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Eric W. Weisstein conjectured , and McKay et al . ( 2004 ) proved , that the same numbers count the ( 0 @,@ 1 ) matrices for which all eigenvalues are positive real numbers . The proof is bijective : a matrix A is an adjacency matrix of a DAG if and only if A + I is a ( 0 @,@ 1 ) matrix with all eigenvalues positive ,...
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= = = Related families of graphs = = =
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A polytree is a directed graph formed by orienting the edges of a free tree . Every polytree is a DAG . In particular , this is true of the arborescences formed by directing all edges outwards from the roots of a tree .
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A multitree ( also called a strongly unambiguous graph or a mangrove ) is a directed graph in which there is at most one directed path ( in either direction ) between any two vertices ; equivalently , it is a DAG in which , for every vertex v , the subgraph reachable from v forms a tree .
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= = Computational problems = =
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= = = Topological sorting and recognition = = =
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Topological sorting is the algorithmic problem of finding a topological ordering of a given DAG . It can be solved in linear time . Kahn 's algorithm for topological sorting builds the vertex ordering directly . It maintains a list of vertices that have no incoming edges from other vertices that have not already been ...
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It is also possible to check whether a given directed graph is a DAG in linear time , either by attempting to find a topological ordering and then testing for each edge whether the resulting ordering is valid or alternatively , for some topological sorting algorithms , by verifying that the algorithm successfully orde...
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= = = Construction from cyclic graphs = = =
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Any undirected graph may be made into a DAG by choosing a total order for its vertices and directing every edge from the earlier endpoint in the order to the later endpoint . The resulting orientation of the edges is called an acyclic orientation . Different total orders may lead to the same acyclic orientation , so a...
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Any directed graph may be made into a DAG by removing a feedback vertex set or a feedback arc set , a set of vertices or edges ( respectively ) that touches all cycles . However , the smallest such set is NP @-@ hard to find . An arbitrary directed graph may also be transformed into a DAG , called its condensation , b...
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= = = Transitive closure and transitive reduction = = =
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The transitive closure of a given DAG , with n vertices and m edges , may be constructed in time O ( mn ) by using either breadth @-@ first search or depth @-@ first search to test reachability from each vertex . Alternatively , it can be solved in time O ( nω ) where ω < 2 @.@ 373 is the exponent for fast matrix mult...
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In all of these transitive closure algorithms , it is possible to distinguish pairs of vertices that are reachable by at least one path of length two or more from pairs that can only be connected by a length @-@ one path . The transitive reduction consists of the edges that form length @-@ one paths that are the only ...
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= = = Closure problem = = =
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The closure problem takes as input a directed acyclic graph with weights on its vertices and seeks the minimum ( or maximum ) weight of a closure , a set of vertices with no outgoing edges . ( The problem may be formulated for directed graphs without the assumption of acyclicity , but with no greater generality , beca...
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= = = Path algorithms = = =
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Some algorithms become simpler when used on DAGs instead of general graphs , based on the principle of topological ordering . For example , it is possible to find shortest paths and longest paths from a given starting vertex in DAGs in linear time by processing the vertices in a topological order , and calculating the...
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= = Applications = =
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= = = Scheduling = = =
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Directed acyclic graphs representations of partial orderings have many applications in scheduling for systems of tasks with ordering constraints . An important class of problems of this type concern collections of objects that need to be updated , such as the cells of a spreadsheet after one of the cells has been chan...
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For instance , when one cell of a spreadsheet changes , it is necessary to recalculate the values of other cells that depend directly or indirectly on the changed cell . For this problem , the tasks to be scheduled are the recalculations of the values of individual cells of the spreadsheet . Dependencies arise when an...
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A somewhat different DAG @-@ based formulation of scheduling constraints is used by the program evaluation and review technique ( PERT ) , a method for management of large human projects that was one of the first applications of DAGs . In this method , the vertices of a DAG represent milestones of a project rather tha...
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= = = Data processing networks = = =
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A directed acyclic graph may be used to represent a network of processing elements . In this representation , data enters a processing element through its incoming edges and leaves the element through its outgoing edges .
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For instance , in electronic circuit design , static combinational logic blocks can be represented as an acyclic system of logic gates that computes a function of an input , where the input and output of the function are represented as individual bits . In general , the output of these blocks cannot be used as the inp...
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Dataflow programming languages describe systems of operations on data streams , and the connections between the outputs of some operations and the inputs of others . These languages can be convenient for describing repetitive data processing tasks , in which the same acyclically @-@ connected collection of operations ...
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In compilers , straight line code ( that is , sequences of statements without loops or conditional branches ) may be represented by a DAG describing the inputs and outputs of each of the arithmetic operations performed within the code . This representation allows the compiler to perform common subexpression eliminatio...
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= = = Causal structures = = =
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Graphs that have vertices representing events , and edges representing causal relations between events , are often acyclic – arranging the vertices in linear order of time , all arrows point in the same direction as time , from parent to child ( due to causality affecting the future , not the past ) , and thus have no...
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For instance , a Bayesian network represents a system of probabilistic events as vertices in a directed acyclic graph , in which the likelihood of an event may be calculated from the likelihoods of its predecessors in the DAG . In this context , the moral graph of a DAG is the undirected graph created by adding an ( u...
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Another type of graph with a similar causal structure is an influence diagram , the vertices of which represent either decisions to be made or unknown information , and the edges of which represent causal influences from one vertex to another . In epidemiology , for instance , these diagrams are often used to estimate...
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= = = Genealogy and version history = = =
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Family trees may be seen as directed acyclic graphs , with a vertex for each family member and an edge for each parent @-@ child relationship . Despite the name , these graphs are not necessarily trees because of the possibility of marriages between relatives ( so a child has a common ancestor on both the mother 's an...
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For the same reason , the version history of a distributed revision control system generally has the structure of a directed acyclic graph , in which there is a vertex for each revision and an edge connecting pairs of revisions that were directly derived from each other . These are not trees in general due to merges ....
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In many randomized algorithms in computational geometry , the algorithm maintains a history DAG representing the version history of a geometric structure over the course of a sequence of changes to the structure . For instance in a randomized incremental algorithm for Delaunay triangulation , the triangulation changes...
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= = = Data compression = = =
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Directed acyclic graphs may also be used as a compact representation of a collection of sequences . In this type of application , one finds a DAG in which the paths form the given sequences . When many of the sequences share the same subsequences , these shared subsequences can be represented by a shared part of the D...
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The same idea of using a DAG to represent a family of paths occurs in the binary decision diagram , a DAG @-@ based data structure for representing binary functions . In a binary decision diagram , each non @-@ sink vertex is labeled by the name of a binary variable , and each sink and each edge is labeled by a 0 or 1...
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= August ( Fringe ) =
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" August " is the eighth episode of the American science fiction drama television series Fringe 's second season . The episode was co @-@ written by J. H. Wyman and Jeff Pinkner , and directed by Dennis Smith . The episode marked the first prominent appearance of more than one Observer , and follows the events that oc...
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The episode first aired on November 19 , 2009 in the United States to mostly positive reviews , with many critics praising the new revelations about the Observers . An estimated 5 @.@ 746 million viewers watched the episode on its first broadcast .
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= = Plot = =
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An Observer , " August " ( Peter Woodward ) abducts Christine Hollis ( Jennifer Missoni ) , a 27 @-@ year @-@ old art student in Boston . Olivia Dunham ( Anna Torv ) and Peter Bishop ( Joshua Jackson ) learn of the events and realize the assailant matches the description of the Observer . However , after viewing video...
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At Massive Dynamic , Brandon ( Ryan McDonald ) theorizes to the team that Observers are time travelers , as they have been documented during several major events in history . They write in an incomprehensible language , and the number of Observer sightings has increased over the past few months , leaving the team wond...
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The team are later made aware of Christine 's location at a motel outside the city . However , Donald is on the trail also . August attempts to stop him , but Donald shoots him several times , before Peter and Olivia arrive to kill the assassin . September picks up August and while driving , September asks August why ...
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= = Production = =
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" August " was co @-@ written by co @-@ showrunners J. H. Wyman and Jeff Pinkner , while being directed by NCIS veteran Dennis Smith . They began shooting the episode during the second half of September 2009 , right after wrapping production on " Of Human Action " . Supervising producer Josh Singer later noted how " A...
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Up to the point the episode " August " aired , only one character that was part of a group known as " Observers " had been introduced . In this episode , two more such individuals were revealed : August ( played by Peter Woodward ) and December ( played by Eugene Lipinski ) . The creation of Observers was one of the f...
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Before the second season premiere aired in September 2009 , co @-@ creator J.R. Orci hinted that the audience was going to meet " many Observers " , and that in the season 's eighth episode , " You 're going to find out their role in the world , what they 're named after , and their connection to some of these charact...
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Actress Anna Torv stated in an interview with MTV News that " August " was one of her favorite episodes because " We sort of get to meet the Observers . At the moment what we know about them , they ... seemingly just observe . That 's kind of it , but [ in ] the episode that we have coming up , we 're not sure if all ...
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= = Reception = =
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= = = Ratings = = =
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" August " premiered to an estimated 5 @.@ 746 million viewers in the United States , with a 2 @.@ 0 rating . The episode was down 9 % from the previous week 's episode " Of Human Action " , which had a rating of 2 @.@ 2 .
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= = = Reviews = = =
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MTV 's Josh Wigler thought the episode was " a touching , sad tale with a healthy mix of mythological advancement , " and couldn 't wait for more episodes about the Observers . Ramsey Isler of IGN gave the episode 7 @.@ 6 / 10 , writing that despite the hype , the episode was " just plain average " . He did however ap...
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= Ghost in the Shell ( 1995 film ) =
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Ghost in the Shell , known in Japan as Mobile Armored Riot Police : Ghost In The Shell ( 攻殻機動隊 GHOST IN THE SHELL , Kōkaku Kidōtai Gōsuto In Za Sheru ) , is a 1995 science fiction anime film based on manga of the same title by Masamune Shirow . The film was written by Kazunori Itō , directed by Mamoru Oshii , animated...
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Ghost in the Shell follows the hunt by the public @-@ security agency Section 9 for a mysterious hacker known as the Puppet Master . With the assistance of her team , Motoko Kusanagi tracks and finds their suspect , only to be drawn into a complex sequence of political intrigue and a cover @-@ up as to the identity an...
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The overarching philosophical themes of the film include self @-@ identity in a technologically advanced world . The music , composed by Kenji Kawai , included an ancient Japanese language in a wedding song that serves as a key piece of music leading up to the climax of the movie . Widely considered one of the greates...
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In 2004 , Oshii directed Ghost in the Shell 2 : Innocence , billed as a separate work and not a true sequel . In 2008 , Oshii released an updated version of the original film , Ghost in the Shell 2 @.@ 0 , that features new audio and updated 3D animation . A live @-@ action Hollywood Ghost in the Shell remake is sched...
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= = Plot = =
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In 2029 , the world is interconnected by a vast electronic network that permeates every aspect of life . Much of humanity has access to this network through cybernetic bodies , or " shells " , which possess their consciousness and can give them superhuman abilities .
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Major Motoko Kusanagi , an assault @-@ team leader for the Public Security Section 9 , is assigned to capture an elusive hacker known as the Puppet Master . Her team , Batou and Ishikawa , use triangulation to seek out the Puppet Master . Their suspect is a garbageman who believes he is using a program obtained from a...
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A facility is hacked and programmed to assemble a female cybernetic body . The body escapes but is hit by a truck ; Section 9 investigates and examines the body , which seems to have a human " ghost " inside — perhaps the Puppet Master himself . Officials from rival agency Section 6 visit Section 9 and explain that th...
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The information from the body leads Section 9 to uncover the mysterious Project 2501 . Section 6 claims the project was created to catch the hacker , but it was initiated before his appearance . Section 9 speculates that the project itself created the Puppet Master , who then escaped , and Section 6 now wants him back...
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The getaway car carrying the Puppet Master meets another , and they split off . Batou stops the first car and realizes it is a decoy . Kusanagi follows the second car to an abandoned building , where she is ambushed by a spider @-@ like armored vehicle . Batou arrives in time to save the badly damaged Kusanagi . With ...
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Batou tries to disconnect the dive , but the Puppet Master ghost @-@ hacks him . Helicopters from Section 6 arrive with orders to destroy everyone inside to cover up Project 2501 . The Puppet Master disrupts their targeting systems . As he starts merging with Kusanagi , snipers blow their heads off , along with Batou ...
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Kusanagi wakes up in a child @-@ sized cyborg body in Batou 's safehouse . Batou explains that her original body was destroyed in the fight ; he recovered her head and attached it to the new body . Kusanagi acknowledges she is now neither herself nor the Puppet Master , but a combination of both . Batou says he will a...
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= = Voice cast = =
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= = Production = =
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= = = Development = = =
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Director Mamoru Oshii stated , " My intuition told me that this story about a futuristic world carried an immediate message for our present world . I am also interested in computers through my own personal experience with them . I had the same feeling about Patlabor and I thought it would be interesting to make a film...
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= = = Design = = =
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Hiroyuki Okiura , the character designer and key animation supervisor , designed a more mature and serious Motoko than Masamune Shirow 's original portrayal of the character in the manga . Okiura chose to depict a physically mature person to match Motoko 's mental age , instead of the youthful twenty @-@ something app...
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Oshii based the setting for Ghost in the Shell on Hong Kong . Oshii commented that his first thought to find an image of the future setting was an Asian city , but finding a suitable cityscape of the future would be impossible . Oshii chose to use the real streets of Hong Kong as his model . He also said that Hong Kon...
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The Hong Kong setting is alluded to by the scene wherein the characters are drinking San Miguel Beer a cultural staple of the East Asian megalopolis .
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= = = Animation = = =
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Ghost in the Shell used a novel process called " digitally generated animation " ( DGA ) , which is a combination of cel animation , computer graphics ( CG ) , and audio that is entered as digital data . In 1995 , DGA was thought to be the future of animation , which mixed traditional animation with the emerging use o...
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The digital cel work included both original illustrations , compositions and manipulation with traditional cel animation to create a sense of depth and evoke emotion and feelings . Utilized as background , filters like a lens effect were used to create a sense of depth and motion , by distorting the front background a...
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Some special effects , like Motoko 's " thermo @-@ optical camouflage " , were rendered through the use of TIMA software . The process uses a single illustration and manipulates the image as necessary to produce distortions for effect in combination with a background without altering the original illustration . The ef...
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The opening credits of the film were produced by the CG director , Seichi Tanaka . Tanaka converted code in a computer language displayed in romanized Japanese letters to numbers before inserting them into the computer to generate the credits . The origin of this code is the names of the film 's staff as written in a ...
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Animation director Toshihiko Nishikubo was responsible for the realism and strove for accurate depictions of movement and effects . The pursuit of realism included the staff conducting firearms research at a facility in Guam . Nishikubo has highlighted the tank scene as an example of the movie 's realism , noting that...
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= = = Sound and music = = =
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Ghost in the Shell 's recording was done with a high @-@ end studio to achieve superior sound throughout the film . A spatializer was used to alter the sound , specifically in the electronic brain conversations , to modify the voices .
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Composer Kenji Kawai scored the film . For the main theme , Kawai tried to imagine the setting and convey the essence of that world in the music . He used the ancient Japanese language of Yamato in the opening theme " Making of a Cyborg " . The composition is a mixture of Bulgarian harmony and traditional Japanese not...
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= = = Ghost in the Shell 2 @.@ 0 = = =
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An updated version of the original film , titled Ghost in the Shell 2 @.@ 0 ( GHOST IN THE SHELL / 攻殻機動隊 2 @.@ 0 , Gōsuto in za sheru / Kōkaku kidōtai 2 @.@ 0 ) , was made in celebration for the release of The Sky Crawlers in 2008 . The Ghost in the Shell 2 @.@ 0 release features replacements of the original animation...
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The original soundtrack was also re @-@ arranged and re @-@ recorded . Kenji Kawai remixed the Version 2 @.@ 0 soundtrack in 6 @.@ 1 Channel Surround . Randy Thom of Skywalker Sound reprised his role as sound designer , having worked previously on Ghost in the Shell 2 : Innocence . In the new soundtrack , the Japanese...
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= = Related media = =
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Kenji Kawai 's original soundtrack for the film was released on November 22 , 1995 . The last track included Yoshimasa Mizuno 's pop song " See You Everyday " . After the release of Ghost in the Shell 2 @.@ 0 , an updated version of the soundtrack was released on December 17 , 2008 .
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A Photo @-@ CD of the film was released in Japan on November 20 , 1995 . A spin @-@ off novel written by Endo Akira , titled Ghost in the Shell : Burning City ( 攻殻機動隊灼熱の都市 , Kōkaku kidōtai shakunetsu no toshi ) , was published by Kodansha and released on November 1995 . It was followed by a sequel , titled Ghost in th...
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= = Releases = =
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The film had its world premiere at the Tokyo International Film Festival in October 1995 , before its general release in November . In Japan , the film was released on VHS on April 26 , 1996 . The DVD version was released on 25 February 2004 , and the Blu @-@ ray on 24 August 2007 . A special edition was released in D...
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The " 2 @.@ 0 " version was released in theatres in Tokyo , Osaka , Nagoya , Fukuoka , and Sapporo on July 12 , 2008 . The film was released in DVD and Blu @-@ ray on December 19 , 2008 , in Japan .
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In North America , the film was released on VHS on June 18 , 1996 through Manga Entertainment , and on DVD on March 31 , 1998 by Anchor Bay Entertainment . Manga Entertainment released the film on Blu @-@ ray on 24 November 2009 ; this version contains the original film and the remastering , but omits the audio commen...
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= = Reception = =
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The film was a box office hit when released in Japan and received positive reviews from film critics . It holds a 95 % approval rating on the review aggregator website Rotten Tomatoes , based on 31 reviews . The website 's critical consensus reads , " A stunning feat of modern animation , Ghost in the Shell offers a t...
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Niels Matthijs of Twitch Film praised the film , stating , " Not only is Kokaku Kidotai an essential film in the canon of Japanese animation , together with Kubrick 's 2001 and Tarkovsky 's Solyaris it completes a trio of book adaptations that transcend the popularity of their originals and [ give ] a new meaning to a...
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Ghost in the Shell was the first anime video to reach Billboard 's # 1 video slot at the time of its release . The film ranked as the ninth top selling anime DVD movie in 2006 . It ranked 35 on Total Film 's 2010 top list of 50 Animated Films . The film ranked # 4 on Wizards Anime Magazine on their " Top 50 Anime rele...
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