operations that make sense only for flowgraphs like nesting and sequencing. So, it probably doesn't makes sense to put "condensations" (or whatever they might be called) of flowgraphs on other, more general graph pages. 188.27.81.64 (talk) 15:36, 19 July 2014 (UTC)

Short description and Definition express different things
In the short description in the top it says: "In the mathematical theory of directed graphs,a graph is said to be strongly connected if every vertex is reachable from every other vertex". This is congruent to the picture given. In the Definitions-Section though, it states: "A directed graph is called strongly connected if there is a path in each direction between each pair of vertices of the graph.". This is a much harder and totally different criteria to be strongly connected.Now we need a duplex-connection between nodes. --BookRings (talk) 11:14, 26 July 2015 (UTC)
 * When it says "a path in each direction" it means two different paths. It doesn't have to be the sme path! In fact it can't possibly be the same path, because a path in a directed graph has to be consistently directed from its start towards its end. So the two definitions are the same. —David Eppstein (talk) 18:15, 26 July 2015 (UTC)

Also: Short description and Definition express different things
The short description does not require that SCCs are maximal. The definition using the equivalence on strongly connected nodes implies that SCCs are maximal. For the example: {a,b,e} is an SCC for the short describtion but not for the definition. — Preceding unsigned comment added by 2001:638:807:20D:FAB1:56FF:FEA6:40DF (talk) 16:09, 15 November 2019 (UTC)
 * The short description is both inaccurate as you say and too long. Any suggestions for how to make it both shorter and more accurate? —David Eppstein (talk) 18:39, 15 November 2019 (UTC)

Suggestion (Note that the article is about "strongly connected components" and not about the property of "strongly connected"). In the mathematical theory of directed graphs, a strongly connected component (or diconnected component) of a graph G is a maximal subgraph of G in which every vertex is reachable from every other vertex. The rest of the intro: "The strongly connected components (or diconnected components) of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected. It is possible to test the strong connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(V+E))." seems to be covered by the article. — Preceding unsigned comment added by 2001:638:807:20D:FAB1:56FF:FEA6:40DF (talk) 10:00, 18 November 2019 (UTC)
 * The short description needs to be a noun phrase rather than a noun, and ideally only maybe ten syllables long. —David Eppstein (talk) 17:01, 18 November 2019 (UTC)

Removed alternative name 'diconnected'
I've removed the synonym 'diconnected' from the article for the following reasons:

 * 1) It is not commonly used. The major references use only 'strongly connected'.
 * 2) It is easy to misread as 'disconnected' which has the opposite meaning to 'strongly connected' and so could cause confusion.
 * 3) Editors are repeatedly 'fixing' it to read 'disconnected' which means the article is just wrong.

Perokema (talk) 10:25, 5 March 2020 (UTC)

title: Talk:Strongly connected component


text:
User:BrianWilloughby

Artist, guitarist, inventor, electrical engineer, software developer, photographer, bassist, mastering engineer, sole proprietor

http://www.audiobanshee.com/

title: User:BrianWilloughby


text:
Glass cliff

The glass cliff is a hypothesized phenomenon in which women are more likely to break the "glass ceiling" (i.e. achieve leadership roles in business and government) during periods of crisis or downturn when the risk of failure is highest. Other research has expanded the definition of the glass cliff phenomenon to include racial and ethnic minority groups.

Origins
The term was coined in 2005 by British professors Michelle K. Ryan and Alexander Haslam of University of Exeter, United Kingdom. In a study, Ryan and Haslam examined the performance of FTSE 100 companies before and after the appointment of new board members, and found that companies that appointed women to their boards were likelier than others to have experienced consistently bad performance in the preceding five months. This work eventually developed into the identification of a phenomenon known as the glass cliff— analogous to the concept of a glass ceiling, but implying the inability to perceive the dangers of the cliff's transparent edge rather than the false promise of elevated organizational positions which can be "seen" through a ceiling of glass but which are actually unattainable. Since the term originated, its use has expanded beyond the corporate world to also encompass politics and other domains.

Overview
Ryan and Haslam's research showed that once women break through the glass ceiling and take on positions of leadership, they often have experiences that are different from those of their male counterparts. More specifically, women are more likely to occupy positions that are precarious and thus have a higher risk of failure—either because they are appointed to lead organizations (or organizational units) that are in crisis or because they are not given the resources and support needed for success.

Extending the metaphor of the glass ceiling, Ryan and Haslam evoked the notion of the "glass cliff" to refer to a danger which involves exposure to risk of falling but which is not readily apparent. CEO tenure is typically shorter at companies which are struggling, compared to those which are stable.

Evidence of the glass cliff phenomenon has been documented in the field of law. A 2006 study found law students were much likelier to assign a high-risk case to a female lead counsel rather than a male one. A 2010 study found undergraduate students in British political science likelier to select a male politician to run for a safe seat in a by-election, and much likelier to select a female candidate when the seat was described as hard to get. A 2014 analysis of US Fortune 500 leadership found that firms with weak performance were likely to promote women into CEO positions over white men.

Additional studies have found that women are likely to be primed as candidates in hard-to-win districts. Specifically in the United Kingdom, women of the Conservative Party are more likely selected by party elites to run in less winnable seats than conservative men, though they performed worse than men in elections. This occurs both with experienced and inexperienced women candidates, and those with both conventional and nonconventional political backgrounds, indicating a glass cliff phenomenon as opposed to any other explanation. Though the Conservative Party has begun to incorporate equality guarantee strategies, women candidates are still often specifically posed as candidates in hard to win districts.

In contrast, a 2007 study of corporate performance preceding CEO appointments showed that women executives are no more likely to be selected for precarious leadership positions than males.

Explanation
Many theories have been advanced to explain the existence of the glass cliff.

University of Houston psychology professor Kristin J. Anderson says companies may offer glass cliff positions to women because they consider women "more expendable and better scapegoats." She says the organizations that offer women tough jobs believe they win either way: if the woman succeeds, the company is better off. If she fails, the company is no worse off, she can be blamed, the company gets credit for having been egalitarian and progressive, and can return to its prior practice of appointing men.

Haslam and Ryan's initial studies indicate that people believe women are better-suited to lead stressed, unhappy companies because they are felt to be more nurturing, creative, and intuitive. These researchers argue that female leaders are not necessarily expected to improve the situation, but are seen as good people managers who can take the blame for organizational failure.

Haslam has shown that women executives are likelier than men to accept glass cliff positions because they do not have access to the high-quality information and support that would ordinarily warn executives away. Additional research has indicated that women and other minorities view risky job offers as the only chance they are likely to get.

A 2007 study found that female news consumers in the United Kingdom were likelier than male ones to accept that the glass cliff exists and is dangerous and unfair to women executives. Female study participants attributed the existence of the glass cliff to a lack of other opportunities for women executives, sexism, and men's in-group favoritism. Male study participants said that women are less suited than men to difficult leadership roles or strategic decision-making, or that the glass cliff is unrelated to gender.

Additional research has suggested that women see precarious glass cliff opportunities as the only chances for advancement. While men may view the same opportunities as risky, women candidates might be more willing to accept these positions out of necessity for career advancement purposes. Additionally, women are more likely than men to maintain their positions at any level during times of crisis, making them more readily available for advancement opportunities during times of crisis than male counterparts.

Women with traditionally feminine traits are sought out in times of crisis due to a perceived ability to better handle employee issues. Stereotypically feminine traits, including creativity, helpfulness and awareness of emotion are all associated with better being able to handle failure. Though these traits generally diminish the desirability of women for leadership positions, in times of crisis they are viewed as valuable assets that aid in leadership changes. These skill sets offer opportunities for non-traditional leadership styles, viewed favorably in times of crisis.

Glass cliff situations are likely only to arise under certain conditions, in which women leaders have access to resources they view as favorable to leaders. Research has indicated that in times of crisis, women view leadership positions with a greater amount of social resources more positively than they do positions lacking in social resources. However, they view positions lacking financial resources equally as positively as those with a wide range of social resources.

Glass cliff for racial and ethnic minority leaders
The glass cliff concept has also been used to describe employment discrimination experienced by leaders who are members of minorities or disabled.

Research analyzing the head coaches of NCAA sports teams found that men of racial and ethnic minority groups were promoted to higher leadership positions in times of crisis. Within historically Black colleges and universities, minority leaders were more often appointed than white leaders under all circumstances, but in other universities, minority leaders were appointed to leadership positions primarily in times of crisis. These leaders are also likely to suffer from high visibility, scrutiny and performance pressures that their white counterparts do not receive. The study also found evidence for the savior effect, the idea that organizations will look for "saviors", usually white, when minority leaders are unable to deliver high-quality performance results in times of crisis. Outside of the NCAA, this has occurred in the political sphere. Often times, the 2008 election of Barack Obama, the first Black president of the United States of America, in the midst of a global financial crisis is viewed as evidence of the glass cliff phenomenon for racial and ethnic minority groups.

In British politics, research has indicated that the Conservative Party sent Black and minority ethnic candidates to contest parliamentary seats that are harder to win than other candidates, indicating similar findings other research on the political glass cliff for women candidates. This phenomenon is specific, however, to the Conservative Party, which has traditionally promoted anti-immigration sentiments that may contribute to this. The rise of Rishi Sunak as the United Kingdom's first prime minister of South Asian heritage, following scandals that brought down two prime ministers within a year, was described as an example of the glass cliff effect.

Minority women face a duplicated glass cliff, being affected by both their gender and race. Black women are often given unsustainable amounts of work in higher positions, creating barriers in their careers. It has additionally been argued Black women may be promoted to leadership positions due to outdated stereotypes related to masculine traits Black women are perceived to have. In addition to struggles related to leadership, Black women are also likely to face an added weight of microaggressions and increased questioning of qualifications.

Implications for women and minority group executives
Glass cliff positions risk hurting the women executives' reputations and career prospects because, when a company does poorly, people tend to blame its leadership without taking into account situational or contextual variables. Additionally, women who are appointed to glass cliff positions may be subject to increased criticism from shareholders, who may lack confidence in their leadership. In contrast, Men who assume leadership in times of crisis are less likely to experience this backlash, and suffer fewer reputation based consequences. Researchers have found that female leaders find it harder than male ones to get second chances once they have failed due to having fewer mentors and sponsors and less access to a protective "old boys' network".

The glass cliff phenomenon adds to the breadth of work on why women are less likely than men to succeed in leadership positions across a wide range of opportunities, from local school districts to the corporate sphere. As a method of descriptive representation, women who see women leaders disposed of as a result of glass cliff leadership may be less likely to see themselves in positions of power, and be less likely to express interest in career advancement.

However, some researchers argue that companies in bad situations offer more opportunities for power and influence compared with companies that are stable.

A study examining glass cliff effects on women leaders in Turkey, a country which has high levels of femininity, found that the preference for female candidates was higher in times of good performance than in times of poor performance. Additional research has affirmed this finding in other countries.

Examples
News media have described the following as examples of the glass cliff.

Political examples

 * In 1990, two female Premiers were appointed in Australia: Joan Kirner inherited a significant deficit in Victoria, while Carmen Lawrence headed a party that had previously been accused of corruption. In 2009, Kristina Keneally was appointed Premier of New South Wales amid low polling for her party and their eventual defeat in 2011. Julia Gillard was appointed as Australia's first female prime minister and subsequently ousted amid procedural complaints about the leadership spill.
 * In 1993, the Canadian Progressive Conservative Party, facing low approval ratings and almost assured loss in the upcoming general elections, elected Kim Campbell, then Defense Minister, to replace Brian Mulroney as its leader. The election dealt the Progressive Conservatives one of the most devastating defeats in Canadian history, reducing them from 156 seats to 2.
 * In 2009, Indonesian Finance Minister Sri Mulyani was accused of misappropriating the country's funds to conduct an alleged unauthorized bailout for Bank Century a year prior which was failing at the time. She contested that the Rp. 6,7 Trillion ($710 Million) bailout was necessary, in order to prevent the country's economy from crashing and received a warning of the bank's impending failure from the central bank. She decided to resign as finance minister in 2010 after 5 years and 7 months in office during Susilo Bambang Yudhoyono's presidency, keeping the country's economy stable during the world financial crisis.[[File:A presidente Dilma Rousseff durante cerimônia contra o impeachment em 31 de março de 2016.jpg|thumb|Dilma Rousseff during her 2016 impeachment trial]]
 * In 2010, Dilma Rousseff was appointed candidate for president of Brazil by the Partido dos Trabalhadores (Workers' Party) when they were being investigated by the Federal Police for allegations of corruption schemes. She won the presidential election and was reelected for a second term in 2014. She was then impeached in 2016.
 * In 2016, Theresa May became leader of the Conservative Party and Prime Minister of the United Kingdom shortly after a referendum result to leave the EU caused the pound to drop in value to levels not seen in 30+ years.
 * In 2020, Agnès Buzyn replaced Benjamin Griveaux as the LREM candidate for Mayor of Paris, after the initial candidate's alleged sexts with a woman were leaked.
 * In 2020, Chrystia Freeland was appointed as Canada's first female federal finance minister during the economic crisis caused by the COVID-19 pandemic. Her appointment to minister of finance was a direct result of former minister Bill Morneau's WE Charity Scandal.
 * In 2021, U.S. Vice President Kamala Harris was tapped to lead the response to challenges at the southern border, which has historically been a significant and polarized issue in American politics.
 * In 2022, Liz Truss became leader of the Conservative Party and Prime Minister of the United Kingdom following Boris Johnson's resignation after a government crisis, and amid a surge in global inflation and the domestic cost of living. She resigned on her fiftieth day in office, following a second government crisis.

Corporate and business examples

 * In 2002, then-unprofitable telecommunications company Lucent Technologies appointed Patricia Russo CEO, and then replaced her with Ben Verwaayen.
 * In 2008 after the Icelandic banking crisis, various women were appointed to repair the industry with the rationale that broader perspectives would prevent the same mistakes from occurring.
 * In 2011, "a horrible time for newspapers", Jill Abramson was appointed editor of The New York Times, and in 2014 she was fired.
 * In 2012, Marissa Mayer was appointed as the CEO of Yahoo after it lost significant market share to Google.
 * In 2015, Ellen Pao resigned amidst controversy after several months as CEO of Reddit. Much of the furore was directed at the firing of popular Reddit employee Victoria Taylor, though former Reddit CEO Yishan Wong revealed that this was the decision of cofounder Alexis Ohanian, not Pao.
 * In 2021, Alexis George was appointed as the CEO of the troubled Australian financial services company AMP Limited.
 * In 2021, Jen Oneal was appointed the first female lead of Blizzard Entertainment after the California Department of Fair Employment and Housing v. Activision Blizzard lawsuit which alleged the company had a culture of sexual misconduct. Following Activision Blizzard's acquisition by Microsoft in 2023, Johanna Faries, the general manager of the Call of Duty series, was named Blizzard Entertainment's new president effective on February 5, 2024. Faries' appointment was a significant change for Blizzard Entertainment, whose leaders have in the past come up through the ranks of gaming and tech.
 * In 2023, Linda Yaccarino was appointed as the CEO of Twitter while the company was facing an uncertain future and a number of challenges, including outages, user discontent and advertiser skepticism. The company lost more than half of its value since its acquisition by Elon Musk six months prior.

title: Glass cliff


text:
The Dawn Parade

The Dawn Parade were a British rock band from Bury St Edmunds formed in 2000. Greg McDonald was the main songwriter, and also provided vocals and guitar.

The band performed 200 gigs in the UK and received critical acclaim from Rolling Stone and John Peel, for the latter of whom the band performed a number of live sessions.

Biography
In 1998 friends from Thurston Community College, Greg McDonald, Nick Morley, Tom Weller and Ben Jennings formed a band, The Hip Down. The band played a small festival as their debut performance and later recorded a ten track demo at Meadowside Studios in Wisbech. Shortly into 1999 Weller departed to University, leaving the band without a permanent bassist. In late 1999, singer-songwriter Seymour Glass briefly joined on bass before leaving to front another local band, Miss Black America.

Auditioning many bass players and managing to win a local band competition covering "Bohemian Rhapsody", they formed a new incarnation of the band in 2001, with Rob Brown (guitar) and Dave Jago (bass) under the new name The Dawn Parade. The band's name came from McDonald's term for his walk back to his village on a Monday morning as the sun came up, having spent the money needed for a taxi home in bars the previous night. The new band played several shows and recorded a self-funded, self-titled debut EP, which the band distributed themselves. Shortly before the release of the EP, Jago left to concentrate on his own project, grindcore band Becky Jago, and was replaced by the longstanding permanent bassist Barney Wade.

Several months later the band made an appearance on an early form of internet television station 'MP3TV' which led them to finally releasing their first official single, "Good Luck Olivia", under the station's show host Susan Hyatt's Not Your Common Records. Then came their second, "Hole in my Heart", in 2002 via the Cambridge based independent record label, Repeat Records, leading the band to tour extensively around the UK for six weeks. Soon after this the band recorded its first Peel Session. The second took place in March 2003, live with a studio audience at BBC Maida Vale (MV4). The band further gigged extensively across the country until July 2003, when Morley, Jennings and Wade decided to leave and focus on their own musical projects, such as the Brighton based ‘Enid Blitz’.

The band re-formed with a new line-up of McDonald on guitar and vocals, Jeremy Jones (lead guitar), Neil Rayson (bass guitar), Mark Sewell (drums, vocals) and Claire Pruden (backing vocals). Rayson was soon replaced by Steve McLoughlin. The first single of this lineup was "The Fortune Line". The band changed its name to The Visions in late 2005, shortly after finishing recording their debut album in Wales with producer Chris Brown. By August 2006 the band split and finally released their debut album in November 2006 on Repeat Records under their original name The Dawn Parade.

Following the Dawn Parade's split, McDonald continued as a solo artist; he has, to date, recorded two full-length solo albums, partly in collaboration with former Hip Down/Dawn Parade members Jeremy Jones, Nick Morley and Seymour Glass (credited as Seymour Patrick) and continues to play live throughout the UK.

Singles / EPs

 * "The Dawn Parade EP" (2001)
 * "Good Luck Olivia" (2001)
 * "Electric Fence Your Gentleness EP" (2002)
 * "Caffeine Row" (January 2003)
 * "Strung Out On Nowhere" (August 2003)
 * "The Underground" (November 2004)

Albums

 * The Dawn Parade (2006)

title: The Dawn Parade


text:
Jing (Chinese medicine)

Jing is the Chinese word for "essence", specifically Kidney essence. Along with qi and shen, it is considered one of the Three Treasures of traditional Chinese medicine.

Description
According to Traditional Chinese Medical theory, jing or essence can be summarised in two parts: the Yin, being congenital or prenatal, and the Yang, being postnatal or acquired. Prenatal jing is acquired at birth from the parents: the father's sperm and the mother's ovum. Postnatal jing is acquired after birth through food, water, oxygen, as well as environmental and social conditions. The concept is expounded in the Chinese theoretical cosmological treatise called the Bagua and within the I Ching.

The Yin and Yang jing transform to create and replenish each other. The Yang jing circulates through the eight extraordinary vessels and transforms to become and replenish yin; in turn the marrow becomes blood, body fluid and semen.

Jing should not be confused with the related concept of jin (勁; "strength" or "energy"), as in Neijin meaning "internal power", nor with jīng (經; "classic"), which appears in many early Chinese book titles, such as the Huangdi Neijing, Yijing, and Chajing.

The characteristics which constitute signs of good jing (e.g. facial structure, teeth, hair, strength of adrenals or Kidneys) share the embryological origin of neural crest cells. These cells undergo immense and challenging cellular migrations requiring great organization. As such, jing may simply represent the strength of embryological self-organization in the organism. This will be manifested most strongly in those cells which require most organization; that is, the neural crest cells.

Allocation
One is said to be born with a fixed amount of jing (prenatal jing is sometimes called yuanqi) and also can acquire jing from food and various forms of stimulation (exercise, study, meditation).

Theoretically, jing is consumed continuously in life; by everyday stress, illness, substance abuse, sexual intemperance, etc.

Prenatal jing is very difficult to be renewed, and it is said it is completely consumed upon dying.

Restoration
Jing is therefore considered quite important for longevity in traditional Chinese medicine (TCM); many disciplines related to qigong are devoted to the replenishment of "lost" jing by restoration of the post-natal jing and transformation of shen. In particular, the internal martial arts tai chi, the Circle Walking of Baguazhang and the middle path of Wuxingheqidao may be used to preserve pre-natal jing and build post-natal jing, if performed correctly. In Traditional Chinese herbal medicine Ginseng is widely used to bolster and support the jing or Essence.

An early mention of the term in this sense is in a 4th-century BCE chapter called Neiye "Inner Training" of a larger text compiled during the Han dynasty, the Guanzi.

Further references

 * Chang, Stephen T. The Great Tao ; Tao Longevity; ISBN 0-942196-01-5 Stephen T. Chang
 * Kaptchuck, Ted J., The Web That Has No Weaver ; Congdon & Weed; ISBN 978-0-8092-2933-8
 * Maciocia, Giovanni, The Foundations of Chinese Medicine: A Comprehensive Text for Acupuncturists and Herbalists ; Churchill Livingstone; ISBN 0-443-03980-1
 * Ni, Mao-Shing, The Yellow Emperor's Classic of Medicine : A New Translation of the Neijing Suwen with Commentary ; Shambhala, 1995; ISBN 1-57062-080-6
 * Holland, Alex Voices of Qi: An Introductory Guide to Traditional Chinese Medicine ; North Atlantic Books, 2000; ISBN 1-55643-326-3
 * Unschuld, Paul U., Medicine in China: A History of Ideas ; University of California Press, 1985; ISBN 0-520-05023-1
 * Graham, A.C. Disputers of the Tao: Philosophical Argument in Ancient China (Open Court, 1993). ISBN 0-8126-9087-7
 * Scheid, Volker, Chinese Medicine in Contemporary China: Plurality and Synthesis ; Duke University Press, 2002; ISBN 0-8223-2857-7
 * Porkert, Manfred The Theoretical Foundations of Chinese Medicine MIT Press, 1974 ISBN 0-262-16058-7
 * Hongyi, L., Hua, T., Jiming, H., Lianxin, C., Nai, L., Weiya, X., Wentao, M. (2003) Perivascular Space: Possible anatomical substrate for the meridian. Journal of Complementary and Alternative Medicine. 9:6 (2003) pp851–859
 * Wang, Mu. Foundations of Internal Alchemy: The Taoist Practice of Neidan. Golden Elixir Press, 2011. ISBN 978-0-9843082-5-5.
 * Wile, Douglas Lost T'ai-chi Classics from the late Ch'ing Dynasty (1996) State University of New York Press, Albany. ISBN 0-7914-2653-X

title: Jing (Chinese medicine)


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Richard Hodges (archaeologist)

Richard Hodges, (born 29 September 1952) is a British archaeologist and past president of The American University of Rome. A former professor and director of the Institute of World Archaeology at the University of East Anglia (1996–2007), Hodges is also the former Williams Director of the University of Pennsylvania Museum of Archaeology and Anthropology in Philadelphia (October 2007- 2012). His published research primarily concerns trade and economics during the early part of the Middle Ages in Europe. His earlier works include Dark Age Economics (1982), Mohammed, Charlemagne and the Origins of Europe (1983) and Light in the Dark Ages: The Rise and Fall of San Vincenzo Al Volturno (1997).

Academic career
Hodges's academic career has focussed upon the archaeology of the later Roman world and the early Middle Ages in western Europe. Many of his excavations and publications have highlighted the transformation of classical antiquity and the birth of Europe. Beginning with Dark Age Economics (1982), he reviewed the changing regional patterns of urban phenomena – especially emporia – in the making of north-west Europe. Following this, with David Whitehouse, in Mohammed, Charlemagne and the Origins of Europe (1983), he reappraised Henri Pirenne's celebrated historical thesis about the collapse of antiquity and the rise of Europe in the Carolingian age. Perhaps his most significant contribution to this theme was the 18-year (1980–98) excavations at San Vincenzo al Volturno, an Italian Benedictine monastery of the Carolingian renaissance, where together with the art historian, John Mitchell, the history and culture was unearthed and set within a European context. In the many reports on these excavations the architectural history and the art history, including well preserved cycles of paintings in the crypt of San Vincenzo Maggiore, were situated within the changing social and economic circumstances of 9th-century Italy.

Hodges pursued a similar approach at the UNESCO World Heritage Site of Butrint, the Graeco-Roman town in southern Albania, where over 20 years (1993-2012) representing the Butrint Foundation (Lords Rothschild and Sainsbury), and partnering with the Packard Humanities Institute, he developed a large-scale research programme (with many publications) and a concurrent cultural heritage programme. The project examined all archaeological periods at this site, including the formerly unknown Middle Byzantine periods.

As of 2015–20 Hodges is the principal investigator of a European Research Council project known as nEU-Med (no. 670792) with the University of Siena entitled 'The creation of economic and monetary union (7th to 12th centuries): mining, landscapes and political strategies in a Mediterranean region'. This project involves excavations at Vetricella, a complex 9th- to 11th- century elite site near Scarlino, a study of Portus Scabris on the Tyrrhenian Sea, environmental and archaeological studies of the Pegora valley corridor, and a major analysis of Italian early Medieval silver coinage with a view to identifying silver extracted from the Colline Metallifere.

Throughout his career Hodges has written articles for public audiences. Foremost amongst these are his bi-monthly column for Current World Archaeology, a collection of which has been published as Travels with an Archaeologist (2017).

Academic management
As a lecturer at Sheffield University (1976–88) Hodges created the Roystone Grange Archaeological Trail (1988-87). This teaching exercise, with the Peak District National Park, was intended as an innovative heritage feature in the National Park. A second teaching project focussed upon the Montarrenti project (1982–87), with Siena University and the Province of Siena. This was designed as a programme to make a park using the castle with its Romanesque to Renaissance tower-houses as well as the associated lost village.

As Director of the British School at Rome (1988–95) Hodges was faced with running an institution as government policy on higher education was being radically changed. He oversaw reforms of the institutional structures (charter, committees, staffing, programmes etc.) with a prominent emphasis upon activity-led projects aimed at raising the School's profile and winning support for refurbishing the it building (originally constructed by Sir Edwin Lutyens). Among the initiatives during his administration were the creation of an art gallery and an active archaeological unit. He also oversaw the refurbishment of the School's celebrated neo-classical façade with funds from the British government. During this period Hodges also wrote Visions of Rome (2000), a biography of the School's third director, the archaeologist, Thomas Ashby.

As Director at the Prince of Wales's Institute (1996–98) Hodges was charged with its re-positioning because it was attracting academic and journalistic criticism. He worked with two chairmen to reduce the trustees to a small working group, and then tackled the academic programme with reviews, and concurrently began the process of re-establishing the Institute within the Prince's group of trusts devoted to sustainability and the built environment.

As a professor in the School of World Art Studies, University of East Anglia, Norwich (1995–2007) Hodges set up a research institute, the Institute of World Archaeology (1996-2007). This was conceived as a research constellation with an emphasis upon cultural heritage activity. The main projects were in Albania and involved the making of a sustainable archaeological park at Butrint, as well as creating a post-communist archaeological community in serving a transition economy.

During this period, Hodges was supported by the Open Foundation to be international adviser in Tirana to the Albanian Minister of Culture, Edi Rama. Hodges also advised the Packard Humanities Institute on archaeological and other projects, notably the rescue excavations of the Roman city of Zeugma, Turkey, the conservation of Herculaneum, and the research and conservation of Chersonesos in the Crimea (Ukraine).

As Williams Director of the University of Pennsylvania Museum of Archaeology and Anthropology (2007–12) Hodges, at the request of the university's Provost, embarked upon a programme to create a modern museum accessible to Penn students and to K-12 schoolchildren and Philadelphians. Restructuring the museum involved re-positioning the research staff, modernizing the curatorial and exhibition programmes, as well as changing the education, catering, marketing and gallery programmes. This led to a successful campaign to refurbish the Museum's West Wing, to install new teaching facilities, to install new travelling exhibition galleries, and to implement a digital programme to put the museum's international collections online.

As President of the American University of Rome (2012–present) Hodges has established a new mission for the university, promoting it as primarily a 4-year international university in the liberal arts, business administration and international relations. Giving it a new identity of working with international academics, and, in effect, beginning an overhaul of every aspect of the university, the university is on course to become a major accredited American university in the Mediterranean region.

Hodges has also served as a specialist archaeological consultant to the York Archaeological Trust for the Roşia Montană gold mines in Romania (2014), and to the Norwegian power company, Statkraft in the Devoll valley dams, Albania (2016).

Books and research monographs

 * 1982. Edited (with G. Barker), Archaeology and Italian Society. Oxford: British Archaeological Reports.
 * 1982. Dark Age Economics: The Origins of Town and Trade. London/New York: Duckworth / St. Martin's Press (new edition 1989).
 * 1983. Edited (with P. Davey), Ceramics and Trade. Sheffield: Department of Archaeology and Prehistory Sheffield University.
 * 1983. (with D. Whitehouse), Mohammed, Charlemagne, and the Origins of Europe: The Pirenne Thesis in the Light of Archaeology. London / Ithaca: Duckworth / Cornell (new edition 1989). Revised French edition published as Mahomet, Charlemagne et les Origines de l'Europe. Paris: Pierre Zech, 1996.
 * 1985. Edited (with J. Mitchell), San Vincenzo al Volturno: the Archaeology, Art and Territory of an Early Medieval Monastery. Oxford: British Archaeological Reports.
 * 1988. Primitive and Peasant Markets. Oxford: Basil Blackwell.
 * 1988. Edited (with B. Hobley), The Rebirth of Towns in the West AD 700-1050. London: Council for British Archaeology Research Report.
 * 1989. The Anglo-Saxon Achievement: Archaeology and the Beginnings of English Society. London/Ithaca: Duckworth/ Cornell.
 * 1991. Wall-to-Wall History: The Story of Roystone Grange. London: Duckworth (Winner of British Archaeological Book of the Year 1992); (republished as Roystone Grange. 6000 years of a Peakland landscape, Stroud, Tempus, 2006)
 * 1991. Early Medieval archaeology in Western Europe: its history and development. Bangor: Headstart History.
 * 1991. Edited (with K. Smith), Recent Developments in the Archaeology of the Peak District. Sheffield: Department of Archaeology and Prehistory Sheffield University.
 * 1993. Edited, San Vincenzo al Volturno 1: the 1980-86 Excavations Part 1. London: The British School at Rome.
 * 1995. Edited, San Vincenzo al Volturno 2: the 1980-86 Excavations Part 2. London: The British School at Rome.
 * 1995. (with J. Mitchell), La basilica di Giosue a San Vincenzo al Volturno. Montecassino: Edizione CEP. Revised English edition published in 1996 as The Abbey of Abbot Joshua at San Vincenzo al Volturno.
 * 1996. Edited (with G. Brogiolo, S. Gelichi, R. Francovich and H. Steuer), Archaeology and History of the Middle Ages. XIII International Congress of Prehistoric and Protohistoric Sciences. Forli.
 * 1997. Light in the Dark Ages. The Rise and Fall of San Vincenzo al Volturno. London/ Ithaca: Duckworth / Cornell University Press.
 * 1998. Edited (with W. Bowden), The Sixth Century: Production, Distribution and Consumption. The Hague: E. J. Brill (Volume 2 in the European Science Foundation's Transformation of the Roman World project).
 * 2000. Towns and Trade in the Age Charlemagne. London: Duckworth.
 * 2000. Visions of Rome: Thomas Ashby, Archaeologist. London: The British School at Rome.
 * 2003. (with R. Francovich) Villa to Village. The Transformation of the Roman Landscape in Italy. London: Duckworth.
 * 2004. (with W. Bowden & K. Lako), Byzantine Butrint: excavations and surveys 1994-99. Oxford: Oxbow Books.
 * 2006. Goodbye to the Vikings? Re-reading Early Medieval Archaeology. London: Duckworth.
 * 2006. Eternal Butrint. A Unesco World Heritage Site in Albania. London: Periplus. (translated by Diana Ndrenika) Butrinti I Përjetshëm, Tirana: Botimet Toena 2011.
 * 2006. Edited (with L.Bejko), New Directions in Albanian Archaeology. Tirana: ICAA.
 * 2006. Edited (with K. Bowes and K.Francis), Between text and territory. San Vincenzo 4. London: British School at Rome.
 * 2007. Edited (with I.L. Hansen), Roman Butrint: An Assessment. Oxford: Oxbow Books. 2007
 * 2008. Shkëlqimi dhe rënia e Butrintit bizantin / The Rise and Fall of Byzantine Butrint. London/Tirana: Butrint Foundation.
 * 2011. (with W. Bowden) Butrint 3. Excavations of the Triconch Palace. Oxford: Oxbow Books.
 * 2011. (with S. Leppard and J. Mitchell) San Vincenzo 5. San Vincenzo Maggiore and its Workshops. London: British School at Rome.
 * 2012. Dark Age Economics: A New Audit. London: Bloomsbury Academic.
 * 2012. Edited (with S. Gelichi) From One Sea to Another. Turnhout: Brepols.
 * 2013. Edited (with I.L.Hansen and S.Leppard) Butrint 4. The Archaeology and Histories of an Ionian Town. Oxford: Oxbow Books.
 * 2015. Edited with S. Gelichi, New Directions in European Medieval Archaeology. Essays for Riccardo Francovich. Turnhout: Brepols.
 * 2016. The Archaeology of Mediterranean Placemaking: Butrint and the Global Heritage Industry. London: Bloomsbury Academic.
 * 2017. Travels of an Archaeologist: Finding A Sense of Place. London: Bloomsbury Academic.
 * 2017. Travels of an Archaeologist: Finding A Sense of Place. London: Bloomsbury Academic.

title: Richard Hodges (archaeologist)


text:
Benesh Movement Notation

Benesh Movement Notation (BMN), also known as Benesh notation or choreology, is the literacy of body language, it is a dance and movement notation system used to document dance and other types of human movement. Invented by Joan and Rudolf Benesh in the late 1940s, the system uses abstract symbols based on figurative representations of the human body. It is used in choreography and physical therapy, and by the Royal Academy of Dance to teach ballet.

Benesh notation is recorded on a five-line staff from left to right, with vertical bar lines to mark the passage of time. Because of its similarity to modern staff music notation, Benesh notation can be displayed alongside (typically below) and in synchronization with musical accompaniment.

History
Benesh Movement Notation was created by Joan Benesh and her husband Rudolph Benesh. In 1955, Rudolf Benesh publicly introduced Benesh notation as an "aesthetic and scientific study of all forms of human movement by movement notation". In 1997, the Benesh Institute (an organisation focused on Benesh notation) merged with the Royal Academy of Dance.

Notation system

Benesh notation plots the position of a dancer as seen from behind as if the dancer is superimposed on a staff that extends from the top of the head down to the feet. From top to bottom, the five lines of the staff coincide with the head, shoulders, waist, knees and feet. Additional symbols are used to notate the. A frame is one complete representation of the dancer.

A short horizontal line is used to represent the location of a hand or foot that passes through the Coronal plane which extends from the sides of the body. A short vertical line represents a hand or foot at a plane in front of the body, whereas a dot represents a hand or foot at a plane behind the body. The height of the hands and feet from the floor and their distance from the mid-line of the body are shown visually. A line drawn in the top space of the staff shows the position of the head when it changes position. A direction sign is placed below the staff when the direction changes.

title: Benesh Movement Notation


text:
Rabin–Karp algorithm

In computer science, the Rabin–Karp algorithm or Karp–Rabin algorithm is a string-searching algorithm created by that uses hashing to find an exact match of a pattern string in a text. It uses a rolling hash to quickly filter out positions of the text that cannot match the pattern, and then checks for a match at the remaining positions. Generalizations of the same idea can be used to find more than one match of a single pattern, or to find matches for more than one pattern.

To find a single match of a single pattern, the expected time of the algorithm is linear in the combined length of the pattern and text, although its worst-case time complexity is the product of the two lengths. To find multiple matches, the expected time is linear in the input lengths, plus the combined length of all the matches, which could be greater than linear. In contrast, the Aho–Corasick algorithm can find all matches of multiple patterns in worst-case time and space linear in the input length and the number of matches (instead of the total length of the matches).

A practical application of the algorithm is detecting plagiarism. Given source material, the algorithm can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation. Because of the abundance of the sought strings, single-string searching algorithms are impractical.

Overview
A naive string matching algorithm compares the given pattern against all positions in the given text. Each comparison takes time proportional to the length of the pattern, and the number of positions is proportional to the length of the text. Therefore, the worst-case time for such a method is proportional to the product of the two lengths. In many practical cases, this time can be significantly reduced by cutting short the comparison at each position as soon as a mismatch is found, but this idea cannot guarantee any speedup.

Several string-matching algorithms, including the Knuth–Morris–Pratt algorithm and the Boyer–Moore string-search algorithm, reduce the worst-case time for string matching by extracting more information from each mismatch, allowing them to skip over positions of the text that are guaranteed not to match the pattern. The Rabin–Karp algorithm instead achieves its speedup by using a hash function to quickly perform an approximate check for each position, and then only performing an exact comparison at the positions that pass this approximate check.

A hash function is a function which converts every string into a numeric value, called its hash value; for example, we might have. If two strings are equal, their hash values are also equal. For a well-designed hash function, the inverse is true, in an approximate sense: strings that are unequal are very unlikely to have equal hash values. The Rabin–Karp algorithm proceeds by computing, at each position of the text, the hash value of a string starting at that position with the same length as the pattern. If this hash value equals the hash value of the pattern, it performs a full comparison at that position.

In order for this to work well, the hash function should be selected randomly from a family of hash functions that are unlikely to produce many false positives, that is, positions of the text which have the same hash value as the pattern but do not actually match the pattern. These positions contribute to the running time of the algorithm unnecessarily, without producing a match. Additionally, the hash function used should be a rolling hash, a hash function whose value can be quickly updated from each position of the text to the next. Recomputing the hash function from scratch at each position would be too slow.

The algorithm
The algorithm is as shown:

Lines 2, 4, and 6 each require O(m) time. However, line 2 is only executed once, and line 6 is only executed if the hash values match, which is unlikely to happen more than a few times. Line 5 is executed O(n) times, but each comparison only requires constant time, so its impact is O(n). The issue is line 4.

Naively computing the hash value for the substring  requires O(m) time because each character is examined. Since the hash computation is done on each loop, the algorithm with a naive hash computation requires O(mn) time, the same complexity as a straightforward string matching algorithm. For speed, the hash must be computed in constant time. The trick is the variable  already contains the previous hash value of. If that value can be used to compute the next hash value in constant time, then computing successive hash values will be fast.

The trick can be exploited using a rolling hash. A rolling hash is a hash function specially designed to enable this operation. A trivial (but not very good) rolling hash function just adds the values of each character in the substring. This rolling hash formula can compute the next hash value from the previous value in constant time: s[i+1..i+m] = s[i..i+m-1] - s[i] + s[i+m] This simple function works, but will result in statement 5 being executed more often than other more sophisticated rolling hash functions such as those discussed in the next section.

Good performance requires a good hashing function for the encountered data. If the hashing is poor (such as producing the same hash value for every input), then line 6 would be executed O(n) times (i.e. on every iteration of the loop). Because character-by-character comparison of strings with length m takes O(m) time, the whole algorithm then takes a worst-case O(mn) time.

Hash function used
The key to the Rabin–Karp algorithm's performance is the efficient computation of hash values of the successive substrings of the text. The Rabin fingerprint is a popular and effective rolling hash function. The hash function described here is not a Rabin fingerprint, but it works equally well. It treats every substring as a number in some base, the base being usually the size of the character set.

For example, if the substring is "hi", the base is 256, and prime modulus is 101, then the hash value would be  [(104 × 256 ) % 101  + 105] % 101  =  65 (ASCII of 'h' is 104 and of 'i' is 105) '%' is 'mod' or modulo, or remainder after integer division, operator

Technically, this algorithm is only similar to the true number in a non-decimal system representation, since for example we could have the "base" less than one of the "digits". See hash function for a much more detailed discussion. The essential benefit achieved by using a rolling hash such as the Rabin fingerprint is that it is possible to compute the hash value of the next substring from the previous one by doing only a constant number of operations, independent of the substrings' lengths.

For example, if we have text "abracadabra" and we are searching for a pattern of length 3, the hash of the first substring, "abr", using 256 as the base, and 101 as the prime modulus is: // ASCII a = 97, b = 98, r = 114. hash("abr") = [ ( [ ( [  (97 × 256) % 101 + 98 ] % 101 ) × 256 ] %  101 ) + 114 ]   % 101   =  4

We can then compute the hash of the next substring, "bra", from the hash of "abr" by subtracting the number added for the first 'a' of "abr", i.e. 97 × 2562, multiplying by the base and adding for the last a of "bra", i.e. 97 × 2560. Like so:

//          old hash   (-ve avoider)*   old 'a'   left base offset      base shift    new 'a'    prime modulus hash("bra") =    [ ( 4   + 101         -  97 * [(256%101)*256] % 101 ) * 256         +    97 ] % 101              =  30

 * (-ve avoider) = "underflow avoider". Necessary if using unsigned integers for calculations. Because we know all hashes $h \leq p$ for prime modulus $p$, we can ensure no underflow by adding p to the old hash before subtracting the value corresponding to the old 'a' (mod p).

the last '* 256' is the shift of the subtracted hash to the left

although ((256%101)*256)%101 is the same as 2562 % 101, to avoid overflowing integer maximums when the pattern string is longer (e.g. 'Rabin-Karp' is 10 characters, 2569 is the offset without modulation ), the pattern length base offset is pre-calculated in a loop, modulating the result each iteration

If we are matching the search string "bra", using similar calculation of hash("abr"),

hash'("bra") = [ ( [ ( [ ( 98 × 256) %101  + 114] % 101 ) × 256 ] % 101) + 97 ] % 101 = 30

If the substrings in question are long, this algorithm achieves great savings compared with many other hashing schemes.

Theoretically, there exist other algorithms that could provide convenient recomputation, e.g. multiplying together ASCII values of all characters so that shifting substring would only entail dividing the previous hash by the first character value, then multiplying by the new last character's value. The limitation, however, is the limited size of the integer data type and the necessity of using modular arithmetic to scale down the hash results, (see hash function article). Meanwhile, naive hash functions do not produce large numbers quickly, but, just like adding ASCII values, are likely to cause many hash collisions and hence slow down the algorithm. Hence the described hash function is typically the preferred one in the Rabin–Karp algorithm.

Multiple pattern search
The Rabin–Karp algorithm is inferior for single pattern searching to Knuth–Morris–Pratt algorithm, Boyer–Moore string-search algorithm and other faster single pattern string searching algorithms because of its slow worst case behavior. However, it is a useful algorithm for multiple pattern search.

To find any of a large number, say k, fixed length patterns in a text, a simple variant of the Rabin–Karp algorithm uses a Bloom filter or a set data structure to check whether the hash of a given string belongs to a set of hash values of patterns we are looking for:

We assume all the substrings have a fixed length m.

A naïve way to search for k patterns is to repeat a single-pattern search taking O(n+m) time, totaling in O((n+m)k) time. In contrast, the above algorithm can find all k patterns in O(n+km) expected time, assuming that a hash table check works in O(1) expected time.

title: Rabin–Karp algorithm


text:
Distance measuring equipment

In aviation, distance measuring equipment (DME) is a radio navigation technology that measures the slant range (distance) between an aircraft and a ground station by timing the propagation delay of radio signals in the frequency band between 960 and 1215 megahertz (MHz). Line-of-visibility between the aircraft and ground station is required. An interrogator (airborne) initiates an exchange by transmitting a pulse pair, on an assigned 'channel', to the transponder ground station. The channel assignment specifies the carrier frequency and the spacing between the pulses. After a known delay, the transponder replies by transmitting a pulse pair on a frequency that is offset from the interrogation frequency by 63 MHz and having specified separation.

DME systems are used worldwide, using standards set by the International Civil Aviation Organization (ICAO), RTCA, the European Union Aviation Safety Agency (EASA) and other bodies. Some countries require that aircraft operating under instrument flight rules (IFR) be equipped with a DME interrogator; in others, a DME interrogator is only required for conducting certain operations.

While stand-alone DME transponders are permitted, DME transponders are usually paired with an azimuth guidance system to provide aircraft with a two-dimensional navigation capability. A common combination is a DME colocated with a VHF omnidirectional range (VOR) transmitter in a single ground station. When this occurs, the frequencies of the VOR and DME equipment are paired. Such a configuration enables an aircraft to determine its azimuth angle and distance from the station. A VORTAC (a VOR co-located with a TACAN) installation provides the same capabilities to civil aircraft but also provides 2-D navigation capabilities to military aircraft.

Low-power DME transponders are also associated with some instrument landing system (ILS), ILS localizer and microwave landing system (MLS) installations. In those situations, the DME transponder frequency/pulse spacing is also paired with the ILS, LOC or MLS frequency.

ICAO characterizes DME transmissions as ultra high frequency (UHF). The term L-band is also used.

Developed in Australia, DME was invented by James "Gerry" Gerrand under the supervision of Edward George "Taffy" Bowen while employed as Chief of the Division of Radiophysics of the Commonwealth Scientific and Industrial Research Organisation (CSIRO). Another engineered version of the system was deployed by Amalgamated Wireless Australasia Limited in the early 1950s operating in the 200 MHz VHF band. This Australian domestic version was referred to by the Federal Department of Civil Aviation as DME(D) (or DME Domestic), and the later international version adopted by ICAO as DME(I). DME is similar in principle to secondary radar ranging function, except the roles of the equipment in the aircraft and on the ground are reversed. DME was a post-war development based on the identification friend or foe (IFF) systems of World War II. To maintain compatibility, DME is functionally identical to the distance measuring component of TACAN.

Operation
In its first iteration, a DME-equipped airplane used the equipment to determine and display its distance from a land-based transponder by sending and receiving pulse pairs. The ground stations are typically collocated with VORs or VORTACs. A low-power DME can be collocated with an ILS or MLS where it provides an accurate distance to touchdown, similar to that otherwise provided by ILS marker beacons (and, in many instances, permitting removal of the latter).

A newer role for DMEs is DME/DME area navigation (RNAV). Owing to the generally superior accuracy of DME relative to VOR, navigation using two DMEs (using trilateration/distance) permits operations that navigating with VOR/DME (using azimuth/distance) does not. However, it requires that the aircraft have RNAV capabilities, and some operations also require an inertial reference unit.

A typical DME ground transponder for en-route or terminal navigation will have a 1 kW peak pulse output on the assigned UHF channel.

Hardware

The DME system comprises a UHF (L-band) transmitter/receiver (interrogator) in the aircraft and a UHF (L-band) receiver/transmitter (transponder) on the ground.

Search mode
150 interrogation pulse-pairs per second. The aircraft interrogates the ground transponder with a series of pulse-pairs (interrogations) and, after a precise time delay (typically 50 microseconds), the ground station replies with an identical sequence of pulse-pairs. The DME receiver in the aircraft searches for reply pulse-pairs (X-mode = 12-microsecond spacing) with the correct interval and reply pattern to its original interrogation pattern. (Pulse-pairs that are not coincident with the individual aircraft's interrogation pattern e.g. not synchronous, are referred to as filler pulse-pairs, or squitter. Also, replies to other aircraft that are therefore non-synchronous also appear as squitter).

Track mode
Less than 30 interrogation Pulse-pairs per second, as the average number of pulses in SEARCH and TRACK is limited to max 30 pulse pairs per second. The aircraft interrogator locks on to the DME ground station once it recognizes a particular reply pulse sequence has the same spacing as the original interrogation sequence. Once the receiver is locked on, it has a narrower window in which to look for the echoes and can retain lock.

Distance calculation
A radio signal takes approximately 12.36 microseconds to travel 1 nmi to the target and back. The time difference between interrogation and reply minus the 50 microsecond ground transponder delay, and the pulse spacing of the reply pulses (12 microseconds in X mode and 30 microseconds in Y mode), is measured by the interrogator's timing circuitry and converted to a distance measurement (slant range), in nautical miles, then displayed on the cockpit DME display.

The distance formula, distance = rate * time, is used by the DME receiver to calculate its distance from the DME ground station. The rate in the calculation is the velocity of the radio pulse, which is the speed of light (roughly 300000000 m/s). The time in the calculation is C. ½(total time − reply delay), where C is the speed of light.

Accuracy
The accuracy of DME ground stations is 185 m (±0.1 nmi). It's important to understand that DME provides the physical distance between the aircraft antenna and the DME transponder antenna. This distance is often referred to as 'slant range' and depends trigonometrically upon the aircraft altitude above the transponder as well as the ground distance between them.

For example, an aircraft directly above the DME station at 6,076 ft (1 nmi) altitude would still show 1.0 nmi on the DME readout. The aircraft is technically a mile away, just a mile straight up. Slant range error is most pronounced at high altitudes when close to the DME station.

Radio-navigation aids must keep a certain degree of accuracy, given by international standards, FAA, EASA, ICAO, etc. To assure this is the case, flight inspection organizations check periodically critical parameters with properly equipped aircraft to calibrate and certify DME precision.

ICAO recommends accuracy of less than the sum of 0.25 nmi plus 1.25% of the distance measured.

Specification
A typical DME ground-based transponder beacon has a limit of 2700 interrogations per second (pulse pairs per second – pps). Thus it can provide distance information for up to 100 aircraft at a time—95% of transmissions for aircraft in tracking mode (typically 25 pps) and 5% in search mode (typically 150 pps). Above this limit the transponder avoids overload by limiting the sensitivity (gain) of the receiver. Replies to weaker (normally the more distant) interrogations are ignored to lower the transponder load.

Radio frequency and modulation data
DME frequencies are paired to VOR frequencies and a DME interrogator is designed to automatically tune to the corresponding DME frequency when the associated VOR frequency is selected. An airplane's DME interrogator uses frequencies from 1025 to 1150 MHz. DME transponders transmit on a channel in the 962 to 1213 MHz range and receive on a corresponding channel between 1025 and 1150 MHz. The band is divided into 126 channels for interrogation and 126 channels for reply. The interrogation and reply frequencies always differ by 63 MHz. The spacing and bandwidth of each channel is 1 MHz and a bandwidth of 1MHz.

Technical references to X and Y channels relate only to the spacing of the individual pulses in the DME pulse pair, 12 microsecond spacing for X channels and 30 microsecond spacing for Y channels.

DME facilities identify themselves with a 1,350 Hz Morse code three letter identity. If collocated with a VOR or ILS, it will have the same identity code as the parent facility. Additionally, the DME will identify itself between those of the parent facility. The DME identity is 1,350 Hz to differentiate itself from the 1,020 Hz tone of the VOR or the ILS localizer.

DME transponder types
The U.S. FAA has installed three DME transponder types (not including those associated with a landing system): Terminal transponders (often installed at an airport) typically provide service to a minimum height above ground of 12,000 ft and range of 25 nmi; Low altitude transponders typically provide service to a minimum height of 18,000 ft and range of 40 nmi; and High altitude transponders, which typically provide service to a minimum height of 45,000 ft and range of 130 nmi. However, many have operational restrictions largely based on line-of-sight blockage, and actual performance may be different. The U.S. Aeronautical Information Manual states, presumably referring to high altitude DME transponders: "reliable signals may be received at distances up to 199 nmi at line−of−sight altitude".

DME transponders associated with an ILS or other instrument approach are intended for use during an approach to a particular runway, either one or both ends. They are not authorized for general navigation; neither a minimum range nor height is specified.

Frequency usage/channelization
DME frequency usage, channelization and pairing with other navaids (VOR, ILS, etc.) are defined by ICAO. 252 DME channels are defined by the combination of their interrogation frequency, interrogation pulse spacing, reply frequency, and reply pulse spacing. These channels are labeled 1X, 1Y, 2X, 2Y, ... 126X, 126Y. X channels (which came first) have both interrogation and reply pulse pairs spaced by 12 microseconds. Y channels (which were added to increase capacity) have interrogation pulse pairs spaced by 36 microseconds and reply pulse pairs spaced by 30 microseconds.

A total of 252 frequencies are defined (but not all used) for DME interrogations and replies—specifically, 962, 963, ... 1213 megahertz. Interrogation frequencies are 1025, 1026, ... 1150 megahertz (126 total), and are the same for X and Y channels. For a given channel, the reply frequency is 63 megahertz below or above the interrogation frequency. The reply frequency is different for X and Y channels, and different for channels numbered 1-63 and 64-126.

Not all defined channels/frequencies are assigned. There are assignment 'holes' centered on 1030 and 1090 megahertz to provide protection for the secondary surveillance radar (SSR) system. In many countries, there is also an assignment 'hole' centered on 1176.45 megahertz to protect the GPS L5 frequency. These three 'holes' remove approximately 60 megahertz from the frequencies available for use.

Precision DME (DME/P), a component of the Microwave Landing System, is assigned to Z channels, which have a third set of interrogation and reply pulse spacings. The Z channels are multiplexed with the Y channels and do not materially affect the channel plan.

Future
In 2020 one company presented its 'Fifth-Generation DME'. Although compatible with existing equipment, this iteration provides greater accuracy (down to 5 meters using DME/DME triangulation), with a further reduction to 3 meters using a further refinement. The 3-meter equipment is being considered as part of Europe's SESAR project, with possible deployment by 2023.

In the twenty-first century, aerial navigation has become increasingly reliant on satellite guidance. However, ground-based navigation will continue, for three reasons:
 * The satellite signal is extremely weak, can be spoofed, and is not always available;
 * A European Union rule requires member states to keep and maintain ground-based navigation aids;
 * A feeling of sovereignty, or control over a state's own navigational means. "Some states want navigation over their territory to rely on means they control. And not every country has its constellation like the U.S.' GPS or Europe's Galileo."

One advantage of the fifth-generation equipment proposed in 2020 is its ability to be function-checked by drone flights, which will significantly reduce the expense and delays of previous manned certification flight tests.

title: Distance measuring equipment