Early history.

A high-speed rail line, LGV Nord, has been in operation between the Channel Tunnel and the outskirts of Paris since the Tunnel's opening in 1994. This has enabled Eurostar rail services to travel at for this part of their journey. A similar high-speed line in Belgium, from the French border to Brussels, HSL 1, opened in 1997. In Britain, Eurostar trains had to run at a maximum of on existing tracks between London Waterloo and the Channel Tunnel. These tracks were shared with local traffic, limiting the number of services that could be run, and jeopardising reliability. The case for a high-speed line similar to the continental part of the route was recognised by policymakers, and the construction of the line was authorised by Parliament with the Channel Tunnel Rail Link Act 1996, which was amended by the Channel Tunnel Rail Link (Supplementary Provisions) Act 2008.  An early plan conceived by British Rail in the early 1970s for a route passing through Tonbridge met considerable opposition on environmental and social grounds, especially from the Leigh Action Group and Surrey & Kent Action on Rail (SKAR). A committee was set up to examine the proposal under Sir Alexander Cairncross; but in due course environment minister Anthony Crosland announced that the project had been cancelled, together with the plan for the tunnel itself.  The next plan for the Channel Tunnel Rail Link involved a tunnel reaching London from the south-east, and an underground terminus in the vicinity of King's Cross station. A late change in the plans, principally driven by the then Deputy Prime Minister Michael Heseltine's desire for urban regeneration in east London, led to a change of route, with the new line approaching London from the east. This opened the possibility of reusing the underused St Pancras station as the terminus, with access via the North London Line that crosses the throat of the station.  The idea of using the North London line proved illusory, and it was rejected in 1994 by the then Transport Secretary, John MacGregor, as too difficult to construct and environmentally damaging. The idea of using St Pancras station as the core of the new terminus was retained, albeit now linked by of specially built tunnels to Dagenham via Stratford.  London & Continental Railways (LCR) was chosen by the UK government in 1996 to build the line and to reconstruct St Pancras station as its terminus, and to take over the British share of the Eurostar operation, Eurostar (UK). The original LCR consortium members were National Express, Virgin Group, S. G. Warburg & Co, Bechtel and London Electric. While the project was under development by British Rail it was managed by "Union Railways", which became a wholly owned subsidiary of "LCR". On 14 November 2006, LCR adopted "High Speed 1" as the brand name for the completed railway. Official legislation, documentation and line-side signage have continued to refer to "CTRL".

The project.

As the 1987 Channel Tunnel Act made government funding for a Channel tunnel rail link unlawful, construction did not take place as it was not financially viable. Construction was delayed until passage of the Channel Tunnel Rail Link Act 1996 which provided construction powers that ran for the following 10 years. The chief executive of the time Rob Holden stated that it was the "largest land acquisition programme since the Second World War".  The whole route was to have been built as a single project, but in 1998 serious financial difficulties arose, and extensive changes came with a British government rescue plan. To reduce risk, the line was split into two separate phases, to be managed by "Union Railways (South)" and "Union Railways (North)". A recovery programme was agreed whereby LCR sold government-backed bonds worth £1.6 billion to pay for the construction of section 1, with the future of section 2 still not settled.  The original intention had been for the new railway, once completed, to be run by Union Railways as a separate line from the rest of the British railway network. As part of the 1998 rescue it was agreed that, following completion, section 1 would be purchased by Railtrack with an option to purchase section 2. In return, Railtrack was committed to operate the whole route as well as St Pancras railway station, which, unlike all other former British Rail stations, had been transferred to LCR/Union Railways in 1996.  In 2001, Railtrack announced that, due to its own financial problems, it would not undertake to purchase section 2, triggering a second restructuring. The 2002 plan agreed that the two sections would have different owners (Railtrack for section 1, LCR for section 2) but with common Railtrack management. Following further financial problems at Railtrack, its interest was sold back to LCR, which then sold the operating rights for the completed line to Network Rail, Railtrack's successor. Under this arrangement LCR became the sole owner of both sections of the CTRL and the St Pancras property, as per the original 1996 plan. Amendments were made in 2001 for the new station at Stratford International and connections to the West Coast Main Line.  As a consequence of the restructuring, in 2006 the LCR consortium consisted of engineering consultants and construction firms Arup, Bechtel, Halcrow and Systra (which form "Rail Link Engineering" (RLE)); transport operators National Express and SNCF (which operates the "Eurostar (UK)" share of the Eurostar service with the National Railway Company of Belgium and British Airways); electricity company EDF; and UBS Investment Bank. On completion of section 1 by RLE, the line was handed over to Union Railways (South), which then handed it over to "London & Continental Stations and Property" (LCSP), the long-term owners of the line. Once section 2 of the line had been completed it was handed over to Union Railways (North), which handed it over to LCSP. The entire line, including St Pancras, is managed, operated and maintained by Network Rail (CTRL).  In February 2006 there were rumours that a 'third party' (believed to be a consortium headed by banker Sir Adrian Montague) had expressed an interest in buying out the present partners in the project. LCR shareholders rejected the proposal, and the government, which effectively could overrule shareholders' decisions as a result of LCR's reclassification as a state-owned body, decided that discussions with shareholders would not take place imminently, effectively backing shareholders' views on the proposed takeover.  By May 2009 LCR had become insolvent and the government received agreement to use state aid to purchase the line and also to open it up to competition to allow other services to use it apart from Eurostar. LCR's hitherto wholly owned subsidiary, HS1 Ltd, thus became the property of the Secretary of State for Transport. On 12 October 2009 a proposal was announced to sell £16 billion of state assets including HS1 Ltd in the following two years to cut UK public debt. The government announced on 5 November 2010 that a concession to operate the line for 30 years had been sold for £2.1 billion to a consortium of Canadian investors. Under the concession, HS1 Ltd has the rights to sell access to track and to the four international stations (St Pancras, Stratford, Ebbsfleet and Ashford) on a commercial basis, under the scrutiny of the Office of Rail Regulation. At the end of 30 years, ownership of the assets will revert to government.

Building cost.

The cost of construction was £6.84 billion. At £51 million per mile, this was higher than other projects in other countries; the French LGV Est, a line built largely through open and flat countryside (save for the Saverne Tunnel) and which terminates outside the urban centres (Vaires-sur-Marne for Paris and Vendenheim for Strasbourg), phase one being completed in 2007 and phase two in 2016, cost £22 million per mile.

Route.

The high-speed railway operates as a "seven-day railway", with full availability on all days. The line is closed for 40 minutes in the middle of the day shortly after noon for a "white period" () and "daylight inspection period". Any heavy maintenance is performed overnight. track access charges were capped at approximate £71.35 per minute. In 2008 the cost of running a train along the full length of the line between St Pancras and the Channel Tunnel was £2,244; with lower costs of £2,192 for a domestic service to Ashford International, or £1,044 for St Pancras to Ebbsfleet International. A discounted rate of £4.00 per kilometre was made available for night-time-only railfreight operation until 31 March 2015.

Section 1.

"Section 1" of the Channel Tunnel Rail Link, opened on 28 September 2003, is a section of high-speed track from the Channel Tunnel to Fawkham Junction in north Kent with a maximum speed of. Its completion cut the London–Paris journey time by around 21 minutes, to 2 hours 35 minutes. The line includes the Medway Viaduct, a 1.2 km (3⁄4 mile) bridge over the River Medway, and the North Downs Tunnel, a long, diameter tunnel. In safety testing on the section prior to opening, a new UK rail speed record of was set. Much of the new line runs alongside the M2 and M20 motorways through Kent. After its completion, Eurostar trains continued to use suburban lines to enter London, arriving at Waterloo International.  There were several deaths of employees working on the CTRL over the construction period. One occurred on 28 March 2003 near Folkestone when a worker came into contact with the energised power supply. Another death occurred two months later, in May 2003, when a scaffolder fell seven metres at Thurrock, Essex. Three companies were found guilty of breaching health and safety legislation by omitting to provide barriers, resulting in Deverson Direct Ltd. being ordered to pay a fine of £50,000, J.Murphy & Sons Ltd. £25,000, and Hochtief AG £25,000. Two more deaths resulted from a fire on board a train carrying wires, one mile () inside a tunnel under the Thames between Swanscombe, Kent, and Thurrock, Essex on 16 August 2005. The train shunter died at the scene and the train driver later died in hospital. It has been suggested that a large amount of blame for accidents throughout the project lay with individual behaviour, becoming such a problem that an internal programme was launched to tackle problem behaviour during the construction.  Unlike most LGV stations in France, the through tracks for Ashford International station are off to one side rather than going through, partly because the station pre-dates the line. High Speed 1 approaches Ashford International from the north in a cut-and-cover "box"; the southbound line rises out of this cutting and crosses over the main tracks to enter the station. The main tracks then rise out of the cutting and over a flyover. On leaving Ashford, southbound Eurostars return to the high-speed line by travelling under this flyover and joining from the outside. The international platforms at Ashford are supplied with both overhead 25 kV AC and third-rail 750 V DC power, avoiding the need to switch power supplies.

Section 2.

"Section 2" of the project opened on 14 November 2007 and is a stretch of track from the newly built Ebbsfleet station in Kent to London St Pancras with a maximum speed of. Completion of the section cut journey times by a further 20 minutes (London–Paris in 2h 15 m; London–Brussels in 1h 51 m). The route starts with a tunnel which dives under the Thames on the edge of Swanscombe, then runs alongside the London, Tilbury and Southend Railway as far as Dagenham, where it enters a tunnel (), much of which is directly under the North London Line, before emerging over the East Coast Main Line near St Pancras. The tunnels are divided into "London East" and "London West" sections, between which a 1-kilometre stretch runs close to the surface to serve Stratford International and the Temple Mills Depot.  The new depot at Temple Mills, to the north of Stratford, replaced the North Pole depot in the west of London. In testing, the first Eurostar train ran into St Pancras on 6 March 2007. All CTRL connections are fully grade-separated.

Stations.

Ashford International.

This station was rebuilt as Ashford International during the early 1990s for international services from mainland Europe; this included the addition of two platforms to the north of station (the original down island platform had been taken over by international services). Unlike normal LGV stations in France, the through tracks for Ashford International railway station are off to one side rather than going through. The number of services was reduced after the opening of the Ebbsfleet station. A high-speed domestic service operated by Southeastern to London St Pancras began on 29 June 2009.

Ebbsfleet International.

Ebbsfleet International railway station in the borough of Dartford, Kent is outside the eastern boundary of Greater London and opened to the public on 19 November 2007. It is now Eurostar's main station in Kent. Two of the platforms are designed for international passenger trains and four for high-speed domestic services.

St Pancras International.

The terminus for the high-speed line in London is St Pancras railway station. During the 2000s, towards the end of the construction of the CTRL, the entire station complex was renovated, expanded and rebranded as St Pancras International, with a new security-sealed terminal area for Eurostar trains to continental Europe. In addition, it retained traditional domestic connections to the north and south of England. The new extension doubled the length of the central platforms now used for Eurostar services; new platforms have been provided for existing domestic East Midlands Trains and the Southeastern high-speed services that run along High Speed 1 to Kent. New platforms on the Thameslink line across London were built beneath the western margins of the station, and the station at King's Cross Thameslink was closed.  A complex junction has been built north of St Pancras with connections to the East Coast Main Line, North London Line (for West Coast Main Line) and Midland Main Line, allowing for a wide variety of potential destinations albeit on conventional rails. As part of the works, tunnels connecting the East Coast Main Line to the Thameslink route were also built in readiness for the forthcoming Thameslink Programme.

Stratford International.

Stratford International railway station was not part of the original government plans for the CTRL. Despite its name, no international services call there. Completed in April 2006, it opened on 30 November 2009 when the domestic preview Southeastern highspeed services started calling there. An extension of the Docklands Light Railway opened to Stratford International in August 2011. It forms part of the complex of railway stations for the main site where the 2012 Summer Olympics were held.  Temple Mills Depot in Leyton is used for storage and servicing of Eurostar trains and off-peak berthing of Class 395 Southeastern high-speed trains.

Infrastructure.

The railway is maintained from Singlewell Infrastructure Maintenance Depot.

Track.

Both track and signalling technology (TVM-430 + KVB) are based on or identical to the standards used on the French LGV high-speed lines. The areas around St Pancras and Gare du Nord use colour light and KVB signalling with the whole of the high-speed route to Paris (CTRL, Channel Tunnel, LGV Nord) using TVM-430. Traffic is controlled from the Ashford signalling centre. Signalling tests before opening were performed by the SNCF-owned "Lucie" test car.  The track is cleared to a larger modern European GC loading gauge enabling GC gauge freight as far as the yards at Barking. The line is electrified entirely using overhead lines with 25 kV AC railway electrification.

Tunnels.

After local protests, early plans were modified to put more of the route into tunnels up until a point approximately from St Pancras. Previously the CTRL was planned to run on an elevated section alongside the North London Line on approach into the line's terminus. The twin tunnels bored under London were driven from Stratford westwards towards St Pancras, eastwards towards Dagenham and from Dagenham westwards to connect with the tunnel from Stratford. The tunnel boring machines were 120 metres long and weighed 1,100 tonnes. The depth of the tunnels varies from 24 metres to 50 metres.  The construction works were complex, and many contractors were involved in delivering them. The CTRL Section 2 construction works had caused considerable disruption around the Kings Cross area of London; in their wake redevelopment was stimulated. The large redevelopment area includes the run-down areas of post-industrial and ex-railway land close to King's Cross and St Pancras, a conservation area with many listed buildings; this was promoted as one of the benefits for building the CTRL. It has been postulated that this development was actually suppressed by the construction project, and some affected districts were said still to be in a poor state in 2005.

Connection line to Waterloo.

A connecting line providing access for Waterloo International leaves High Speed 1 at Southfleet Junction using a grade-separated junction; the main CTRL tracks continue uninterrupted through to CTRL Section 2 underneath the southbound flyover. The connection joins the Chatham Main Line at Fawkham Junction with a flat crossing. The retention of Eurostar services to Waterloo after the line to St Pancras opened was ruled out on cost grounds. Waterloo International closed upon opening of the section two of the CTRL in November 2007; Eurostar now serves the refurbished St Pancras as its only London terminal, so this connecting line is no longer used in regular service, but can be used in emergencies by Class 395 passenger trains.

Services.

High Speed 1 was built to allow eight trains per hour through to the Channel Tunnel. As of May 2014, Eurostar runs two to three trains per hour in each direction between London and the Channel Tunnel. Southeastern runs in the high peak eight trains per hour between London and Ebbsfleet, two of these continuing to Ashford. During the 2012 Olympic Games, Southeastern provided the Olympic Javelin service with up to twelve trains per hour from Stratford into London.

Freight.

The route was built with freight provision from the beginning. It has spurs leading to and from the freight terminal at Dollands Moor (Folkestone) and the freight depot at Barking (Ripple Lane), north of the River Thames. Long passing loops to hold freight trains while passenger trains overtake them were built at Lenham Heath and Singlewell.  Freight trains operated by EWS first ran over CTRL Section 1, on the consecutive evenings of 3–4 April 2004. Five freight trains that would have run via the classic lines were diverted to run over the Channel Tunnel Rail Link instead: three southbound intermodal trains on 3 April 2004 and two northbound intermodal trains on 4 April 2004.

Ownership.

In November 2010, the HS1 concession was awarded for a duration of thirty years to an investment consortium bringing together two Canadian public pension funds: Ontario Municipal Employees Retirement System (through its subsidiary Borealis Infrastructure) and Ontario Teachers' Pension Plan At the time, UK pension investors had generally limited interest for such long-term, illiquid, ‘infrastructure assets’ In 2017, the sale of HS1 was announced to funds advised and managed by InfraRed Capital Partners Ltd and Equitix Investment Management Ltd.; participants include HICL Infrastructure and South Korea's National Pension Service.

Operators.

The railway is operated on an open access basis. Trains are operated by several organisations all operating over the same track. HS1 Ltd. is the network manager for the line, stations, and other infrastructure.

Network Rail (High Speed) Ltd.

HS1 Ltd is responsible for overall managing and running of the line—along with the international railway stations at St Pancras, Stratford, Ashford and Ebbsfleet—with responsibility for the infrastructure itself sub-contracted to Network Rail (High Speed) Ltd (formerly known as Network Rail (CTRL) acting as the controller and infrastructure manager. Network Rail (CTRL) Limited was created as a subsidiary of Network Rail on 26 September 2003 for £57 million to take over the assets of the CTRL renewal and maintenance operations. Network Rail (High Speed) operates engineering, track maintenance machines, rescue locomotives, and infrastructure- and test trains. Eurotunnel's subsidiary Europorte 2 operates its Eurotunnel Class 0001 (Krupp/MaK 6400) rescue locomotives on the line when required.  Various track recording trains run as necessary, including visits by the New Measurement Train. On the night of 4/5 May 2011 the SNCF TGV Iris 320 laboratory train took over, being hauled from Coquelles to St Pancras and back, towed by Eurotunnel Krupp locomotives numbers 4 and 5. The Iris 320 runs for Network Rail (High Speed) are an extension of the monitoring cycle already undertaken by SNCF International since December 2010 for Eurotunnel every two months.

Eurostar.

The Eurostar service uses about 40% of the capacity of High Speed 1, which in November 2007 became the company's route for all its services. Eurostar trains are for international traffic only, passing along the high-speed line from London St Pancras railway station to the Channel Tunnel, with the majority terminating at either Paris Gare du Nord in France or Brussels-South railway station in Belgium. A Eurostar train was used to set a new British rail speed record of on 30 July 2003. Prior to the formation of Eurostar International Limited, the British component of the Eurostar grouping was owned by London and Continental Railways, which had also previously owned the High Speed 1 infrastructure.  The fastest regular-service Eurostar journeys on record are 2 hours, 3 minutes and 39 seconds from Paris Gare du Nord to St Pancras, set on 4 September 2007; and 1 hour 43 minutes from Brussels South to St Pancras, set on 19 September 2007.

Southeastern.

Domestic high-speed services on High Speed 1 are operated by Southeastern. Having been in planning since 2004, a preview service of the British Rail Class 395 trains, popularly known as "Javelins", started in June 2009, and regular services began on 13 December 2009. The quickest journey time from Ashford to London St Pancras is 35 minutes, compared with 80 minutes for the service to London Charing Cross via Tonbridge. This service on Section 2 of the CTRL, known previously as CTRL-DS, was a factor in London's successful 2012 Olympic Bid, promising a seven-minute journey time from the Olympic Park at Stratford to the London terminus at St Pancras.

DB Cargo UK.

DB Cargo is a global freight operator with a large interest in freight over rail in Europe. While High Speed 1 was constructed with freight loops, no freight traffic had run upon the line since opening in 2003. On 16 April 2009 DB Schenker signed an agreement with HS1 Ltd, the owner of High Speed 1, for a partnership to develop TVM modifications for class 92 freight locomotives to run on the line. On 25 March 2011 for the first time a modified class 92 locomotive travelled from Dollands Moor to Singlewell using the TVM430 signalling system. A loaded container train ran for the first time on 27 May 2011, to Novara in Italy. Following further trials with loaded wagons DB is to upgrade five Class 92 locomotives to allow them to run on High Speed 1. From 11 November 2011 a weekly service using European-sized swap body containers has run between London and Poland using High Speed 1.

Future operations.

At present, only Deutsche Bahn has applied for use of the line and in 2009 regulations were relaxed to allow its trains to use the Channel Tunnel. Other proposals are yet to be formalised.

Deutsche Bahn.

In November 2007, it was reported that Deutsche Bahn, Germany's national train company, had applied to use the Channel Tunnel and High Speed 1 into London. This was denied by Deutsche Bahn, and the bi-national Channel Tunnel Safety Authority confirmed that it had not received such an application. The plan was delayed by safety regulations as Deutsche Bahn's fleet of ICE 3M high-speed trains could not be divided in the tunnel in an emergency.  In December 2008, it was reported that Deutsche Bahn (DB) was interested in buying the British share in Eurostar, which in practice means buying Eurostar (UK) Ltd., the 100% subsidiary of London and Continental Railways (LCR), which the British government intends to break up and sell just as it does the other rail-related subsidiary of L&CR, HS1 Ltd. The buyer of EUKL would become the owner of the 11 British "Three Capitals" Class 373 trainsets plus all seven "North of London" sets, and would also be responsible for the operations of Eurostar traffic within Britain once the management contract with ICRR expires in 2010. Guillaume Pépy, the president of SNCF, who held a press conference the same day, described DB's interest as "premature, presumptuous and arrogant". SNCF claims to own 62% of the shares of Eurostar Group Ltd. Hartmut Mehdorn, then CEO of Deutsche Bahn, confirmed DB's interest but insisted in a letter to Pépy that DB had only informally requested information and not made any official requests to Britain's Department for Transport.  In 2009, Eurotunnel (the owners of the Channel Tunnel) announced that it was prepared to start relaxing the fire safety regulations, in order to permit other operators, such as Deutsche Bahn, to transport passengers via the Tunnel using other forms of rolling stock. Under the deregulation of European railway service, high-speed lines were opened up to access by other operators on 1 January 2010; the Inter-Governmental Commission on the Channel Tunnel (IGC) announced that it was considering relaxing the safety requirements concerning train splitting. LCR suggested that high-speed rail services between London and Cologne could commence before the 2012 Olympics.  In March 2010 Eurotunnel, HS1 Ltd, DB and other interested train operators formed a working group to discuss changes to the safety rules, including allowing 200-metre trains. The Intergovernmental Commission currently requires trains to be 400 m long. Deutsche Bahn carried out evacuation trials in the tunnel on 17 October 2010 with two 200m-long ICE3 trains, and displayed one of them at St Pancras station on 19 October. The current Velaro ICE3 sets do not meet the fire safety requirements for passenger services through the tunnel, but the Siemens Velaro D sets on order include the necessary additional fire-proofing. In March 2011, the European Rail Agency decided to allow trains with distributed traction to operate in the Channel Tunnel. DB is planning three services a day to Frankfurt (5h from London), Rotterdam (3h) and Amsterdam (4h) via Brussels from 2015. This had originally planned to be 2013, but has been delayed due to the availability of the Channel Tunnel version of the Siemens Velaro D trains, high rental costs of the French rail network and border controls in their stations. As of 2016, nothing yet has come to fruition, but the High Speed One website continues to state that "HS1 Ltd are working with Deutsche Bahn on plans to incorporate three additional international return journeys, between Frankfurt and London via Cologne, Brussels and Lille. This will include connections from Amsterdam via Rotterdam to London."  In March 2017 it was announced that Deutsche Bahn had revived plans for a London to Frankfurt train service with the service beginning as early as 2020. The service would take around 5 hours and could rival airlines and become the first competitor for Eurostar. However, in June 2018, Deutsche Bahn stated the plans have been shelved due to a "significantly changed economic environment".

Veolia.

In September 2008, Air France-KLM indicated a desire to take advantage of the change in the law and apply to run rail services, in co-operation with Veolia, from London to Paris and from Paris to Amsterdam, in competition with Eurostar and Thalys respectively, with the intention of purchasing or leasing the new AGV multiple units currently being tested. In October 2009 Air France withdrew its interest. This led to Veolia looking for new partners, with the announcement that it would begin working on new proposals in co-operation with Trenitalia to run services from Paris to Strasbourg, London and Brussels.

Renfe.

Spanish railway operator RENFE said in 2009 that it was interested in running AVE services from Spain to London via Paris, Lyon, Barcelona, Madrid and Lisbon (using the Madrid–Barcelona high-speed rail line) once its AVE network was connected to France via the Barcelona to Figueres and Perpignan to Figueres lines in 2012.

Services to Bordeaux.

It was revealed in March 2020 that High Speed 1 Ltd, along with SNCF and Lisea, are looking for an operator for a future London St Pancras-Bordeaux St Jean train service.

High Speed 1 (HS1), legally the Channel Tunnel Rail Link (CTRL), is a high-speed railway linking London with the Channel Tunnel.

High Speed 1 (HS1), ursprünglich als Channel Tunnel Rail Link (CTRL) bezeichnet, ist eine 108 km lange Schnellfahrstrecke, die London mit dem Eurotunnel unter dem Ärmelkanal verbindet und eine Geschwindigkeit von 300 km/h zulässt. Die Strecke ist der erste größere Eisenbahnneubau in Großbritannien seit mehr als hundert Jahren und ersetzt die alte Route durch die Grafschaft Kent, auf der die Eurostar-Hochgeschwindigkeitszüge mit maximal 100 mph (160 km/h) unterwegs waren.


Usage.

Dzongkha and its dialects are the native tongue of eight western districts of Bhutan ("viz." Wangdue Phodrang, Punakha, Thimphu, Gasa, Paro, Ha, Dagana and Chukha). There are also some native speakers near the Indian town of Kalimpong, once part of Bhutan but now in North Bengal.  Dzongkha was declared the national language of Bhutan in 1971. Dzongkha study is mandatory in all schools, and the language is the "lingua franca" in the districts to the south and east where it is not the mother tongue. The 2003 Bhutanese film "Travellers and Magicians" is in Dzongkha.

Writing system.

The Tibetan alphabet used to write Dzongkha has thirty basic letters, sometimes known as "radicals", for consonants. Dzongkha is usually written in Bhutanese forms of the Uchen script, forms of the Tibetan alphabet known as "Jôyi" "cursive longhand" and "Jôtshum" "formal longhand". The print form is known simply as "Tshûm".

Romanization.

There are various ways of romanization and transliteration systems for Dzongkha, however all possible systems failed to represent the true phonetic sound. A phonetic transcription system known as Roman Dzongkha, devised by the linguist George van Driem, was adopted as the standard romanization system of Dzongkha by the Bhutanese government in 1991.

Phonology.

Dzongkha is a tone language and has two register tones: high and low. The tone of a syllable determines the allophone of the onset and the phonation type of the nuclear vowel.

Consonants.

All consonants may begin a syllable. In the onsets of low-tone syllables, consonants are voiced. Aspirated consonants (indicated by the superscript "h"),, and are not found in low-tone syllables. The rhotic is usually a trill or a fricative trill, and is voiceless in the onsets of high-tone syllables.  Only a few consonants are found in syllable-final positions. Most common among them are. Syllable-final is often elided and results in the preceding vowel nasalized and prolonged, especially word-finally. Syllable-final is most often omitted when word-final as well, unless in formal speech. In literary pronunciation, liquids and may also end a syllable. Though rare, is also found in syllable-final positions. No other consonants are found in syllable-final positions.

Phonotactics.

Many words in Dzongkha are monosyllabic. Syllables usually take the form of CVC, CV, or VC. Syllables with complex onsets are also found, but such an onset must be a combination of an unaspirated bilabial stop and a palatal affricate. The bilabial stops in complex onsets are often omitted in colloquial speech.

Classification and related languages.

Dzongkha is considered a South Tibetic language. It is closely related to and partially intelligible with Sikkimese, and to some other Bhutanese languages such as Chocangaca, Brokpa, Brokkat and Lakha.  Dzongkha bears a close linguistic relationship to J'umowa, which is spoken in the Chumbi Valley of Southern Tibet. It has a much more distant relationship to Standard Tibetan. Although spoken Dzongkha and Tibetan are largely mutually unintelligible, the literary forms of both are both highly influenced by the liturgical (clerical) Classical Tibetan language, known in Bhutan as "Chöke," which has been used for centuries by Buddhist monks. Chöke was used as the language of education in Bhutan until the early 1960s when it was replaced by Dzongkha in public schools.  Although descended from Classical Tibetan, Dzongkha shows a great many irregularities in sound changes that make the official spelling and standard pronunciation more distant from each other than is the case with Standard Tibetan. "Traditional orthography and modern phonology are two distinct systems operating by a distinct set of rules."

Sample text.

The following is a sample text in Dzongkha of Article 1 of the Universal Declaration of Human Rights:  Dzongkha in the Tibetan alphabet  Translation

Dzongkha (, ), is a Sino-Tibetan language spoken by over half a million people in Bhutan; it is the sole official and national language of the Kingdom of Bhutan. The Tibetan alphabet is used to write Dzongkha.

Dzongkha (tibetische Schreibweise:, auch "Bhutanische Sprache, Jonkha, Bhotia, Zongkhar, Drukke") ist die Amtssprache in Bhutan und wird außerdem in Indien, vornehmlich im direkt an Bhutan grenzenden indischen Bundesstaat Sikkim, gesprochen. 226.000 Sprecher leben in Bhutan (Bhutan hat etwa 672.000 Einwohner laut Volkszählung 2005). Total hat Dzongkha etwa 237.000 Sprecher weltweit.


The paradox.

Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms, where the pigeonhole principle would apply.

Finitely many new guests.

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room "n" to room "n"+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests.

Infinitely many new guests.

It is also possible to accommodate a "countably infinite" number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and, in general, the guest occupying room "n" to room 2"n" (2 times "n"), and all the odd-numbered rooms (which are countably infinite) will be free for the new guests.

Infinitely many coaches with infinitely many guests each.

It is possible to accommodate countably infinitely many coachloads of countably infinite passengers each, by several different methods. Most methods depend on the seats in the coaches being already numbered (or use the axiom of countable choice). In general any pairing function can be used to solve this problem. For each of these methods, consider a passenger's seat number on a coach to be formula_1, and their coach number to be formula_2, and the numbers formula_1 and formula_2 are then fed into the two arguments of the pairing function.

Prime powers method.

Empty the odd numbered rooms by sending the guest in room formula_5 to room formula_6, then put the first coach's load in rooms formula_7, the second coach's load in rooms formula_8; for coach number formula_2 we use the rooms formula_10 where formula_11 is the formula_2th odd prime number. This solution leaves certain rooms empty (which may or may not be useful to the hotel); specifically, all odd numbers that are not prime powers, such as 15 or 847, will no longer be occupied. (So, strictly speaking, this shows that the number of arrivals is "less than or equal to" the number of vacancies created. It is easier to show, by an independent means, that the number of arrivals is also "greater than or equal to" the number of vacancies, and thus that they are "equal", than to modify the algorithm to an exact fit.) (The algorithm works equally well if one interchanges formula_1 and formula_2, but whichever choice is made, it must be applied uniformly throughout.)

Prime factorization method.

You can put each person of a certain seat formula_15 and coach formula_2 into room formula_17 (presuming "c"=0 for the people already in the hotel, 1 for the first coach, etc....). Because every number has a unique prime factorization, it's easy to see all people will have a room, while no two people will end up in the same room. For example, the person in room 2592 (formula_18) was sitting in on the 4th coach, on the 5th seat. Like the prime powers method, this solution leaves certain rooms empty.  This method can also easily be expanded for infinite nights, infinite entrances, etc.... ( formula_19 )

Interleaving method.

For each passenger, compare the lengths of formula_1 and formula_2 as written in any positional numeral system, such as decimal. (Treat each hotel resident as being in coach #0.) If either number is shorter, add leading zeroes to it until both values have the same number of digits. Interleave the digits to produce a room number: its digits will be [first digit of coach number]-[first digit of seat number]-[second digit of coach number]-[second digit of seat number]-etc. The hotel (coach #0) guest in room number 1729 moves to room 01070209 (i.e., room 1,070,209). The passenger on seat 1234 of coach 789 goes to room 01728394 (i.e., room 1,728,394).  Unlike the prime powers solution, this one fills the hotel completely, and we can reconstruct a guest's original coach and seat by reversing the interleaving process. First add a leading zero if the room has an odd number of digits. Then de-interleave the number into two numbers: the seat number consists of the odd-numbered digits and the coach number is the even-numbered ones. Of course, the original encoding is arbitrary, and the roles of the two numbers can be reversed (seat-odd and coach-even), so long as it is applied consistently.

Triangular number method.

Those already in the hotel will be moved to room formula_22, or the formula_1th triangular number. Those in a coach will be in room formula_24, or the formula_25 triangular number plus formula_1. In this way all the rooms will be filled by one, and only one, guest.  This pairing function can be demonstrated visually by structuring the hotel as a one-room-deep, infinitely tall pyramid. The pyramid's topmost row is a single room: room 1; its second row is rooms 2 and 3; and so on. The column formed by the set of rightmost rooms will correspond to the triangular numbers. Once they are filled (by the hotel's redistributed occupants), the remaining empty rooms form the shape of a pyramid exactly identical to the original shape. Thus, the process can be repeated for each infinite set. Doing this one at a time for each coach would require an infinite number of steps, but by using the prior formulas, a guest can determine what his room "will be" once his coach has been reached in the process, and can simply go there immediately.

Arbitrary enumeration method.

Let formula_27. formula_28 is countable since formula_29 is countable, hence we may enumerate its elements formula_30. Now if formula_31, assign the formula_32th guest of the formula_33th coach to the formula_1th room (consider the guests already in the hotel as guests of the formula_35th coach). Thus we have a function assigning each person to a room; furthermore, this assignment does not skip over any rooms.

Further layers of infinity.

Suppose the hotel is next to an ocean, and an infinite number of car ferries arrive, each bearing an infinite number of coaches, each with an infinite number of passengers. This is a situation involving three "levels" of infinity, and it can be solved by extensions of any of the previous solutions.  The prime factorization method can be applied by adding a new prime number for every additional layer of infinity ( formula_36, with formula_37 the ferry).  The prime power solution can be applied with further exponentiation of prime numbers, resulting in very large room numbers even given small inputs. For example, the passenger in the second seat of the third bus on the second ferry (address 2-3-2) would raise the 2nd odd prime (5) to 49, which is the result of the 3rd odd prime (7) being raised to the power of his seat number (2). This room number would have over thirty decimal digits.  The interleaving method can be used with three interleaved "strands" instead of two. The passenger with the address 2-3-2 would go to room 232, while the one with the address 4935-198-82217 would go to room #008,402,912,391,587 (the leading zeroes can be removed).  Anticipating the possibility of any number of layers of infinite guests, the hotel may wish to assign rooms such that no guest will need to move, no matter how many guests arrive afterward. One solution is to convert each arrival's address into a binary number in which ones are used as separators at the start of each layer, while a number within a given layer (such as a guest's coach number) is represented with that many zeroes. Thus, a guest with the prior address 2-5-1-3-1 (five infinite layers) would go to room 10010000010100010 (decimal 295458).  As an added step in this process, one zero can be removed from each section of the number; in this example, the guest's new room is 101000011001 (decimal 2585). This ensures that every room could be filled by a hypothetical guest. If no infinite sets of guests arrive, then only rooms that are a power of two will be occupied.

Infinite layers of nesting.

Although a room can be found for any finite number of nested infinities of people, the same is not always true for an infinite number of layers, even if a finite number of elements exists at each layer.  The set of real numbers, and the set of guests in this example, is uncountably infinite. Because no one-to-one pairing can be made between countable and uncountable sets, rooms at the hotel cannot be made for all of these guests, although any countably infinite subset of them can still be accommodated.  If this variant is modified in certain ways, then the set of people is countable again. For example, suppose there "were" a largest ship, directly containing a finite (or countably infinite) number of both ships and people, and each of these ships in turn contained both ships and people, and so forth. This time, any given person is a finite number of levels "down" from the top, and thus can be identified with a unique finite address. The set of people is countable again, even if the total number of layers is infinite, because we do not have to consider an "infinitieth layer" in either direction.

Analysis.

Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true. The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.  Initially, this state of affairs might seem to be counter-intuitive. The properties of "infinite collections of things" are quite different from those of "finite collections of things". The paradox of Hilbert's Grand Hotel can be understood by using Cantor's theory of transfinite numbers. Thus, while in an ordinary (finite) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms. However, in Hilbert's aptly named Grand Hotel, the quantity of odd-numbered rooms is not smaller than the total "number" of rooms. In mathematical terms, the cardinality of the subset containing the odd-numbered rooms is the same as the cardinality of the set of all rooms. Indeed, infinite sets are characterized as sets that have proper subsets of the same cardinality. For countable sets (sets with the same cardinality as the natural numbers) this cardinality is formula_38.  Rephrased, for any countably infinite set, there exists a bijective function which maps the countably infinite set to the set of natural numbers, even if the countably infinite set contains the natural numbers. For example, the set of rational numbers—those numbers which can be written as a quotient of integers—contains the natural numbers as a subset, but is no bigger than the set of natural numbers since the rationals are countable: there is a bijection from the naturals to the rationals.

Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often. The idea was introduced by David Hilbert in a 1924 lecture "Über das Unendliche", reprinted in, and was popularized through George Gamow's 1947 book "One Two Three... Infinity".

Hilberts Hotel ist ein vom Mathematiker David Hilbert erdachtes Paradoxon bzw. Gedankenexperiment zur Veranschaulichung verblüffender Konsequenzen der Nutzung des Unendlichkeitsbegriffes in der Mathematik. Damit lässt sich zeigen, dass die Mengen der natürlichen Zahlen, der ganzen Zahlen und der rationalen Zahlen gleichmächtig sind.


Characteristics.

Writer Vladimir Nabokov, in his lectures at Cornell University, said: "In an Anglo-Saxon thriller, the villain is generally punished, and the strong silent man generally wins the weak babbling girl, but there is no governmental law in Western countries to ban a story that does not comply with a fond tradition, so that we always hope that the wicked but romantic fellow will escape scot-free and the good but dull chap will be finally snubbed by the moody heroine."  Thrillers may be defined by the primary mood that they elicit: suspenseful excitement. In short, if it "thrills", it is a thriller. As the introduction to a major anthology says:

Suspense.

Suspense is a crucial characteristic of the thriller genre. It gives the viewer a feeling of pleasurable fascination and excitement mixed with apprehension, anticipation and tension. These develop from unpredictable, mysterious and rousing events during the narrative, which makes the viewer or reader think about the outcome of certain actions. Suspense builds in order to make those final moments, no matter how short, the most memorable. The suspense in a story keeps the person hooked to reading or watching more until the climax is reached.  In terms of narrative expectations, it may be contrasted with curiosity and surprise. The objective is to deliver a story with sustained tension, surprise, and a constant sense of impending doom. As described by film director Alfred Hitchcock, an audience experiences suspense when they expect something bad to happen and have (or believe they have) a superior perspective on events in the drama's hierarchy of knowledge, yet they are powerless to intervene to prevent it from happening.  Suspense in thrillers is often intertwined with hope and anxiety, which are treated as two emotions aroused in anticipation of the conclusion - the hope that things will turn out all right for the appropriate characters in the story, and the fear that they may not. The second type of suspense is the "...anticipation wherein we either know or else are fairly certain about what is going to happen but are still aroused in anticipation of its actual occurrence."  According to Greek philosopher Aristotle in his book "Poetics", suspense is an important building block of literature, and this is an important convention in the thriller genre.  Thriller music has been shown to create a distrust and ominous uncertainty between the viewer of a film and the character on screen at the time when the music is playing.

Themes and characters.

Common methods and themes in crime and action thrillers are mainly ransoms, captivities, heists, revenge, kidnappings. Common in mystery thrillers are investigations and the whodunit technique. Common elements in dramatic and psychological thrillers include plot twists, psychology, obsession and mind games. Common elements of science-fiction thrillers are killing robots, machines or aliens, mad scientists and experiments. Common in horror thrillers are serial killers, stalking, deathtraps and horror-of-personality. Elements such as fringe theories, false accusations and paranoia are common in paranoid thrillers. Threats to entire countries, spies, espionage, conspiracies, assassins and electronic surveillance are common in spy thrillers.  Characters may include criminals, stalkers, assassins, innocent victims (often on the run), menaced women, psychotic individuals, spree killers, sociopaths, agents, terrorists, cops and escaped cons, private eyes, people involved in twisted relationships, world-weary men and women, psycho-fiends, and more. The themes frequently include terrorism, political conspiracy, pursuit, or romantic triangles leading to murder. Plots of thrillers involve characters which come into conflict with each other or with outside forces.  The protagonist of these films is set against a problem. No matter what subgenre a thriller film falls into, it will emphasize the danger that the protagonist faces. The protagonists are frequently ordinary citizens unaccustomed to danger, although commonly in crime and action thrillers, they may also be "hard men" accustomed to danger such as police officers and detectives. While protagonists of thrillers have traditionally been men, women lead characters are increasingly common. In psychological thrillers, the protagonists are reliant on their mental resources, whether it be by battling wits with the antagonist or by battling for equilibrium in the character's own mind. The suspense often comes from two or more characters preying upon one another's minds, either by playing deceptive games with the other or by merely trying to demolish the other's mental state.

Story and setting.

An atmosphere of menace and sudden violence, such as crime and murder, characterize thrillers. The tension usually arises when the character(s) is placed in a dangerous situation, or a trap from which escaping seems impossible. Life is threatened, usually because the principal character is unsuspectingly or unknowingly involved in a dangerous or potentially deadly situation.  Hitchcock's films often placed an innocent victim (an average, responsible person) into a strange, life-threatening or terrorizing situation, in a case of mistaken identity or wrongful accusation.  Thrillers take place mostly in ordinary suburbs and cities, although sometimes they may take place wholly or partly in exotic settings such as foreign cities, deserts, polar regions, or the high seas. These usually tough, resourceful, but essentially ordinary heroes are pitted against villains determined to destroy them, their country, or the stability of the free world. Often in a thriller movie, the protagonist is faced with what seem to be insurmountable problems in his mission, carried out against a ticking clock, the stakes are high and although resourceful, they face personal dilemmas along the way forcing them to make sacrifices for others.

History in literature.

Ancient epic poems such as the "Epic of Gilgamesh", Homer's "Odyssey" and the "Mahābhārata" may have used similar narrative techniques to modern thrillers. "The Three Apples", a tale in the "One Thousand and One Nights" ("Arabian Nights"), is a murder mystery with multiple plot twists and detective fiction elements. In this tale, a fisherman discovers a heavy locked chest along the Tigris river and he sells it to the Abbasid Caliph, Harun al-Rashid, who then has the chest broken open only to find inside it the dead body of a young woman who was cut into pieces. Harun orders his vizier, Ja'far ibn Yahya, to solve the crime and find the murderer within three days. This whodunit mystery has also been considered a detective story, though it lacks a sleuth.  "The Count of Monte Cristo" (1844) is a swashbuckling revenge thriller about a man named Edmond Dantès who is betrayed by his friends and sent to languish in the notorious Château d'If. His only companion is an old man who teaches him everything from philosophy to mathematics to swordplay. Just before the old man dies, he reveals to Dantès the secret location of a great treasure. Shortly after, Dantès engineers a daring escape and uses the treasure to reinvent himself as the Count of Monte Cristo. Thirsting for vengeance, he sets out to punish those who destroyed his life.  The first recognizable modern thriller was Erskine Childer’s "The Riddle of the Sands" (1903), in which two young Englishmen stumble upon a secret German armada preparing to invade their homeland.  "The Thirty-Nine Steps" (1915) is an early thriller by John Buchan, in which an innocent man becomes the prime suspect in a murder case and finds himself on the run from both the police and enemy spies.  "The Manchurian Candidate" (1959) by Richard Condon is a classic of Cold War paranoia. A squad of American soldiers is kidnapped and brainwashed by Communists. False memories are implanted, along with a subconscious trigger that turns them into assassins at a moment's notice. They are soon reintegrated into American society as sleeper agents. One of them, Major Bennett Marco, senses that not all is right, setting him on a collision course with his former comrade Sergeant Raymond Shaw, who has been activated as an assassin.  "The Spy Who Came in from the Cold" (1963) by John le Carré is set in the world of Cold War espionage and helped to usher in an era of more realistic thriller fiction, based around professional spies and the battle of wits between rival spymasters.  "The Bourne Identity" (1980) is one of the first thrillers to be written in the modern style that we know today. A man with gunshot wounds is found floating unconscious in the Mediterranean Sea. Brought ashore and nursed back to health, he wakes up with amnesia. Fiercely determined to uncover the secrets of his past, he embarks on a quest that sends him spiraling into a web of violence and deceit. He is astounded to learn that knowledge of hand-to-hand combat, firearms, and trade craft seem to come naturally to him.

Television.

There have been at least two television series called simply "Thriller", one made in the U.S. in the 1960s and one made in the UK in the 1970s. Although in no way linked, both series consisted of one-off dramas, each utilising the familiar motifs of the genre.  "The Twilight Zone" consists of suspenseful unrelated dramas depicting characters dealing with paranormal, futuristic, supernatural, or otherwise disturbing or unusual events. Characters who find themselves dealing with these strange, sometimes inexplicable happenings are said to have crossed over into "The Twilight Zone". Each story typically features a moral and a surprise ending.  "24" is a fast-paced television series with a premise inspired by the War on Terror. Each season takes place over the course of twenty-four hours, with each episode happening in "real time". Featuring a split-screen technique and a ticking onscreen clock, "24" follows the exploits of federal agent Jack Bauer as he races to foil terrorist threats.  "Lost", which deals with the survivors of a plane crash, sees the castaways on the island forced to deal with a monstrous being that appears as a cloud of black smoke, a conspiracy of "Others" who have kidnapped or killed their fellow castaways at various points, a shadowy past of the island itself that they are trying to understand, polar bears, and the fight against these and other elements as they struggle simply to stay alive and get off of the island.  "Prison Break" follows Michael Scofield, an engineer who has himself incarcerated in a maximum-security prison in order to break out his brother, who is on death row for a crime he did not commit. In the first season Michael must deal with the hazards of prison life, the other inmates and prison staff, and executing his elaborate escape plan, while outside the prison Michael's allies investigate the conspiracy that led to Lincoln being framed. In the second season, Michael, his brother and several other inmates escape the prison and must evade the nationwide manhunt for their re-capture, as well as those who want them dead.  "The Fugitive" was a television series in which Dr. Richard Kimble was on the run from authorities while trying to find the man whom he claimed murdered his wife.

Thriller is a genre of fiction, having numerous, often overlapping subgenres. Thrillers are characterized and defined by the moods they elicit, giving viewers heightened feelings of suspense, excitement, surprise, anticipation and anxiety. Successful examples of thrillers are the films of Alfred Hitchcock.

Der Thriller [] (Lehnwort aus engl. "" „Schauer, Erregung, Sensation“) ist sowohl ein Literatur- als auch ein Filmgenre mit verschiedenen, sich teilweise überlappenden Subgenres. Charakteristisch für Thriller ist das Erzeugen eines Thrills, einer Spannung, die nicht nur in kurzen Passagen, sondern während des gesamten Handlungsverlaufs präsent ist, ein beständiges Spiel zwischen Anspannung und Erleichterung. Häufig anzutreffen sind weitläufige Spannungsbögen, Spannungsmusik, Cliffhanger und Red Herrings.


Plot.

In the 22nd century, rising sea levels from global warming have wiped out coastal cities, reducing the world's population. Mecha, humanoid robots seemingly capable of complex thought but lacking in emotions, have been created. In Madison, New Jersey, David, a prototype Mecha child capable of experiencing love, is given to Henry Swinton and his wife Monica, whose son Martin contracted a rare disease and has been placed in suspended animation. Monica feels uneasy with David, but eventually warms to him and activates his imprinting protocol, causing him to have an enduring childlike love for her. David seeks to have Monica express the same love towards him. David is befriended by Teddy, a robotic teddy bear which belonged to Martin. Martin is unexpectedly cured of his disease and brought home. Martin becomes jealous of David, and taunts him to perform worrisome acts, such as cutting off locks of Monica's hair while she is sleeping. At a pool party, one of Martin's friends pokes David with a knife, triggering his self-protection programming. David grabs onto Martin, and they both fall into the pool. Martin is saved before he drowns, and Henry convinces Monica to return David to his creators to be destroyed. On the way there, Monica has a change of heart and spares David from destruction by leaving him in the woods. With Teddy as his only accompaniment, David recalls "The Adventures of Pinocchio" and decides to find the Blue Fairy so that she may turn him into a real boy, which he believes will win back Monica's love.  David and Teddy are captured by a Flesh Fair, where obsolete Mecha are destroyed before jeering crowds. David is nearly destroyed himself and pleads for his life. The audience, deceived by David's realistic nature, revolts and allows David to escape alongside Gigolo Joe, a male prostitute Mecha on the run from authorities after being charged with murder. David, Teddy and Joe go to the decadent resort town of Rouge City, where "Dr. Know", a holographic answer engine, directs them to the top of Rockefeller Center in the flooded ruins of Manhattan and has also provided fairy tale information interpreted by David as suggesting that a Blue Fairy has the power to help him. Above the ruins of Manhattan, David meets Professor Hobby, his creator, who tells him that their meeting demonstrates David's ability to love and desire. David finds many copies of himself, including a female variant Darlene, boxed and ready to be shipped. Disheartened by his lost sense of individuality, David attempts suicide by falling from a skyscraper into the ocean. While underwater, David catches sight of a figure resembling the Blue Fairy before Joe rescues him in an amphibious aircraft. Before David can explain, Joe is captured via electromagnet by authorities. David and Teddy take control of the aircraft to see the Fairy, which turns out to be a statue from an attraction on Coney Island. The two become trapped when the Wonder Wheel falls on their vehicle. Believing the Blue Fairy to be real, David asks the statue to turn him into a real boy, and repeats this request until his internal power source is depleted.  Two thousand years later, humans are extinct and Manhattan is buried under glacial ice. The Mecha have evolved into an advanced form called Specialists, and have become interested in learning about humanity. They find and revive David and Teddy. David walks to the frozen Blue Fairy statue, which collapses when he touches it. The Specialists reconstruct the Swinton family home from David's memories and explain to him, via an interactive image of the Blue Fairy, that it is impossible to make David a real boy. However, at David's insistence, they recreate Monica through genetic material from the strand of hair that Teddy kept. This Monica can only live for one day, and the process cannot be repeated. David spends his happiest day with Monica, and as she falls asleep in the evening, she tells David that she has always loved him: "the everlasting moment he had been waiting for", the narrator says. David falls asleep as well and goes to that place "where dreams are born".

Production.

Development.

Kubrick began development on an adaptation of "Super-Toys Last All Summer Long" in the late 1970s, hiring the story's author, Brian Aldiss, to write a film treatment. In 1985, Kubrick asked Steven Spielberg to direct the film, with Kubrick producing. Warner Bros. agreed to co-finance "A.I." and cover distribution duties. The film labored in development hell, and Aldiss was fired by Kubrick over creative differences in 1989. Bob Shaw briefly served as writer, leaving after six weeks due to Kubrick's demanding work schedule, and Ian Watson was hired as the new writer in March 1990. Aldiss later remarked, "Not only did the bastard fire me, he hired my enemy [Watson] instead." Kubrick handed Watson "The Adventures of Pinocchio" for inspiration, calling "A.I." "a picaresque robot version of "Pinocchio"".  Three weeks later, Watson gave Kubrick his first story treatment, and concluded his work on "A.I." in May 1991 with another treatment of 90 pages. Gigolo Joe was originally conceived as a G.I. Mecha, but Watson suggested changing him to a male prostitute. Kubrick joked, "I guess we lost the kiddie market." Meanwhile, Kubrick dropped "A.I." to work on a film adaptation of "Wartime Lies", feeling computer animation was not advanced enough to create the David character. However, after the release of Spielberg's "Jurassic Park", with its innovative computer-generated imagery, it was announced in November 1993 that production of "A.I." would begin in 1994. Dennis Muren and Ned Gorman, who worked on "Jurassic Park", became visual effects supervisors, but Kubrick was displeased with their previsualization, and with the expense of hiring Industrial Light & Magic.

Pre-production.

In early 1994, the film was in pre-production with Christopher "Fangorn" Baker as concept artist, and Sara Maitland assisting on the story, which gave it "a feminist fairy-tale focus". Maitland said that Kubrick never referred to the film as "A.I.", but as "Pinocchio". Chris Cunningham became the new visual effects supervisor. Some of his unproduced work for "A.I." can be seen on the DVD, "The Work of Director Chris Cunningham". Aside from considering computer animation, Kubrick also had Joseph Mazzello do a screen test for the lead role. Cunningham helped assemble a series of "little robot-type humans" for the David character. "We tried to construct a little boy with a movable rubber face to see whether we could make it look appealing," producer Jan Harlan reflected. "But it was a total failure, it looked awful." Hans Moravec was brought in as a technical consultant. Meanwhile, Kubrick and Harlan thought "A.I." would be closer to Steven Spielberg's sensibilities as director. Kubrick handed the position to Spielberg in 1995, but Spielberg chose to direct other projects, and convinced Kubrick to remain as director. The film was put on hold due to Kubrick's commitment to "Eyes Wide Shut" (1999). After the filmmaker's death in March 1999, Harlan and Christiane Kubrick approached Spielberg to take over the director's position. By November 1999, Spielberg was writing the screenplay based on Watson's 90-page story treatment. It was his first solo screenplay credit since "Close Encounters of the Third Kind" (1977). Spielberg remained close to Watson's treatment, but removed various sex scenes with Gigolo Joe. Pre-production was briefly halted during February 2000, because Spielberg pondered directing other projects, which were "Harry Potter and the Philosopher's Stone", "Minority Report", and "Memoirs of a Geisha". The following month Spielberg announced that "A.I." would be his next project, with "Minority Report" as a follow-up. When he decided to fast track "A.I.", Spielberg brought Chris Baker back as concept artist. Ian Watson reported that the final script was very faithful to Kubrick's vision, even the ending, which is normally attributed to Spielberg, saying, "The final 20 minutes are pretty close to what I wrote for Stanley, and what Stanley wanted, faithfully filmed by Spielberg without added schmaltz."

Filming.

The original start date was July 10, 2000, but filming was delayed until August. Aside from a couple of weeks shooting on location in Oxbow Regional Park in Oregon, "A.I." was shot entirely using sound stages at Warner Bros. Studios and the Spruce Goose Dome in Long Beach, California. Spielberg copied Kubrick's obsessively secretive approach to filmmaking by refusing to give the complete script to cast and crew, banning press from the set, and making actors sign confidentiality agreements. Social robotics expert Cynthia Breazeal served as technical consultant during production. Costume designer Bob Ringwood studied pedestrians on the Las Vegas Strip for his influence on the Rouge City extras.

Soundtrack.

The film's soundtrack was released by Warner Sunset Records in 2001. The original score was composed and conducted by John Williams and featured singers Lara Fabian on two songs and Josh Groban on one. The film's score also had a limited release as an official "For your consideration Academy Promo", as well as a complete score issue by La-La Land Records in 2015. The band Ministry appears in the film playing the song "What About Us?" (but the song does not appear on the official soundtrack album).

Release.

Marketing.

Warner Bros. used an alternate reality game titled "The Beast" to promote the film. Over forty websites were created by Atomic Pictures in New York City (kept online at Cloudmakers.org) including the website for Cybertronics Corp. There were to be a series of video games for the Xbox video game console that followed the storyline of "The Beast", but they went undeveloped. To avoid audiences mistaking "A.I." for a family film, no action figures were created, although Hasbro released a talking Teddy following the film's release in June 2001.  "A.I." had its premiere at the Venice Film Festival in 2001.

Home media.

"A.I. Artificial Intelligence" was released on VHS and DVD in the US by DreamWorks Home Entertainment on March 5, 2002 in widescreen and full-screen 2-disc special editions featuring an extensive sixteen-part documentary detailing the film's development, production, music and visual effects. The bonus features also included interviews with Haley Joel Osment, Jude Law, Frances O'Connor, Steven Spielberg, and John Williams, two teaser trailers for the film's original theatrical release and an extensive photo gallery featuring production stills and Stanley Kubrick's original storyboards. It was released overseas by Warner Home Video.  The film was first released on Blu-ray Disc in Japan by Warner Home Video on December 22, 2010, followed shortly after with a U.S release by Paramount Home Media Distribution (former owners of the DreamWorks catalog) on April 5, 2011. This Blu-ray featured the film newly remastered in high-definition and incorporated all the bonus features previously included on the 2-disc special-edition DVD.

Box office.

The film opened in 3,242 theaters in the United States on June 29, 2001, earning $29,352,630 during its opening weekend. "A.I" went on to gross $78.62 million in US totals as well as $157.31 million in foreign countries, coming to a worldwide total of $235.93 million.

Reception.

Based on 193 reviews collected by Rotten Tomatoes, 74% of critics gave the film positive notices with a score of 6.6/10. The website's critical consensus reads, "A curious, not always seamless, amalgamation of Kubrick's chilly bleakness and Spielberg's warm-hearted optimism. "A.I." is, in a word, fascinating." By comparison, Metacritic collected an average score of 65, based on 32 reviews, which is considered favorable.  Producer Jan Harlan stated that Kubrick "would have applauded" the final film, while Kubrick's widow Christiane also enjoyed "A.I". Brian Aldiss admired the film as well: "I thought what an inventive, intriguing, ingenious, involving film this was. There are flaws in it and I suppose I might have a personal quibble but it's so long since I wrote it." Of the film's ending, he wondered how it might have been had Kubrick directed the film: "That is one of the 'ifs' of film history—at least the ending indicates Spielberg adding some sugar to Kubrick's wine. The actual ending is overly sympathetic and moreover rather overtly engineered by a plot device that does not really bear credence. But it's a brilliant piece of film and of course it's a phenomenon because it contains the energies and talents of two brilliant filmmakers." Richard Corliss heavily praised Spielberg's direction, as well as the cast and visual effects.  Roger Ebert gave the film three stars, saying that it was "wonderful and maddening." Ebert later gave the film four stars and added the film to his "Great Movies" list in 2011. Leonard Maltin, on the other hand, gives the film two stars out of four in his "Movie Guide", writing: "[The] intriguing story draws us in, thanks in part to Osment's exceptional performance, but takes several wrong turns; ultimately, it just doesn't work. Spielberg rewrote the adaptation Stanley Kubrick commissioned of the Brian Aldiss short story 'Super Toys Last All Summer Long'; [the] result is a curious and uncomfortable hybrid of Kubrick and Spielberg sensibilities." However, he calls John Williams' music score "striking". Jonathan Rosenbaum compared "A.I." to "Solaris" (1972), and praised both "Kubrick for proposing that Spielberg direct the project and Spielberg for doing his utmost to respect Kubrick's intentions while making it a profoundly personal work." Film critic Armond White, of the "New York Press", praised the film noting that "each part of David's journey through carnal and sexual universes into the final eschatological devastation becomes as profoundly philosophical and contemplative as anything by cinema's most thoughtful, speculative artists – Borzage, Ozu, Demy, Tarkovsky." Filmmaker Billy Wilder hailed "A.I." as "the most underrated film of the past few years." When British filmmaker Ken Russell saw the film, he wept during the ending.  Mick LaSalle gave a largely negative review. ""A.I." exhibits all its creators' bad traits and none of the good. So we end up with the structureless, meandering, slow-motion endlessness of Kubrick combined with the fuzzy, cuddly mindlessness of Spielberg." Dubbing it Spielberg's "first boring movie", LaSalle also believed the robots at the end of the film were aliens, and compared Gigolo Joe to the "useless" Jar Jar Binks, yet praised Robin Williams for his portrayal of a futuristic Albert Einstein. Peter Travers gave a mixed review, concluding "Spielberg cannot live up to Kubrick's darker side of the future." But he still put the film on his top ten list that year for best movies. David Denby in "The New Yorker" criticized "A.I." for not adhering closely to his concept of the Pinocchio character. Spielberg responded to some of the criticisms of the film, stating that many of the "so called sentimental" elements of "A.I.", including the ending, were in fact Kubrick's and the darker elements were his own. However, Sara Maitland, who worked on the project with Kubrick in the 1990s, claimed that one of the reasons Kubrick never started production on "A.I." was because he had a hard time making the ending work. James Berardinelli found the film "consistently involving, with moments of near-brilliance, but far from a masterpiece. In fact, as the long-awaited 'collaboration' of Kubrick and Spielberg, it ranks as something of a disappointment." Of the film's highly debated finale, he claimed, "There is no doubt that the concluding 30 minutes are all Spielberg; the outstanding question is where Kubrick's vision left off and Spielberg's began."  Screenwriter Ian Watson has speculated, "Worldwide, "A.I." was very successful (and the 4th-highest earner of the year) but it didn't do quite so well in America, because the film, so I'm told, was too poetical and intellectual in general for American tastes. Plus, quite a few critics in America misunderstood the film, thinking for instance that the Giacometti-style beings in the final 20 minutes were aliens (whereas they were robots of the future who had evolved themselves from the robots in the earlier part of the film) and also thinking that the final 20 minutes were a sentimental addition by Spielberg, whereas those scenes were exactly what I wrote for Stanley and exactly what he wanted, filmed faithfully by Spielberg." [Despite Mr. Watson's reference to worldwide box office of 4th, the movie actually finished 16th worldwide among 2001 movie releases.]  In 2002, Spielberg told film critic Joe Leydon that "People pretend to think they know Stanley Kubrick, and think they know me, when most of them don't know either of us". "And what's really funny about that is, all the parts of "A.I." that people assume were Stanley's were mine. And all the parts of "A.I." that people accuse me of sweetening and softening and sentimentalizing were all Stanley's. The teddy bear was Stanley's. The whole last 20 minutes of the movie was completely Stanley's. The whole first 35, 40 minutes of the film—all the stuff in the house—was word for word, from Stanley's screenplay. This was Stanley's vision." "Eighty percent of the critics got it all mixed up. But I could see why. Because, obviously, I've done a lot of movies where people have cried and have been sentimental. And I've been accused of sentimentalizing hard-core material. But in fact it was Stanley who did the sweetest parts of "A.I.", not me. I'm the guy who did the dark center of the movie, with the Flesh Fair and everything else. That's why he wanted me to make the movie in the first place. He said, 'This is much closer to your sensibilities than my own. He also added: "While there was divisiveness when A.I. came out, I felt that I had achieved Stanley’s wishes, or goals."  Upon rewatching the film many years after its release, BBC film critic Mark Kermode apologized to Spielberg in an interview in January 2013 for "getting it wrong" on the film when he first viewed it in 2001. He now believes the film to be Spielberg's "enduring masterpiece".

Accolades.

Visual effects supervisors Dennis Muren, Stan Winston, Michael Lantieri, and Scott Farrar were nominated for the Academy Award for Best Visual Effects, while John Williams was nominated for Best Original Music Score. Steven Spielberg, Jude Law and Williams received nominations at the 59th Golden Globe Awards. "A.I." was successful at the Saturn Awards, winning five awards, including Best Science Fiction Film along with Best Writing for Spielberg and Best Performance by a Younger Actor for Osment.

A.I. Artificial Intelligence (also known as A.I.) is a 2001 American science fiction drama film directed by Steven Spielberg. The screenplay by Spielberg and screen story by Ian Watson were loosely based on the 1969 short story "Supertoys Last All Summer Long" by Brian Aldiss. The film was produced by Kathleen Kennedy, Spielberg and Bonnie Curtis. It stars Haley Joel Osment, Jude Law, Frances O'Connor, Brendan Gleeson and William Hurt. Set in a futuristic post-climate change society, "A.I." tells the story of David (Osment), a childlike android uniquely programmed with the ability to love.

A.I. – Künstliche Intelligenz ist ein Science-Fiction-Film von Steven Spielberg nach der Kurzgeschichte "Supertoys Last All Summer Long" von Brian Aldiss. Ursprünglich war dies ein Filmprojekt von Stanley Kubrick, das er aber vor seinem Tod an Steven Spielberg übergeben hatte. Der Film ist zugleich eine moderne Adaption des Pinocchio-Themas. Der Film startete am 13. September 2001 in den deutschen Kinos.


History.

Orsha was first mentioned in 1067 as Rsha, making it one of the oldest towns in Belarus. The town was named after the river, which was originally also named Rsha, probably from a Baltic root *"rus"'slowly flowing.'  In 1320, Orsha became a part of the Grand Duchy of Lithuania. In 1398–1407, the Orsha castle was built. On September 8, 1514 the famous Battle of Orsha occurred, between allied Grand Duchy of Lithuania with Kingdom of Poland and Muscovite army. The Muscovites suffered significant defeat; however, the victorious Grand Duchy of Lithuania did not fully avail its victory.  In 1555, Mikołaj "the Black" Radziwiłł founded a Calvinist (Protestant) order in Orsha, one of the first in the Belarusian lands. From the sixteenth to eighteenth centuries Orsha was a notable religious centre, with dozens of Orthodox, Protestant and Catholic churches and orders. The town was also home to a large Jewish population.  Orsha was granted Magdeburg Rights in 1620. In 1630, S. Sobal opened the first printing house at the Kuciejna monastery, which became a well-known centre of Cyrillic-alphabet publishing. The town was damaged during the Russo-Polish War (1654-1667), which was a disaster for the Grand Duchy of Lithuania. During the First Polish partition the city was taken over by the Russian Empire in 1772, and became part of the Mogilyov Gubernia. Under Russian rule, it was stripped of its Magdeburg Rights in 1776 and went into cultural and economic decline. The population dropped sharply to just about 2,000 inhabitants. The city symbol in 1781 was changed to one which included the symbol of the Russian empire and five arrows.  In 1812, the city was badly burned during Napoleon's invasion. At the time of Orsha had been taken under control of French troops, there was a French writer Marie-Henri Beyle (also known under the pen name Stendhal) in a rank of intendant. According to the census of 1897, on a total population of 13,161, about 7,000 are Jews. During the First World War, the city was occupied by German forces in February–October 1918. From February 2, 1919, Orsha became a part of Homyel region (Vitebsk region, 1920) of Soviet Russia. After the formation of the Soviet Union, it was transferred to the Byelorussian SSR in 1924.  The population before World War II was about 37,000. The city was occupied by Germany on July 16, 1941. The occupiers founded several concentration camps in the city, where an estimated 19,000 people were killed.  Orsha was one of the centers of the Belarusian general strike in April 1991. Hundreds of thousands of coal miners had been on strike across the Soviet Union since March 1. On April 3, the day after the central government had imposed consumer price increases, workers at several Minsk factories walked out raising the miners' demand for wages indexed to inflation. Virtually the entire labor force of that city followed on the 4th, joined soon thereafter by strikes across the Belarusian SSR. Mass demonstrations voted for additional demands (including the dissolution of the Union and Belarusian governments and the end of the Communist Party's privileges) and elected delegates from each enterprise to citywide strike committees, which in turn sent representatives to a central Belarusian Strike Committee (SKB). On April 23, the SKB resumed the general strike after the deadline for its demands to be met had passed. The next morning, Gorbachev, Yeltsin, and leaders of eight of the other Soviet republics published a joint declaration in the papers agreeing to democratic elections for the Soviet parliament and the presidency, a new union treaty that would "radically increase the role of the union republics," and measures to soften the impact of the price increase, but also the introduction of a "special work regime" in many industries.  In response, the Orsha strike committee issued a proposal for all local workers to block the railway junction, strategically located on the line linking Moscow and Leningrad to Eastern and Western Europe. This was quickly endorsed by votes to "lie down on the rails" at a citywide meeting at the railway station. On the 25th, the Belarusian authorities concentrated the republic's KGB and riot police forces on Orsha, but were resisted by the strikers who sent fuel trains primed to explode down the tracks. Gorbachev mobilized the nearby military forces in Pskov with instructions to restore order over the railway; however many officers declared their refusal to comply, and brigade commander Gennady Sidorov professed a "lack of understanding" of the mission. Meanwhile, workers in other cities throughout Belarus held rallies threatening to retaliate if a drop of blood was shed in Orsha. Fearing a clash, and seizing on the government's offer to negotiate with its representatives and grant it radio and air time, the SKB suspended the general strike that evening.

Sports.

The bandy club Start has produced players for the Belarus national bandy team.

Transportation.

Orsha became an important transportation center after the construction of a Dnieper River port. The coming of railway lines in the second half of the nineteenth century greatly contributed to the city growth:  Today, Orsha is a major railway node where the Minsk–Moscow crosses the northern Vitebsk line, which branches south to Mogilev and Krychaw. All trains from Moscow and Saint-Petersburg bound for Western Europe pass through Orsha.  The city is also a junction of the important motorways: The M1 (E30) Moscow-Brest and the M8/M20 (E95) Saint Petersburg - Odessa.

Military.

OSGOEINT recently reported on the 571st Aircraft Repair Plant (ARP) located at Orsha Airfield (Balbasovo Air Base). Accordingly, the 571st ARP repairs Mi-8-17 HIP, Mi-24-35 HIND, as well as the Tu-134 CRUSTY and possibly the IL-76 CANDID. The report goes on to mention recent investment agreements with the Ukraine where private firms plan on providing $12 million to finance facility upgrades during the 2012-2016 period. Press reporting states that the investors plan on building a modern warehouse terminal as well as office buildings for customs services, banking, and a leasing company.

Health problems.

Recently, a high rate of oncological diseases attracted attention to this city. Before 1987 there were less than 100 new cancer patients registered each year. Since then the number grew fivefold, with more than 500 new patients registered per year as of 2004. The biggest growth was registered in 2003–04 (178%). This was widely reported in independent media, but Belarusian officials are silent about the alarming health situation and possible reasons for this high cancer rate. Two possible factors mentioned in the independent media are old Soviet military installations in Orsha, and the Chernobyl disaster.

Twin towns - sister cities.

Orsha is twinned with:

Orsha (; ;, ) is a city in Belarus in the Vitebsk Region, on the fork of the Dnieper and Arshytsa rivers.

Orscha (; ;, weißrussisch inoffiziell auch Ворша/"Worscha") ist eine am Dnepr (weißrussisch ) gelegene Industriestadt im Nordosten Weißrusslands in der Wizebskaja Woblasz, kurz vor der Grenze zu Russland mit 125.347 Einwohnern. Sie ist administratives Zentrum des Rajon Orscha.


Definitions.

Probability mass function.

The following conditions characterize the hypergeometric distribution:  A random variable formula_19 follows the hypergeometric distribution if its probability mass function (pmf) is given by  where  The is positive when formula_26.  A random variable distributed hypergeometrically with parameters formula_13, formula_14 and formula_12 is written formula_30 and has probability mass function formula_31 above.

Combinatorial identities.

As required, we have  which essentially follows from Vandermonde's identity from combinatorics.  Also note that  This identify can be shown by expressing the binomial coefficients in terms of factorials and rearranging the latter, but it also follows from the symmetry of the problem. Indeed, consider two rounds of drawing without replacement. In the first round, formula_14 out of formula_13 neutral marbles are drawn from an urn without replacement and coloured green. Then the coloured marbles are put back. In the second round, formula_12 marbles are drawn without replacement and coloured red. Then, the number of marbles with both colours on them (that is, the number of marbles that have been drawn twice) has the hypergeometric distribution. The symmetry in formula_14 and formula_12 stems from the fact that the two rounds are independent, and one could have started with drawing formula_12 balls and colouring them red first.

Properties.

Working example.

The classical application of the hypergeometric distribution is sampling without replacement. Think of an urn with two types of marbles, red ones and green ones. Define drawing a green marble as a success and drawing a red marble as a failure (analogous to the binomial distribution). If the variable "N" describes the number of all marbles in the urn (see contingency table below) and "K" describes the number of green marbles, then "N" − "K" corresponds to the number of red marbles. In this example, "X" is the random variable whose outcome is "k", the number of green marbles actually drawn in the experiment. This situation is illustrated by the following contingency table:  Now, assume (for example) that there are 5 green and 45 red marbles in the urn. Standing next to the urn, you close your eyes and draw 10 marbles without replacement. What is the probability that exactly 4 of the 10 are green? "Note that although we are looking at success/failure, the data are not accurately modeled by the binomial distribution, because the probability of success on each trial is not the same, as the size of the remaining population changes as we remove each marble."  This problem is summarized by the following contingency table: The probability of drawing exactly "k" green marbles can be calculated by the formula  Hence, in this example calculate  Intuitively we would expect it to be even more unlikely that all 5 green marbles will be among the 10 drawn.  As expected, the probability of drawing 5 green marbles is roughly 35 times less likely than that of drawing 4.

Symmetries.

Swapping the roles of green and red marbles:  Swapping the roles of drawn and not drawn marbles:  Swapping the roles of green and drawn marbles:

Order of draws.

The probability of drawing any set of green and red marbles (the hypergeometric distribution) depends only on the numbers of green and red marbles, not on the order in which they appear; i.e., it is an exchangeable distribution. As a result, the probability of drawing a green marble in the formula_46 draw is  This is an ex ante probability—that is, it is based on not knowing the results of the previous draws.

Tail bounds.

Let formula_48 and formula_49. Then for formula_50 we can derive the following bounds:  where  is the Kullback-Leibler divergence and it is used that formula_53.  If "n" is larger than "N"/2, it can be useful to apply symmetry to "invert" the bounds, which give you the following:

Statistical Inference.

Hypergeometric test.

The hypergeometric test uses the hypergeometric distribution to measure the statistical significance of having drawn a sample consisting of a specific number of formula_15 successes (out of formula_12 total draws) from a population of size formula_13 containing formula_14 successes. In a test for over-representation of successes in the sample, the hypergeometric p-value is calculated as the probability of randomly drawing formula_15 or more successes from the population in formula_12 total draws. In a test for under-representation, the p-value is the probability of randomly drawing formula_15 or fewer successes.  The test based on the hypergeometric distribution (hypergeometric test) is identical to the corresponding one-tailed version of Fisher's exact test ). Reciprocally, the p-value of a two-sided Fisher's exact test can be calculated as the sum of two appropriate hypergeometric tests (for more information see ).

Related distributions.

Let formula_62 and formula_49.  where formula_83 is the standard normal distribution function  The following table describes four distributions related to the number of successes in a sequence of draws:

Multivariate hypergeometric distribution.

The model of an urn with green and red marbles can be extended to the case where there are more than two colors of marbles. If there are "K" marbles of color "i" in the urn and you take "n" marbles at random without replacement, then the number of marbles of each color in the sample ("k","k"...,"k") has the multivariate hypergeometric distribution. This has the same relationship to the multinomial distribution that the hypergeometric distribution has to the binomial distribution—the multinomial distribution is the "with-replacement" distribution and the multivariate hypergeometric is the "without-replacement" distribution.  The properties of this distribution are given in the adjacent table, where "c" is the number of different colors and formula_88 is the total number of marbles.

Example.

Suppose there are 5 black, 10 white, and 15 red marbles in an urn. If six marbles are chosen without replacement, the probability that exactly two of each color are chosen is

Occurrence and applications.

Application to auditing elections.

Election audits typically test a sample of machine-counted precincts to see if recounts by hand or machine match the original counts. Mismatches result in either a report or a larger recount. The sampling rates are usually defined by law, not statistical design, so for a legally defined sample size "n", what is the probability of missing a problem which is present in "K" precincts, such as a hack or bug? This is the probability that "k" = 0. Bugs are often obscure, and a hacker can minimize detection by affecting only a few precincts, which will still affect close elections, so a plausible scenario is for "K" to be on the order of 5% of "N". Audits typically cover 1% to 10% of precincts (often 3%), so they have a high chance of missing a problem. For example, if a problem is present in 5 of 100 precincts, a 3% sample has 86% probability that "k" = 0 so the problem would not be noticed, and only 14% probability of the problem appearing in the sample (positive "k"):  The sample would need 45 precincts in order to have probability under 5% that "k" = 0 in the sample, and thus have probability over 95% of finding the problem:

Application to Texas hold'em poker.

In hold'em poker players make the best hand they can combining the two cards in their hand with the 5 cards (community cards) eventually turned up on the table. The deck has 52 and there are 13 of each suit. For this example assume a player has 2 clubs in the hand and there are 3 cards showing on the table, 2 of which are also clubs. The player would like to know the probability of one of the next 2 cards to be shown being a club to complete the flush.  There are 4 clubs showing so there are 9 clubs still unseen. There are 5 cards showing (2 in the hand and 3 on the table) so there are formula_92 still unseen.  The probability that one of the next two cards turned is a club can be calculated using hypergeometric with formula_93 and formula_94. (about 31.6%)  The probability that both of the next two cards turned are clubs can be calculated using hypergeometric with formula_95 and formula_94. (about 3.3%)  The probability that neither of the next two cards turned are clubs can be calculated using hypergeometric with formula_97 and formula_94. (about 65.0%)

\, formula_9 formula_10 In statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific formula_15 successes (out of formula_12 total draws) from the aforementioned population. The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30).

Die hypergeometrische Verteilung ist eine Wahrscheinlichkeitsverteilung in der Stochastik. Sie ist univariat und zählt zu den diskreten Wahrscheinlichkeitsverteilungen. In Abgrenzung zur allgemeinen hypergeometrischen Verteilung wird sie auch klassische hypergeometrische Verteilung genannt.


Sources.

The original source region has since become an area of carr with poor water quality. The water of the Schwalm comes mainly from "Rheinbraun's" waste water pits. This brown coal open cast mine is required to feed the waste water into the surface water. Otherwise it would fill the mine, which is up to 230 metres deep.This is achieved by means of shafts ("Schlitzschächten") through which the water flows back into the groundwater. If it were not for these shafts, the rivers Niers and Schwalm would long since have dried up. This would also destroy the mixed alder and ash wet woodland typical of the region.

Course.

The source of the Schwalm is in a wetland area south of the German village of Wegberg-Tüschenbroich at an elevation of about. From there the river flows mainly through the Maas-Schwalm-Nette Nature Park, its riverbed running between the rivers Rur, Nette and Niers.  Of its total length from this source to its mouth on the Meuse, near the village of Swalmen at about, 13 kilometres of the river run through Dutch territory.  Parts of the river which, for example, run past the villages of Wegberg, Niederkrüchten, Schwalmtal, Brüggen-Born, Brüggen and Swalmen, form natural meanders.  The catchment area of the Schwalm is 268.7 square kilometres, of which around 27 square kilometres lie in the Netherlands.

Flora and fauna.

The carr and heath/bog areas along the Schwalm provide a diverse habitat for fauna and flora. Frogs, dragonflies, damselflies, bluethroat, kingfisher and golden oriole are to be found as are water crowfoot, bog myrtle and other rare plants. brown trout, barbel and chub are at home in the river; along the river banks are also various members of the eter water rat family.

The Schwalm (German) or Swalm (Dutch), is a small river in Germany and the Netherlands, tributary to the river Meuse. Its source is near Wegberg, in the district Heinsberg, south-west of Mönchengladbach, in North Rhine-Westphalia (Germany). The Schwalm flows through Wegberg and Brüggen before flowing into the Meuse across the border with the Netherlands, in Swalmen. Its total length is 45 km.

Die Schwalm () ist ein 45,3 km langer, südöstlicher und rechter Nebenfluss der Maas in Nordrhein-Westfalen (Deutschland) und in den Niederlanden.