AI Image Generators

Explore the best AI Image Generators — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

Computer audition

Computer audition (CA) or machine listening is the general field of study of algorithms and systems for audio interpretation by machines. Since the notion of what it means for a machine to "hear" is very broad and somewhat vague, computer audition attempts to bring together several disciplines that originally dealt with specific problems or had a concrete application in mind. The engineer Paris Smaragdis, interviewed in Technology Review, talks about these systems — "software that uses sound to locate people moving through rooms, monitor machinery for impending breakdowns, or activate traffic cameras to record accidents." Inspired by models of human audition, CA deals with questions of representation, transduction, grouping, use of musical knowledge and general sound semantics for the purpose of performing intelligent operations on audio and music signals by the computer. Technically this requires a combination of methods from the fields of signal processing, auditory modelling, music perception and cognition, pattern recognition, and machine learning, as well as more traditional methods of artificial intelligence for musical knowledge representation. == Applications == Like computer vision versus image processing, computer audition versus audio engineering deals with understanding of audio rather than processing. It also differs from problems of speech understanding by machine since it deals with general audio signals, such as natural sounds and musical recordings. Applications of computer audition are widely varying, and include search for sounds, genre recognition, acoustic monitoring, music transcription, score following, audio texture, music improvisation, emotion in audio and so on. == Related disciplines == Computer Audition overlaps with the following disciplines: Music information retrieval: methods for search and analysis of similarity between music signals. Auditory scene analysis: understanding and description of audio sources and events. Computational musicology and mathematical music theory: use of algorithms that employ musical knowledge for analysis of music data. Computer music: use of computers in creative musical applications. Machine musicianship: audition driven interactive music systems. == Areas of study == Since audio signals are interpreted by the human ear–brain system, that complex perceptual mechanism should be simulated somehow in software for "machine listening". In other words, to perform on par with humans, the computer should hear and understand audio content much as humans do. Analyzing audio accurately involves several fields: electrical engineering (spectrum analysis, filtering, and audio transforms); artificial intelligence (machine learning and sound classification); psychoacoustics (sound perception); cognitive sciences (neuroscience and artificial intelligence); acoustics (physics of sound production); and music (harmony, rhythm, and timbre). Furthermore, audio transformations such as pitch shifting, time stretching, and sound object filtering, should be perceptually and musically meaningful. For best results, these transformations require perceptual understanding of spectral models, high-level feature extraction, and sound analysis/synthesis. Finally, structuring and coding the content of an audio file (sound and metadata) could benefit from efficient compression schemes, which discard inaudible information in the sound. Computational models of music and sound perception and cognition can lead to a more meaningful representation, a more intuitive digital manipulation and generation of sound and music in musical human-machine interfaces. The study of CA could be roughly divided into the following sub-problems: Representation: signal and symbolic. This aspect deals with time-frequency representations, both in terms of notes and spectral models, including pattern playback and audio texture. Feature extraction: sound descriptors, segmentation, onset, pitch and envelope detection, chroma, and auditory representations. Musical knowledge structures: analysis of tonality, rhythm, and harmonies. Sound similarity: methods for comparison between sounds, sound identification, novelty detection, segmentation, and clustering. Sequence modeling: matching and alignment between signals and note sequences. Source separation: methods of grouping of simultaneous sounds, such as multiple pitch detection and time-frequency clustering methods. Auditory cognition: modeling of emotions, anticipation and familiarity, auditory surprise, and analysis of musical structure. Multi-modal analysis: finding correspondences between textual, visual, and audio signals. === Representation issues === Computer audition deals with audio signals that can be represented in a variety of fashions, from direct encoding of digital audio in two or more channels to symbolically represented synthesis instructions. Audio signals are usually represented in terms of analogue or digital recordings. Digital recordings are samples of acoustic waveform or parameters of audio compression algorithms. One of the unique properties of musical signals is that they often combine different types of representations, such as graphical scores and sequences of performance actions that are encoded as MIDI files. Since audio signals usually comprise multiple sound sources, then unlike speech signals that can be efficiently described in terms of specific models (such as source-filter model), it is hard to devise a parametric representation for general audio. Parametric audio representations usually use filter banks or sinusoidal models to capture multiple sound parameters, sometimes increasing the representation size in order to capture internal structure in the signal. Additional types of data that are relevant for computer audition are textual descriptions of audio contents, such as annotations, reviews, and visual information in the case of audio-visual recordings. === Features === Description of contents of general audio signals usually requires extraction of features that capture specific aspects of the audio signal. Generally speaking, one could divide the features into signal or mathematical descriptors such as energy, description of spectral shape etc., statistical characterization such as change or novelty detection, special representations that are better adapted to the nature of musical signals or the auditory system, such as logarithmic growth of sensitivity (bandwidth) in frequency or octave invariance (chroma). Since parametric models in audio usually require very many parameters, the features are used to summarize properties of multiple parameters in a more compact or salient representation. === Musical knowledge === Finding specific musical structures is possible by using musical knowledge as well as supervised and unsupervised machine learning methods. Examples of this include detection of tonality according to distribution of frequencies that correspond to patterns of occurrence of notes in musical scales, distribution of note onset times for detection of beat structure, distribution of energies in different frequencies to detect musical chords and so on. === Sound similarity and sequence modeling === Comparison of sounds can be done by comparison of features with or without reference to time. In some cases an overall similarity can be assessed by close values of features between two sounds. In other cases when temporal structure is important, methods of dynamic time warping need to be applied to "correct" for different temporal scales of acoustic events. Finding repetitions and similar sub-sequences of sonic events is important for tasks such as texture synthesis and machine improvisation. === Source separation === Since one of the basic characteristics of general audio is that it comprises multiple simultaneously sounding sources, such as multiple musical instruments, people talking, machine noises or animal vocalization, the ability to identify and separate individual sources is very desirable. Unfortunately, there are no methods that can solve this problem in a robust fashion. Existing methods of source separation rely sometimes on correlation between different audio channels in multi-channel recordings. The ability to separate sources from stereo signals requires different techniques than those usually applied in communications where multiple sensors are available. Other source separation methods rely on training or clustering of features in mono recording, such as tracking harmonically related partials for multiple pitch detection. Some methods, before explicit recognition, rely on revealing structures in data without knowing the structures (like recognizing objects in abstract pictures without attributing them meaningful labels) by finding the least complex data representations, for instance describing audio scenes as generated by a few tone patterns and their trajectories (polyphonic voices) and acoustical contours drawn by a tone (c
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Project Debater

Project Debater is an IBM artificial intelligence project, designed to participate in a full live debate with expert human debaters. It follows on from the Watson project which played Jeopardy! == Development == Project Debater was developed at IBM's lab in Haifa, Israel. The project was proposed by Noam Slonim in 2011 as the IBM Research next Grand Challenge, following Deep Blue and the victory of Watson in Jeopardy! It was exposed for the first time in a closed media event at June 18, 2018, in San Francisco, under the leadership of Ranit Aharonov and Slonim, both from the IBM Research lab in Haifa, Israel. The AI technology debated two human debaters, Noa Ovadia, who was the 2016 Israeli debate champion and Dan Zafrir. The two debated on the topics "We should subsidize space exploration" and "Should we increase the use of telemedicine." A demonstration of Project Debater also aired on the Discovery Channel in June 2018 debating the question of whether sports gambling should be legalized. == Live Debate == On February 11, 2019, Project Debater was revealed to the world in a live debate in San Francisco. Nonpartisan media group Intelligence Squared U.S. Debates hosted the debate which was moderated by journalist John Donvan. The debate took place between Project Debater and Harish Natarajan, who holds the world record in number of debate competition victories. The motion was “We should subsidize preschools.” == That's Debatable Television Show == Project Debater was featured in a television series called “That’s Debatable” presented by Intelligence Squared U.S. Debates and Bloomberg Media. For each episode of “That’s Debatable,” Project Debater provided insight into three distinct debate topics on the redistribution of wealth, modern monetary theory, and a US-China space race. More than 5,000 arguments were submitted online from around the world across the three topics, which were then analyzed and distilled into key points that were highlighted on the television show and discussed by human debaters. == Artificial Intelligence Capabilities == To develop Project Debater, the IBM Research team had to endow the system with the following AI capabilities: Data-driven speech writing and delivery: Project Debater is the first demonstration of a computer that can digest massive corpora, and given a short description of a controversial topic, write a well-structured speech, and deliver it with clarity and purpose, while even incorporating humor where appropriate. Listening comprehension: the ability to identify the key concepts and claims hidden within long continuous spoken language. Four minutes of persuasive speech: the guarantee of producing four minutes of persuasive speech. Modeling human dilemmas: modeling the world of human controversy and dilemmas in a unique knowledge representation, enabling the system to suggest principled arguments as needed. An article on the project was published in Nature in March 2021.
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Federal Virtual World Challenge

The Federal Virtual Challenge, formerly The Federal Virtual Worlds Challenge is a competition led by the Simulation and Training Technology Center (United States Army Research, Development and Engineering Command). The event is conducted in order to reach a global development community that will create innovative and interactive training and analysis services in virtual worlds. The inaugural event began in 2009 with the awards being conducted during March 2010 GameTech conference in Orlando, Florida. == Description == The focus of the challenge is training or analysis capability conducted wholly in a virtual environment. The training and analysis audience includes all United States Federal Agencies including, Department of Defense, Department of Homeland Security, Department of Transportation, and Department of Health and Human Services, NASA, DOT, and many more.
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Paranoia (role-playing game)

Paranoia is a dystopian science-fiction tabletop role-playing game originally designed and written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and first published in 1984 by West End Games. Since 2004 the game has been published under license by Mongoose Publishing. The game won the Origins Award for Best Roleplaying Rules of 1984 and was inducted into the Origins Awards Hall of Fame in 2007. Paranoia is notable among tabletop games for being more competitive than co-operative, with players encouraged to betray one another for their own interests, as well as for keeping a light-hearted, tongue in cheek tone despite its dystopian setting. Several editions of the game have been published since the original version, and the franchise has spawned several spin-offs, novels and comic books based on the game. == Premise == The game is set in a dystopian future city controlled by the Computer (also known as "Friend Computer"), and where information (including the game rules) are restricted by color-coded "security clearance". Player characters are initially enforcers of the Computer's authority known as Troubleshooters, and are given missions to seek out and eliminate threats to the Computer's control. They are also part of prohibited underground movements, and have secret objectives including theft from and murder of other player characters. == Tone == Paranoia is a humorous role-playing game set in a dystopian future along the lines of Nineteen Eighty-Four, Brave New World, Logan's Run, and THX 1138; however, the tone of the game is rife with black humor, frequently tongue-in-cheek rather than dark and heavy. Most of the game's humor is derived from the players' (usually futile) attempts to complete their assignment while simultaneously adhering to the Computer's arbitrary, contradictory and often nonsensical security directives. The Paranoia rulebook is unusual in a number of ways; demonstrating any knowledge of the rules is forbidden, and most of the rulebook is written in an easy, conversational tone that often makes fun of the players and their characters, while occasionally taking digs at other notable role-playing games. === Setting === The game's main setting is an immense, futuristic city called Alpha Complex. Alpha Complex is controlled by the Computer, a civil service AI construct (a literal realization of the "Influencing Machine" that some schizophrenics fear). The Computer serves as the game's principal antagonist, and fears a number of threats to its 'perfect' society, such as the Outdoors, mutants, and secret societies (especially Communists). To deal with these threats, the Computer employs Troubleshooters, whose job is to go out, find trouble, and shoot it. Player characters are usually Troubleshooters, although later game supplements have allowed the players to take on other roles, such as High-Programmers of Alpha Complex. The player characters frequently receive mission instructions from the Computer that are incomprehensible, self-contradictory, or obviously fatal if adhered to, and side-missions (such as Mandatory Bonus Duties) that conflict with the main mission. Failing a mission generally results in termination of the player character, but succeeding can just as often result in the same fate, after being rewarded for successfully concluding the mission. They are issued equipment that is uniformly dangerous, faulty, or "experimental" (i.e., almost certainly dangerous and faulty). Additionally, each player character is generally an unregistered mutant and a secret society member (which are both termination offenses in Alpha Complex), and has a hidden agenda separate from the group's goals, often involving stealing from or killing teammates. Thus, missions often turn into a comedy of errors, as everyone on the team seeks to double-cross everyone else while keeping their own secrets. The game's manual encourages suspicion between players, offering several tips on how to make the gameplay as paranoid as possible. Every player's character is assigned six clones, known as a six-pack, which are used to replace the preceding clone upon his or her death. The game lacks a conventional health system; most wounds the player characters can suffer are assumed to be fatal. As a result, Paranoia allows characters to be routinely killed, yet the player can continue instead of leaving the game. This easy spending of clones tends to lead to frequent firefights, gruesome slapstick, and the horrible yet humorous demise of most if not all of the player character's clone family. Additional clones can be purchased if one gains sufficient favour with the Computer. === Security clearances === Paranoia features a security clearance system based on colors of the visible spectrum which heavily restricts what the players can and cannot legally do; everything from corridors to food and equipment have security restrictions. The lowest rating is Infrared, but the lowest playable security clearance is Red; the game usually begins with the characters having just been promoted to Red grade. Interfering with anything which is above that player's clearance carries significant risk. The full order of clearances from lowest to highest is Infrared (visually represented by black), Red, Orange, Yellow, Green, Blue, Indigo, Violet, and Ultraviolet (visually represented by white). Within the game, Infrared-clearance citizens live dull lives of mindless drudgery and are heavily medicated, while higher clearance characters may be allowed to demote or even summarily execute those of a lower rank and those with Ultraviolet clearance are almost completely unrestricted and have a great deal of access to the Computer; they are the only citizens that may (legally) access and modify the Computer's programming, and thus Ultraviolet citizens are also referred to as "High Programmers". Security clearance is not related to competence but is instead the result of the Computer's often insane and unjustified calculus of trust concerning a citizen. It is suggested that it may in fact be the High Programmers' meddling with The Computer's programming that resulted in its insanity. === Secret societies === In the game, secret societies tend to be based on sketchy and spurious knowledge of historical matters. For example, previous editions included societies such as the "Seal Club" that idolizes the Outdoors but is unsure what plants and animals actually look like. Other societies include the Knights of the Circular Object (based on the Knights of the Round Table), the Trekkies, and the First Church of Christ Computer Programmer. In keeping with the theme of paranoia, many secret societies have spies or double agents in each other's organizations. The first edition also included secret societies such as Programs Groups (the personal agents and spies of the High Programmers at the apex of Alpha Complex society) and Spy For Another Alpha Complex. The actual societies which would be encountered in a game depends on the play style; some societies are more suited for more light-hearted games (Zap-style, or the lighter end of Classic), whereas others represent a more serious threat to Alpha Complex and are therefore more suitable for Straight or the more dark sort of Classic games. == Publication history == Six editions have been published. Three of these were published by West End Games — the first, second, and fifth editions — whereas the later three editions (Paranoia XP, the 25th Anniversary edition and the "Red Clearance" edition) were published by Mongoose Publishing. In addition to these six published editions, it is known that West End Games were working on a third edition — to replace the poorly received fifth edition — in the late 1990s, but their financial issues would prevent this edition from being published, except for being included in one tournament adventure. === First edition === The first edition, was written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and published in 1984 by West End Games. In 1985, this edition of Paranoia won the Origins Award for Best Roleplaying Rules of 1984. This edition, while encouraging dark humour in-game, took a fairly serious dystopian tone; the supplements and adventures released to accompany it emphasised the lighter side, however, establishing the freewheeling mix of slapstick, intra-team backstabbing and satire that is classically associated with a game of Paranoia. === Second edition === The second edition, is credited to Costikyan, Gelber, Goldberg, Ken Rolston, and Paul Murphy, was published in 1987 by West End Games. This edition can be seen as a response to the natural development of the line towards a rules-light, fast and entertaining play style. Here, the humorous possibilities of life in a paranoid dystopia are emphasised, and the rules are simplified. ==== Metaplot and the second edition ==== Many of the supplements released for the second edition fall into a story arc set up by new writers and line editors
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Google Gadgets

Google Gadgets are dynamic web content that can be embedded on a web page. They can be added to and interact strongly with Google's iGoogle personalized home page (discontinued in November 2013, although iGoogle Gadgets still work on other websites) and the Google Desktop (discontinued in September 2011) application, as well as Google Wave (also no longer supported by Google) and Google Sites. Webmasters can add and customize a gadget to their own business or personal web site, a process called "syndication". Gadgets are developed by Google and third-party developers using the Google Gadgets API, using basic web technologies such as XML and JavaScript. == Multi-user persistent - Wave Gadgets == With the advent of Google Wave (now Apache Wave), gadgets became able to have persistent storage and multi-user capabilities and better state management. Gadgets using Google Wave in this way were simply known as 'Wave Gadgets'. For instance, a game written using a Google Gadget could use Google Wave technology to record a list of users and high scores without having to worry about how to permanently store the scores on a hosted server. The use of Google Wave would give the gadget multi-user and permanent storage capabilities. For example, scores could be stored in a Google Wave hosted permanently by Google at no cost to the user. As of early 2013, Google Gadgets were deprecated in Google Spreadsheets. Shortly after, they were removed from all spreadsheets. == Technology == Google Gadgets are written in XML and can have HTML and JavaScript components, and were able to use Google Wave. Here is an example of a Hello World program written using Google Gadget technology. Google Gadgets API is a Google API which allows developers to create Google Gadgets easily.
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Ideogram (text-to-image model)

Ideogram is a freemium text-to-image model developed by Ideogram, Inc. using deep learning methodologies to generate digital images from natural language descriptions known as prompts. The model is capable of generating legible text in the images compared to other text-to-image models. == History == Ideogram was founded in 2022 by Mohammad Norouzi, William Chan, Chitwan Saharia, and Jonathan Ho to develop a better text-to-image model. It was first released with its 0.1 model on August 22, 2023, after receiving $16.5 million in seed funding, which itself was led by Andreessen Horowitz and Index Ventures. In February 2024, Ideogram raised $80 million after its 1.0 model release in the same year. In August 2024, Ideogram released its 2.0 model. This model has several styles such as realistic, design, 3D, and anime and better capability in generating text. In February 2025, Ideogram released 2a model. This model was designed for speed and optimized for graphics design and photography generation. In March 2025, Ideogram released its 3.0 model. This model has improved realism and understanding of complex text layout, although like other generative AI models, it still struggles with ambigram creation.
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Fuzzy control system

A fuzzy control system is a control system based on fuzzy logic – a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectively). Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, such that that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans. == History and applications == Fuzzy logic was proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables", which in this article equates to a variable defined as a fuzzy set. Other research followed, with the first industrial application, a cement kiln built in Denmark, coming on line in 1976. Fuzzy systems were initially implemented in Japan. Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of Hitachi, who in 1985 provided simulations that demonstrated the feasibility of fuzzy control systems for the Sendai Subway. Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the Namboku Line opened in 1987. In 1987, Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an "inverted pendulum" experiment. This is a classic control problem, in which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth. Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases. Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field. Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering (LIFE), a cooperative arrangement between 48 companies to pursue fuzzy research. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years. Japanese consumer goods often incorporate fuzzy systems. Matsushita vacuum cleaners use microcontrollers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly. Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent. Canon developed an autofocusing camera that uses a charge-coupled device (CCD) to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot. The camera's fuzzy control system uses 12 inputs: 6 to obtain the current clarity data provided by the CCD and 6 to measure the rate of change of lens movement. The output is the position of the lens. The fuzzy control system uses 13 rules and requires 1.1 kilobytes of memory. An industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an inverter, a compressor valve, and a fan motor. Compared to the previous design, the fuzzy controller heats and cools five times faster, reduces power consumption by 24%, increases temperature stability by a factor of two, and uses fewer sensors. Other applications investigated or implemented include: character and handwriting recognition; optical fuzzy systems; robots, including one for making Japanese flower arrangements; voice-controlled robot helicopters (hovering is a "balancing act" rather similar to the inverted pendulum problem); rehabilitation robotics to provide patient-specific solutions (e.g. to control heart rate and blood pressure ); control of flow of powders in film manufacture; elevator systems; and so on. Work on fuzzy systems is also proceeding in North America and Europe, although on a less extensive scale than in Japan. The US Environmental Protection Agency has investigated fuzzy control for energy-efficient motors, and NASA has studied fuzzy control for automated space docking: simulations show that a fuzzy control system can greatly reduce fuel consumption. Firms such as Boeing, General Motors, Allen-Bradley, Chrysler, Eaton, and Whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors. In 1995 Maytag introduced an "intelligent" dishwasher based on a fuzzy controller and a "one-stop sensing module" that combines a thermistor, for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measures scattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate. The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water. It even adjusts for dried-on foods by tracking the last time the door was opened, and estimates the number of dishes by the number of times the door was opened. Xiera Technologies Inc. has developed the first auto-tuner for the fuzzy logic controller's knowledge base known as edeX. This technology was tested by Mohawk College and was able to solve non-linear 2x2 and 3x3 multi-input multi-output problems. Research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive "genetic" software systems, with the ultimate goal of building "self-learning" fuzzy-control systems. These systems can be employed to control complex, nonlinear dynamic plants, for example, human body. == Fuzzy sets == The input variables in a fuzzy control system are in general mapped by sets of membership functions similar to this, known as "fuzzy sets". The process of converting a crisp input value to a fuzzy value is called "fuzzification". The fuzzy logic based approach had been considered by designing two fuzzy systems, one for error heading angle and the other for velocity control. A control system may also have various types of switch, or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another. Given "mappings" of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form: IF brake temperature IS warm AND speed IS not very fast THEN brake pressure IS slightly decreased. In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have values like "static" or "slightly increased" or "slightly decreased" etc. === Fuzzy control in detail === Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. From three to seven curves are generally appropriate to cover the required range of an input value, or the "universe of discourse" in fuzzy jargon. As discussed earlier, the processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the "antecedent" and the THEN part is called the "consequent". Typical fuzzy
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SQLf

SQLf is a SQL extended with fuzzy set theory application for expressing flexible (fuzzy) queries to traditional (or ″Regular″) Relational Databases. Among the known extensions proposed to SQL, at the present time, this is the most complete, because it allows the use of diverse fuzzy elements in all the constructions of the language SQL. SQLf is the only known proposal of flexible query system allowing linguistic quantification over set of rows in queries, achieved through the extension of SQL nesting and partitioning structures with fuzzy quantifiers. It also allows the use of quantifiers to qualify the quantity of search criteria satisfied by single rows. Several mechanisms are proposed for query evaluation, the most important being the one based on the derivation principle. This consists in deriving classic queries that produce, given a threshold t, a t-cut of the result of the fuzzy query, so that the additional processing cost of using a fuzzy language is diminished. == Basic block == The fundamental querying structure of SQLf is the multi-relational block. The conception of this structure is based on the three basic operations of the relational algebra: projection, cartesian product and selection, and the application of fuzzy sets’ concepts. The result of a SQLf query is a fuzzy set of rows that is a fuzzy relation instead of a regular relation. A basic block in SQLf consists of a SELECT clause, a FROM clause and an optional WHERE clause. The semantic of this query structure is: The SELECT clause corresponds to the projection. It specifies the relations’ attributes (or attribute expressions) that will be selected. The resulting table is a fuzzy set and it is given in decreasing ordered of satisfaction degree. The SELECT clause specifies also a calibration that is intended to restrict the set of rows retrieved. There are two kinds of calibrations: quantitative and qualitative. In quantitative calibration the user specifies the number of results to be retrieved, so that the query will retrieve the rows with highest membership degrees up to the number of required answers. In qualitative calibration the user specifies a minim level of satisfaction that must have any retrieved row. The FROM clause corresponds to the Cartesian Product. The consult is made on the Cartesian Product of the relations that are specified in this clause. The WHERE clause corresponds to the selection. It specifies the condition for which the satisfaction degree will be calculated. Rows that do not satisfy at all the condition are rejected. This condition is a fuzzy predicate that may involve any attribute of the relations. The following is an example of a SELECT query that returns a list of hotels that are cheap. The query retrieves all rows from the Hotels table that satisfice the fuzzy predicate cheap defined by the fuzzy set μ=(∞, ∞, 25, 30). The result is sorted in descending order by the membership degree of the query.
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Tensor operator

In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ⁡ ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin ⁡ θ ℏ n ^ ⋅ J − 1 − cos ⁡ θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ⁡ ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ⁡ ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos ⁡ θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ⁡ ϕ sin ⁡ θ e x + s
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Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y
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European Conference on Artificial Intelligence

The European Conference on Artificial Intelligence (ECAI) is the leading conference in the field of Artificial Intelligence in Europe, and is commonly listed together with IJCAI and AAAI as one of the three major general AI conferences worldwide. The conference series has been held without interruption since 1974, originally under the name AISB. The conference was originally held biennially, but has been organized annually since ECAI 2022. The conferences are held under the auspices of the European Coordinating Committee for Artificial Intelligence (ECCAI) and organized by one of the member societies. The journal AI Communications, sponsored by the same society, regularly publishes special issues in which conference attendees report on the conference. Publication of a paper in ECAI is considered by some journals to be archival: the paper should be considered equivalent to a journal publication and that the contents of ECAI papers cannot be reformulated as separate journal submissions unless a significant amount of new material is added. == List of ECAI conferences == ECAI-1992 took place in Vienna, Austria. ECAI-1996 took place in Budapest, Hungary. ECAI-1998 tool place in Brighton, United Kingdom. ECAI-2000 took place in Berlin, Germany. ECAI-2004 took place in Valencia, Spain. ECAI-2006 took place in Riva del Garda, Italy. ECAI-2008 took place in Patras, Greece. ECAI-2010 took place in Lisbon, Portugal. ECAI-2012 took place in Montpellier, France. ECAI-2014 took place in Prague, Czech Republic. ECAI-2016 took place in The Hague, Netherlands. ECAI-2018 took place in Stockholm, Sweden. ECAI-2020 took place in Santiago de Compostela, Spain. ECAI-2022 took place in Vienna, Austria. ECAI-2023 took place in Kraków, Poland. ECAI-2024 took place in Santiago de Compostela, Spain. ECAI-2025 took place in Bologna, Italy.
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Hyperion Cantos

The Hyperion Cantos is a series of science fiction novels by Dan Simmons. The title was originally used for the collection of the first pair of books in the series, Hyperion and The Fall of Hyperion, and later came to refer to the overall storyline, including Endymion, The Rise of Endymion, and a number of short stories. More narrowly, inside the fictional storyline, after the first volume, the Hyperion Cantos is an epic poem written by the character Martin Silenus covering in verse form the events of the first two books. Of the four novels, Hyperion received the Hugo and Locus Awards in 1990; The Fall of Hyperion won the Locus and British Science Fiction Association Awards in 1991; and The Rise of Endymion received the Locus Award in 1998. All four novels were also nominated for various science fiction awards. == Works == === Hyperion (1989) === First published in 1989, Hyperion has the structure of a frame story, similar to Geoffrey Chaucer's Canterbury Tales and Giovanni Boccaccio's Decameron. The story weaves the interlocking tales of a diverse group of travelers sent on a pilgrimage to the Time Tombs on Hyperion. The travelers have been sent by the Hegemony (the government of the human star systems), the All Thing, and the Church of the Final Atonement, alternately known as the Shrike Church, to make a request of the Shrike. As they progress in their journey, each of the pilgrims tells their tale. === The Fall of Hyperion (1990) === This book concludes the story begun in Hyperion. It abandons the storytelling frame structure of the first novel, and is instead presented primarily as a series of dreams by John Keats. === Endymion (1996) === The story commences 274 years after the events in the previous novel. Few main characters from the first two books are present in the later two. The main character is Raul Endymion, an ex-soldier who receives a death sentence after an unfair trial. He is rescued by Martin Silenus and asked to perform a series of rather extraordinarily difficult tasks. The main task is to rescue and protect the daughter of Brawne Lamia (one of the main characters of Hyperion), Aenea, a messiah coming from the time period just after the first books via time travel. The Catholic Church has become a dominant force in the human universe and views Aenea as a potential threat to their power. The group of Aenea, Endymion, and A. Bettik (an android) evades the Church's forces on several worlds through use of the Consul's spaceship, ending the story on Earth. === The Rise of Endymion (1997) === This final novel in the series finishes the story begun in Endymion, expanding on the themes in Endymion, as Raul and Aenea battle the Church and meet their respective destinies. === Short stories === The series also includes three short stories: "Remembering Siri" (1983, included almost verbatim in Hyperion) "The Death of the Centaur" (1990) "Orphans of the Helix" (1999) == Development == The Hyperion universe originated when Simmons was an elementary school teacher, as an extended tale he told at intervals to his young students; this is recorded in "The Death of the Centaur", and its introduction. It then inspired his short story "Remembering Siri", which eventually became the nucleus around which Hyperion and The Fall of Hyperion formed. After the quartet was published came the short story "Orphans of the Helix". "Orphans" is currently the final work in the Cantos, both chronologically and internally. The original Hyperion Cantos has been described as a novel published in two volumes, published separately at first for reasons of length. In his introduction to "Orphans of the Helix", Simmons elaborates: Some readers may know that I've written four novels set in the "Hyperion Universe"—Hyperion, The Fall of Hyperion, Endymion, and The Rise of Endymion. A perceptive subset of those readers—perhaps the majority—know that this so-called epic actually consists of two long and mutually dependent tales, the two Hyperion stories combined and the two Endymion stories combined, broken into four books because of the realities of publishing. == Influences == Much of the appeal of the series stems from its extensive use of references and allusions from a wide array of thinkers such as Teilhard de Chardin, John Muir, Norbert Wiener, and to the poetry of John Keats, the famous 19th-century English Romantic poet, Norse mythology, and the monk Ummon. A large number of technological elements are acknowledged by Simmons to be inspired by elements of Out of Control: The New Biology of Machines, Social Systems, and the Economic World. The Hyperion series has many echoes of Jack Vance, explicitly acknowledged in one of the later books. The title of the first novel, "Hyperion", is taken from one of Keats's poems, the unfinished epic Hyperion. Similarly, the title of the third novel is from Keats' poem Endymion. Quotes from actual Keats poems and the fictional Cantos of Martin Silenus are interspersed throughout the novels. Simmons goes so far as to have two artificial reincarnations of John Keats ("cybrids": artificial intelligences in human bodies) play a major role in the series. == Setting == Much of the action in the series takes place on the planet Hyperion. It is described as having one-fifth less gravity than Earth standard. Hyperion has a number of peculiar indigenous flora and fauna, notably Tesla trees, which are essentially large electricity-spewing trees. It is also a "labyrinthine" planet, which means that it is home to ancient subterranean labyrinths of unknown purpose. Most importantly, Hyperion is the location of the Time Tombs, large artifacts surrounded by "anti-entropic" fields that allow them to move backward through time. In the fictional universe of the Hyperion Cantos, the Hegemony of Man encompasses over 200 planets. Faster than light communications technology, Fatlines, are said to operate through tachyon bursts. However, in later books it is revealed that they operate through the Void Which Binds. The Farcaster network was given to humanity by the TechnoCore and again it was another use of the Void Which Binds that allowed this instantaneous travel between worlds. The Hawking Drive was developed by human scientists, allowing the faster than light travel which led to the Hegira (from the Arabic word هجرة Hijra, meaning 'migration'). The Gideon drive, a Core-provided starship drive, allows for near-instantaneous travel between any two points in human-occupied space. The drive's use kills any human on board a Gideon-propelled starship; thus, the technology is only of use with remote probes or when used in conjunction with the Pax's resurrection technology. The resurrection creche can regenerate someone carrying a cruciform from their remains. Treeships are living trees that are propelled by ergs (spider-like solid-state alien being that emits force fields) through space. === The Shrike === The region of the Tombs is also the home of the Shrike, a menacing half-mechanical, half-organic four-armed creature that features prominently in the series. It appears in all four Hyperion Cantos books and is an enigma in the initial two; its purpose is not revealed until the second book, but is still left nebulous. The Shrike appears to act both autonomously and as a servant of some unknown force or entity. In the first two Hyperion books, it exists solely in the area around the Time Tombs on the planet Hyperion. Its portrayal is changed significantly in the last two books, Endymion and The Rise of Endymion. In these novels, the Shrike appears effectively unfettered and protects the heroine Aenea against assassins of the opposing TechnoCore. Surrounded in mystery, the object of fear, hatred, and even worship by members of the Church of the Final Atonement (the Shrike Cult), the Shrike's origins are described as uncertain. It is portrayed as composed of razorwire, thorns, blades, and cutting edges, having fingers like scalpels and long, curved toe blades. It has the ability to control the flow of time, and may thus appear to travel infinitely fast. The Shrike may kill victims in a flash or it may transport them to an eternity of impalement upon an enormous artificial 'Tree of Thorns,' or 'Tree of Pain' in Hyperion's distant future. The Tree of Thorns is described as an unimaginably large, metallic tree, alive with the agonized writhing of countless human victims of all ages and races. It is also hinted in the second book that the Tree of Thorns is actually a simulation generated by a mystical interface which connects to human brains via a strong and pulsing (as if it were alive) cord. The name Shrike seems a reference to birds of the shrike family, a family of birds that impales their victims on thorns, spines, or twigs. === Worlds and Systems === In the fictional universe of the Hyperion Cantos, the Hegemony of Man encompasses over 200 planets. The following planets appear or are specifically mentioned in the Hyperion Cantos. Planets of
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Brill tagger

The Brill tagger is an inductive method for part-of-speech tagging. It was described and invented by Eric Brill in his 1993 PhD thesis. It can be summarized as an "error-driven transformation-based tagger". It is: a form of supervised learning, which aims to minimize error; and, a transformation-based process, in the sense that a tag is assigned to each word and changed using a set of predefined rules. In the transformation process, if the word is known, it first assigns the most frequent tag, or if the word is unknown, it naively assigns the tag "noun" to it. High accuracy is eventually achieved by applying these rules iteratively and changing the incorrect tags. This approach ensures that valuable information such as the morphosyntactic construction of words is employed in an automatic tagging process. == Algorithm == The algorithm starts with initialization, which is the assignment of tags based on their probability for each word (for example, "dog" is more often a noun than a verb). Then "patches" are determined via rules that correct (probable) tagging errors made in the initialization phase: Initialization: Known words (in vocabulary): assigning the most frequent tag associated to a form of the word Unknown word == Rules and processing == The input text is first tokenized, or broken into words. Typically in natural language processing, contractions such as "'s", "n't", and the like are considered separate word tokens, as are punctuation marks. A dictionary and some morphological rules then provide an initial tag for each word token. For example, a simple lookup would reveal that "dog" may be a noun or a verb (the most frequent tag is simply chosen), while an unknown word will be assigned some tag(s) based on capitalization, various prefix or suffix strings, etc. (such morphological analyses, which Brill calls Lexical Rules, may vary between implementations). After all word tokens have (provisional) tags, contextual rules apply iteratively, to correct the tags by examining small amounts of context. This is where the Brill method differs from other part of speech tagging methods such as those using Hidden Markov Models. Rules are reapplied repeatedly, until a threshold is reached, or no more rules can apply. Brill rules are of the general form: tag1 → tag2 IF Condition where the Condition tests the preceding and/or following word tokens, or their tags (the notation for such rules differs between implementations). For example, in Brill's notation: IN NN WDPREVTAG DT while would change the tag of a word from IN (preposition) to NN (common noun), if the preceding word's tag is DT (determiner) and the word itself is "while". This covers cases like "all the while" or "in a while", where "while" should be tagged as a noun rather than its more common use as a conjunction (many rules are more general). Rules should only operate if the tag being changed is also known to be permissible, for the word in question or in principle (for example, most adjectives in English can also be used as nouns). Rules of this kind can be implemented by simple Finite-state machines. See Part of speech tagging for more general information including descriptions of the Penn Treebank and other sets of tags. Typical Brill taggers use a few hundred rules, which may be developed by linguistic intuition or by machine learning on a pre-tagged corpus. == Code == Brill's code pages at Johns Hopkins University are no longer on the web. An archived version of a mirror of the Brill tagger at its latest version as it was available at Plymouth Tech can be found on Archive.org. The software uses the MIT License.
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Whisper (speech recognition system)

Whisper is a machine learning model for speech recognition and transcription, created by OpenAI and first released as open-source software in September 2022. It is capable of transcribing speech in English and multiple other languages, and can translate several non-English languages into English. Whisper is a weakly-supervised deep learning acoustic model, made using an encoder-decoder transformer architecture. OpenAI claims that the combination of different training data and post-training filtering used in its development has led to improved recognition of accents, background noise, and jargon compared to previous approaches. While the model does not outperform larger, more specialized models and still experiences AI hallucination, it has been showed to be useful for general sound recognition and has many applications across different industries. == Background == Speech recognition has had a long history in research; the first approaches made use of statistical methods, such as dynamic time warping, and later hidden Markov models. At around the 2010s, deep neural network approaches became more common for speech recognition models, which were enabled by the availability of large datasets ("big data") and increased computational performance. Early approaches to deep learning in speech recognition included convolutional neural networks, which were limited due to their inability to capture sequential data, which later led to developments of Seq2seq approaches, which include recurrent neural networks, which made use of long short-term memory. Transformers, introduced in 2017 by Google, displaced many prior state-of-the-art approaches across a wide range in machine learning, and started becoming the core neural architecture in fields such as language modeling and computer vision. Weakly-supervised approaches to training acoustic models were recognized in the early 2020s as promising for speech recognition approaches using deep neural networks. According to a NYT report, in 2021 OpenAI believed they exhausted sources of higher-quality data to train their large language models and decided to complement scraped web text with transcriptions of YouTube videos and podcasts, and developed Whisper to solve this task. Whisper Large V2 was released on December 8, 2022, followed by Whisper Large V3 being released in November 2023, during the OpenAI Dev Day. In March 2025, OpenAI released new transcription models based on GPT-4o and GPT-4o mini, both of which have lower error rates than Whisper. == Architecture == The Whisper architecture is based on an encoder-decoder transformer. Input audio is resampled to 16,000 Hertz (Hz) and converted to an 80-channel Log-magnitude Mel spectrogram using 25 ms windows with a 10 ms stride. The spectrogram is then normalized to a [-1, 1] range with near-zero mean. The encoder takes this Mel spectrogram as input and processes it. It first passes through two convolutional layers. Sinusoidal positional embeddings are added. It is then processed by a series of Transformer encoder blocks (with pre-activation residual connections). The encoder's output is layer normalized. The decoder is a standard transformer decoder. It has the same width and Transformer blocks as the encoder. It uses learned positional embeddings and tied input-output token representations (using the same weight matrix for both the input and output embeddings). It uses a byte-pair encoding tokenizer, of the same kind as used in GPT-2. English-only models use the GPT-2 vocabulary, while multilingual models employ a re-trained multilingual vocabulary with the same number of words. Special tokens are used to allow the decoder to perform multiple tasks: Tokens that denote language (one unique token per language). Tokens that specify task (<|transcribe|> or <|translate|>). Tokens that specify if no timestamps are present (<|notimestamps|>). If the token is not present, then the decoder predicts timestamps relative to the segment, and quantized to 20 ms intervals. <|nospeech|> for voice activity detection. <|startoftranscript|>, and <|endoftranscript|> . Any text that appears before <|startoftranscript|> is not generated by the decoder, but given to the decoder as context. Loss is only computed over non-contextual parts of the sequence, i.e. tokens between these two special tokens. == Training data == The training dataset consists of 680,000 hours of labeled audio-transcript pairs sourced from the internet using semi-supervised learning. This includes 117,000 hours in 96 non-English languages and 125,000 hours of X→English translation data, where X stands for any non-English language. Preprocessing involved standardization of transcripts, filtering to remove machine-generated transcripts using heuristics (e.g., punctuation, capitalization), language identification and matching with transcripts, fuzzy deduplication, and deduplication with evaluation datasets to avoid data contamination. Speechless segments were also included to allow voice activity detection training. For the files still remaining after the filtering process, audio files were then broken into 30-second segments paired with the subset of the transcript that occurs within that time. If this predicted spoken language differed from the language of the text transcript associated with the audio, that audio-transcript pair was not used for training the speech recognition models, but instead for training translation. The model was trained using the AdamW optimizer with gradient norm clipping and a linear learning rate decay with warmup, with batch size 256 segments. Training proceeded for 1 million updates (approximately 2-3 epochs). No data augmentation or regularization, except for the Large V2 model, which used SpecAugment, Stochastic Depth, and BPE Dropout. The training used data parallelism with float16, dynamic loss scaling, and activation checkpointing. === Post-training filtering === After training the first model, researchers ran it on different subsets of the training data, each representing a distinct source. Data sources were ranked by a combination of their error rate and size. Manual inspection of the top-ranked sources (high error, large size) helped determine if the source was low quality (e.g., partial transcriptions, inaccurate alignment). After training, it was fine-tuned to suppress the prediction of speaker names and low-quality sources were then removed. == Capacity == While Whisper does not outperform models which specialize in the LibriSpeech dataset, when tested across many datasets, it is more robust and makes 55.2% fewer errors than other models. Whisper has a differing error rate with respect to transcribing different languages, with a higher word error rate in languages not well-represented in the training data. The authors found that multi-task learning improved overall performance compared to models specialized to one task. They conjectured that the best Whisper model trained is still underfitting the dataset, and larger models and longer training can result in better models. Third-party evaluations have found varying levels of AI hallucination. A study of transcripts of public meetings found hallucinations in eight out of every 10 transcripts, while an engineer discovered hallucinations in "about half" of 100 hours of transcriptions and a developer identified them in "nearly every one" of 26,000 transcripts. A study of 13,140 short audio segments (averaging 10 seconds) found 187 hallucinations (1.4%), 38% of which generated text that could be harmful because it inserted false references to things like race, non-existent medications, or violent events that were not in the audio. == Applications == The model has been used as the base for many applications, such as a unified model for speech recognition and more general sound recognition. Whisper has also been integrated into the workflow of biomedical research. In 2025, a study on Alzheimer's disease detection used the model to transcribe spontaneous speech recordings. The transcripts that were generated by the model were combined with LLM vector embeddings and traditional classifiers to help classify the patients' health. Another application is when OVALYTICS incorporated Whisper to transcribe YouTube videos and automate content moderation systems, which improved its detection of offensive content. The model has also been used in academic libraries and cultral heritage institutions to generate transcripts and captions for their digitized audiovisual collections. In a 2025 case study, Emory University Libraries found that Whisper reduced the labor used in transcription by around 30-35%, shifting work from text creation to text correction. However, human review is still necessary to make sure accuracy, formatting, and accessibility are all standard.
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Fuzzy finite element

The fuzzy finite element method combines the well-established finite element method with the concept of fuzzy numbers, the latter being a special case of a fuzzy set. The advantage of using fuzzy numbers instead of real numbers lies in the incorporation of uncertainty (on material properties, parameters, geometry, initial conditions, etc.) in the finite element analysis. One way to establish a fuzzy finite element (FE) analysis is to use existing FE software (in-house or commercial) as an inner-level module to compute a deterministic result, and to add an outer-level loop to handle the fuzziness (uncertainty). This outer-level loop comes down to solving an optimization problem. If the inner-level deterministic module produces monotonic behavior with respect to the input variables, then the outer-level optimization problem is greatly simplified, since in this case the extrema will be located at the vertices of the domain.
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