Granular computing is an emerging computing paradigm of information processing that concerns the processing of complex information entities called "information granules", which arise in the process of data abstraction and derivation of knowledge from information or data. Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like. At present, granular computing is more a theoretical perspective than a coherent set of methods or principles. As a theoretical perspective, it encourages an approach to data that recognizes and exploits the knowledge present in data at various levels of resolution or scales. In this sense, it encompasses all methods which provide flexibility and adaptability in the resolution at which knowledge or information is extracted and represented. == Types of granulation == As mentioned above, granular computing is not an algorithm or process; there is no particular method that is called "granular computing". It is rather an approach to looking at data that recognizes how different and interesting regularities in the data can appear at different levels of granularity, much as different features become salient in satellite images of greater or lesser resolution. On a low-resolution satellite image, for example, one might notice interesting cloud patterns representing cyclones or other large-scale weather phenomena, while in a higher-resolution image, one misses these large-scale atmospheric phenomena but instead notices smaller-scale phenomena, such as the interesting pattern that is the streets of Manhattan. The same is generally true of all data: At different resolutions or granularities, different features and relationships emerge. The aim of granular computing is to try to take advantage of this fact in designing more effective machine-learning and reasoning systems. There are several types of granularity that are often encountered in data mining and machine learning, and we review them below: === Value granulation (discretization/quantization) === One type of granulation is the quantization of variables. It is very common that in data mining or machine-learning applications the resolution of variables needs to be decreased in order to extract meaningful regularities. An example of this would be a variable such as "outside temperature" (temp), which in a given application might be recorded to several decimal places of precision (depending on the sensing apparatus). However, for purposes of extracting relationships between "outside temperature" and, say, "number of health-club applications" (club), it will generally be advantageous to quantize "outside temperature" into a smaller number of intervals. ==== Motivations ==== There are several interrelated reasons for granulating variables in this fashion: Based on prior domain knowledge, there is no expectation that minute variations in temperature (e.g., the difference between 80–80.7 °F (26.7–27.1 °C)) could have an influence on behaviors driving the number of health-club applications. For this reason, any "regularity" which our learning algorithms might detect at this level of resolution would have to be spurious, as an artifact of overfitting. By coarsening the temperature variable into intervals the difference between which we do anticipate (based on prior domain knowledge) might influence number of health-club applications, we eliminate the possibility of detecting these spurious patterns. Thus, in this case, reducing resolution is a method of controlling overfitting. By reducing the number of intervals in the temperature variable (i.e., increasing its grain size), we increase the amount of sample data indexed by each interval designation. Thus, by coarsening the variable, we increase sample sizes and achieve better statistical estimation. In this sense, increasing granularity provides an antidote to the so-called curse of dimensionality, which relates to the exponential decrease in statistical power with increase in number of dimensions or variable cardinality. Independent of prior domain knowledge, it is often the case that meaningful regularities (i.e., which can be detected by a given learning methodology, representational language, etc.) may exist at one level of resolution and not at another. For example, a simple learner or pattern recognition system may seek to extract regularities satisfying a conditional probability threshold such as p ( Y = y j | X = x i ) ≥ α . {\displaystyle p(Y=y_{j}|X=x_{i})\geq \alpha .} In the special case where α = 1 , {\displaystyle \alpha =1,} this recognition system is essentially detecting logical implication of the form X = x i → Y = y j {\displaystyle X=x_{i}\rightarrow Y=y_{j}} or, in words, "if X = x i , {\displaystyle X=x_{i},} then Y = y j {\displaystyle Y=y_{j}} ". The system's ability to recognize such implications (or, in general, conditional probabilities exceeding threshold) is partially contingent on the resolution with which the system analyzes the variables. As an example of this last point, consider the feature space shown to the right. The variables may each be regarded at two different resolutions. Variable X {\displaystyle X} may be regarded at a high (quaternary) resolution wherein it takes on the four values { x 1 , x 2 , x 3 , x 4 } {\displaystyle \{x_{1},x_{2},x_{3},x_{4}\}} or at a lower (binary) resolution wherein it takes on the two values { X 1 , X 2 } . {\displaystyle \{X_{1},X_{2}\}.} Similarly, variable Y {\displaystyle Y} may be regarded at a high (quaternary) resolution or at a lower (binary) resolution, where it takes on the values { y 1 , y 2 , y 3 , y 4 } {\displaystyle \{y_{1},y_{2},y_{3},y_{4}\}} or { Y 1 , Y 2 } , {\displaystyle \{Y_{1},Y_{2}\},} respectively. At the high resolution, there are no detectable implications of the form X = x i → Y = y j , {\displaystyle X=x_{i}\rightarrow Y=y_{j},} since every x i {\displaystyle x_{i}} is associated with more than one y j , {\displaystyle y_{j},} and thus, for all x i , {\displaystyle x_{i},} p ( Y = y j | X = x i ) < 1. {\displaystyle p(Y=y_{j}|X=x_{i})<1.} However, at the low (binary) variable resolution, two bilateral implications become detectable: X = X 1 ↔ Y = Y 1 {\displaystyle X=X_{1}\leftrightarrow Y=Y_{1}} and X = X 2 ↔ Y = Y 2 {\displaystyle X=X_{2}\leftrightarrow Y=Y_{2}} , since every X 1 {\displaystyle X_{1}} occurs iff Y 1 {\displaystyle Y_{1}} and X 2 {\displaystyle X_{2}} occurs iff Y 2 . {\displaystyle Y_{2}.} Thus, a pattern recognition system scanning for implications of this kind would find them at the binary variable resolution, but would fail to find them at the higher quaternary variable resolution. ==== Issues and methods ==== It is not feasible to exhaustively test all possible discretization resolutions on all variables in order to see which combination of resolutions yields interesting or significant results. Instead, the feature space must be preprocessed (often by an entropy analysis of some kind) so that some guidance can be given as to how the discretization process should proceed. Moreover, one cannot generally achieve good results by naively analyzing and discretizing each variable independently, since this may obliterate the very interactions that we had hoped to discover. A sample of papers that address the problem of variable discretization in general, and multiple-variable discretization in particular, is as follows: Chiu, Wong & Cheung (1991), Bay (2001), Liu et al. (2002), Wang & Liu (1998), Zighed, Rabaséda & Rakotomalala (1998), Catlett (1991), Dougherty, Kohavi & Sahami (1995), Monti & Cooper (1999), Fayyad & Irani (1993), Chiu, Cheung & Wong (1990), Nguyen & Nguyen (1998), Grzymala-Busse & Stefanowski (2001), Ting (1994), Ludl & Widmer (2000), Pfahringer (1995), An & Cercone (1999), Chiu & Cheung (1989), Chmielewski & Grzymala-Busse (1996), Lee & Shin (1994), Liu & Wellman (2002), Liu & Wellman (2004). === Variable granulation (clustering/aggregation/transformation) === Variable granulation is a term that could describe a variety of techniques, most of which are aimed at reducing dimensionality, redundancy, and storage requirements. We briefly describe some of the ideas here, and present pointers to the literature. ==== Variable transformation ==== A number of classical methods, such as principal component analysis, multidimensional scaling, factor analysis, and structural equation modeling, and their relatives, fall under the genus of "variable transformation." Also in this category are more modern areas of study such as dimensionality reduction, projection pursuit, and independent component analysis. The common goal of these methods in general is to find a representation of the data in terms of new variables, which are a linear or nonlinear transformation of the original variables, and in which important stati
NNDB
The Notable Names Database (NNDB) is an online database of biographical details of over 40,000 people. Soylent Communications, a sole proprietorship that also hosted the later defunct Rotten.com, describes NNDB as an "intelligence aggregator" of noteworthy persons, highlighting their interpersonal connections. The Rotten.com domain was registered in 1996 by former Apple and Netscape software engineer Thomas E. Dell, who was also known by his internet alias, "Soylent". == Entries == Each entry has an executive summary followed by a brief narrative about their life. It also lists date and cause of death if deceased. Businesspeople and government officials are listed with chronologies of their posts, positions, and board memberships. As of 2022, the site is no longer updated. == NNDB Mapper == The NNDB Mapper, a visual tool for exploring connections between people, was made available in May 2008. It required Adobe Flash 7.
Argument mining
Argument mining, or argumentation mining, is a research area within the natural language processing field. The goal of argument mining is the automatic extraction and identification of argumentative structures from natural language text with the aid of computer programs. Such argumentative structures include the premise, conclusions, the argument scheme and the relationship between the main and subsidiary argument, or the main and counter-argument within discourse. The Argument Mining workshop series is the main research forum for argument mining related research. == Applications == Argument mining has been applied in many different genres including the qualitative assessment of social media content (e.g. Twitter, Facebook), where it provides a powerful tool for policy-makers and researchers in social and political sciences. Other domains include legal documents, product reviews, scientific articles, online debates, newspaper articles and dialogical domains. Transfer learning approaches have been successfully used to combine the different domains into a domain agnostic argumentation model. Argument mining has been used to provide students individual writing support by accessing and visualizing the argumentation discourse in their texts. The application of argument mining in a user-centered learning tool helped students to improve their argumentation skills significantly compared to traditional argumentation learning applications. == Challenges == Given the wide variety of text genres and the different research perspectives and approaches, it has been difficult to reach a common and objective evaluation scheme. Many annotated data sets have been proposed, with some gaining popularity, but a consensual data set is yet to be found. Annotating argumentative structures is a highly demanding task. There have been successful attempts to delegate such annotation tasks to the crowd but the process still requires a lot of effort and carries significant cost. Initial attempts to bypass this hurdle were made using the weak supervision approach.
TuVox
TuVox is a company that produces VXML-based telephone speech-recognition applications to replace DTMF touch-tone systems for their clients. == History == TuVox was founded in 2001 by Steven S. Pollock and Ashok Khosla, formerly of Apple Computer Corporation and Claris Corporation. Since then, TuVox has grown to over 150 employees and has US offices in Cupertino, California and Boca Raton, Florida as well as international offices in London, Vancouver and Sydney. In 2005, TuVox acquired the customers and hosting facilities of Net-By-Tel. In 2007, the company raised $20m for its speech recognition, and phone menu software. On July 22, 2010, West Interactive — a subsidiary of West Corporation — announced its acquisition of TuVox. == Customers == TuVox clients include: 1-800-Flowers.com, AMC Entertainment, American Airlines, British Airways, M&T Bank, Canon Inc., Gateway, Inc., Motorola, Progress Energy Inc., Telecom New Zealand, Time, Inc., BECU, Virgin America and USAA.
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
Pixelmator
Pixelmator is a series of graphics editors developed by Apple for macOS, iOS, and iPadOS. Pixelmator apps leverage Apple-specific technologies such as CoreML and Metal. Pixelmator uses a proprietary format across their apps (.PXD), but supports editing a variety of file types including Photoshop, RAW, and WebP. == History == Pixelmator Team was founded in 2007 by Lithuanian brothers Saulius and Aidas Dailidė, and released Pixelmator (now Pixelmator Classic) 1.0 in September of the same year. The company resided in Vilnius, Lithuania. In November 2024, Pixelmator Team agreed to be acquired by Apple for an unknown monetary amount, which was completed on 11 February 2025, the company was later folded into Apple with its products coming under them fully. == Pixelmator Classic == Pixelmator Classic was the original version of Pixelmator released for Mac on 25 September 2007. It uses a palette-style interface with floating toolbars compared to Pixelmator Pro's single-window interface. It is no longer being updated and has been delisted from the Mac App Store. == Pixelmator iOS == Pixelmator for iOS launched on 23 October 2014 as an iPad-exclusive app with touch-optimized versions of Pixelmator's desktop features. In May 2015, Pixelmator for iOS 2.0 was released with support for the iPhone. Apple no longer updates Pixelmator for iOS as of 13 January 2026, shortly before the release of Pixelmator Pro for iPad. == Pixelmator Pro == Pixelmator Pro is an image, video, and vector editing software for macOS that launched on 29 November 2017. It was a paid upgrade for Pixelmator Classic users, featuring a redesigned interface, a graphics pipeline rewritten using Metal, Apple silicon support and a greater focus on ML/AI editing features. On 28 January 2026, Apple announced Apple Creator Studio, a subscription bundle for their professional software that contains Pixelmator Pro. They also brought Pixelmator Pro to iPad, shortly after discontinuing Pixelmator iOS. == Photomator == Photomator (formerly Pixelmator Photo) is a photo-oriented editing app which launched on iPad in 2019, on iOS in 2021, and macOS in 2022. After launching the macOS version, the app moved from a one-time purchase to a subscription; however, a lifetime license can still be purchased for $99. Photomator differentiates itself from other Pixelmator apps with features such as batch editing of full photoshoots and AI-powered color correction. Edits in Photomator are made on a single layer and are non-destructive.
Fuzzy pay-off method for real option valuation
The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.