title: The Bear (1988 film)

text: Some reviewers were critical of the film's dream sequences, which heavily utilize special effects and deviate from the overall naturalistic feel of the film. In his review for the "St. Petersburg Times", Hal Lipper called the dream sequences "existential flights of fancy are accompanied by psychedelic images that seem better suited for '60s 'happenings.'" In addition, one scene in which the male grizzly mates with a female bear while the cub looks on was criticized as being unfriendly for children viewers. David Denby of "New York Magazine" stated as much in his review of the film, noting "I would like to be able to recommend "The Bear" as a movie that parents and children could see together, but I'm afraid there's a scene in the middle that would have to be... "explained"."


title: The Bear (1988 film)

text: A small campaign was launched for the 62nd Academy Awards to secure Bart a nomination for the Academy Award for Best Actor, with proponents arguing the bear gave such a moving performance he should be the first animal actor to receive consideration for an award. However, the campaign was dismissed by the Academy, who stated they would not permit non-human actors to be nominated for awards, in the Best Actor category or any other.


title: Web analytics

text: Web analytics is the measurement, collection, analysis, and reporting of web data to understand and optimize web usage. Web analytics is not just a process for measuring web traffic but can be used as a tool for business and market research and assess and improve website effectiveness. Web analytics applications can also help companies measure the results of traditional print or broadcast advertising campaigns. It can be used to estimate how traffic to a website changes after launching a new advertising campaign. Web analytics provides information about the number of visitors to a website and the number of page views, or create user behavior profiles. It helps gauge traffic and popularity trends, which is useful for market research.


title: Web analytics

text: Another essential function developed by the analysts for the optimization of the websites are the experiments


title: Web analytics

text: The goal of A/B testing is to identify and suggest changes to web pages that increase or maximize the effect of a statistically tested result of interest.


title: Web analytics

text: Each stage impacts or can impact (i.e., drives) the stage preceding or following it. So, sometimes the data that is available for collection impacts the online strategy. Other times, the online strategy affects the data collected.


title: Web analytics

text: Historically, web analytics has been used to refer to on-site visitor measurement. However, this meaning has become blurred, mainly because vendors are producing tools that span both categories. Many different vendors provide on-site web analytics software and services. There are two main technical ways of collecting the data. The first and traditional method, "server log file analysis", reads the logfiles in which the web server records file requests by browsers. The second method, "page tagging", uses JavaScript embedded in the webpage to make image requests to a third-party analytics-dedicated server, whenever a webpage is rendered by a web browser or, if desired, when a mouse click occurs. Both collect data that can be processed to produce web traffic reports.


title: Web analytics

text: The fundamental goal of web analytics is to collect and analyze data related to web traffic and usage patterns. The data mainly comes from four sources:


title: Web analytics

text: Web servers record some of their transactions in a log file. It was soon realized that these log files could be read by a program to provide data on the popularity of the website. Thus arose web log analysis software.


title: Web analytics

text: In the early 1990s, website statistics consisted primarily of counting the number of client requests (or "hits") made to the web server. This was a reasonable method initially since each website often consisted of a single HTML file. However, with the introduction of images in HTML, and websites that spanned multiple HTML files, this count became less useful. The first true commercial Log Analyzer was released by IPRO in 1994.


title: Web analytics

text: Two units of measure were introduced in the mid-1990s to gauge more accurately the amount of human activity on web servers. These were "page views" and "visits" (or "sessions"). A "page view" was defined as a request made to the web server for a page, as opposed to a graphic, while a "visit" was defined as a sequence of requests from a uniquely identified client that expired after a certain amount of inactivity, usually 30 minutes.


title: Web analytics

text: The emergence of search engine spiders and robots in the late 1990s, along with web proxies and dynamically assigned IP addresses for large companies and ISPs, made it more difficult to identify unique human visitors to a website. Log analyzers responded by tracking visits by cookies, and by ignoring requests from known spiders.


title: Web analytics

text: The extensive use of web caches also presented a problem for log file analysis. If a person revisits a page, the second request will often be retrieved from the browser's cache, and so no request will be received by the web server. This means that the person's path through the site is lost. Caching can be defeated by configuring the web server, but this can result in degraded performance for the visitor and bigger load on the servers.


title: Web analytics

text: Concerns about the accuracy of log file analysis in the presence of caching, and the desire to be able to perform web analytics as an outsourced service, led to the second data collection method, page tagging or "web beacons".


title: Web analytics

text: In the mid-1990s, Web counters were commonly seen — these were images included in a web page that showed the number of times the image had been requested, which was an estimate of the number of visits to that page. In the late 1990s, this concept evolved to include a small invisible image instead of a visible one, and, by using JavaScript, to pass along with the image request certain information about the page and the visitor. This information can then be processed remotely by a web analytics company, and extensive statistics generated.


title: Web analytics

text: The web analytics service also manages the process of assigning a cookie to the user, which can uniquely identify them during their visit and in subsequent visits. Cookie acceptance rates vary significantly between websites and may affect the quality of data collected and reported.


title: Web analytics

text: Collecting website data using a third-party data collection server (or even an in-house data collection server) requires an additional DNS lookup by the user's computer to determine the IP address of the collection server. On occasion, delays in completing successful or failed DNS lookups may result in data not being collected.


title: Web analytics

text: With the increasing popularity of Ajax-based solutions, an alternative to the use of an invisible image is to implement a call back to the server from the rendered page. In this case, when the page is rendered on the web browser, a piece of JavaScript code would call back to the server and pass information about the client that can then be aggregated by a web analytics company.


title: Web analytics

text: Both logfile analysis programs and page tagging solutions are readily available to companies that wish to perform web analytics. In some cases, the same web analytics company will offer both approaches. The question then arises of which method a company should choose. There are advantages and disadvantages to each approach.


title: Web analytics

text: Logfile analysis is almost always performed in-house. Page tagging can be performed in-house, but it is more often provided as a third-party service. The economic difference between these two models can also be a consideration for a company deciding which to purchase.


title: Web analytics

text: Which solution is cheaper to implement depends on the amount of technical expertise within the company, the vendor chosen, the amount of activity seen on the websites, the depth and type of information sought, and the number of distinct websites needing statistics.


title: Web analytics

text: Regardless of the vendor solution or data collection method employed, the cost of web visitor analysis and interpretation should also be included. That is, the cost of turning raw data into actionable information. This can be from the use of third party consultants, the hiring of an experienced web analyst, or the training of a suitable in-house person. A cost-benefit analysis can then be performed. For example, what revenue increase or cost savings can be gained by analyzing the web visitor data?


title: Web analytics

text: Some companies produce solutions that collect data through both log files and page tagging and can analyze both kinds. By using a hybrid method, they aim to produce more accurate statistics than either method on its own. An early hybrid solution was produced in 1998 by Rufus Evison.


title: Web analytics

text: With IP geolocation, it is possible to track visitors' locations. Using an IP geolocation database or API, visitors can be geolocated to city, region, or country level.


title: Web analytics

text: IP Intelligence, or Internet Protocol (IP) Intelligence, is a technology that maps the Internet and categorizes IP addresses by parameters such as geographic location (country, region, state, city and postcode), connection type, Internet Service Provider (ISP), proxy information, and more. The first generation of IP Intelligence was referred to as geotargeting or geolocation technology. This information is used by businesses for online audience segmentation in applications such as online advertising, behavioral targeting, content localization (or website localization), digital rights management, personalization, online fraud detection, localized search, enhanced analytics, global traffic management, and content distribution.


title: Web analytics

text: Click analytics, also known as Clickstream is a special type of web analytics that gives special attention to clicks.


title: Web analytics

text: Commonly, click analytics focuses on on-site analytics. An editor of a website uses click analytics to determine the performance of his or her particular site, with regards to where the users of the site are clicking.


title: Web analytics

text: Also, click analytics may happen real-time or "unreal"-time, depending on the type of information sought. Typically, front-page editors on high-traffic news media sites will want to monitor their pages in real-time, to optimize the content. Editors, designers or other types of stakeholders may analyze clicks on a wider time frame to help them assess performance of writers, design elements or advertisements etc.


title: Web analytics

text: Data about clicks may be gathered in at least two ways. Ideally, a click is "logged" when it occurs, and this method requires some functionality that picks up relevant information when the event occurs. Alternatively, one may institute the assumption that a page view is a result of a click, and therefore log a simulated click that led to that page view.


title: Web analytics

text: Customer lifecycle analytics is a visitor-centric approach to measuring that falls under the umbrella of lifecycle marketing. Page views, clicks and other events (such as API calls, access to third-party services, etc.) are all tied to an individual visitor instead of being stored as separate data points. Customer lifecycle analytics attempts to connect all the data points into a marketing funnel that can offer insights into visitor behavior and website optimization.


title: Web analytics

text: Other methods of data collection are sometimes used. Packet sniffing collects data by sniffing the network traffic passing between the web server and the outside world. Packet sniffing involves no changes to the web pages or web servers. Integrating web analytics into the webserver software itself is also possible. Both these methods claim to provide better real-time data than other methods.


title: Web analytics

text: There are no globally agreed definitions within web analytics as the industry bodies have been trying to agree on definitions that are useful and definitive for some time. The main bodies who have had input in this area have been the IAB (Interactive Advertising Bureau), JICWEBS (The Joint Industry Committee for Web Standards in the UK and Ireland), and The DAA (Digital Analytics Association), formally known as the WAA (Web Analytics Association, US). However, many terms are used in consistent ways from one major analytics tool to another, so the following list, based on those conventions, can be a useful starting point:


title: Web analytics

text: Off-site web analytics is based on open data analysis, social media exploration, share of voice on web properties.


title: Web analytics

text: It is usually used to understand how to market a site by identifying the keywords tagged to this site, either from social media or from other websites.


title: Web analytics

text: The hotel problem is generally the first problem encountered by a user of web analytics. The problem is that the unique visitors for each day in a month do not add up to the same total as the unique visitors for that month. This appears to an inexperienced user to be a problem in whatever analytics software they are using. In fact it is a simple property of the metric definitions.


title: Web analytics

text: The way to picture the situation is by imagining a hotel. The hotel has two rooms (Room A and Room B).


title: Web analytics

text: As the table shows, the hotel has two unique users each day over three days. The sum of the totals with respect to the days is therefore six.


title: Web analytics

text: During the period each room has had two unique users. The sum of the totals with respect to the rooms is therefore four.


title: Web analytics

text: Actually only three visitors have been in the hotel over this period. The problem is that a person who stays in a room for two nights will get counted twice if they are counted once on each day, but are only counted once if the total for the period is looked at. Any software for web analytics will sum these correctly for the chosen time period, thus leading to the problem when a user tries to compare the totals.


title: Web analytics

text: As the internet has matured, the proliferation of automated bot traffic has become an increasing problem for the reliability of web analytics. As bots traverse the internet, they render web documents in ways similar to organic users, and as a result may incidentally trigger the same code that web analytics use to count traffic. Jointly, this incidental triggering of web analytics events impacts interpretability of data and inferences made upon that data. IPM provided a proof of concept of how Google Analytics as well as their competitors are easily triggered by common bot deployment strategies.


title: Web analytics

text: Historically, vendors of page-tagging analytics solutions have used third-party cookies sent from the vendor's domain instead of the domain of the website being browsed. Third-party cookies can handle visitors who cross multiple unrelated domains within the company's site, since the cookie is always handled by the vendor's servers.


title: Web analytics

text: However, third-party cookies in principle allow tracking an individual user across the sites of different companies, allowing the analytics vendor to collate the user's activity on sites where he provided personal information with his activity on other sites where he thought he was anonymous. Although web analytics companies deny doing this, other companies such as companies supplying banner ads have done so. Privacy concerns about cookies have therefore led a noticeable minority of users to block or delete third-party cookies. In 2005, some reports showed that about 28% of Internet users blocked third-party cookies and 22% deleted them at least once a month.


title: Web analytics

text: Most vendors of page tagging solutions have now moved to provide at least the option of using first-party cookies (cookies assigned from the client subdomain).


title: Web analytics

text: Another problem is cookie deletion. When web analytics depend on cookies to identify unique visitors, the statistics are dependent on a persistent cookie to hold a unique visitor ID. When users delete cookies, they usually delete both first- and third-party cookies. If this is done between interactions with the site, the user will appear as a first-time visitor at their next interaction point. Without a persistent and unique visitor id, conversions, click-stream analysis, and other metrics dependent on the activities of a unique visitor over time, cannot be accurate.


title: Web analytics

text: Cookies are used because IP addresses are not always unique to users and may be shared by large groups or proxies. In some cases, the IP address is combined with the user agent in order to more accurately identify a visitor if cookies are not available. However, this only partially solves the problem because often users behind a proxy server have the same user agent. Other methods of uniquely identifying a user are technically challenging and would limit the trackable audience or would be considered suspicious. Cookies reach the lowest common denominator without using technologies regarded as spyware.


title: Web analytics

text: It may be good to be aware that third-party information gathering is subject to any network limitations and security applied. Countries, Service Providers and Private Networks can prevent site visit data from going to third parties.


title: Web analytics

text: All the methods described above (and some other methods not mentioned here, like sampling) have the central problem of being vulnerable to manipulation (both inflation and deflation). This means these methods are imprecise and insecure (in any reasonable model of security). This issue has been addressed in several papers, but to date the solutions suggested in these papers remain theoretical.


title: Madagascar: A Little Wild

text: Madagascar: A Little Wild (also known as A Little Wild) is an American computer-animated streaming television series produced by DreamWorks Animation Television. The series, which is a prequel to the 2005 film, features Alex the Lion, Marty the Zebra, Gloria the Hippo, and Melman the Giraffe residing in a rescue habitat at the Central Park Zoo as children. The series premiered on Hulu and Peacock on September 7, 2020. It concluded with its eighth and final season on June 30, 2022.


title: Madagascar: A Little Wild

text: Outside of the United States, it aired on Family Jr. in Canada on January 9, 2021. The series aired on DreamWorks Channel Asia as part of the DW Jr. block in 2022. The series is available for Latin America, on HBO Max.


title: Bruce Wayne (1989 film series character)

text: Bruce Wayne, better known by his vigilante superhero alias Batman, is a fictional character who appears as the main protagonist in Tim Burton's "Batman" and "Batman Returns", which are part of the "Batman" film series (1989–1997), and later in the DC Extended Universe (DCEU) film "The Flash". He is based on the DC Comics character of the same name and was originally portrayed by Michael Keaton.


text: This version of the character was critically acclaimed, and an influence on later interpretations. Keaton is set to reprise the role in the DCEU film "The Flash" (2023), which retroactively incorporates him into DCEU continuity. He was also expected to reprise the role in "Batgirl" before the film's cancellation.


text: The character was recast with Val Kilmer and George Clooney in Joel Schumacher's "Batman Forever" (1995) and "Batman & Robin" (1997) respectively.


text: Multiple actors were considered for the role of Batman during production. In Tom Mankiewicz's original script which "Ghostbusters" director Ivan Reitman was attached to, actor Bill Murray was considered for the role in a script that featured Eddie Murphy as Dick Grayson / Robin. "Gremlins" director Joe Dante was attached to the project as well at one point. The script was intended as a comedy, but was altered significantly after Tim Burton's involvement. Mel Gibson, Kevin Costner, Charlie Sheen, Tom Selleck, Harrison Ford, Pierce Brosnan, Ray Liotta, Willem Dafoe, Alec Baldwin, Patrick Swayze, Kyle MacLachlan, Steven Seagal, Dennis Quaid and Jean-Claude Van Damme were all considered for the role. Eventually, producer Jon Peters suggested Michael Keaton, claiming he had the right "edgy, tormented quality" for the role, and based his argument on Keaton's dramatic performance in the film "Clean and Sober". At the time, Keaton was primarily known for comedic parts in "Mr. Mom" and "Beetlejuice", the latter also being directed by Burton. Keaton's casting as the character caused an uproar from fans of the character, who claimed Keaton was too comedic and too short for the role. Over 50,000 recorded protest letters were sent to Warner Bros. offices, and the casting was questioned by screenwriter Sam Hamm, producer Michael Uslan and even Batman co-creator Bob Kane.


text: For the two later films, Keaton decided not to reprise the role of Batman and Val Kilmer ("Batman Forever") and George Clooney ("Batman & Robin") were cast.


text: The Batsuit worn by Keaton was designed by costume designer Bob Ringwood. Ringwood turned down the opportunity to work on James Bond film "Licence to Kill" to work on "Batman". Ringwood stated that designing the Batsuit was difficult, claiming "the image of Batman in the comics is this huge, big six-foot-four hunk with a dimpled chin. Michael Keaton is a guy with average build. The problem was to make somebody who was average-sized and ordinary-looking into this bigger-than-life creature." Producer Jon Peters had requested for the Batsuit to feature a Nike product-placement, but was shot down by Burton and Ringwood, feeling that it would not be intimidating. 28 latex designs of the suit were made, as well as 25 different capes and 6 different heads. It was decided the use of spandex as in the comics and previous adaptations would not be intimidating enough, so the character was given black armor pieces.


text: The Batsuit was upgraded for "Batman Returns", using more flexible foam latex, as well as a more traditional chest emblem. The updated Batsuit also featured a zipper to allow for urination in between takes and an updated plated armor torso that did not resemble sculpted muscles. Keaton still had difficulty hearing but found the neck movement much less restrictive than with the first costume. Due to the second costume's much thinner cowl with increased flexibility, a greater range of head-turning was allowed but could still leave gaps folding away from the cheek. The infamous "Bat-Turn" movement became an iconic part of the character's body language despite not truly needing to depend upon it, contrary to speculation from contemporary pundits. The wardrobe department spent seven weeks sculpting "Batman Forever" costumes on his body cast, preceding under the assumption that he would be returning. The addition of nipples and an enlarged codpiece to the Batsuit and Robin's costume in "Batman & Robin" was the subject of criticism.


text: As a child, Wayne watches the film "The Mark of Zorro" with his parents, Thomas and Martha. As the Waynes walk down an alley, Thomas and Martha are shot and killed by a mugger. After this, he is raised by Alfred Pennyworth (Michael Gough), the family butler. At his parents' funeral, he runs away and discovered a cave filled with bats on the family grounds, and decides to take the image and use it to put fear into the hearts of criminals. After decades of training, the adult Wayne had his company purchased equipment and built an advanced combat suit and the Batcave, a secret lair under Wayne Manor, and begins fighting crime in Gotham City as a vigilante who dresses as a bat.


text: Years later as an adult, there have been numerous sightings of the "Bat vigilante" and a criminal, Johnny Gobbs, who died after accidentally falling off from a roof, creates a rumor that the vigilante killed Gobbs in a manner of a vampire that feeds on blood and cannot be killed. The vigilante's reputation as a menacing creature of the night that hunts wrongdoers strikes fear in the city's criminal element.


text: Wayne hosts a fundraiser at Wayne Manor to help fund the Gotham City 200th Anniversary Parade, where he meets photographer Vicki Vale (Kim Basinger).


text: Wayne finds in reviewing the Manor's surveillance cameras that Commissioner James Gordon (Pat Hingle), who left the party unexpectedly, had been summoned to Axis Chemicals due to a break-in by Jack Napier (Jack Nicholson), crime lord Carl Grissom's (Jack Palance) right-hand man. Wayne suits up as the vigilante, now known as Batman, and during the fight, Napier falls into a vat of chemicals, transforming him into the insane, disfigured criminal mastermind the Joker.


text: On the 20th anniversary of his parents' murder, Wayne leaves lunch with Vale, and witnesses the Joker killing one of Grissom's associates. As Batman, he discovers that the Joker has poisoned various consumer products with his Joker venom. Wayne is informed by Alfred that he has a date with Vale at the Flugelheim Museum. Wayne states he has no plans to meet Vale that day, and realizes that the meeting was set up by the Joker to gain information on Batman.


text: After a battle with the Joker's men, Batman and Vale return to the Batcave, where he reveals his investigation of Joker's lethal chemicals to Vale, giving her his research to publish. Wayne nearly reveals to Vale that he is Batman, but they are interrupted by the Joker. The master criminal shoots Wayne, who survives because he is wearing body armor.


text: Wayne recognizes the Joker as the mugger who killed his parents. Wayne comes across the Joker's parade float during the 200th Anniversary Parade, where the Joker plans to kill thousands of people with his toxin. Batman foils the Joker's plan, however, and pursues him and Vale into the cathedral, eventually finding them at the top level. Batman confronts the Joker over killing his parents, and gets into brutal hand-to-hand combat with the villain. As the Joker tries to escape on a helicopter, Batman uses his grappling gun to tie one of the cathedral's gargoyles to the Joker's leg; when the gargoyle breaks free from its foundations, the Joker falls to his death. In the aftermath, Batman gives the Gotham City Police Department (GCPD) his own personalized signal as a way of contacting him for help.


text: During Gotham's Christmas celebrations, Batman discovers the Red Triangle Gang has interrupted the annual tree lighting ceremony. Despite managing to fight them off, he is too late to stop them taking billionaire industrialist Max Shreck (Christopher Walken) hostage. The next day, a member of the gang kidnaps the mayor's infant son, but the child is saved by the Penguin (Danny DeVito), a deformed mystery man who has lived in the sewers ever since his parents threw him into Gotham's reservoir. Though Penguin is immediately accepted by the public and allowed inside the Hall of Records to find his birth parents, Batman remains suspicious, and discovers the Penguin may have once been a performer in the Red Triangle Circus and connected to a series of missing children cases. He deduces that the Penguin is the gang's leader and is planning something else, already knowing who his parents are. Penguin becomes popular with the citizens of Gotham, and they discover his name is Oswald Cobblepot, with his parents having died years earlier. Meanwhile, Wayne meets with Shreck, who had been blackmailed into helping Oswald return to the surface, to contest his plans to build a new power plant, and meets Shreck's secretary Selina Kyle (Michelle Pfeiffer), unaware that she is the masked vigilante Catwoman, who is planning to kill Shreck as revenge for trying to kill her when she discovered that his power plant will actually drain Gotham of its energy and leave the city at the mercy of the Shreck family.


text: On Shreck's urging, the Penguin officially announces his plans to run for Mayor of Gotham City, and later, Wayne and Kyle discover that Cobblepot attempted to frame Batman by kidnapping the Ice Princess (Cristi Conaway), who was to relight the tree, and leaving behind a batarang. While Batman investigates the kidnapping, the Red Triangle Gang sabotages the Batmobile to allow the Penguin remote control access. Batman finds the Ice Princess standing on the edge of a rooftop, but the Penguin arrives and startles the girl by opening one of his trick-umbrellas and releasing a swarm of bats, which knocks her off the roof to her death. She lands on the button used to light the tree, causing a mass swarm of bats to attack the onlookers. Batman is forced to flee, now the chief suspect in the murder.


text: Batman returns to the Batmobile, but the car, having been hacked by the Penguin, takes him on a destructive joyride, though Batman is able to disable the signal and escape. With Alfred's help, Batman hacks into the Gotham Plaza's speakers during one of the Penguin's speeches and plays a recording of the villain bragging about having manipulated the entire city, causing a backlash from the crowd. At Shreck's masked ball, Kyle tells Wayne her plans to kill Shreck, and the two deduce each other's secret identities. At that moment, the Penguin crashes through the floor of the room, announcing his plans to kill all of the first-born sons of Gotham and takes Shreck hostage. Batman arrives and interrogates Penguin's right-hand man, learning of the Penguin's hideout underneath the Arctic World exhibit at the abandoned Gotham Zoo.


text: Batman foils the Penguin's plan to massacre Gotham by sending his penguins to fire missiles at the city and, with Pennyworth's help, reprograms the penguins to fire upon the Penguin's hideout. Batman and Penguin fight until the Penguin falls into the toxic waters in the sewer, eventually causing him to die. Batman attempts to stop Kyle from killing Shreck, and reveals his secret identity. Kyle kills Shreck by kissing him with a taser in her mouth, but mysteriously disappears. After the GCPD seize the Penguin's destroyed lair, Wayne finds Kyle's black cat, Miss Kitty, in an alleyway, implies that a very much alive Catwoman is watching him from a rooftop while the Bat Signal shines in the sky.


text: Batman is called to stop the gangster Two-Face (Tommy Lee Jones) from destroying the Gotham Statue of Liberty, with help from Gordon and psychologist Chase Meridian (Nicole Kidman), who becomes instantly attracted to him. Two-Face was once Gotham's District Attorney, Harvey Dent, before a criminal scarred half of his face with acid, for which he blames Batman. The Dark Knight stops Two-Face from destroying the statue, but Two-Face escapes.


text: The next day, Bruce Wayne visits Wayne Enterprises and becomes acquainted with Edward Nygma (Jim Carrey), an employee who is obsessed with him. Nygma has developed the Box, a machine capable of transmitting television signals directly into the human brain. He asks Wayne to fund his invention, but Wayne turns him down. Seeking revenge, Nygma reinvents himself as "the Riddler" and allies himself with Two-Face in a plot to destroy both Batman and Bruce Wayne, whom Nygma has discovered are one and the same.


text: During a charity circus performance, Wayne witnesses Two-Face attack and murder a family of acrobats dubbed the Flying Graysons, leaving their youngest son, Dick (Chris O'Donnell), an orphan. Feeling a kinship with Dick, Wayne takes him in as his ward. Dick soon discovers Wayne's secret identity, and asks Wayne to take him on as his crimefighting partner so he can kill Two-Face and avenge his family. Wayne, who still feels responsible for his parents' deaths, refuses, not wanting to be responsible for another lost life.


text: Meanwhile, Wayne soon starts a romantic relationship with Meridian, who tries help him move on the trauma of his parents' deaths. Wayne decides to abandon his war on crime and lead a normal life with her. Before he can tell her, however, Riddler and Two-Face attack Wayne Manor, take Meridian hostage, and destroy the Batcave. Batman tracks the villainous duo to their hideout, with help from Dick, whom he has finally accepted as his crimefighting partner, Robin.


text: Two-Face and the Riddler take Meridian and Robin hostage, setting a trap that would force Batman to choose between saving one life or the other. Instead, Batman destroys the Box, driving the Riddler insane, and saves Meridan and Robin. Two-Face corners them at gunpoint, and while flipping his coin to decide their fates, Batman throws a handful of coins at him, causing him to fall to his death, avenging Dick's family.


text: New villain Mr. Freeze (Arnold Schwarzenegger) surfaces and commits a string of diamond thefts, catching the attention of Batman and Robin. After Freeze freezes but spares Robin in order to escape, Wayne chastises Dick, who has begun to chafe under Wayne's leadership. Wayne deduces that Freeze is Dr. Victor Fries, whose wife, Nora, is suffering from MacGregor's syndrome and was placed in cryogenic sleep until Freeze finds a cure. In his prior research, Fries accidentally fell backwards into a tank of modified liquid nitrogen, rendering him unable to survive outside of a subzero environment. In order to lure Freeze in, Wayne hosts a charity ball auctioning off the Wayne family diamonds with himself and Dick attending as Batman and Robin, leading to an ensuing battle and Freeze's capture. Wayne and Grayson become acquainted with Dr. Pamela Isley, who is secretly the metahuman ecoterrorist Poison Ivy, and who seduces Robin and allies with Freeze, breaking him out of Arkham Asylum. Ivy then unplugs Nora's life support and convinces Freeze that Batman is responsible.


text: Alfred's niece Barbara Wilson (Alicia Silverstone) comes to visit Wayne Manor, at about the same time that Wayne discovers that Alfred is dying of McGregor's Syndrome. She soon discovers the Batcave, and becomes Batgirl. Batman and Robin reluctantly allow her to help them defeat Freeze and Ivy, who are trying to turn Gotham City into a giant polar ice cap with a giant freeze ray that Freeze invented. Batgirl defeats Ivy, and the three head to the observatory to stop Freeze. Robin and Batgirl defeat Ivy's minion Bane (Robert Swenson) while Batman faces and subdues Freeze, redirecting the telescope's satellites to reflect sunlight to thaw Gotham, but Freeze detonates several bombs that he had placed around the freeze ray, destroying it. Nevertheless, Robin and Batgirl are still able to thaw the city. Batman reveals to a defeated Freeze that Nora is still alive, having been rescued in time.


text: Batman appeals to Freeze's humanity and asks him for the cure to MacGregor's syndrome's early stages to save Pennyworth. Freeze provides him with the cure and returns to Arkham to torment Ivy, his new cellmate, while Pennyworth makes a full recovery and reunites with Wayne, Grayson, and Barbara.


text: A comic adaptation of Tim Burton's "Batman" titled "Batman: The Official Comic Adaptation of the Warner Bros Motion Picture" was released in June 1989. Longtime Batman editor at DC Dennis O'Neil adapted the screenplay, with art provided by Jerry Ordway.


text: A comic adaptation for "Batman Returns" titled "Batman Returns: The Official Comic Adaptation of the Warner Bros Motion Picture" was released in June 1992. The story was once again adapted by Dennis O' Neil, with pencils provided by Steve Erwin and inked embellishments by José Luis García-López. Many of the illustrations García-López did for the film's style guide were re-purposed for the comic adaptation.


text: A comic continuation that was to chronicle the events of Tim Burton's failed third Batman film titled "Batman '89" was submitted to DC Comics written by Joe Quinones and Kath Leth in March 2016. The run was inspired by DC's recent comic run "Batman '66", which was a continuation of the 1966 television series starring Adam West and Burt Ward. The story was to be a direct sequel to Burton's Batman films, with visual allusions to Michael Keaton as Batman, Billy Dee Williams (who portrayed a pre-disfigurement Harvey Dent in "Batman") as Two-Face, Marlon Wayans as Robin, Michelle Pfeiffer as Catwoman, and Robin Williams as The Riddler. The story would also introduce iterations of Barbara Gordon, Poison Ivy and Harley Quinn into the story's fictional universe. However, the comic run was initially rejected by DC.


text: In February 2021, it was confirmed that DC would in fact be proceeding to develop a canonical comic continuation of Burton's "Batman" films, with "Batman" screenwriter Sam Hamm returning to write the script while Joe Quinones provides the comic's art.


text: Michael Keaton's portrayal as Batman was seen as hugely influential towards further adaptations of the character. Keaton's portrayal inspired the portrayal by Kevin Conroy in "". As the first version of the character to carry a grapple device with a motorized reel, as well a cape that can harden and transform into a hang-glider, these concepts would become highly influential for most contemporary appearances of the character. Keaton's grim, monosyllabic persona in-costume has been paid tribute to throughout multiple adaptations of the character, including video game appearances and homages.


text: This adaptation of the character was also seen as the first to change their voice while in costume as Batman, something which future actors Kevin Conroy, Ben Affleck and Christian Bale would also add to their interpretations. Michael Keaton's portrayal of the character appears on AFI's 100 Years...100 Heroes & Villains at #46 on the heroes side, while Jack Nicholson's portrayal as the Joker ranked 45th on the villains side.


text: Due to his involvement in the film, Michael Keaton's role in the film "Birdman" directed by Alejandro G. Iñárritu has been compared to Keaton's own experiences as Batman. Many people have come to the conclusion that the film is a reflection of Michael Keaton's life post-Batman, as the film itself focuses on Riggan Thompson, a struggling, aging actor who is best known for having played a winged superhero earlier in his career.


text: When Iñárritu contacted Keaton about taking the role of Riggan, Keaton asked him if he was making fun of him for playing Batman. Despite comparisons between Riggan and Keaton and many people believing that the role was taken by the actor to let out frustration at the role, Keaton has claimed that he loves talking about his time as Batman, and is extremely grateful for the role.


text: Keaton was nominated for the Academy Award for Best Actor for his performance in "Birdman", his first-ever nomination, and this was what helped him gain the villainous role of Adrian Toomes / Vulture in "" (2017) and "Morbius" (2022), which are respectively set in the Marvel Cinematic Universe (MCU) and Sony's Spider-Man Universe (SSU).


title: First Portuguese Republic

text: The First Portuguese Republic (; officially: "República Portuguesa", Portuguese Republic) spans a complex 16-year period in the history of Portugal, between the end of the period of constitutional monarchy marked by the 5 October 1910 revolution and the 28 May 1926 "coup d'état". The latter movement instituted a military dictatorship known as "Ditadura Nacional" (national dictatorship) that would be followed by the corporatist "Estado Novo" (new state) regime of António de Oliveira Salazar.


title: First Portuguese Republic

text: The sixteen years of the First Republic saw nine presidents and 44 ministries, and were altogether more of a transition between the Kingdom of Portugal and the Estado Novo than they were a coherent period of governance.


title: First Portuguese Republic

text: The First Republic was intensely anti-clerical. Historian Stanley Payne points out, "The majority of Republicans took the position that Catholicism was the number one enemy of individualist middle-class radicalism and must be completely broken as a source of influence in Portugal." Under the leadership of Afonso Costa, the Minister of Justice, the revolution immediately targeted the Catholic Church; the provisional government began devoting its entire attention to an anti-religious policy, in spite of the disastrous economic situation. On 8th October the religious orders in Portugal were expelled, and their property was confiscated. On 10 October – five days after the inauguration of the Republic – the new government decreed that all convents, monasteries and religious orders were to be suppressed. All residents of religious institutions were expelled and their goods confiscated. The Jesuits were forced to forfeit their Portuguese citizenship. A series of anti-Catholic laws and decrees followed each other in rapid succession. On 3 November, a law legalizing divorce was passed and then there were laws to recognize the legitimacy of children born outside wedlock, authorize cremation, secularize cemeteries, suppress religious teaching in the schools and prohibit the wearing of the cassock. In addition, the ringing of church bells to signal times of worship was subjected to certain restraints, and the public celebration of religious feasts was suppressed. The government also interfered in the running of seminaries, reserving the right to appoint professors and determine curricula. This whole series of laws authored by Afonso Costa culminated in the law of Separation of Church and State, which was passed on 20 April 1911.


title: First Portuguese Republic

text: The republicans were anticlerical and had a "hostile" approach to the issue of church and state separation, like that of the French Revolution, and the future Mexican Constitution of 1917 and Spanish Constitution of 1931. On 24 May 1911, Pope Pius X issued the encyclical "Iamdudum" which condemned the anticlericalism of the new republic for its deprivation of religious civil liberties and the "incredible series of excesses and crimes which has been enacted in Portugal for the oppression of the Church."


title: First Portuguese Republic

text: The First Portuguese Republic was an unstable period in the History of Portugal. In a period of 16 years (1910–1926) Portugal had 8 Presidents of the Republic, 1 Provisional Government, 38 Prime Ministers and 1 Constitutional "Junta":


title: First Portuguese Republic

text: Most historians have emphasized the failure and collapse of the republican dream by the 1920s. José Miguel Sardica in 2011 summarized the consensus of historians:


title: Between the World and Me

text: Between the World and Me is a 2015 nonfiction book written by American author Ta-Nehisi Coates and published by Spiegel & Grau. It is written as a letter to the author's teenage son about the feelings, symbolism, and realities associated with being Black in the United States. Coates recapitulates American history and explains to his son the "racist violence that has been woven into American culture." Coates draws from an abridged, autobiographical account of his youth in Baltimore, detailing the ways in which institutions like the school, the police, and even "the streets" discipline, endanger, and threaten to disembody black men and women. The work takes structural and thematic inspiration from James Baldwin's 1963 epistolary book "The Fire Next Time". Unlike Baldwin, Coates sees white supremacy as an indestructible force, one that Black Americans will never evade or erase, but will always struggle against.


title: Between the World and Me

text: The novelist Toni Morrison wrote that Coates filled an intellectual gap in succession to James Baldwin. Editors of "The New York Times" and "The New Yorker" described the book as exceptional. The book won the 2015 National Book Award for Nonfiction and was a finalist for the 2016 Pulitzer Prize for General Non-Fiction.


title: Between the World and Me

text: Coates was inspired to write "Between the World and Me" following a 2013 meeting with sitting United States President Barack Obama. Coates, a writer for "The Atlantic", had been reading James Baldwin's 1963 "The Fire Next Time" and was determined to make his second meeting with the president less deferential than his first. As he left for Washington, D.C., his wife encouraged him to think like Baldwin, and Coates recalled an unofficial, fiery meeting between Baldwin, Black activists, and Robert F. Kennedy in 1963. When it was his turn, Coates debated with Obama whether his policy sufficiently addressed racial disparities in the universal health care rollout. After the event, Obama and Coates spoke privately about a blog post Coates had written criticizing the president's call for more personal responsibility among African Americans. Obama disagreed with the criticism and told Coates not to despair.


title: Between the World and Me

text: As Coates walked to the train station, he thought about how Baldwin would not have shared Obama's optimism, the same optimism that supported many Civil Rights Movement activists' belief that justice was inevitable. Instead, Coates saw Baldwin as being fundamentally "cold," without "sentiment and melodrama" in his acknowledgment that the movement could fail and that requital was not guaranteed. Coates found this idea "freeing" and called his book editor, Christopher Jackson, to ask "why no one wrote like Baldwin anymore." Jackson proposed that Coates try.


title: Between the World and Me

text: "Between the World and Me" is Coates's second book, following his 2008 memoir "The Beautiful Struggle". Since then, and especially in the 18 months including the Ferguson unrest preceding his new book's release, Coates somberly believed less in the soul and its aspirational sense of eventual justice. Coates felt that he had become more radicalized.


title: Between the World and Me

text: The book's title comes from Richard Wright's poem "Between the World and Me," originally published in the July/August 1935 issue of "Partisan Review". Wright's poem is about a Black man discovering the site of a lynching and becoming incapacitated with fear, creating a barrier between himself and the world. Despite many changes in "Between the World and Me", Coates always planned to end the book with the story of Mabel Jones. The only endorsement Coates sought was that of novelist Toni Morrison, which he received. "Between the World and Me" was published by Spiegel & Grau in 2015.


title: Between the World and Me

text: "Between the World and Me" takes the form of a book-length letter from the author to his son, adopting the structure of Baldwin's "The Fire Next Time"; the latter is directed, in part, towards Baldwin's nephew, while the former addresses Coates's 15-year-old son. Coates's letter is divided into three parts, recounting Coates's experiences as a young man, after the birth of his son, and during a visit with Mabel Jones. Coates contemplates the feelings, symbolism, and realities associated with being Black in the United States. He recapitulates the American history of violence against Black people and the incommensurate policing of Black youth. The book's tone is poetic and bleak, guided by his experiences growing up poor and always at risk of bodily harm. He prioritizes the physical security of African-American bodies over the tradition in Black Christianity of optimism, "uplift," and faith in eventual justice (i.e., being on God's side). As Coates discussed in a 2015 interview at the Chicago Humanities Festival, he was inspired by his college professor Eileen Boris who utilized an extended metaphor of the physical body for exploitation by objectification in her course, “History of Women in America" at Howard University. Her teachings inspired Coates's theme of the physical and visceral experience of racism on the body. His background, which he describes as "physicality and chaos," leads him to emphasize the daily corporeal concerns he experiences as an African-American in U.S. culture. Coates's position is that absent the religious rhetoric of "hope and dreams and faith and progress," only systems of White supremacy remain along with no real evidence that those systems are bound to change. In this way, he disagrees with Martin Luther King, Jr.'s optimism about integration and Malcolm X's optimism about nationalism.


title: Between the World and Me

text: Coates gives an abridged, autobiographical account of his youth "always on guard" in Baltimore and his fear of the physical harm threatened by both the police and the streets. He also feared the rules of code-switching to meet the clashing social norms of the streets, the authorities, and the professional world. He contrasts these experiences with neat suburban life, which he calls "the Dream" because it is an exclusionary fantasy for White people who are enabled by, yet largely ignorant of, their history of privilege and suppression. To become conscious of their gains from slavery, segregation, and voter suppression would shatter that Dream. The book ends with a story about Mabel Jones, the daughter of a sharecropper, who worked and rose in social class to give her children comfortable lives, including private schools and European trips. Her son, Coates's college friend Prince Carmen Jones Jr., was "mistakenly" tracked and killed by a policeman. Coates uses his friend's story to argue that racism and related tragedy affects Black people of means as well.


title: Between the World and Me

text: After reading "Between the World and Me", novelist Toni Morrison wrote that Coates fills "the intellectual void" left by James Baldwin's death 28 years prior. A. O. Scott of "The New York Times" said the book is "essential, like water or air." David Remnick of "The New Yorker" described it as "extraordinary."


title: Between the World and Me

text: Michiko Kakutani of "The New York Times" wrote that "Between the World and Me" functioned as a sequel to Coates's 2008 memoir, which displayed Coates's talents as an emotional and lyrical writer. Coates's use of "the Dream" (in reference to paradisal suburban life) confused her, and she thought Coates stretched beyond what is safely generalizable. In particular, she felt that the phrasing of his comments on 9/11 could be easily misread. Kakutani thought that Coates did not consistently acknowledge racial progress achieved over the course of centuries and that some parts read like the author's internal debate. Benjamin Wallace-Wells of "New York" magazine said that a sense of fear for one's children propels the book, and Coates's atheism gives the book a sense of urgency.


title: Between the World and Me

text: On November 18, 2015, it was announced that Coates had won the National Book Award for "Between the World and Me". NPR's Colin Dwyer had considered it the favorite to win the prize, given the book's reception. It also won the 2015 Kirkus Prize for nonfiction.


title: Between the World and Me

text: The book topped "The New York Times" Best Seller list for nonfiction on August 2, 2015, and remained number 1 for three weeks. It topped the same list again during the week of January 24, 2016.


title: Between the World and Me

text: The book was selected by Washington University in St. Louis and Augustana College in 2016, as the book for all first-year students to read and discuss in the fall 2016 semester. In the same year, the book was ranked 7th on "The Guardian"s list of the 100 best books of the 21st century.


title: Between the World and Me

text: On September 30, 2020, HBO announced that it had adapted "Between the World and Me" as an 80-minute-long television special, which premiered on November 21, 2020. "Between the World and Me" was initially adapted and staged in 2018 by the Apollo Theater in Harlem, New York. The HBO adaption of "Between the World and Me" combines elements of the 2018 production at the Apollo Theater, readings from the book, and documentary footage from the actors’ home lives. Both the Apollo and HBO versions are directed by Kamilah Forbes. The HBO special included appearances by around 20 celebrities and civil rights activists including Oprah Winfrey, Phylicia Rashad, Angela Davis, Mahershala Ali, Joe Morton, Yara Shahidi and Angela Bassett. The production used Baltimore street scene photographs by John Clark Mayden, which the "Baltimore Sun" called "powerful images".


title: Clifford algebra

text: In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford.


title: Clifford algebra

text: The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as ("pseudo-")"Riemannian Clifford algebras", as distinct from "symplectic Clifford algebras".


title: Clifford algebra

text: A Clifford algebra is a unital associative algebra that contains and is generated by a vector space over a field , where is equipped with a quadratic form . The Clifford algebra is the "freest" unital associative algebra generated by subject to the condition


title: Clifford algebra

text: where the product on the left is that of the algebra, and the is its multiplicative identity. The idea of being the "freest" or "most general" algebra subject to this identity can be formally expressed through the notion of a universal property, as done below.


title: Clifford algebra

text: Where is a finite-dimensional real vector space and is nondegenerate, may be identified by the label , indicating that has an orthogonal basis with elements with , with , and where indicates that this is a Clifford algebra over the reals; i.e. coefficients of elements of the algebra are real numbers. This basis may be found by orthogonal diagonalization.


title: Clifford algebra

text: The free algebra generated by may be written as the tensor algebra , that is, the sum of the tensor product of copies of over all , and so a Clifford algebra would be the quotient of this tensor algebra by the two-sided ideal generated by elements of the form for all elements . The product induced by the tensor product in the quotient algebra is written using juxtaposition (e.g. ). Its associativity follows from the associativity of the tensor product.


title: Clifford algebra

text: The Clifford algebra has a distinguished subspace , being the image of the embedding map. Such a subspace cannot in general be uniquely determined given only a -algebra isomorphic to the Clifford algebra.


title: Clifford algebra

text: If the characteristic of the ground field is not , then one can rewrite the fundamental identity above in the form


title: Clifford algebra

text: Quadratic forms and Clifford algebras in characteristic form an exceptional case. In particular, if it is not true that a quadratic form uniquely determines a symmetric bilinear form satisfying , nor that every quadratic form admits an orthogonal basis. Many of the statements in this article include the condition that the characteristic is not , and are false if this condition is removed.


title: Clifford algebra

text: Clifford algebras are closely related to exterior algebras. Indeed, if then the Clifford algebra is just the exterior algebra . For nonzero there exists a canonical "linear" isomorphism between and whenever the ground field does not have characteristic two. That is, they are naturally isomorphic as vector spaces, but with different multiplications (in the case of characteristic two, they are still isomorphic as vector spaces, just not naturally). Clifford multiplication together with the distinguished subspace is strictly richer than the exterior product since it makes use of the extra information provided by .


title: Clifford algebra

text: More precisely, Clifford algebras may be thought of as "quantizations" (cf. quantum group) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra.


title: Clifford algebra

text: Weyl algebras and Clifford algebras admit a further structure of a *-algebra, and can be unified as even and odd terms of a superalgebra, as discussed in CCR and CAR algebras.


title: Clifford algebra

text: Let be a vector space over a field , and let be a quadratic form on . In most cases of interest the field is either the field of real numbers , or the field of complex numbers , or a finite field.


title: Clifford algebra

text: A Clifford algebra is a pair , where is a unital associative algebra over and is a linear map satisfying for all in , defined by the following universal property: given any unital associative algebra over and any linear map such that


title: Clifford algebra

text: (where denotes the multiplicative identity of ), there is a unique algebra homomorphism such that the following diagram commutes (i.e. such that ):


title: Clifford algebra

text: The quadratic form may be replaced by a (not necessarily symmetric) bilinear form that has the property , in which case an equivalent requirement on is


title: Clifford algebra

text: When the characteristic of the field is not , this may be replaced by what is then an equivalent requirement,


title: Clifford algebra

text: where the bilinear form may additionally be restricted to being symmetric without loss of generality.


title: Clifford algebra

text: A Clifford algebra as described above always exists and can be constructed as follows: start with the most general algebra that contains , namely the tensor algebra , and then enforce the fundamental identity by taking a suitable quotient. In our case we want to take the two-sided ideal in generated by all elements of the form


title: Clifford algebra

text: The ring product inherited by this quotient is sometimes referred to as the Clifford product to distinguish it from the exterior product and the scalar product.


title: Clifford algebra

text: It is then straightforward to show that contains and satisfies the above universal property, so that is unique up to a unique isomorphism; thus one speaks of "the" Clifford algebra . It also follows from this construction that is injective. One usually drops the and considers as a linear subspace of .


title: Clifford algebra

text: The universal characterization of the Clifford algebra shows that the construction of is in nature. Namely, can be considered as a functor from the category of vector spaces with quadratic forms (whose morphisms are linear maps preserving the quadratic form) to the category of associative algebras. The universal property guarantees that linear maps between vector spaces (preserving the quadratic form) extend uniquely to algebra homomorphisms between the associated Clifford algebras.


title: Clifford algebra

text: Since comes equipped with a quadratic form , in characteristic not equal to there exist bases for that are orthogonal. An orthogonal basis is one such that for a symmetric bilinear form


title: Clifford algebra

text: This makes manipulation of orthogonal basis vectors quite simple. Given a product formula_16 of "distinct" orthogonal basis vectors of , one can put them into a standard order while including an overall sign determined by the number of pairwise swaps needed to do so (i.e. the signature of the ordering permutation).


title: Clifford algebra

text: The empty product () is defined as the multiplicative identity element. For each value of there are basis elements, so the total dimension of the Clifford algebra is


title: Clifford algebra

text: The most important Clifford algebras are those over real and complex vector spaces equipped with nondegenerate quadratic forms.


title: Clifford algebra

text: Each of the algebras and is isomorphic to or , where is a full matrix ring with entries from , , or . For a complete classification of these algebras see "Classification of Clifford algebras".


title: Clifford algebra

text: Clifford algebras are also sometimes referred to as geometric algebras, most often over the real numbers.


title: Clifford algebra

text: Every nondegenerate quadratic form on a finite-dimensional real vector space is equivalent to the standard diagonal form:


title: Clifford algebra

text: where is the dimension of the vector space. The pair of integers is called the signature of the quadratic form. The real vector space with this quadratic form is often denoted The Clifford algebra on is denoted The symbol means either or depending on whether the author prefers positive-definite or negative-definite spaces.


title: Clifford algebra

text: A standard basis for consists of mutually orthogonal vectors, of which square to +1 and of which square to −1. Of such a basis, the algebra will therefore have vectors that square to +1 and vectors that square to −1.


title: Clifford algebra

text: One can also study Clifford algebras on complex vector spaces. Every nondegenerate quadratic form on a complex vector space of dimension "n" is equivalent to the standard diagonal form


title: Clifford algebra

text: Thus, for each dimension , up to isomorphism there is only one Clifford algebra of a complex vector space with a nondegenerate quadratic form. We will denote the Clifford algebra on with the standard quadratic form by .


title: Clifford algebra

text: In this section, Hamilton's quaternions are constructed as the even sub algebra of the Clifford algebra


title: Clifford algebra

text: Let the vector space be real three-dimensional space and the quadratic form be the negative of the usual Euclidean metric. Then, for in we have the bilinear form (or scalar product)


title: Clifford algebra

text: The linear combination of the even degree elements of defines the even subalgebra with the general element


title: Clifford algebra

text: In this section, dual quaternions are constructed as the even Clifford algebra of real four-dimensional space with a degenerate quadratic form.


title: Clifford algebra

text: Let the vector space be real four-dimensional space and let the quadratic form be a degenerate form derived from the Euclidean metric on For in introduce the degenerate bilinear form


title: Clifford algebra

text: Denote a set of mutually orthogonal unit vectors of as then the Clifford product yields the relations


title: Clifford algebra

text: The general element of the Clifford algebra has 16 components. The linear combination of the even degree elements defines the even subalgebra with the general element


title: Clifford algebra

text: The exchanges of and alternate signs an even number of times, and show the dual unit commutes with the quaternion basis elements


title: Clifford algebra

text: For , if has diagonalization , that is there is a non-zero vector such that , then is algebra-isomorphic to a -algebra generated by an element satisfying , the quadratic algebra .


title: Clifford algebra

text: In particular, if (that is, is the zero quadratic form) then is algebra-isomorphic to the dual numbers algebra over .


title: Clifford algebra

text: For , if has diagonalization with non-zero and (which always exists if is non-degenerate), then is isomorphic to a -algebra generated by elements and satisfying , and .


title: Clifford algebra

text: Thus is isomorphic to the (generalized) quaternion algebra . We retrieve Hamilton's quaternions when , since .


title: Clifford algebra

text: Given a vector space , one can construct the exterior algebra , whose definition is independent of any quadratic form on . It turns out that if does not have characteristic then there is a natural isomorphism between and considered as vector spaces (and there exists an isomorphism in characteristic two, which may not be natural). This is an algebra isomorphism if and only if . One can thus consider the Clifford algebra as an enrichment (or more precisely, a quantization, cf. the Introduction) of the exterior algebra on with a multiplication that depends on (one can still define the exterior product independently of ).


title: Clifford algebra

text: The easiest way to establish the isomorphism is to choose an "orthogonal" basis for and extend it to a basis for as described above. The map is determined by


title: Clifford algebra

text: Note that this only works if the basis is orthogonal. One can show that this map is independent of the choice of orthogonal basis and so gives a natural isomorphism.


title: Clifford algebra

text: If the characteristic of is , one can also establish the isomorphism by antisymmetrizing. Define functions by


title: Clifford algebra

text: where the sum is taken over the symmetric group on elements, . Since is alternating it induces a unique linear map . The direct sum of these maps gives a linear map between and . This map can be shown to be a linear isomorphism, and it is natural.


title: Clifford algebra

text: A more sophisticated way to view the relationship is to construct a filtration on . Recall that the tensor algebra has a natural filtration: , where contains sums of tensors with order . Projecting this down to the Clifford algebra gives a filtration on . The associated graded algebra


title: Clifford algebra

text: is naturally isomorphic to the exterior algebra . Since the associated graded algebra of a filtered algebra is always isomorphic to the filtered algebra as filtered vector spaces (by choosing complements of in for all ), this provides an isomorphism (although not a natural one) in any characteristic, even two.


title: Clifford algebra

text: Clifford algebras are Z-graded algebras (also known as superalgebras). Indeed, the linear map on "V" defined by (reflection through the origin) preserves the quadratic form "Q" and so by the universal property of Clifford algebras extends to an algebra automorphism


title: Clifford algebra

text: Since is an involution (i.e. it squares to the identity) one can decompose into positive and negative eigenspaces of


title: Clifford algebra

text: where the bracketed superscripts are read modulo 2. This gives the structure of a Z-graded algebra. The subspace forms a subalgebra of , called the "even subalgebra". The subspace is called the "odd part" of (it is not a subalgebra). This Z-grading plays an important role in the analysis and application of Clifford algebras. The automorphism is called the "main involution" or "grade involution". Elements that are pure in this Z-grading are simply said to be even or odd.


title: Clifford algebra

text: "Remark". In characteristic not 2 the underlying vector space of inherits an N-grading and a Z-grading from the canonical isomorphism with the underlying vector space of the exterior algebra . It is important to note, however, that this is a "vector space grading only". That is, Clifford multiplication does not respect the N-grading or Z-grading, only the Z-grading: for instance if , then , but , not in . Happily, the gradings are related in the natural way: . Further, the Clifford algebra is Z-filtered:


title: Clifford algebra

text: The even subalgebra of a Clifford algebra is itself isomorphic to a Clifford algebra. If is the orthogonal direct sum of a vector of nonzero norm and a subspace , then is isomorphic to , where is the form restricted to and multiplied by . In particular over the reals this implies that:


title: Clifford algebra

text: In addition to the automorphism , there are two antiautomorphisms that play an important role in the analysis of Clifford algebras. Recall that the tensor algebra comes with an antiautomorphism that reverses the order in all products of vectors:


title: Clifford algebra

text: Since the ideal is invariant under this reversal, this operation descends to an antiautomorphism of called the "transpose" or "reversal" operation, denoted by . The transpose is an antiautomorphism: . The transpose operation makes no use of the Z-grading so we define a second antiautomorphism by composing and the transpose. We call this operation "Clifford conjugation" denoted formula_49


title: Clifford algebra

text: Note that all of these operations are involutions. One can show that they act as ±1 on elements which are pure in the Z-grading. In fact, all three operations depend only on the degree modulo 4. That is, if "x" is pure with degree "k" then


title: Clifford algebra

text: When the characteristic is not 2, the quadratic form "Q" on "V" can be extended to a quadratic form on all of (which we also denoted by "Q"). A basis-independent definition of one such extension is


title: Clifford algebra

text: One can check that this reduces to the original bilinear form when restricted to "V". The bilinear form on all of is nondegenerate if and only if it is nondegenerate on "V".


title: Clifford algebra

text: The operator of left (respectively right) Clifford multiplication by the transpose "a" of an element "a" is the adjoint of left (respectively right) Clifford multiplication by "a" with respect to this inner product. That is,


title: Clifford algebra

text: "In this section we assume that characteristic is not 2, the vector space "V" is finite-dimensional and that the associated symmetric bilinear form of "Q" is nondegenerate."


title: Clifford algebra

text: A central simple algebra over is a matrix algebra over a (finite-dimensional) division algebra with center . For example, the central simple algebras over the reals are matrix algebras over either the reals or the quaternions.


title: Clifford algebra

text: The structure of Clifford algebras can be worked out explicitly using the following result. Suppose that has even dimension and a non-singular bilinear form with discriminant , and suppose that is another vector space with a quadratic form. The Clifford algebra of is isomorphic to the tensor product of the Clifford algebras of and , which is the space with its quadratic form multiplied by . Over the reals, this implies in particular that


title: Clifford algebra

text: These formulas can be used to find the structure of all real Clifford algebras and all complex Clifford algebras; see the classification of Clifford algebras.


title: Clifford algebra

text: Notably, the Morita equivalence class of a Clifford algebra (its representation theory: the equivalence class of the category of modules over it) depends only on the signature . This is an algebraic form of Bott periodicity.


title: Clifford algebra

text: The class of Lipschitz groups ( Clifford groups or Clifford–Lipschitz groups) was discovered by Rudolf Lipschitz.


title: Clifford algebra

text: An action on the elements of a Clifford algebra by its group of units may be defined in terms of a twisted conjugation: twisted conjugation by maps , where is the "main involution" defined above.


title: Clifford algebra

text: The Lipschitz group is defined to be the set of invertible elements that "stabilize the set of vectors" under this action, meaning that for all in we have:


title: Clifford algebra

text: This formula also defines an action of the Lipschitz group on the vector space "V" that preserves the quadratic form "Q", and so gives a homomorphism from the Lipschitz group to the orthogonal group. The Lipschitz group contains all elements "r" of "V" for which "Q"("r") is invertible in "K", and these act on "V" by the corresponding reflections that take "v" to . (In characteristic these are called orthogonal transvections rather than reflections.)


title: Clifford algebra

text: If "V" is a finite-dimensional real vector space with a non-degenerate quadratic form then the Lipschitz group maps onto the orthogonal group of "V" with respect to the form (by the Cartan–Dieudonné theorem) and the kernel consists of the nonzero elements of the field "K". This leads to exact sequences


title: Clifford algebra

text: Over other fields or with indefinite forms, the map is not in general onto, and the failure is captured by the spinor norm.


title: Clifford algebra

text: It is a homomorphism from the Lipschitz group to the group "K" of non-zero elements of "K". It coincides with the quadratic form "Q" of "V" when "V" is identified with a subspace of the Clifford algebra. Several authors define the spinor norm slightly differently, so that it differs from the one here by a factor of −1, 2, or −2 on Γ. The difference is not very important in characteristic other than 2.


title: Clifford algebra

text: The nonzero elements of "K" have spinor norm in the group ("K") of squares of nonzero elements of the field "K". So when "V" is finite-dimensional and non-singular we get an induced map from the orthogonal group of "V" to the group "K"/("K"), also called the spinor norm. The spinor norm of the reflection about "r", for any vector "r", has image "Q"("r") in "K"/("K"), and this property uniquely defines it on the orthogonal group. This gives exact sequences:


title: Clifford algebra

text: From the point of view of Galois cohomology of algebraic groups, the spinor norm is a connecting homomorphism on cohomology. Writing "μ" for the algebraic group of square roots of 1 (over a field of characteristic not 2 it is roughly the same as a two-element group with trivial Galois action), the short exact sequence


title: Clifford algebra

text: The 0th Galois cohomology group of an algebraic group with coefficients in "K" is just the group of "K"-valued points: , and , which recovers the previous sequence


title: Clifford algebra

text: The pin group is the subgroup of the Lipschitz group of elements of spinor norm , and similarly the spin group is the subgroup of elements of Dickson invariant in . When the characteristic is not , these are the elements of determinant . The spin group usually has index in the pin group.


title: Clifford algebra

text: Recall from the previous section that there is a homomorphism from the Lipschitz group onto the orthogonal group. We define the special orthogonal group to be the image of . If does not have characteristic this is just the group of elements of the orthogonal group of determinant . If does have characteristic , then all elements of the orthogonal group have determinant , and the special orthogonal group is the set of elements of Dickson invariant .


title: Clifford algebra

text: There is a homomorphism from the pin group to the orthogonal group. The image consists of the elements of spinor norm . The kernel consists of the elements and , and has order unless has characteristic . Similarly there is a homomorphism from the Spin group to the special orthogonal group of .


title: Clifford algebra

text: In the common case when is a positive or negative definite space over the reals, the spin group maps onto the special orthogonal group, and is simply connected when has dimension at least . Further the kernel of this homomorphism consists of and . So in this case the spin group, , is a double cover of . Please note, however, that the simple connectedness of the spin group is not true in general: if is for and both at least then the spin group is not simply connected. In this case the algebraic group is simply connected as an algebraic group, even though its group of real valued points is not simply connected. This is a rather subtle point, which completely confused the authors of at least one standard book about spin groups.


title: Clifford algebra

text: Clifford algebras , with even, are matrix algebras which have a complex representation of dimension . By restricting to the group we get a complex representation of the Pin group of the same dimension, called the spin representation. If we restrict this to the spin group then it splits as the sum of two "half spin representations" (or "Weyl representations") of dimension .


title: Clifford algebra

text: If is odd then the Clifford algebra is a sum of two matrix algebras, each of which has a representation of dimension , and these are also both representations of the Pin group . On restriction to the spin group these become isomorphic, so the spin group has a complex spinor representation of dimension .


title: Clifford algebra

text: More generally, spinor groups and pin groups over any field have similar representations whose exact structure depends on the structure of the corresponding Clifford algebras: whenever a Clifford algebra has a factor that is a matrix algebra over some division algebra, we get a corresponding representation of the pin and spin groups over that division algebra.


title: Clifford algebra

text: To describe the real spin representations, one must know how the spin group sits inside its Clifford algebra. The pin group, is the set of invertible elements in that can be written as a product of unit vectors:


title: Clifford algebra

text: Comparing with the above concrete realizations of the Clifford algebras, the pin group corresponds to the products of arbitrarily many reflections: it is a cover of the full orthogonal group . The spin group consists of those elements of that are products of an even number of unit vectors. Thus by the Cartan–Dieudonné theorem Spin is a cover of the group of proper rotations .


title: Clifford algebra

text: Let be the automorphism which is given by the mapping acting on pure vectors. Then in particular, is the subgroup of whose elements are fixed by . Let


title: Clifford algebra

text: The irreducible representations of restrict to give representations of the pin group. Conversely, since the pin group is generated by unit vectors, all of its irreducible representation are induced in this manner. Thus the two representations coincide. For the same reasons, the irreducible representations of the spin coincide with the irreducible representations of .


title: Clifford algebra

text: To classify the pin representations, one need only appeal to the classification of Clifford algebras. To find the spin representations (which are representations of the even subalgebra), one can first make use of either of the isomorphisms (see above)


title: Clifford algebra

text: One of the principal applications of the exterior algebra is in differential geometry where it is used to define the bundle of differential forms on a smooth manifold. In the case of a (pseudo-)Riemannian manifold, the tangent spaces come equipped with a natural quadratic form induced by the metric. Thus, one can define a Clifford bundle in analogy with the exterior bundle. This has a number of important applications in Riemannian geometry. Perhaps more important is the link to a spin manifold, its associated spinor bundle and manifolds.


title: Clifford algebra

text: Clifford algebras have numerous important applications in physics. Physicists usually consider a Clifford algebra to be an algebra with a basis generated by the matrices called Dirac matrices which have the property that


title: Clifford algebra

text: where is the matrix of a quadratic form of signature (or corresponding to the two equivalent choices of metric signature). These are exactly the defining relations for the Clifford algebra , whose complexification is which, by the classification of Clifford algebras, is isomorphic to the algebra of complex matrices . However, it is best to retain the notation , since any transformation that takes the bilinear form to the canonical form is "not" a Lorentz transformation of the underlying spacetime.


title: Clifford algebra

text: The Clifford algebra of spacetime used in physics thus has more structure than . It has in addition a set of preferred transformations – Lorentz transformations. Whether complexification is necessary to begin with depends in part on conventions used and in part on how much one wants to incorporate straightforwardly, but complexification is most often necessary in quantum mechanics where the spin representation of the Lie algebra sitting inside the Clifford algebra conventionally requires a complex Clifford algebra. For reference, the spin Lie algebra is given by


title: Clifford algebra

text: The Dirac matrices were first written down by Paul Dirac when he was trying to write a relativistic first-order wave equation for the electron, and give an explicit isomorphism from the Clifford algebra to the algebra of complex matrices. The result was used to define the Dirac equation and introduce the Dirac operator. The entire Clifford algebra shows up in quantum field theory in the form of Dirac field bilinears.


title: Clifford algebra

text: The use of Clifford algebras to describe quantum theory has been advanced among others by Mario Schönberg, by David Hestenes in terms of geometric calculus, by David Bohm and Basil Hiley and co-workers in form of a hierarchy of Clifford algebras, and by Elio Conte et al.


title: Clifford algebra

text: Clifford algebras have been applied in the problem of action recognition and classification in computer vision. Rodriguez et al. propose a Clifford embedding to generalize traditional MACH filters to video (3D spatiotemporal volume), and vector-valued data such as optical flow. Vector-valued data is analyzed using the Clifford Fourier Transform. Based on these vectors action filters are synthesized in the Clifford Fourier domain and recognition of actions is performed using Clifford correlation. The authors demonstrate the effectiveness of the Clifford embedding by recognizing actions typically performed in classic feature films and sports broadcast television.


title: Cho Jin-woong

text: Cho Jin-woong (born Jo Won-jun; March 3, 1976) is a South Korean actor. He is best known for his roles as Sejong's loyal bodyguard in "Deep Rooted Tree" (2011), a mobster in "" (2012), and a mysterious villain in "A Hard Day" (2014). He also gained recognition and praise for his performance as a detective in the television series "Signal" (2016).


title: Cho Jin-woong

text: In 2021 he was selected as Jury member for Actor and Actress of the Year Award in 26th Busan International Film Festival held in October.


title: Roger Ibañez

text: Roger Ibañez da Silva (born 23 November 1998) is a Brazilian professional footballer who plays for Serie A club Roma and the Brazil national team. Mainly a central defender, he can also play as a defensive midfielder.


title: Roger Ibañez

text: Born in Canela, Rio Grande do Sul to an Uruguayan mother, Ibañez only started his career in 2016, aged 18, at . Playing as a midfielder, he joined later in that year, and made his senior debut during the 2016 Copa Serrana, which was the club's first professional competition.


title: Roger Ibañez

text: On 5 December 2016, Ibañez signed for Sergipe on loan for the season. The following 4 March, however, after featuring rarely, he was recalled. Upon returning, he became a regular starter during PRS' Campeonato Gaúcho Série B campaign.


title: Roger Ibañez

text: In the middle of 2017, Ibañez joined Fluminense and was initially assigned to the under-20 squad. Promoted to the first team for the 2018 season by manager Abel Braga, he made his professional debut on 20 January 2018, starting in a 0–0 Campeonato Carioca home draw against Botafogo.


title: Roger Ibañez

text: On 28 February 2018, Ibãnez had his federative rights purchased by "Flu", and he signed a new five-year deal with the club. He made his Série A debut on 15 April, starting in a 2–1 away loss against Corinthians, and finished the campaign with 14 league appearances.


title: Roger Ibañez

text: On 29 January 2019, Ibañez signed with the Italian club Atalanta. Having been inserted in the squad in February, Ibañez received his debut on 11 May, coming on for the final few minutes of their 2–1 victory over Genoa. He replaced attacker Josip Iličić as the club was in the heat of battle for a top-four Serie A finish and UEFA Champions League qualification for the first time in their history, which they eventually achieved.


title: Roger Ibañez

text: Ibañez made his first appearance the following season on the final day of Atalanta's group stage campaign in the Champions League. Needing a win away to Shakhtar Donetsk, Ibañez came on for centre-forward Luis Muriel for the final 20 minutes with Atalanta leading 0–1 and having previously abandoned their regular back three for a back four while in search of the winning goal. Ibañez had only been included in one of the previous five match day squads, but the suspension of Rafael Toloi and an injury to Simon Kjær paved the way for his inclusion. Atalanta would win the game 0–3, qualifying for the knockout stage.


title: Roger Ibañez

text: On 27 January 2020, he moved to Serie A club Roma and signed a four-and-a-half-year contract with the club. The transfer is initially a loan until 30 June 2021, which will convert to the permanent transfer for a predetermined fee of €8 million if certain conditions are met.


title: Roger Ibañez

text: On 9 September 2022, Ibañez received his first call up to the Brazil national team, for friendlies against Ghana and Tunisia. He made his debut against Tunisia on 27 September, in a 5–1 win.


title: Federal voting rights in Puerto Rico

text: Voting rights of United States citizens who live in Puerto Rico, like the voting rights of residents of other United States territories, differ from those of United States citizens in each of the fifty states and the District of Columbia. Residents of Puerto Rico and other U.S. territories do not have voting representation in the United States Congress, and are not entitled to electoral votes for president. The United States Constitution grants congressional voting representation to U.S. states, which Puerto Rico and other U.S. territories are not, specifying that members of Congress shall be elected by direct popular vote and that the president and the vice president shall be elected by electors chosen by the states.


title: Federal voting rights in Puerto Rico

text: Puerto Rico is a territory under the sovereignty of the federal government, but is not part of any state nor is it a state itself. It has been organized (given a measure of self-rule by the Congress) subject to the Congress' plenary powers under the territorial clause of Article IV, sec. 3, of the U.S. Constitution. In the U.S. House of Representatives, Puerto Rico is entitled to a resident commissioner, a delegate who is not allowed to vote on the floor of the House but can vote on procedural matters and in House committees. In most other U.S. overseas (and historically pre-state) territories, as well as the District of Columbia, a similar representative position is styled Delegate.


title: Federal voting rights in Puerto Rico

text: The lack of direct voting representation in Congress for residents of the territory has been an issue since the U.S. Congress granted U.S. citizenship to Puerto Rico citizens in 1917. All judicial claims have been met with political or constitutional challenges; therefore, there has been no change in Puerto Rico's representation in the Congress or representation on the electoral college for the U.S. citizens residing in Puerto Rico.


title: Federal voting rights in Puerto Rico

text: Like other territories, Puerto Rico holds presidential primary elections in the spring of each presidential election year in which the parties choose delegates to the Republican and Democratic national conventions. While these delegates do vote for their pledged candidate at their respective convention, this marks the end of the territory's participation in the presidential election.


title: Federal voting rights in Puerto Rico

text: Puerto Rico is an insular area—a United States territory that is neither a part of one of the fifty states nor a part of the District of Columbia, the nation's federal district. Insular areas, including Puerto Rico, the U.S. Virgin Islands and Guam, are not allowed to choose electors in U.S. presidential elections or elect voting members of the U.S. Congress. This grows out of Articles One and Two of the United States Constitution, which state that electors are to be chosen by "the People of the several States." In 1961, the 23rd amendment extended the right to choose electors to the District of Columbia; the insular areas, however, were not addressed in that Amendment.


title: Federal voting rights in Puerto Rico

text: On December 29, 2003, The Inter-American Commission on Human Rights of the Organization of American States concluded that the United States is responsible for violations of the District of Columbia's rights under Articles II and XX of the American Declaration of the Rights and Duties of Man by denying District of Columbia citizens an effective opportunity to participate in their federal legislature. On October 17, 2006, Pedro Rosselló, a former governor of Puerto Rico, and the Unfinished Business of American Democracy Committee on behalf of the approximately four million U.S. citizens residing in the Commonwealth of Puerto Rico, presented a petition to the Inter-American Commission on Human Rights of the Organization of American States seeking the Commission's aid in obtaining enfranchisement.


title: Federal voting rights in Puerto Rico

text: Any U.S. citizen who resides in Puerto Rico is effectively disenfranchised at the national level, as are all U.S. citizen residents of U.S. unincorporated territories. Although the Republican Party and Democratic Party chapters in Puerto Rico have selected voting delegates to the national nominating conventions participating in U.S. presidential primaries or caucuses, U.S. citizens without a voting residence in one of the 50 states or in the District of Columbia may not vote in federal elections.


title: Federal voting rights in Puerto Rico

text: Both the Puerto Rican Independence Party and the New Progressive Party reject the status quo that permits disenfranchisement (from their distinct respective positions on the ideal enfranchised status for the island-nation of Puerto Rico). The remaining political organization, the Popular Democratic Party, has officially stated that it favors fixing the remaining "deficits of democracy" that the Bill Clinton and George W. Bush administrations have publicly recognized in writing through reports of the President's Task Force on Puerto Rico's Status.


title: Federal voting rights in Puerto Rico

text: In 2003, attorney Gregorio Igartúa and others in a third round of litigation (Igartúa III) filed suit seeking to enfranchise U.S. citizens residents of Puerto Rico with the right to vote for the U.S. President and Vice President.


title: Federal voting rights in Puerto Rico

text: The U.S. Court of Appeals decision in 2005, on appeal of the decision in Igartúa III, "Igartua-de la Rosa v. United States", 417 F.3d 145 (1st Cir. P.R. 2005), reads in part:


title: Federal voting rights in Puerto Rico

text: Judges Campbell and Lipez concurred in the decision. Judge Torruella dissented, opening his dissent as follows:


title: Federal voting rights in Puerto Rico

text: In 2008, attorney Gregorio Igartúa and others in a fourth round of litigation (Igartúa IV) attempted to bring a class action suit claiming they and other U.S. citizen-residents of Puerto Rico have a right to vote for a Representative to the U.S. House of Representatives from Puerto Rico and a right to have Representatives from Puerto Rico in that body.


title: Federal voting rights in Puerto Rico

text: In 1961, just a few years after the United Nations first ratified the ICCPR, the Twenty-third Amendment to the United States Constitution was passed, allowing United States citizens residing in the District of Columbia to vote for the executive offices. a bill was pending in Congress that would treat the District of Columbia as "a congressional district for purposes of representation in the House of Representatives", and permit United States citizens residing in the capital to vote for members of the House of Representatives. However, the United States has not taken similar steps with regard to the four million United States citizens and nationals who reside in the U.S. territories, of which close to three million are residents of Puerto Rico. In an opinion concurring in part and dissenting in part in a judicial decision, Circuit Judge Juan R. Torruella, who is Puerto Rican, wrote that this inaction is in clear violation of the United States' obligations under the ICCPR.


title: Federal voting rights in Puerto Rico

text: In August 2017, the "en banc" First Circuit rejected another lawsuit by Igartúa challenging Puerto Rico's exclusion from United States congressional apportionment, over the dissents of Judges Torruella, Kermit Lipez, and Ojetta Rogeriee Thompson.


title: Ben 10: Alien Swarm

text: Ben 10: Alien Swarm is a 2009 American superhero film directed by Alex Winter. It is based on the Cartoon Network animated series "" and is a standalone sequel to 2007's "". The film stars Ryan Kelley, Galadriel Stineman, Nathan Keyes, Alyssa Diaz, Herbert Siguenza, and Barry Corbin. The film held its world premiere in London on November 15, 2009, and premiered on Cartoon Network on November 25, 2009, where it was watched by 4.02 million viewers. The events of the film takes place between the second season's finale and the first episode of the third season of "Ben 10: Alien Force" due to the fact that Gwen and Kevin changed their clothes later in the movie.


title: Ben 10: Alien Swarm

text: The film opens as fifteen-year-old cousins Ben and Gwen Tennyson, and their friend sixteen-year-old Kevin Levin are negotiating with a group of black market dealers attempting to sell them alien nanochips, which are causing interference with the Omnitrix. One of them reveals herself to be Elena Validus, a childhood friend of Ben and Gwen. Elena explains that she had set up negotiations to lure Ben out into the open to seek his help in finding her abducted scientist father.


title: Ben 10: Alien Swarm

text: As Ben agrees to help her, the chips spring to life and attack, controlled by a man on a catwalk. The group fights them, and in the process the suspicious man and the dealers escape. While Elena claims she is not responsible for the attack, Kevin and Gwen are suspicious of her.


title: Ben 10: Alien Swarm

text: At their headquarters, the trio, along with Grandpa Max, study one of the chips salvaged from the fight, learning that they are a hybrid of organic and technological components. Elena, having followed the trio, breaks in and Max orders her to leave, explaining that Elena's father, Victor Validus, was an apprentice of his who was dishonorably discharged after stealing the original chips. Ben refuses to believe that Elena is like her father, and breaks ranks with his grandfather and teammates to help her.


title: Ben 10: Alien Swarm

text: While Max is away, Gwen and Kevin investigate Victor Validus and discover a video of Max interrogating Victor, in which Victor insists that "the Hive", the mind intelligence behind the chips, is coming to take over the planet as they are revealed to be able to possess people.


title: Ben 10: Alien Swarm

text: Meanwhile, Ben and Elena arrive at Victor's old laboratory. It has been cleared out by the Hive, but they find evidence that Victor was studying and upgrading the chips. Elena reveals that her father had become erratic before disappearing, and had stopped returning home. He also appears to be the man from the rafters controlling the chips. A mob under the control of the chips ambush Ben and Elena, forcing them to retreat. The Omnitrix again experiences interference around the chips and keeps Ben from transforming, but Ben utilizes a scanning function on it to temporarily repel the mob and allow him and Elena to escape. They head to the Ship-It building to investigate further, though Ben is now somewhat suspicious of Elena himself, realizing the mob expected him and Elena to go to the lab and set a trap for them. Ben finds an order slip made out for that day, when Elena claimed that Victor had already been missing for weeks.


title: Ben 10: Alien Swarm

text: Gwen and Kevin, having reached the building first, are too late to stop the distribution of the chips. Instead, they are met by one of the Ship-It employees, who is also under the chips' control. He summons another larger chip swarm, now capable of forming solid, weaponizable shapes, to attack Gwen and Kevin, damaging Kevin's car during a lengthy chase. Ben, upon joining them, uses Humongousaur to defeat the swarm, destroying Kevin's car in the process.


title: Ben 10: Alien Swarm

text: By the time they return to headquarters, the chips have spread across the globe, and number in the millions. Gwen realizes the swarm's new ability is a sign that they can adapt to threats and become smarter. The group also deduces the chips have a queen, as the chip's hosts have mentioned her. They believed that they can stop the chips by destroying her, but during their search, Max is possessed. Pulling together, the group notice that while world population centers are all infected, Barren Rock, Missouri, has the highest concentration, an apparent anomaly in their distribution.


title: Ben 10: Alien Swarm

text: Infiltrating the factory, populated by multiple infected, including Max, the group discovers that the Queen infected Elena's father, and his body is being used as a hive to rapidly mass-produce the chips. Fearing being possessed by the chips while in his alien forms, Ben uses the Omnitrix to transform into a new alien that he calls "Nanomech", but before he could turn into it he was instead shrunken down as a human. He then notices the giant feet of Kevin and Gwen in front of him. Gwen begins to scrap her gigantic heavy foot across the floor which causes a loud scratching sound which goes to show the massive difference in both size and mass between Gwen and now her shrunken cousin. Ben realises that he is small then after a few seconds then finally transforms into Nanomech, which was created by scanning the DNA of the chips. He flies into Victor's head and battles the Queen, who briefly tries to assert dominance on him, though he resists, while Gwen, Kevin, and Elena fight the infected. As the dormant chips in the factory activate, Nanomech uses the chips ability to adapt to overwhelm and destroy the Queen, freeing everyone from the chips' control.


title: Ben 10: Alien Swarm

text: In the aftermath, Max, after apologizing to Victor, decides to retire and leave his position as leader to Ben, but Ben refuses to allow him to do so. The film ends as Ben, Gwen, Kevin, and Elena drive home.