The noisy channel model is a framework used in spell checkers, question answering, speech recognition, and machine translation. In this model, the goal is to find the intended word given a word where the letters have been scrambled in some manner. == In spell-checking == See Chapter B of. Given an alphabet Σ {\displaystyle \Sigma } , let Σ ∗ {\displaystyle \Sigma ^{}} be the set of all finite strings over Σ {\displaystyle \Sigma } . Let the dictionary D {\displaystyle D} of valid words be some subset of Σ ∗ {\displaystyle \Sigma ^{}} , i.e., D ⊆ Σ ∗ {\displaystyle D\subseteq \Sigma ^{}} . The noisy channel is the matrix Γ w s = Pr ( s | w ) {\displaystyle \Gamma _{ws}=\Pr(s|w)} , where w ∈ D {\displaystyle w\in D} is the intended word and s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} is the scrambled word that was actually received. The goal of the noisy channel model is to find the intended word given the scrambled word that was received. The decision function σ : Σ ∗ → D {\displaystyle \sigma :\Sigma ^{}\to D} is a function that, given a scrambled word, returns the intended word. Methods of constructing a decision function include the maximum likelihood rule, the maximum a posteriori rule, and the minimum distance rule. In some cases, it may be better to accept the scrambled word as the intended word rather than attempt to find an intended word in the dictionary. For example, the word schönfinkeling may not be in the dictionary, but might in fact be the intended word. === Example === Consider the English alphabet Σ = { a , b , c , . . . , y , z , A , B , . . . , Z , . . . } {\displaystyle \Sigma =\{a,b,c,...,y,z,A,B,...,Z,...\}} . Some subset D ⊆ Σ ∗ {\displaystyle D\subseteq \Sigma ^{}} makes up the dictionary of valid English words. There are several mistakes that may occur while typing, including: Missing letters, e.g., leter instead of letter Accidental letter additions, e.g., misstake instead of mistake Swapping letters, e.g., recieved instead of received Replacing letters, e.g., fimite instead of finite To construct the noisy channel matrix Γ {\displaystyle \Gamma } , we must consider the probability of each mistake, given the intended word ( Pr ( s | w ) {\displaystyle \Pr(s|w)} for all w ∈ D {\displaystyle w\in D} and s ∈ Σ ∗ {\displaystyle s\in \Sigma ^{}} ). These probabilities may be gathered, for example, by considering the Damerau–Levenshtein distance between s {\displaystyle s} and w {\displaystyle w} or by comparing the draft of an essay with one that has been manually edited for spelling. == In machine translation == One naturally wonders if the problem of translation could conceivably be treated as a problem in cryptography. When I look at an article in Russian, I say: 'This is really written in English, but it has been coded in some strange symbols. I will now proceed to decode. See chapter 1, and chapter 25 of. Suppose we want to translate a foreign language to English, we could model P ( E | F ) {\displaystyle P(E|F)} directly: the probability that we have English sentence E given foreign sentence F, then we pick the most likely one E ^ = arg max E P ( E | F ) {\displaystyle {\hat {E}}=\arg \max _{E}P(E|F)} . However, by Bayes law, we have the equivalent equation: E ^ = argmax E ∈ English P ( F ∣ E ) ⏞ translation model P ( E ) ⏞ language model {\displaystyle {\hat {E}}={\underset {E\in {\text{ English }}}{\operatorname {argmax} }}\overbrace {P(F\mid E)} ^{\text{translation model }}\overbrace {P(E)} ^{\text{language model}}} The benefit of the noisy-channel model is in terms of data: If collecting a parallel corpus is costly, then we would have only a small parallel corpus, so we can only train a moderately good English-to-foreign translation model, and a moderately good foreign-to-English translation model. However, we can collect a large corpus in the foreign language only, and a large corpus in the English language only, to train two good language models. Combining these four models, we immediately get a good English-to-foreign translator and a good foreign-to-English translator. The cost of noisy-channel model is that using Bayesian inference is more costly than using a translation model directly. Instead of reading out the most likely translation by arg max E P ( E | F ) {\displaystyle \arg \max _{E}P(E|F)} , it would have to read out predictions by both the translation model and the language model, multiply them, and search for the highest number. == In speech recognition == Speech recognition can be thought of as translating from a sound-language to a text-language. Consequently, we have T ^ = argmax T ∈ Text P ( S ∣ T ) ⏞ speech model P ( T ) ⏞ language model {\displaystyle {\hat {T}}={\underset {T\in {\text{ Text }}}{\operatorname {argmax} }}\overbrace {P(S\mid T)} ^{\text{speech model }}\overbrace {P(T)} ^{\text{language model}}} where P ( S | T ) {\displaystyle P(S|T)} is the probability that a speech sound S is produced if the speaker is intending to say text T. Intuitively, this equation states that the most likely text is a text that's both a likely text in the language, and produces the speech sound with high probability. The utility of the noisy-channel model is not in capacity. Theoretically, any noisy-channel model can be replicated by a direct P ( T | S ) {\displaystyle P(T|S)} model. However, the noisy-channel model factors the model into two parts which are appropriate for the situation, and consequently it is generally more well-behaved. When a human speaks, it does not produce the sound directly, but first produces the text it wants to speak in the language centers of the brain, then the text is translated into sound by the motor cortex, vocal cords, and other parts of the body. The noisy-channel model matches this model of the human, and so it is appropriate. This is justified in the practical success of noisy-channel model in speech recognition. === Example === Consider the sound-language sentence (written in IPA for English) S = aɪ wʊd laɪk wʌn tuː. There are three possible texts T 1 , T 2 , T 3 {\displaystyle T_{1},T_{2},T_{3}} : T 1 = {\displaystyle T_{1}=} I would like one to. T 2 = {\displaystyle T_{2}=} I would like one too. T 3 = {\displaystyle T_{3}=} I would like one two. that are equally likely, in the sense that P ( S | T 1 ) = P ( S | T 2 ) = P ( S | T 3 ) {\displaystyle P(S|T_{1})=P(S|T_{2})=P(S|T_{3})} . With a good English language model, we would have P ( T 2 ) > P ( T 1 ) > P ( T 3 ) {\displaystyle P(T_{2})>P(T_{1})>P(T_{3})} , since the second sentence is grammatical, the first is not quite, but close to a grammatical one (such as "I would like one to [go]."), while the third one is far from grammatical. Consequently, the noisy-channel model would output T 2 {\displaystyle T_{2}} as the best transcription.
Skipper (computer software)
Skipper is a visualization tool and code/schema generator for PHP ORM frameworks like Doctrine2, Doctrine, Propel, and CakePHP, which are used to create database abstraction layer. Skipper is developed by Czech company Inventic, s.r.o. based in Brno, and was known as ORM Designer prior to rebranding in 2014. == Overview == Generates visual model from the schema definition files Repetitive import/export of schema definitions in supported formats (XML, YML, PHP annotations) Schema definition files are automatically generated from the visual model Visual representation uses ER diagram extended by concepts of inheritance and many-to-many Supports customization using .xml configuration files and JavaScript Does not support direct connections to the database Crude and simplistic visual representation and menus == Architecture == Skipper was built on the Qt framework. Import/export of the schema definitions uses XSL transformations powered by LibXslt library. Imported source files are first converted to XML format: no conversion for XML, simple conversion for YML, creating the Abstract Syntax Tree and its subsequent conversion to XML for PHP annotations. The import/export scripts are configured in JavaScript and can be freely customized. == Supported ORM frameworks == Frameworks supported for visual model and schema files generation: Doctrine2 Doctrine CakePHP == History == Skipper was created as an internal tool for the web applications developed by Inventic. It was first published as a commercial tool under the name ORM Designer in 2009. Application was reworked and optimized in January 2013, and released as ORM Designer 2. In May 2013 ORM Designer became part of the South Moravian Innovation Center Incubator program (support program for innovative technological startups). In June 2014, ORM Designer version 3 was released and rebranded under the name of Skipper
Kialo
Kialo is an online structured debate platform with argument maps in the form of debate trees. It is a collaborative reasoning tool for thoughtful discussion, understanding different points of view, and collaborative decision-making, showing arguments for and against claims underneath user-submitted theses or questions. The deliberative discourse platform is designed to present hundreds of supporting or opposing arguments in a dynamic argument tree and is streamlined for rational civil debate on topics such as philosophical questions, policy deliberations, entertainment, ethics, science questions, and unsolved problems or subjects of disagreement in general. Argument-boxes are structured into hierarchical branches where the root is the main thesis (or theses) of the debate, enabling deliberation and navigable debates between opposing perspectives. A debate is divided into Pro (supporting) and Con (refuting or devaluing) columns where registered users can add arguments and rate the impact on the weight or validity of the parent claim. The arguments are sorted according to the rating average. Its argument tree structure enables detailed scrutiny of claims at all levels of the tree and allows users to for example quickly understand why a decision was made or which of the aggregated arguments swayed it this way. Newcomers can join a debate at any time and look back at the structured discussion history, and then weigh in at the right place with their new argument or their comment on a specific argument. The design presets a structure on debates "that allows participants to easily see, process, and ultimately assess the many facets of competing claims". The word Kialo is Esperanto for "reason". The platform is the world's largest argument mapping and structured debate site. == Overview == Users can comment on every Pro or Con, for example for requesting sources or expansions. Recent activities of a debate are shown in a panel on the right side of the respective debate. Debates can be found through the search or on the Explore page through their descriptions and topic-tags. Mere comments that do not make a constructive point (a self-contained argument backed by reasoning) are not allowed and are picked up by other users and moderators. "Civil language and sensible observations from opposing perspectives" can be seen also in debates about controversial topics. The site by-design incentivizes fair, rigorous, open-minded dialogue. Contributors making claims often also write counterpoints to their own contribution. Claims need to be shorter than 500 characters and can link to external sources. Debate trees can also start off with multiple theses – such as different policy options or hypotheses. Claims can link to related debates or include segments of them. In the discussion tab of each claim, users can make edit proposals (e.g. for accuracy, improving sources, or changing scope), decide if the argument should be moved or copied to another branch, call for archiving a claim, and ask for extra evidence or clarification. Debates can grow large and complex for which a sunburst diagram visualization of the topology of the debate and the search functionality can be useful. Each debate also has a chat-box. In cases where e.g. a "Con" is a point against multiple in the "Pros", users – through moderators – can link these arguments at the respective places to avoid duplication of content and allowing a clean chain for people to understand which points are arguments against each other. Contributions of users are tracked, enabling a board of thought-leaders for every debate. Other gamification elements include a feature to thank users for their contributions. The "Perspectives" feature allows users to see 'Impact' ratings of supporters and opposers of a thesis as well as of the debate's moderators and individual contributors. It thereby enables participants to see a debate from other participants' perspectives and to sort by them. In Kialo Edu, this feature lets teachers view votes for a whole class, individuals, or supporters/opponents of a specific thesis. Users in both versions of Kialo can vote on the overall debate topic as well as on individual claims to express their perspectives or conclusions, with the rationale (i.e. the main causal arguments) why they voted on the veracity of the thesis as they did not being captured. Voting can be done by any registered user while navigating through any debate that has voting enabled or via using the Guided Voting wizard user interface that automatically walks through branches. As of 2021, Kialo doesn't have a mobile app. == Contents == A 2018 report stated the collaborative argument platform hosts more than 10,000 debates in various languages. It also hosts private debates. The website claims that it has over 18,000 public debates as of July 2023, as well as over 1 million votes and over 720,000 claims. Debates can be found via the site's internal search and up to six tags per debate. Preprint studies have scraped public debates on over 1.4K issues with over 130K statements as of October 2019 and 1628 debates, related to over 1120 categories, with 124,312 unique claims as of June 26, 2020. == Kialo Inc. == The site is run by Kialo Inc. It was founded by German-born entrepreneur and London School of Economics and Political Science graduate Errikos Pitsos in August 2017 and is based in Brooklyn and Berlin. According to a 2018 report, the site does not show advertisements and does not sell user's data. The for-profit company was founded in 2011, Pitsos began to develop the concept in 2012 and described various specifics of the system in 2014. In 2018, he stated that they intend to make money by selling the platform to companies as a deliberation and decision-making tool. The site is free to use for the public and in education. According to the site, as of 2023 Kialo.com is a non-revenue generating site with no ads and no reselling of user data. == Applications and adoption == === Adopted applications === Applications of its content or the platform in society include: Teachers and professors, especially in high schools – including the universities Harvard and Princeton, are using Kialo for class discussions and exercises in critical thinking and reasoning, as consolidating understanding of materials covered in recent classes, more useful and engaging learning experiences, for remote/e-learning, for clearing up misconceptions, teaching logical fallacies and rational argumentation, for academic dialogue, teaching media literacy, and for teaching to sufficiently reflect or research before posting online. Like for debaters of the main site, access for schools and universities is free. Kialo Edu is the custom version of Kialo specifically designed for classroom use where debates are private and locked to invited students. Kialo allows teachers to provide feedback to students on their ideas, argument structure, and research quality while it is left to other students to rate the impacts of their peers' arguments. Students can be allowed to contribute anonymously which may be useful for controversial issues as well as for safeguarding privacy in education. Students are or can be encouraged to back up their claims with evidence which can foster digital literacy and research skills. Students and teachers can use it to arrange their thoughts when structuring an essay or project. The site's name was decided on internally using the software. === Prototypical and theoretical applications === Potential, theoretical, prototypical or little-used applications include: Education Improving critical thinking skills of society at large as well as facilitating deep or efficient thinking and deepening research and debates where e.g. discussions are less shallow and the well-known or many arguments have already been made and in many cases aren't unreasonably over- or underrated. Pitsos claimed that "we're training students to be very good test-takers instead of critical thinkers", suggesting teaching people to think things through may be more important or neglected compared to essay writing skills. Many young people and adults are "submerged into a sea of dispersed information", "[b]rowsing and engaging in superficial thinking activities". Kialo could counteract this issue and help people develop good sane reasoning. Academia, R&D and policy Three scholars from three prestigious U.S. universities outlined possible benefits in this domain, including applications beyond higher education such as for academic communication. They suggest the debate platform could be used for structuring the communication of open peer-review by helping those giving feedback to "hone in on[sic] core arguments and pieces of evidence in an even more direct way" than annotated commenting. It could be used to evaluate extracted argument structures and sequences from raw texts, as in a Semantic Web for arguments. Such "argument mining", to which Kialo is the lar
Plants vs. Zombies: Replanted
Plants vs. Zombies: Replanted is a 2025 tower defense video game developed by PopCap Seattle, The Lost Pixels, and published by Electronic Arts. It is a remaster of the 2009 game Plants vs. Zombies, introducing upscaled graphics and new additional content. Plants vs. Zombies: Replanted was released for video game consoles and personal computers on October 23, 2025. It received generally positive reviews from critics, but was criticized by the original game's development team for including fabricated concept art and for mishandling the soundtrack. == Gameplay == Plants vs. Zombies: Replanted follows the same gameplay of the original Plants vs. Zombies game with very minor changes. It is a lane-based tower defense game where the player has to defend their home from incoming zombies. The player can place various plants by spending "sun", the game's currency during levels. Sun icons can be collected from the sky during daytime and from sun-producing plants such as sunflowers. Some plants can attack zombies while some can act as defense. If all zombies are defeated in a level, the player wins. If a zombie reaches the left side of the line, a lawn mower—or other similar, relevant object—will activate and clear the row of any zombies, but if the lawn mower has already been used, and another zombie crosses, the game is over. === Replanted features === Plants vs. Zombies: Replanted contains up to 4K upscaled graphics and widescreen support, in comparison to the original game's static 800x600 resolution and 4:3 aspect ratio. Replanted now has full controller support and features local multiplayer modes ported from the original game's seventh generation console ports: co-op, where two players play together with assigned roles; and Versus, where one plays as the plants and the other as the zombies. No online multiplayer is planned, however support for Steam Remote Play was later added in a patch as an alternative for Windows users. Replanted also contains quality-of-life features. Gameplay can now be sped up by the player's will, with a max speed increase of 2.5x. Sun icons can now be mass collected using the "Sun Magnet." On Windows, players can quick-select plants from their seed bank using the number keys as hotkeys. Replanted also introduces two new additional game modes. "Cloudy Day" is a set of non-linear levels in the Adventure campaign. These levels only allow Sunflowers as sun-producing plants. During these levels, the amount of sun dropped from the sky and produced by plants are lowered. At certain times, rain clouds will move over the lawn. While these clouds are present, sun will stop appearing from the sky and from Sunflowers. However, all plants will cost around half their original price and have significantly faster recharge times. "R.I.P. Mode" is a harder difficulty of the Adventure campaign, but the player is forced back to the beginning if they lose a single level. Replanted additionally features "bonus levels" included as non-linear levels in the Adventure campaign. These include 10 new minigames that were previously unused in the original game. In a later update, Replanted added "Survival: Endless" levels to all five areas of the game instead of just the daytime pool. == Development == The existence of a Plants vs. Zombies remaster was revealed in an interview with Janet Robin from The String Revolution, who they did a vinyl collaboration with the franchise in 2025 with Iam8bit. Janet stated that EA commissioned them to record an acoustic composition of the track "Crazy Dave" to be used for an "anniversary edition" of the game. The song would be additionally be a tribute to the song "Bad Guy", which artist Billie Eilish has stated to be somewhat similar to the track. Plants vs. Zombies Replanted was officially announced in a Nintendo Direct presentation in late July 2025. As an incentive, people who pre-ordered the game are given an in-game retro-styled skin of the Peashooter. Replanted was showcased at PAX West on August 25, 2025. A dev diary for Plants vs. Zombies: Replanted was uploaded to YouTube on October 17, 2025. The video features Nick Reinhart, Jake Neri, and Matt Townsend. A developer panel for the game was available during TwitchCon 2025. == Release == Plants vs. Zombies: Replanted was released for Nintendo Switch, Nintendo Switch 2, PlayStation 4, PlayStation 5, Xbox One, Xbox Series X and Series S, and personal computers on October 23, 2025. It was leaked onto the internet on October 17, 2025. Players discovered multiple software bugs, and multiple assets alleged to be upscaled by generative artificial intelligence were found, leading to backlash. Numerous bugs were fixed in a day-one patch on October 23, 2025. == Reception == === Critical response === The versions of Plants vs. Zombies: Replanted for Windows, PlayStation 5, and Nintendo Switch 2 received "generally favorable" reviews from critics, according to review aggregator website Metacritic, while the Xbox Series X version received "mixed or average" reviews. According to OpenCritic, 57% of critics recommended it. IGN's Alessandro Fillari called it "a good way to get re-acquainted with one of the quirkiest puzzle-strategy games of the 2000s", while acknowledging its questionable decisions. Shacknews' David Craddock said it was his favorite version of Plants vs. Zombies, stating, "it packs everything fans loved about the original game, plus lots more" while justifying its US$20 price. The Verge described Replanted as "a time capsule from a simpler, happier time". Kyle Hilliard from Game Informer praised its faithfulness, complimenting the new animations and character designs that did not alter its memorability. Noah Hunter for Final Weapon described the remake as solid, though criticized the lack of certain features and containing bugs that gate it from being excellent. Ben Lyons from Gamereactor stated Replanted is the same as the original overall, despite believing the £18 price is not justified. === Original developers === Rich Werner, the original game's character designer, claims that some concept art contained in the game, speculated to be for Plants vs. Zombies: Garden Warfare (2014), did not originate from the original's development. Werner also stated that concept art for the Disco Zombie is fabricated; the design for the Disco Zombie was created after the estate of Michael Jackson requested the original Dancing Zombie, who resembles Michael Jackson from his Thriller music video, be removed from the game. On October 19, 2026, composer Laura Shigihara expressed her dissatisfaction with the lack of dynamic music in the game. Dynamic music would later be implemented in a later patch. In an interview featuring Rich Werner and user interface designer Matt Holmberg on April 29, 2026, Werner revealed that he and Shigihara were contacted by EA to make a music video to market Replanted. However, after the game was leaked, Werner's response on social media led EA to cancel the collaboration.
Wonder.land
Wonder.land (stylised as wonder.land) is a musical with music by Damon Albarn and lyrics and book by Moira Buffini. Inspired by Lewis Carroll's novels Alice's Adventures in Wonderland (1865) and Through the Looking-Glass (1871), it had its world premiere at the Palace Theatre in Manchester in July 2015 as part of the Manchester International Festival. The musical moved to London's Royal National Theatre in November 2015 before opening at the Théâtre du Châtelet in Paris in 2016. Licencing for potential future smaller scale productions is held by United Agents UK. == Background == The musical is inspired by the novels Alice in Wonderland and Through the Looking-Glass, written by Lewis Carroll. It was announced on 21 January 2015 that the show would premiere in July of that year as part of the Manchester International Festival, with tickets going on sale the following day. The musical, a co-production by the Manchester International Festival, the Royal National Theatre and the Théâtre du Châtelet in Paris, marks the 150th anniversary of the publication of Alice's Adventures in Wonderland. The idea for a musical based on Alice in Wonderland came from Manchester International Festival artistic director Alex Poots. Damon Albarn had collaborated with the festival on Monkey: Journey to the West and Dr Dee. The musical has a book by Moira Buffini. It was directed by Rufus Norris, with set design by Rae Smith, costume design by Katrina Lindsay, lighting design by Paule Constable, projections by 59 Productions and choreography by Javier De Frutos. The musical's score was composed by Damon Albarn, with lyrics by Moira Buffini, sound design by Paul Arditti and musical direction by David Shrubsole. == Production history == The musical began previews at the Palace Theatre in Manchester on 29 June 2015. It opened on 2 July for a limited run until 12 July. A revised version moved to the Royal National Theatre, where it ran at the Olivier Theatre from 27 November 2015 to 30 April 2016. The production had a limited run, from 7 to 16 June 2016, at the Theatre Du Chatelet in Paris. == Synopsis == This synopsis is based on the final version, as seen at the National Theatre and the Théâtre du Châtelet. Earlier performances significantly differed in songs and plot. === Act 1 === AI, the MC, explains that virtual technology is "a portal to boundless lands" ("Prologue"). Aly's mother, Bianca, is exasperated with her for spending the weekend indoors on her phone. Aly accompanies Bianca to the supermarket, and thinks that her life is being ruined by her parents due to dysfunctional problems ("Who's Ruining Your Life?") Her alcoholic father, Matt, is also at the supermarket; he and Bianca argue about their divorce and his gambling. Aly goes home and picks up her phone. She tries to engage with schoolmates, who bully her ("Network"). Aly begins to wish that she is someone else. She finds the virtual online game Wonder.land. In its strange world, Aly creates an avatar: beautiful, kind Alice ("Wonder.land"). Wonder.land has one rule: malice causes deletion from the game. Aly and Alice become friends and encounter the Cheshire Cat, who explains that you can be anyone you want ("Fabulous"). Aly decides to go on a quest; Alice follows the white rabbit down a hole, falling past unusual objects and musical notes ("Falling"). The next morning, Aly is too distracted by Wonder.land to listen to Bianca's complaints about her baby brother Charlie. She plays the game at school before her phone is confiscated by stern headmistress Ms Manxome, who tells her students that taking pleasures from them is for their own good ("I'm Right"). Aly goes to Ms Manxome's office to retrieve her phone. Ms Manxome returns it, warning that if she catches her with it again, "it's a beheading – I mean, detention." Aly sees the girls who bullied her, and they bully her again until a teacher arrives. Aly's friend, Luke, is late and is given detention. Aly goes on her phone and takes out her frustration and sadness on Alice, whose tears form a pool until she is interrupted by the quarrelsome twins Dum and Dee ("Freaks"). Alice tries to befriend them, but they insult her and Aly makes her fight them. Dum and Dee cry, and Aly and Alice see a large mouse who is attracted by Alice's fighting. They are joined by the Dodo, the Mock Turtle and Humpty, who all have problems. The Dodo is stressed because his parents want him to save the planet; Dum and Dee are dancers who hate pressure; Humpty has problems with her parents; the Mock Turtle lacks self-esteem, and the mouse is lustful. Wonderland is a hiding place from teenage life ("Crap Life"). Aly returns to reality when asked a math question she cannot answer. Confronting the three bullies, Aly mocks the facial hair of one and hides in the bathroom. She again immerses herself in Wonder.land, where Alice meets a Caterpillar who is obsessed with identity ("Who are You?"). Aly is interrupted by the girls, who ridicule her father's gambling addiction and poverty before beating her up. Aly seeks understanding from Alice, who tries to get Aly to tell her what is wrong. Aly tells Alice about her family and how she hates her life, and is surprised that Alice has similar problems ("Secrets"). Luke comes into the girls' bathroom because Kieran has threatened him with violence, and hides in a cubicle when Kieran enters. Aly defends Luke, and makes Kieran leave. Luke reveals that the reason Kieran hates him is because, like himself, he is gay. Aly is amazed, and they skip class and play games on their phones. Luke plays Zombie Swarm, and Aly plays Wonder.land. Ms Manxome enters the bathroom; Luke hides his phone, but Aly does not. Ms Manxome confiscates the phone for three months, and Aly and Luke leave. Ms Manxome finds that Aly did not lock her phone, and Alice is calling her. Ms Manxome begins to talk to her, and Alice thinks she is talking to Aly. Aly complains to Luke about her phone being taken away. Matt then takes them out for tea to celebrate his new job at the local garden centre ("In Clover"). At the tea shop, Matt maniacally dances on the tables and plays with spoons; asked to stop, he punches a waiter. Bianca arrives, and they argue again. Aly begins to notice that Wonder.land is invading reality; the MC emerges from a gigantic teapot, and the landscape outside becomes surreal ("Chances"). === Act 2 === Ms Manxome manipulates Alice around Wonder.land on Aly's phone, buys many things, and makes Alice's hair red ("Entre Act"). She tells Alice about her plans to dominate and destroy the online world, and Alice thinks she is talking to Aly ("Me"). Aly, Matt, Bianca, and Charlie are at the police station. PC Rook unsuccessfully tries to get Matt to make a statement (since he is charged with assault and affray), but Matt and Bianca argue again. Aly laments the loss of her family's unity ("Heartless Useless"). In Wonder.land, Ms Manxome is hostile when she meets Dum and Dee, the Mock Turtle, the Dodo, Humpty and the Mouse. She makes Alice chase them away, but Alice and Ms Manxome are driven away by Alice's friends, who are worried about the change in her ("Me (Reprise)"). Bianca learns that Aly missed a detention and had her phone confiscated. Concerned that she is losing Aly to technology, she bans her from the internet ("Gadget"). Charlie vomits, and Aly is left to clean it up. She looks for an internet cafe to go to Wonder.land, the only place she is truly happy ("Everyone Loves Charlie"). At the cafe, Aly cannot log into Wonder.land and her avatar seems to be in use. She sees Alice receive a Vorpal sword, bought by Ms Manxome with the money on Aly's phone. Alice is no longer Alice but the Red Queen, and Ms Manxome tells her to kill her friends. Alice, knowing the person controlling her is not Aly, cannot rebel; she lashes out at her friends, bullying and trying to hurt them. The MC warns that Alice has a deletion warning – any more malice, and she will be deleted. Aly now knows that Ms Manxome controls her phone and avatar ("O Children"). Aly enlists Luke to help and decides to break into Ms. Manxome's office to retrieve the phone. Luke agrees to meet her at the school gates. Matt and Bianca wonder if they should reconcile ("Man of Broken Glass"). At the school, Luke is reluctant to get involved; Aly decides to break into the office anyway. Luke contacts the girls who bullied Aly and tells them about Ms Manxome playing on Aly's stolen phone. They decide to spread the word that it is not Aly ("Fabulous (Reprise)"). Bianca goes to the police because Aly is missing, and gives her phone to Matt. Aly is likely to also be in Wonder.land. The avatars prepare for war against Alice but disagree about a strategy. At the police station, Matt hacks into Wonder.land sees Alice, and realizes that she is controlled by someone other than Aly. The White Rabbit appears (delighting Alice), but Ms Manxome makes Alice push him aside. The borderline between Wonder.land and
Statistical shape analysis
Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. Important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate mean shapes from (possibly random) samples, to estimate shape variability within samples, to perform clustering and to test for differences between shapes. One of the main methods used is principal component analysis (PCA). Statistical shape analysis has applications in various fields, including medical imaging, computer vision, computational anatomy, sensor measurement, and geographical profiling. == Landmark-based techniques == In the point distribution model, a shape is determined by a finite set of coordinate points, known as landmark points. These landmark points often correspond to important identifiable features such as the corners of the eyes. Once the points are collected some form of registration is undertaken. This can be a baseline methods used by Fred Bookstein for geometric morphometrics in anthropology. Or an approach like Procrustes analysis which finds an average shape. David George Kendall investigated the statistical distribution of the shape of triangles, and represented each triangle by a point on a sphere. He used this distribution on the sphere to investigate ley lines and whether three stones were more likely to be co-linear than might be expected. Statistical distribution like the Kent distribution can be used to analyse the distribution of such spaces. Alternatively, shapes can be represented by curves or surfaces representing their contours, by the spatial region they occupy. == Shape deformations == Differences between shapes can be quantified by investigating deformations transforming one shape into another. In particular a diffeomorphism preserves smoothness in the deformation. This was pioneered in D'Arcy Thompson's On Growth and Form before the advent of computers. Deformations can be interpreted as resulting from a force applied to the shape. Mathematically, a deformation is defined as a mapping from a shape x to a shape y by a transformation function Φ {\displaystyle \Phi } , i.e., y = Φ ( x ) {\displaystyle y=\Phi (x)} . Given a notion of size of deformations, the distance between two shapes can be defined as the size of the smallest deformation between these shapes. Diffeomorphometry is the focus on comparison of shapes and forms with a metric structure based on diffeomorphisms, and is central to the field of Computational anatomy. Diffeomorphic registration, introduced in the 90's, is now an important player with existing codes bases organized around ANTS, DARTEL, DEMONS, LDDMM, StationaryLDDMM, and FastLDDMM are examples of actively used computational codes for constructing correspondences between coordinate systems based on sparse features and dense images. Voxel-based morphometry (VBM) is an important technology built on many of these principles. Methods based on diffeomorphic flows are also used. For example, deformations could be diffeomorphisms of the ambient space, resulting in the LDDMM (Large Deformation Diffeomorphic Metric Mapping) framework for shape comparison.
Defuzzification
Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems. These systems will have a number of rules that transform a number of variables into a fuzzy result, that is, the result is described in terms of membership in fuzzy sets. For example, rules designed to decide how much pressure to apply might result in "Decrease Pressure (15%), Maintain Pressure (34%), Increase Pressure (72%)". Defuzzification is interpreting the membership degrees of the fuzzy sets into a specific decision or real value. The simplest but least useful defuzzification method is to choose the set with the highest membership, in this case, "Increase Pressure" since it has a 72% membership, and ignore the others, and convert this 72% to some number. The problem with this approach is that it loses information. The rules that called for decreasing or maintaining pressure might as well have not been there in this case. A common and useful defuzzification technique is center of gravity. First, the results of the rules must be added together in some way. The most typical fuzzy set membership function has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal line somewhere between the top and the bottom, and the top portion were to be removed, the remaining portion forms a trapezoid. The first step of defuzzification typically "chops off" parts of the graphs to form trapezoids (or other shapes if the initial shapes were not triangles). For example, if the output has "Decrease Pressure (15%)", then this triangle will be cut 15% the way up from the bottom. In the most common technique, all of these trapezoids are then superimposed one upon another, forming a single geometric shape. Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value. == Methods == There are many different methods of defuzzification available, including the following: AI (adaptive integration) BADD (basic defuzzification distributions) BOA (bisector of area) CDD (constraint decision defuzzification) COA (center of area) COG (center of gravity) ECOA (extended center of area) EQM (extended quality method) FCD (fuzzy clustering defuzzification) FM (fuzzy mean) FOM (first of maximum) GLSD (generalized level set defuzzification) ICOG (indexed center of gravity) IV (influence value) LOM (last of maximum) MeOM (mean of maxima) MOM (middle of maximum) QM (quality method) RCOM (random choice of maximum) SLIDE (semi-linear defuzzification) WFM (weighted fuzzy mean) The maxima methods are good candidates for fuzzy reasoning systems. The distribution methods and the area methods exhibit the property of continuity that makes them suitable for fuzzy controllers.