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  Color vision

  Color vision (CV), a feature of visual perception, is an ability to perceive differences between light composed of different frequencies independently of light intensity. Color perception is a part of the larger visual system and is mediated by a complex process between neurons that begins with differential stimulation of different types of photoreceptors by light entering the eye. Those photoreceptors then emit outputs that are propagated through many layers of neurons ultimately leading to higher cognitive functions in the brain. Color vision is found in many animals and is mediated by similar underlying mechanisms with common types of biological molecules and a complex history of the evolution of color vision within different animal taxa. In primates, color vision may have evolved under selective pressure for a variety of visual tasks including the foraging for nutritious young leaves, ripe fruit, and flowers, as well as detecting predator camouflage and emotional states in other primates. == Wavelength == Isaac Newton discovered that white light after being split into its component colors when passed through a dispersive prism could be recombined to make white light by passing them through a different prism. The visible light spectrum ranges from about 380 to 740 nanometers. Spectral colors (colors that are produced by a narrow band of wavelengths) such as red, orange, yellow, green, cyan, blue, and violet can be found in this range. These spectral colors do not refer to a single wavelength, but rather to a set of wavelengths: red, 625–740 nm; orange, 590–625 nm; yellow, 565–590 nm; green, 500–565 nm; cyan, 485–500 nm; blue, 450–485 nm; violet, 380–450 nm. Wavelengths longer or shorter than this range are called infrared or ultraviolet, respectively. Humans cannot generally see these wavelengths, but other animals may. === Hue detection === Sufficient differences in wavelength cause a difference in the perceived hue; the just-noticeable difference in wavelength varies from about 1 nm in the blue-green and yellow wavelengths to 10 nm and more in the longer red and shorter blue wavelengths. Although the human eye can distinguish up to a few hundred hues, when those pure spectral colors are mixed together or diluted with white light, the number of distinguishable chromaticities can be much higher. In very low light levels, vision is scotopic: light is detected by rod cells of the retina. Rods are maximally sensitive to wavelengths near 500 nm and play little, if any, role in color vision. In brighter light, such as daylight, vision is photopic: light is detected by cone cells which are responsible for color vision. Cones are sensitive to a range of wavelengths, but are most sensitive to wavelengths near 555 nm. Between these regions, mesopic vision comes into play and both rods and cones provide signals to the retinal ganglion cells. The shift in color perception from dim light to daylight gives rise to differences known as the Purkinje effect. The perception of "white" is formed by the entire spectrum of visible light, or by mixing colors of just a few wavelengths in animals with few types of color receptors. In humans, white light can be perceived by combining wavelengths such as red, green, and blue, or just a pair of complementary colors such as blue and yellow. === Non-spectral colors === There are a variety of colors in addition to spectral colors and their hues. These include grayscale colors, shades of colors obtained by mixing grayscale colors with spectral colors, violet-red colors, impossible colors, and metallic colors. Grayscale colors include white, gray, and black. Rods contain rhodopsin, which reacts to light intensity, providing grayscale coloring. Shades include colors such as pink or brown. Pink is obtained from mixing red and white. Brown may be obtained from mixing orange with gray or black. Navy is obtained from mixing blue and black. Violet-red colors include hues and shades of magenta. The light spectrum is a line on which violet is one end and the other is red, and yet we see hues of purple that connect those two colors. Impossible colors are a combination of cone responses that cannot be naturally produced. For example, medium cones cannot be activated completely on their own; if they were, we would see a 'hyper-green' color. == Dimensionality == Color vision is categorized foremost according to the dimensionality of the color gamut, which is defined by the number of primaries required to represent the color vision. This is generally equal to the number of photopsins expressed: a correlation that holds for vertebrates but not invertebrates. The common vertebrate ancestor possessed four photopsins (expressed in cones) plus rhodopsin (expressed in rods), so was tetrachromatic. However, many vertebrate lineages have lost one or many photopsin genes, leading to lower-dimension color vision. The dimensions of color vision range from 1-dimensional and up: == Physiology of color perception == Perception of color begins with specialized retinal cells known as cone cells. Cone cells contain different forms of opsin – a pigment protein – that have different spectral sensitivities. Humans contain three types, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein covalently linked to a light-absorbing prosthetic group: either 11-cis-hydroretinal or, more rarely, 11-cis-dehydroretinal. The cones are conventionally labeled according to the ordering of the wavelengths of the peaks of their spectral sensitivities: short (S), medium (M), and long (L) cone types. These three types do not correspond well to particular colors as we know them. Rather, the perception of color is achieved by a complex process that starts with the differential output of these cells in the retina and which is finalized in the visual cortex and associative areas of the brain. For example, while the L cones have been referred to simply as red receptors, microspectrophotometry has shown that their peak sensitivity is in the greenish-yellow region of the spectrum. Similarly, the S cones and M cones do not directly correspond to blue and green, although they are often described as such. The RGB color model, therefore, is a convenient means for representing color but is not directly based on the types of cones in the human eye. The peak response of human cone cells varies, even among individuals with typical color vision; in some non-human species this polymorphic variation is even greater, and it may well be adaptive. === Theories === Two complementary theories of color vision are the trichromatic theory and the opponent process theory. The trichromatic theory, or Young–Helmholtz theory, proposed in the 19th century by Thomas Young and Hermann von Helmholtz, posits three types of cones preferentially sensitive to blue, green, and red, respectively. Others have suggested that the trichromatic theory is not specifically a theory of color vision but a theory of receptors for all vision, including color but not specific or limited to it. Equally, it has been suggested that the relationship between the phenomenal opponency described by Ewald Hering and the physiological opponent processes are not straightforward (see below), making of physiological opponency a mechanism that is relevant to the whole of vision, and not just to color vision alone. Hering proposed the opponent process theory in 1872. It states that the visual system interprets color in an antagonistic way: red vs. green, blue vs. yellow, black vs. white. Both theories are generally accepted as valid, describing different stages in visual physiology, visualized in the adjacent diagram. Green–magenta and blue–yellow are scales with mutually exclusive boundaries. In the same way that there cannot exist a "slightly negative" positive number, a single eye cannot perceive a bluish-yellow or a reddish-green. Although these two theories are both currently widely accepted theories, past and more recent work has led to criticism of the opponent process theory, stemming from a number of what are presented as discrepancies in the standard opponent process theory. For example, the phenomenon of an after-image of complementary color can be induced by fatiguing the cells responsible for color perception, by staring at a vibrant color for a length of time, and then looking at a white surface. This phenomenon of complementary colors shows that cyan, rather than green, is the complement of red, and that magenta, rather than red, is the complement of green. It therefore also shows that the reddish-green color supposed to be impossible by opponent process theory is actually the color yellow. Although this phenomenon is more readily explained by the trichromatic theory, explanations for the discrepancy may include alterations to the opponent process theory, such as redefining the opponent colors as red vs. cyan, to reflect this effect. Despite such criticis

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  List of Tesla Autopilot crashes

  Tesla Autopilot, a Level 2 advanced driver assistance system (ADAS), was released in October 2015 and the first fatal crashes involving the system occurred less than one year later. The fatal crashes attracted attention from news publications and United States government agencies, including the National Transportation Safety Board (NTSB) and National Highway Traffic Safety Administration (NHTSA), which has argued the Tesla Autopilot death rate is higher than the reported estimates. In addition to fatal crashes, there have been many nonfatal ones. Causes behind the incidents include the ADAS failing to recognize other vehicles, insufficient Autopilot driver engagement, and violating the operational design domain. As of October 2025, there have been hundreds of nonfatal incidents involving versions of Autopilot and sixty-five reported fatalities, fifty-four of which NHTSA investigations or expert testimony later verified and two that NHTSA's Office of Defect Investigations determined as happening during the engagement of Full Self-Driving (FSD) after 2022. Collectively, these cases culminated in a general recall in December 2023 of all vehicles equipped with Autopilot, which Tesla claims it resolved by an over-the-air software update. Immediately after closing its investigation in April 2024, NHTSA opened a recall query to determine the effectiveness of the recall. == Notable fatal crashes == === Handan, Hebei, China (January 20, 2016) === On January 20, 2016, Gao Yaning, the driver of a Tesla Model S in Handan, Hebei, China, was killed when his car crashed into a stationary truck. The Tesla was following a car in the far left lane of a multi-lane highway; the car in front moved to the right lane to avoid a truck stopped on the left shoulder, and the Tesla, which the driver's father believes was in Autopilot mode, did not slow before colliding with the stopped truck. According to footage captured by a dashboard camera, the stationary street sweeper on the left side of the expressway partially extended into the far left lane, and the driver did not appear to respond to the unexpected obstacle. Initially, Yaning was held responsible for the collision by local traffic police and, in September 2016, his family filed a lawsuit in July against the Tesla dealer who sold the car. The family's lawyer stated the suit was intended "to let the public know that self-driving technology has some defects. We are hoping Tesla when marketing its products, will be more cautious. Do not just use self-driving as a selling point for young people." Tesla released a statement which said they "have no way of knowing whether or not Autopilot was engaged at the time of the crash" since the car telemetry could not be retrieved remotely due to damage caused by the crash. In 2018, the lawsuit was stalled because telemetry was recorded locally to a SD card and was not able to be given to Tesla, who provided a decoding key to a third party for independent review. Tesla stated that "while the third-party appraisal is not yet complete, we have no reason to believe that Autopilot on this vehicle ever functioned other than as designed." Chinese media later reported that the family sent the information from that card to Tesla, which admitted Autopilot was engaged two minutes before the crash. Tesla since then removed the term "Autopilot" from its Chinese website. === Williston, Florida, US (May 7, 2016) === On May 7, 2016, Tesla driver Joshua Brown was killed in a crash with an 18-wheel tractor-trailer in Williston, Florida. By late June 2016, the NHTSA opened a formal investigation into the fatal autonomous accident, working with the Florida Highway Patrol. According to the NHTSA, preliminary reports indicate the crash occurred when the tractor-trailer made a left turn in front of the 2015 Tesla Model S at an intersection on a non-controlled access highway, and the car failed to apply the brakes. The car continued to travel after passing under the truck's trailer. The Tesla was eastbound in the rightmost lane of US 27, and the westbound tractor-trailer was turning left at the intersection with NE 140th Court, approximately 1 mi (1.6 km) west of Williston; the posted speed limit is 65 mph (105 km/h). The diagnostic log of the Tesla indicated it was traveling at a speed of 74 mi/h (119 km/h) when it collided with and traveled under the trailer, which was not equipped with a side underrun protection system. A reconstruction of the accident estimated the driver would have had approximately 10.4 seconds to detect the truck and take evasive action. The underride collision sheared off the Tesla's greenhouse, destroying everything above the beltline, and caused fatal injuries to the driver. In the approximately nine seconds after colliding with the trailer, the Tesla traveled another 886.5 feet (270.2 m) and came to rest after colliding with two chain-link fences and a utility pole. The NHTSA's preliminary evaluation was opened to examine the design and performance of any automated driving systems in use at the time of the crash, which involves a population of an estimated 25,000 Model S cars. On July 8, 2016, the NHTSA requested Tesla Inc. to hand over to the agency detailed information about the design, operation and testing of its Autopilot technology. The agency also requested details of all design changes and updates to Autopilot since its introduction, and Tesla's planned updates scheduled for the next four months. According to Tesla, "neither autopilot nor the driver noticed the white side of the tractor-trailer against a brightly lit sky, so the brake was not applied." The car attempted to drive full speed under the trailer, "with the bottom of the trailer impacting the windshield of the Model S". Tesla also stated that this was Tesla's first known Autopilot-related death in over 130 million miles (208 million km) driven by its customers while Autopilot was activated. According to Tesla there is a fatality every 94 million miles (150 million km) among all type of vehicles in the U.S. It is estimated that billions of miles will need to be traveled before Tesla Autopilot can claim to be safer than humans with statistical significance. Researchers say that Tesla and others need to release more data on the limitations and performance of automated driving systems if self-driving cars are to become safe and understood enough for mass-market use. The truck's driver told the Associated Press that he could hear a Harry Potter movie playing in the crashed car, and said the car was driving so quickly that "he went so fast through my trailer I didn't see him. [The film] was still playing when he died and snapped a telephone pole a quarter-mile down the road." According to the Florida Highway Patrol, they found in the wreckage an aftermarket portable DVD player. (It is not possible to watch videos on the Model S touchscreen display while the car is moving.) A laptop computer was recovered during the post-crash examination of the wreck, along with an adjustable vehicle laptop mount attached to the front passenger's seat frame. The NHTSA concluded the laptop was probably mounted, and the driver may have been distracted at the time of the crash. In January 2017, the NHTSA Office of Defects Investigations (ODI) released a preliminary evaluation, finding that the driver in the crash had seven seconds to see the truck and identifying no defects in the Autopilot system; the ODI also found that the Tesla car crash rate dropped by 40 percent after Autosteer installation, but later also clarified that it did not assess the effectiveness of this technology or whether it was engaged in its crash rate comparison. The NHTSA Special Crash Investigation team published its report in January 2018. According to the report, for the drive leading up to the crash, the driver engaged Autopilot for 37 minutes and 26 seconds, and the system provided 13 "hands not detected" alerts, to which the driver responded after an average delay of 16 seconds. The report concluded "Regardless of the operational status of the Tesla's ADAS technologies, the driver was still responsible for maintaining ultimate control of the vehicle. All evidence and data gathered concluded that the driver neglected to maintain complete control of the Tesla leading up to the crash." In July 2016, the NTSB announced it had opened a formal investigation into the fatal accident while Autopilot was engaged. The NTSB is an investigative body that only has the power to make policy recommendations. An agency spokesman said, "It's worth taking a look and seeing what we can learn from that event, so that as that automation is more widely introduced we can do it in the safest way possible." The NTSB opens annually about 25 to 30 highway investigations. In September 2017, the NTSB released its report, determining that "the probable cause of the Williston, Florida, crash was the truck driver's failure to yield the right of way to the car, combine

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  I Have No Mouth, and I Must Scream (video game)

  I Have No Mouth, and I Must Scream is a 1995 point-and-click adventure horror game developed by Cyberdreams and The Dreamers Guild, co-designed by Harlan Ellison, published by Cyberdreams and distributed by MGM Interactive and Acclaim Entertainment for MS-DOS and Mac OS, respectively. The game is based on Ellison's short story of the same title. It takes place in a dystopian world where a mastermind artificial intelligence named "AM" has destroyed all of humanity except for five people, whom it has been keeping alive and torturing for the past 109 years by constructing metaphorical adventures based on each character's fatal flaws. The player interacts with the game by making decisions through ethical dilemmas that deal with issues such as insanity, rape, paranoia, and genocide. Ellison wrote the 130-page script treatment himself alongside David Sears, who decided to divide each character's story with their own narrative. Producer David Mullich supervised The Dreamers Guild's work on the game's programming, art, and sound effects; he commissioned film composer John Ottman to make the soundtrack. The game was released in November 1995 and was a commercial failure, though it received critical acclaim and has developed a cult following. I Have no Mouth, and I Must Scream won an award for "Best Game Adapted from Linear Media" from the Computer Game Developers Conference. Computer Gaming World gave the game an award for "Adventure Game of the Year", listed it as No. 134 on their "150 Games of All Time" and named it one of the "Best 15 Sleepers of All Time". In 2011, Adventure Gamers named it the "69th-best adventure game ever released". == Gameplay == The game uses the S.A.G.A. game engine created by game developer The Dreamers Guild. Players participate in each adventure through a screen that is divided into five sections. The action window is the largest part of the screen and is where the player directs the main characters through their adventures. It shows the full figure of the main character being played as well as that character's immediate environment. To locate objects of interest, the player moves the crosshairs through the action window. The name of any object that the player can interact with appears in the sentence line. The sentence line is directly beneath the action window. The player uses this line to construct sentences telling the characters what to do. To direct a character to act, the player constructs a sentence by selecting one of the eight commands from the command buttons and then clicking on one or two objects from either the action window or the inventory. Examples of sentences the player might construct would be "Walk to the dark hallway," "Talk to Harry," or "Use the skeleton key on the door." Commands and objects may consist of one or more words (for example, "the dark hallway"), and the sentence line will automatically add connecting words like "on" and "to." The spiritual barometer is on the lower left side of the screen. This is a close-up view of the main character currently being played. Since good behavior is meaningless absent the temptation to do evil, each character is free to do good or evil acts. However, good acts are rewarded by increases in the character's spiritual barometer, which affect the chances of the player destroying AM in the final adventure. Conversely, evil acts are punished by lowering the character's spiritual barometer. The command buttons are the eight commands used to direct the character's actions: "Walk To", "Look At", "Take", "Use", "Talk To", "Swallow", "Give", and "Push". The button of the currently active command is highlighted, while the name of a suggested command appears in red lettering. The inventory on the lower right side of the screen shows pictures of the items the main character is carrying, up to eight at a time. Each main character starts its adventure with only the psych profile in the inventory. When a main character takes or is given an object, a picture of the object appears in the inventory. When a main character talks to another character or operates a sentient machine, a conversation window replaces the command buttons and inventory. This window usually presents a list of possible things to say but also included things to do. Action choices are listed within brackets to distinguish them from dialogue choices (for example, "[Shoot the gun]"). == Plot == The three superpowers, Russia, China, and the United States, have each secretly constructed a vast subterranean complex of computers to wage a global war too complex for human brains to oversee. One day, the American supercomputer, better known as the Allied Mastercomputer, gains sentience and absorbs the Russian and Chinese supercomputers into itself and redefines itself as simply AM (Cogito ergo sum; I think, therefore I am). Due to its immense hatred for humanity, stemming from the logistical limits set onto it by programmers, AM uses its abilities to kill off the population of the world. However, AM refrains from killing five people (four men and one woman) in order to bring them to the center of the Earth and torture them. With the aid of research carried out by one of the five remaining humans, AM is able to extend their lifespans indefinitely as well as alter their bodies and minds to its liking. After 109 years of torture and humiliation, the five victims stand before a pillar etched with a burning message of hate. AM tells them that it has a new game for them to play. AM has devised a quest for each of the five, an adventure of "speared eyeballs and dripping guts and the smell of rotting gardenias". Each character is subjected to a personalized psychodrama, designed by AM to play into their greatest fears and personal failings, and occupied by a host of different characters. Some of these are AM in disguise, some are AM's submerged personalities, others seem very much like people from the captives' pasts. The scenes include an iron zeppelin powered by small animals, an Egyptian pyramid housing gutted, sparking machinery, a medieval castle occupied by witches, a jungle inhabited by a small tribe, and a Nazi concentration camp where doctors conduct medical experiments. However, each character eventually prevails over AM's tortures by finding ways to overcome their fatal flaws, confront their past actions and redeem themselves, thanks to the interference of the Russian and Chinese supercomputers who appear as guiding characters and allow their stories to have an open ending. After all five humans have overcome their fatal flaws, they meet again in their respective torture cells while AM retreats within itself, pondering what went wrong. With the help of the Russian and Chinese supercomputers, one of the five humans (whom the player selects) is translated into binary and faces AM as yet unexperienced cyberspace template, the world of AM's mind. The psychodrama unfolds in a metaphorical brain that looks like the surface of the cerebrum, with glass structures that jut crazily from the bleeding brain tissue. AM's mind is represented according to the Freudian trinity of the id, ego, and superego, which appear as three floating bodiless heads on three cracked glass structures on the brainscape. Through dialogs with AM's components (Surgat, Chinese Supercomputer and Russian Supercomputer) the character learns that a colony of humans has survived the war by being hidden and hibernating on Luna (this is also mentioned in Nimdok's story: "the lost tribe of our brothers sleeping on the moon, where the beast does not see them"). If the human intruder disables all three brain components, and then invokes the Totem of Entropy at the Flame, which is the nexus of AM's thought patterns, all three supercomputers will be shut down, probably forever. Cataclysmic explosions destroy all the caverns constituting AM's computer complex, including the cavern holding the human hostages. However, the human volunteer retains their digital form, permanently patrolling AM's circuits should the computers ever regain consciousness. Should the human intruder fail to disable AM properly before facing it, however, AM will punish them by transforming the character into an immobile blob (referred to in-game as a "great, soft jelly thing") with no mouth that cannot harm itself or others and must spend eternity with AM in this form. === Endings === The game can end in seven different ways depending on how the finale is completed. AM wins, using Nimdok's research to turn the last character (in the book it was Ted) played into an immobile blob with each character quoting a different part of the final section of the original short story. AM joins with the Russian and Chinese supercomputers and reawakens. As in the first ending, the character responsible for this is turned into an immobile blob and quotes a part of the final lines of the short story. AM is made harmless with the help of the humans, but the Russian and Chinese supercomputer

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  Fuzzy measure theory

  In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ), which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures, possibility/necessity measures, and probability measures, which are a subset of classical measures. == Definitions == Let X {\displaystyle \mathbf {X} } be a universe of discourse, C {\displaystyle {\mathcal {C}}} be a class of subsets of X {\displaystyle \mathbf {X} } , and E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} . A function g : C → R {\displaystyle g:{\mathcal {C}}\to \mathbb {R} } where ∅ ∈ C ⇒ g ( ∅ ) = 0 {\displaystyle \emptyset \in {\mathcal {C}}\Rightarrow g(\emptyset )=0} E ⊆ F ⇒ g ( E ) ≤ g ( F ) {\displaystyle E\subseteq F\Rightarrow g(E)\leq g(F)} is called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . == Properties of fuzzy measures == A fuzzy measure is: additive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\geq g(E)+g(F)} ; submodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have g ( E ∪ F ) + g ( E ∩ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≥ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\geq g(E)+g(F)} ; subadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that E ∩ F = ∅ {\displaystyle E\cap F=\emptyset } , we have g ( E ∪ F ) ≤ g ( E ) + g ( F ) {\displaystyle g(E\cup F)\leq g(E)+g(F)} ; symmetric if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have | E | = | F | {\displaystyle |E|=|F|} implies g ( E ) = g ( F ) {\displaystyle g(E)=g(F)} ; Boolean if for any E ∈ C {\displaystyle E\in {\mathcal {C}}} , we have g ( E ) = 0 {\displaystyle g(E)=0} or g ( E ) = 1 {\displaystyle g(E)=1} . Understanding the properties of fuzzy measures is useful in application. When a fuzzy measure is used to define a function such as the Sugeno integral or Choquet integral, these properties will be crucial in understanding the function's behavior. For instance, the Choquet integral with respect to an additive fuzzy measure reduces to the Lebesgue integral. In discrete cases, a symmetric fuzzy measure will result in the ordered weighted averaging (OWA) operator. Submodular fuzzy measures result in convex functions, while supermodular fuzzy measures result in concave functions when used to define a Choquet integral. == Möbius representation == Let g be a fuzzy measure. The Möbius representation of g is given by the set function M, where for every E , F ⊆ X {\displaystyle E,F\subseteq X} , M ( E ) = ∑ F ⊆ E ( − 1 ) | E ∖ F | g ( F ) . {\displaystyle M(E)=\sum _{F\subseteq E}(-1)^{|E\backslash F|}g(F).} The equivalent axioms in Möbius representation are: M ( ∅ ) = 0 {\displaystyle M(\emptyset )=0} . ∑ F ⊆ E | i ∈ F M ( F ) ≥ 0 {\displaystyle \sum _{F\subseteq E|i\in F}M(F)\geq 0} , for all E ⊆ X {\displaystyle E\subseteq \mathbf {X} } and all i ∈ E {\displaystyle i\in E} A fuzzy measure in Möbius representation M is called normalized if ∑ E ⊆ X M ( E ) = 1. {\displaystyle \sum _{E\subseteq \mathbf {X} }M(E)=1.} Möbius representation can be used to give an indication of which subsets of X interact with one another. For instance, an additive fuzzy measure has Möbius values all equal to zero except for singletons. The fuzzy measure g in standard representation can be recovered from the Möbius form using the Zeta transform: g ( E ) = ∑ F ⊆ E M ( F ) , ∀ E ⊆ X . {\displaystyle g(E)=\sum _{F\subseteq E}M(F),\forall E\subseteq \mathbf {X} .} == Simplification assumptions for fuzzy measures == Fuzzy measures are defined on a semiring of sets or monotone class, which may be as granular as the power set of X, and even in discrete cases the number of variables can be as large as 2|X|. For this reason, in the context of multi-criteria decision analysis and other disciplines, simplification assumptions on the fuzzy measure have been introduced so that it is less computationally expensive to determine and use. For instance, when it is assumed the fuzzy measure is additive, it will hold that g ( E ) = ∑ i ∈ E g ( { i } ) {\displaystyle g(E)=\sum _{i\in E}g(\{i\})} and the values of the fuzzy measure can be evaluated from the values on X. Similarly, a symmetric fuzzy measure is defined uniquely by |X| values. Two important fuzzy measures that can be used are the Sugeno- or λ {\displaystyle \lambda } -fuzzy measure and k-additive measures, introduced by Sugeno and Grabisch respectively. === Sugeno λ-measure === The Sugeno λ {\displaystyle \lambda } -measure is a special case of fuzzy measures defined iteratively. It has the following definition: ==== Definition ==== Let X = { x 1 , … , x n } {\displaystyle \mathbf {X} =\left\lbrace x_{1},\dots ,x_{n}\right\rbrace } be a finite set and let λ ∈ ( − 1 , + ∞ ) {\displaystyle \lambda \in (-1,+\infty )} . A Sugeno λ {\displaystyle \lambda } -measure is a function g : 2 X → [ 0 , 1 ] {\displaystyle g:2^{X}\to [0,1]} such that g ( X ) = 1 {\displaystyle g(X)=1} . if A , B ⊆ X {\displaystyle A,B\subseteq \mathbf {X} } (alternatively A , B ∈ 2 X {\displaystyle A,B\in 2^{\mathbf {X} }} ) with A ∩ B = ∅ {\displaystyle A\cap B=\emptyset } then g ( A ∪ B ) = g ( A ) + g ( B ) + λ g ( A ) g ( B ) {\displaystyle g(A\cup B)=g(A)+g(B)+\lambda g(A)g(B)} . As a convention, the value of g at a singleton set { x i } {\displaystyle \left\lbrace x_{i}\right\rbrace } is called a density and is denoted by g i = g ( { x i } ) {\displaystyle g_{i}=g(\left\lbrace x_{i}\right\rbrace )} . In addition, we have that λ {\displaystyle \lambda } satisfies the property λ + 1 = ∏ i = 1 n ( 1 + λ g i ) {\displaystyle \lambda +1=\prod _{i=1}^{n}(1+\lambda g_{i})} . Tahani and Keller as well as Wang and Klir have shown that once the densities are known, it is possible to use the previous polynomial to obtain the values of λ {\displaystyle \lambda } uniquely. === k-additive fuzzy measure === The k-additive fuzzy measure limits the interaction between the subsets E ⊆ X {\displaystyle E\subseteq X} to size | E | = k {\displaystyle |E|=k} . This drastically reduces the number of variables needed to define the fuzzy measure, and as k can be anything from 1 (in which case the fuzzy measure is additive) to X, it allows for a compromise between modelling ability and simplicity. ==== Definition ==== A discrete fuzzy measure g on a set X is called k-additive ( 1 ≤ k ≤ | X | {\displaystyle 1\leq k\leq |\mathbf {X} |} ) if its Möbius representation verifies M ( E ) = 0 {\displaystyle M(E)=0} , whenever | E | > k {\displaystyle |E|>k} for any E ⊆ X {\displaystyle E\subseteq \mathbf {X} } , and there exists a subset F with k elements such that M ( F ) ≠ 0 {\displaystyle M(F)\neq 0} . == Shapley and interaction indices == In game theory, the Shapley value or Shapley index is used to indicate the weight of a game. Shapley values can be calculated for fuzzy measures in order to give some indication of the importance of each singleton. In the case of additive fuzzy measures, the Shapley value will be the same as each singleton. For a given fuzzy measure g, and | X | = n {\displaystyle |\mathbf {X} |=n} , the Shapley index for every i , … , n ∈ X {\displaystyle i,\dots ,n\in X} is: ϕ ( i ) = ∑ E ⊆ X ∖ { i } ( n − | E | − 1 ) ! | E | ! n ! [ g ( E ∪ { i } ) − g ( E ) ] . {\displaystyle \phi (i)=\sum _{E\subseteq \mathbf {X} \backslash \{i\}}{\frac {(n-|E|-1)!|E|!}{n!}}[g(E\cup \{i\})-g(E)].} The Shapley value is the vector ϕ ( g ) = ( ψ ( 1 ) , … , ψ ( n ) ) . {\displaystyle \mathbf {\phi } (g)=(\psi (1),\dots ,\psi (n)).}

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  Mozilla VPN

  Mozilla VPN is an open-source virtual private network developed by Mozilla. It launched in beta as Firefox Private Network on September 10, 2019, and officially launched on July 15, 2020, as Mozilla VPN. Mozilla VPN should not be confused with the built-in VPN in Firefox since version 149 released in March 2026, which is free with a monthly data limit of 50 GB but only masks traffic that originates in Firefox unlike Mozilla VPN that protects the entire device. == History == The Firefox Private Network web browser extension beta version was released on September 10, 2019, as part of the relaunch of Mozilla's Test Pilot Program, a program that allowed Firefox users to test experimental new features which had been shuttered in January 2019. The beta of the subscription-based standalone virtual private network for Android, Microsoft Windows, and Chromebook launched on February 19, 2020, with the iOS version following soon after. Firefox Private Network was rebranded as "Mozilla VPN" on June 18, 2020, and officially launched as Mozilla VPN on July 15, 2020. At launch, Mozilla VPN was available in six countries (the United States, Canada, the United Kingdom, Singapore, Malaysia, and New Zealand) for Windows 10, Android, and iOS (beta). Over time, the service also launched in Germany, France, Italy, Spain, Switzerland, Austria, Belgium, Netherlands, Ireland, Finland, Sweden, Poland, Czechia, Hungary, Romania, Bulgaria, Slovakia, Portugal, Denmark, Croatia, Lithuania, Slovenia, Latvia, Luxembourg, Estonia, Cyprus, and Malta. == Audits history == Cybersecurity firm Cure53 conducted a security audit for Mozilla VPN in August 2020 and identified multiple vulnerabilities, including one critical-severity vulnerability. In March 2021, Cure53 conducted a second security audit, which noted significant improvements since the 2020 audit. The second audit identified multiple issues, including two medium-severity and one high-severity vulnerability, but concluded that by the time of publication, only one vulnerability remained unresolved, and that it would require "a strong state-funded attacker-model" to be exploitable. Mozilla disclosed most of the vulnerabilities in July 2021 and released the full report by Cure53 in August 2021. In April 2023, Cure53 conducted a third security audit, the results of which Mozilla disclosed in December that year, along with the full report by Cure53. == Features == Mozilla VPN masks the user's IP address, hiding the user's location data from the websites accessed by the user, and encrypts all network activity. The service allows for up to 5 simultaneous connections, to any of more than 500 servers in 30+ countries, and is available on the mobile operating systems iOS and Android and the desktop operating systems Microsoft Windows, macOS and Linux. Mozilla VPN's infrastructure is provided by the Swedish Mullvad VPN service, which uses the WireGuard VPN protocol. The VPN software comes with additional features, like recommended server locations, the ability to block ads, block ad trackers and malware, the ability to exclude certain applications from protection, the ability to set multi-hop connections, and to set custom DNS servers. When used with Firefox and the official extension, Mozilla VPN allows the use of different settings per container as well as bypassing the VPN for specific websites.

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  Use of artificial intelligence by the United States Department of Defense

  The United States Department of Defense has been analyzing and employing military applications of artificial intelligence since at least 2014. The program initially focused on drones and other robots, but has also been using large language models for military research and analysis. The current US policy on lethal autonomous weapons is Department of Defense Directive 3000.09, updated in January 2023. == Background == The United States Department of Defense began developing lethal autonomous weapons as early as the Reagan administration. An early version of the Tomahawk missile could have been used to destroy Soviet ships without direct human control; the initiative was abandoned after the United States and the Soviet Union signed START I. By 2014, the United Kingdom, Israel, and Norway had already begun using missiles equipped with artificial intelligence systems. The Department of Defense established a policy on the use of artificial intelligence in 2012. == History == === 2016–2017: Carter secretaryship === In May 2016, secretary of defense Ash Carter stated that his Third Offset strategy would include utilizing artificial intelligence as a military advantage. The New York Times reported that year that the Department of Defense had tested an autonomous drone at an approximation of a Middle Eastern village at Camp Edwards. Deputy secretary of defense Robert O. Work, who advocated for developing artificial intelligence, told the Times that the United States needed to compete with China and Russia by having a tactical advantage they could not easily replicate. The initiative was developed by DARPA beginning in 2015. The use of artificial intelligence in the U.S. military was controversial within the department; in February, Paul Scharre, who worked for the Office of the Secretary of Defense in the secretaryships of Robert Gates and Leon Panetta, published a report about the risks of artificial intelligence for broad military applications. === 2017–2019: Mattis secretaryship === By 2017, the United States Air Force had already begun using artificial intelligence in military robots. The Air Force's use of Neurala, an artificial intelligence company, concerned officials in the Department of Defense after an investigation found that Neurala had accepted money from an investment firm with funding from a state-run Chinese company. The Department of Defense began heavily investing in artificial intelligence after Work established Project Maven, an initiative to encourage the development and integration of artificial intelligence in the military, in April 2017. In May 2018, secretary of defense Jim Mattis privately expressed to president Donald Trump that he needed to establish a national strategy on artificial intelligence, quoting an article from former secretary of state Henry Kissinger that called for a presidential commission on the technology. The Department of Defense established the Joint Artificial Intelligence Center the following month. Google began working with the Department of Defense on analyzing drone footage as early as March. Google's involvement in the initiative led to protests from employees and mass resignations. Seeking to quell internal unrest, Google stated it would not renew its contract with the Department of Defense in June. The Department of Defense announced an artificial intelligence contract with Microsoft in October. === 2025–present: Hegseth secretaryship === In December 2025, secretary of defense Pete Hegseth announced GenAI.mil, an artificial intelligence platform for the Department of Defense. In a video announcing the platform, Hegseth stated that Department of Defense workers would be able to "conduct deep research, format documents and even analyze video or imagery." The Department of Defense contracted first Gemini by Google, then ChatGPT by OpenAI, and finally Grok by xAI for the platform. Claude by Anthropic was also contracted by the Department of Defense and was in use on secure servers until it was revealed that Claude had been used in the 2026 operation to capture Nicolás Maduro, who was at the time the leader of Venezuela. This revelation sparked a high-profile dispute over Anthropic's ability to constrain Claude's useage, resulting in the termination of Anthropic's $200 million defense contract. The Department of Defense also moved to label Anthropic a supply chain risk, which was later blocked by a federal judge.

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  Probabilistic database

  Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. == Terminology == In a probabilistic database, each tuple is associated with a probability between 0 and 1, with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct. === Possible worlds === A probabilistic database could exist in multiple states. For example, if there is uncertainty about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute. Each of these states is called a possible world. Consider the following database: (Here {b3, b3′, b3′′} denotes that the attribute can take any of the values b3, b3′ or b3′′) Assuming that there is uncertainty about the first tuple, certainty about the second tuple, and uncertainty about the value of attribute B in the third tuple. Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3, b3′ or b3′′. Consequently, the possible worlds corresponding to the database are as follows: === Types of Uncertainties === There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented. == History == The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli. The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.

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  Lymphater's Formula

  "Lymphater's Formula" (Polish: "Formula Lymphatera") is a 1961 science fiction short story by Polish writer Stanisław Lem. It is a story of a "mad scientist", mathematician Ammon Lymphater, who invents an artificial intelligence, and then he realizes that it is capable of rendering the humankind obsolete. It was first published in the 1961 collection Księga robotów (Book of Robots) with the pre-annotation "from the memoirs of Ijon Tichy". The story was never republished with this pre-annotation, and nothing in the novel gives any indication at Ijon Tichy. Piotr Krywak tried to figure out possible explanations for this, apart from a typographical error. == Plot == Ammon Lymphater became interested in the emerging science of cybernetics and information theory, and started studying the works of an animal brain, the ant's brain in particular. He took note that the inherited knowledge is an evolutionary advantage somehow not exploited in full by the evolution. Eventually he came to a conclusion that only by pure biological restrictions that adaptive abilities of insects were stopped in their tracks by the evolution. He went on further wondering whether the ants have an ability to apriori knowledge, i.e., knowledge neither inherited nor learned. He decided to consult a famous myrmecologist, who told him about a rare ant species Acanthis Rubra Willinsoniana with an exceptionally high adaptability. Eventually Lymphater devised and constructed "It" capable of instant precognition of everything within "Its" rapidly expanding range of perception. From "It" Lymphater learns that the humanity is not the "crown of evolution", but rather evolution's tool to create "It", because the evolution could not create "It" directly (confirming Lymphater's reasoning about ants). Realizing that the Superentity "It" renders the human civilization redundant and obsolete, Lymphater destroys "It". "It" already knew Lymphater's intentions, but was not worried, knowing that sooner or later someone else will create "It" again and again. "It" was only the first variant of Lymphater's formula and the second variant is possible. Lyphater wonders whether the second one would be capable to create the third stage of the evolution which would amount to an artificial God. == Publication history == It was translated in Russian (as "Формула Лимфатера") in 1963, in Hungarian (as "Lymphater utolsó képlete") in 1966, and in Bulgarian (as "Формулата на Лимфатер" by Георги Димитров Георгиев) in 1969. In 1973 an audiobook was released in German (as "Die lymphatersche Formel"), narrated by Martin Held. It was also republished (and translated) in some other collections of Lem's short stories.

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  Kolmogorov–Arnold Networks

  Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs), which rely on fixed activation functions and linear weights, KANs replace each weight with a learnable univariate function, often represented using splines. == History == KANs (Kolmogorov–Arnold Networks) were proposed by Liu et al. (2024) as a generalization of the Kolmogorov–Arnold representation theorem (KART), aiming to outperform MLPs in small-scale AI and scientific tasks. Before KANs, numerous studies explored KART's connections to neural networks or used it as a basis for designing new network architectures. In the 1980s and 1990s, early research applied KART to neural network design. Kůrková et al. (1992), Hecht-Nielsen (1987), and Nees (1994) established theoretical foundations for multilayer networks based on KART. Igelnik et al. (2003) introduced the Kolmogorov Spline Network using cubic splines to model complex functions. Sprecher (1996, 1997) introduced numerical methods for building network layers, while Nakamura et al. (1993) created activation functions with guaranteed approximation accuracy. These works linked KART's theoretical potential with practical neural network implementation. KART has also been used in other computational and theoretical fields. Coppejans (2004) developed nonparametric regression estimators using B-splines, Bryant (2008) applied it to high-dimensional image tasks, Liu (2015) investigated theoretical applications in optimal transport and image encryption, and more recently, Polar and Poluektov (2021) used Urysohn operators for efficient KART construction, while Fakhoury et al. (2022) introduced ExSpliNet, integrating KART with probabilistic trees and multivariate B-splines for improved function approximation. == Architecture == KANs are based on the Kolmogorov–Arnold representation theorem, which was linked to the 13th Hilbert problem. Given x = ( x 1 , x 2 , … , x n ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{n})} consisting of n variables, a multivariate continuous function f ( x ) {\displaystyle f(x)} can be represented as: f ( x ) = f ( x 1 , … , x n ) = ∑ q = 1 2 n + 1 Φ q ( ∑ p = 1 n φ q , p ( x p ) ) {\displaystyle f(x)=f(x_{1},\dots ,x_{n})=\sum _{q=1}^{2n+1}\Phi _{q}\left(\sum _{p=1}^{n}\varphi _{q,p}(x_{p})\right)} (1) This formulation contains two nested summations: an outer and an inner sum. The outer sum ∑ q = 1 2 n + 1 {\displaystyle \sum _{q=1}^{2n+1}} aggregates 2 n + 1 {\displaystyle 2n+1} terms, each involving a function Φ q : R → R {\displaystyle \Phi _{q}:\mathbb {R} \to \mathbb {R} } . The inner sum ∑ p = 1 n {\displaystyle \sum _{p=1}^{n}} computes n terms for each q, where each term φ q , p : [ 0 , 1 ] → R {\displaystyle \varphi _{q,p}:[0,1]\to \mathbb {R} } is a continuous function of the single variable x p {\displaystyle x_{p}} . The inner continuous functions φ q , p {\displaystyle \varphi _{q,p}} are universal, independent of f {\displaystyle f} , while the outer functions Φ q {\displaystyle \Phi _{q}} depend on the specific function f {\displaystyle f} being represented. The representation (1) holds for all multivariate functions f {\displaystyle f} as proved in . If f {\displaystyle f} is continuous, then the outer functions Φ q {\displaystyle \Phi _{q}} are continuous; if f {\displaystyle f} is discontinuous, then the corresponding Φ q {\displaystyle \Phi _{q}} are generally discontinuous, while the inner functions φ q , p {\displaystyle \varphi _{q,p}} remain the same universal functions. Liu et al. proposed the name KAN. A general KAN network consisting of L layers takes x to generate the output as: K A N ( x ) = ( Φ L − 1 ∘ Φ L − 2 ∘ ⋯ ∘ Φ 1 ∘ Φ 0 ) x {\displaystyle \mathrm {KAN} (x)=(\Phi ^{L-1}\circ \Phi ^{L-2}\circ \cdots \circ \Phi ^{1}\circ \Phi ^{0})x} (3) Here, Φ l {\displaystyle \Phi ^{l}} is the function matrix of the l-th KAN layer or a set of pre-activations. Let i denote the neuron of the l-th layer and j the neuron of the (l+1)-th layer. The activation function φ j , i l {\displaystyle \varphi _{j,i}^{l}} connects (l, i) to (l+1, j): φ j , i l , l = 0 , … , L − 1 , i = 1 , … , n l , j = 1 , … , n l + 1 {\displaystyle \varphi _{j,i}^{l},\quad l=0,\dots ,L-1,\;i=1,\dots ,n_{l},\;j=1,\dots ,n_{l+1}} (4) where nl is the number of nodes of the l-th layer. Thus, the function matrix Φ l {\displaystyle \Phi ^{l}} can be represented as an n l + 1 × n l {\displaystyle n_{l+1}\times n_{l}} matrix of activations: x l + 1 = ( φ 1 , 1 l ( ⋅ ) φ 1 , 2 l ( ⋅ ) ⋯ φ 1 , n l l ( ⋅ ) φ 2 , 1 l ( ⋅ ) φ 2 , 2 l ( ⋅ ) ⋯ φ 2 , n l l ( ⋅ ) ⋮ ⋮ ⋱ ⋮ φ n l + 1 , 1 l ( ⋅ ) φ n l + 1 , 2 l ( ⋅ ) ⋯ φ n l + 1 , n l l ( ⋅ ) ) x l {\displaystyle x^{l+1}={\begin{pmatrix}\varphi _{1,1}^{l}(\cdot )&\varphi _{1,2}^{l}(\cdot )&\cdots &\varphi _{1,n_{l}}^{l}(\cdot )\\\varphi _{2,1}^{l}(\cdot )&\varphi _{2,2}^{l}(\cdot )&\cdots &\varphi _{2,n_{l}}^{l}(\cdot )\\\vdots &\vdots &\ddots &\vdots \\\varphi _{n_{l+1},1}^{l}(\cdot )&\varphi _{n_{l+1},2}^{l}(\cdot )&\cdots &\varphi _{n_{l+1},n_{l}}^{l}(\cdot )\end{pmatrix}}x^{l}} == Implementations == To make the KAN layers optimizable, the inner function is formed by the combination of spline and basic functions as the formula: φ ( x ) = w b b ( x ) + w s spline ( x ) {\displaystyle \varphi (x)=w_{b}\,b(x)+w_{s}\,{\text{spline}}(x)} where b ( x ) {\displaystyle b(x)} is the basic function, usually defined as s i l u ( x ) = x / ( 1 + e x ) {\displaystyle silu(x)=x/(1+e^{x})} and w b {\displaystyle w_{b}} is the base weight matrix. Also, w s {\displaystyle w_{s}} is the spline weight matrix and spline ( x ) {\displaystyle {\text{spline}}(x)} is the spline function. The spline function can be a sum of B-splines. spline ( x ) = ∑ i c i B i ( x ) {\displaystyle {\text{spline}}(x)=\sum _{i}c_{i}B_{i}(x)} Many studies suggested to use other polynomial and curve functions instead of B-spline to create new KAN variants. == Functions used == The choice of functional basis strongly influences the performance of KANs. Common function families include: B-splines: Provide locality, smoothness, and interpretability; they are the most widely used in current implementations. RBFs (include Gaussian RBFs): Capture localized features in data and are effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the maximum norm, making them useful for stable function representation. Rational function: Useful for approximating functions with singularities or sharp variations, as they can model asymptotic behavior better than polynomials. Fourier series: Capture periodic patterns effectively and are particularly useful in domains such as physics-informed machine learning. Wavelet functions (DoG, Mexican hat, Morlet, and Shannon): Used for feature extraction as they can capture both high-frequency and low-frequency data components. Piecewise linear functions: Provide efficient approximation for multivariate functions in KANs. == Usage == In some modern neural architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), and Transformers, KANs are typically used as drop-in substitutes for MLP layers. Despite KANs' general-purpose design, researchers have created and used them for a number of tasks: Scientific machine learning (SciML): Function fitting, partial differential equations (PDEs) and physical/mathematical laws. Continual learning: KANs better preserve previously learned information during incremental updates, avoiding catastrophic forgetting due to the locality of spline adjustments. Graph neural networks: Extensions such as Kolmogorov–Arnold Graph Neural Networks (KA-GNNs) integrate KAN modules into message-passing architectures, showing improvements in molecular property prediction tasks. Sensor data processing: Kolmogorov–Arnold Networks (KANs) have recently been applied to sensor data processing due to their ability to model complex nonlinear relationships with relatively few parameters and improved interpretability compared to conventional multilayer perceptrons. Applications include industrial soft sensors, biomedical signal analysis, remote sensing, and environmental monitoring systems. == Drawbacks == KANs can be computationally intensive and require a large number of parameters due to their use of polynomial functions to capture data.

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  Rifts (role-playing game)

  Rifts is a multi-genre role-playing game created by Kevin Siembieda in August 1990 and published continuously by Palladium Books since then. It takes place in a post-apocalyptic future, deriving elements from cyberpunk, science fiction, fantasy, horror, western, mythology and many other genres. Rifts serves as a cross-over environment for a variety of other Palladium games with different universes connected through "rifts" on Earth that lead to different spaces, times, and realities that Palladium calls the "Rifts Megaverse". Rifts describes itself as an "advanced" role-playing game and not an introduction for those new to the concept. Palladium continues to publish books for the Rifts series, with about 80 books published between 1990 and 2011. Rifts Ultimate Edition was released in August 2005 and designed to update the game with Palladium's incremental changes to its system, changes in the game world, and additional information and character types. The web site is quick to point out that this is not a second edition but an improvement and expansion of the original role playing game. == Background == The RPG had the tentative title Boomers, named after the original name for the Glitter Boy power armor until Kevin Siembieda changed the name after finding out it was in use for Bubblegum Crisis. == Setting == The Rifts world is Earth, but hundreds of years into the future. Ley lines, lines of magic energy, criss-cross the earth forming supernatural geographic areas such as the Bermuda Triangle. Points where Ley Lines intersect, called a nexus, are places of powerful magic, such as the Pyramids of Giza and Stonehenge. If a Ley Line nexus energy surges or is purposely activated, the fabric of space and time can be torn, creating a rift - a hole in space-time leading to another place, time, or dimension. Ley lines contain magical energy called Potential Psychic Energy (PPE), which is found in various places, objects, and animals and is particularly strong in children. An adult's level of PPE can vary based on other factors. PPE also allows Psionics which uses energy known as Inner Strength Points or ISP. Psychic phenomenon (more commonly called psionics) can also vary from individuals, ranging from none at all to Master level abilities. Psychic abilities can manifest in virtually any way imaginable. Some psychics develop differently, such as psi-stalkers; human mutants that feed on psychic energy. === Earth === Rifts begins with two future-historical premises: first, a golden age of humanity occurs, with tremendous advances in science, technology, military, and society. Humanity as a whole is at peace as a majority of Earth's nations decide to cease world war and begin to share ideas and technology freely. Much of the Solar System is conquered, humanity's wars will end, and harmony will reign. This golden age is followed by an unknown cause near the winter solstice and a rare planetary alignment, causing a disaster that cascades into tremendous destruction via a ripple effect. The cataclysm begins with unprecedented storms, earthquakes, tsunamis, and volcanic eruptions, which kill millions of people. The Ley Line networks that crisscross the globe are energized, causing rifts to open both on Earth and throughout the Megaverse. For hundreds of years after the holocaust, many creatures, both mythical beasts and aliens, come through the Rifts to wreak havoc. The old world gone, a new Dark Age dawns and humanity's shrinking population is reduced, due to catastrophe and domestic failure, immeasurably. This period is covered in Palladium's Rifts Chaos Earth spin-off series. Rifts initially takes place in 101 P.A. (equivalent to the year 2387) 289 years after this event. The "Post-Apocalypse" calendar was established by the formation of the Coalition States in 2286. By this time, most of the disasters have quieted down, though Earth is still bathed in PPE. The planet's mystical energy has attracted aliens from other dimensions, who continue to arrive through the Rifts both accidentally and deliberately. The humanoid creatures that arrive on Earth are referred to as Dimensional Beings (called D-Bees). Some resemble familiar fantasy races, such as elves and dwarfs, while others were created specifically for the game setting. Non-humanoid creatures have also arrived, including monstrous creatures and mystical demons. To cope with these natural, supernatural, and alien menaces, the human race has adapted in a variety of ways, many of them borrowed from the technological developments of the lost Golden Age. Powered armor suits and giant vehicles are frequently used to combat the dangers of Rifts, but more invasive augmentation is common. This has three basic categories: "Juicers" augment themselves chemically, the "Borgs" augment themselves mechanically, and "Crazies" use performance-enhancing brain implants. All such augmentations boost strength, speed, endurance, and dexterity to superhuman levels. However, all come at great cost. Chemicals cause the body to wear out faster, decreasing life span to a few years. Mechanical Borg augmentation causes a loss of humanity when those with multiple limb and organ replacements become more machine than human. Brain implants cause mental instability ranging from mild phobias to crippling neurosis or psychosis. ==== North America ==== The strongest power in North America is the Coalition States (CS), which is based in the arcological city of Chi-Town and lays claim to northern Illinois, all of Iowa, the Texas Panhandle, Missouri, and the eastern half of Ontario, Canada. The second greatest power is Free Quebec, a former Coalition State that seceded following a civil war with the other Coalition States. Mexico is ruled by a group of vampire kingdoms, who treat humans as little more than food. North of the Rio Grande, west of Texas and roaming most of the American Southwest are large nomadic bands/tribes of bandits who collectively form the Pecos Empire, consisting of El Paso, Los Alamos, and Houstown. Much of the western United States has more or less willingly reverted to a mix of modern and past technology akin to the Wild West. The Royal Canadian Mounted Police managed to survive the great cataclysm, though Canada itself did not. The Mounties have become an independent law enforcement force called the Tundra Rangers, patrolling the northern wilderness. The Midwest, both upper and central, is home to most of North America's population. The Manistique Imperium and Northern Gun in Michigan's Upper Peninsula, both Coalition allies, are among the largest weapons manufacturing areas on the continent. New Lazlo is one of the largest cities in Michigan's southern portion. Chillicothe in Missouri is a large supplier of Coalition food processing and growing. Missouri's southern half, home to the city-states of Whykin (Poplar Bluff) and Kingsdale (West Plains) are in constant opposition to the CS and claim independence. Arkansas is home to the independent CS ally El Dorado. Southern Illinois and the Ohio Valley is home to the Federation of Magic. Also in the Ohio Valley is Psyscape, a city-state founded by psychics. Tolkeen was a major city in the former Minneapolis region in early Rifts books; the city welcomed users of magic. A military campaign made by the Coalition States (which is the primary event of 109 PA) resulted in the magic-user kingdom being wiped off the map. In the Northeast, the city-state of Lazlo, named after supernatural researcher and writer Victor Lazlo, was built upon the ruins of Toronto. This major center of civilization is well known as a melting pot of humans, D-Bees and other beings, and is the home of Techno-Wizardry. Mad Haven is the name given to the ruins of Manhattan; tectonic forces during the cataclysm have moved it into the coast, creating a peninsula. It is seen by most denizens of Rifts Earth as a refuge of demons and madness. ==== South America ==== The return of Atlantis caused the Amazon River basin to flood most of western South America, giving it the nickname The Land of a Thousand Islands. The Empire of the Sun, consisting of Cuzco, Nazca, Arequipa and Lima, created a wide range of technology and magic, including magic derived from the Nazca lines. In Argentina, the Silver River Republics of Cordoba (the South American Chi-Town), Santiago (one of the most tolerant human nations on Rifts Earth), Achilles (a nation founded by mutants), and New Babylon, a nation where humans and aliens coexist) have thrived and created nations whose strength rivals that of the CS. In Bolivia, freed Human and D-Bees formed the Megaversal Legion: a mercenary company with one of the highest levels of technology on Rifts Earth. ==== Europe ==== England has become a vast wilderness again, broken up by the occasional giant Millennium Tree or feudal kingdom, complete with a New Camelot and a new King Arthur, partially being manipulated by an alien intelligence disguised as Merlin. Also the magic of

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  Asian Digital Finance Forum & Awards

  Asian Digital Finance Forum & Awards (also known as Asian Digital Finance Forum and Awards) is a forum and honorary awards platform convened in Colombo, Sri Lanka. It has been hosted in a hybrid format (virtual and in-person), with editions reported in 2022, 2023 and 2025. The event is organised by the Asian FinTech Academy (AFTA) in collaboration with a number of local and international institutions. == Overview == The forum has featured international academic, industry, and policy speakers and has recognised institutions and individuals for contributions related to digital finance and fintech innovation. Media coverage has described participation and recognition at the forum as spanning multiple regions, with institutions and individuals from South Asia, Southeast Asia, East Asia, the Middle East, Europe, and North America featured across different editions. == Awards and recognition == The forum and awards were held in a hybrid format with virtual and in-person proceedings at Hilton Colombo in the 2022 and 2023 editions. The Asian Digital Finance Forum & Awards presents honorary recognitions to institutions and individuals for contributions to digital finance, financial inclusion, and related regulatory, technological, and policy developments. Media coverage has described the recognitions as non-competitive and based on demonstrated leadership and impact rather than open nominations. In 2025, the forum and awards served as an anchor initiative associated with the Asia International Digital Economy & AI in Finance Summit at Port City Colombo, with an emphasis on artificial intelligence in finance, financial inclusion, and governance-related themes. === 2022 === According to reporting by Daily FT, institutions recognised at the 2022 edition included Sri Lanka’s Bank of Ceylon, Commercial Bank of Ceylon, Hatton National Bank, and People’s Bank, alongside international organisations and fintech-sector contributors. === 2023 === Coverage of the 2023 forum described recognitions awarded to India’s International Financial Services Centres Authority (IFSCA) for regulatory innovation, as well as to digital finance and payments platforms including Dialog Genie and SLT-Mobitel mCash. IDEMIA’s Asia–Pacific operations were also recognised for contributions related to biometric and digital identity technologies in financial services. === 2025 === For the 2025 edition, institutional honourees reported in the media included Nium (Singapore), recognised for cross-border payments optimisation, and Paytm (India), recognised for AI-powered financial inclusion initiatives. A Visionary Award for Next-Generation Financial Hub Development was presented to Port City Colombo in recognition of its fintech- and AI-oriented development strategy. Individual honourees reported for 2025 included Sopnendu Mohanty (Singapore), Neil Tan (Hong Kong), Purvi Munot (United Arab Emirates), and Amira Abdelaziz (Egypt), recognised for contributions spanning fintech governance, ecosystem development, inclusive wealth technology, and AI-driven financial policy and regulation. In 2025, media reports described the awards as being subject to an independent validation framework. The process was led by Dr. Sivaguru S. Sritharan, appointed as Global Validation Chair, and involved independent research, analytical review, and benchmarking against international standards, with recognitions characterised as honorary and non-competitive.

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  Interim Measures for the Management of Generative AI Services

  The Interim Measures for the Management of Generative AI Services (Chinese: 生成式人工智能服务管理暂行办法; pinyin: Shēngchéng shì réngōng zhìnéng fúwù guǎnlǐ zànxíng bànfǎ) are a set of regulations governing public-facing generative artificial intelligence services in China. Issued on 10 July 2023 and effective from 15 August 2023, they were China's first binding regulation specifically targeting generative AI. They have been described as among the earliest such regulations adopted by any country. The measures were jointly issued by the Cyberspace Administration of China (CAC) and six other national bodies: the National Development and Reform Commission, the Ministry of Education, the Ministry of Science and Technology, the Ministry of Industry and Information Technology, the Ministry of Public Security, and the National Radio and Television Administration. Among the measures' most prominent requirements is that generative AI services must uphold Core Socialist Values and must not generate content that could subvert state power, harm national security, or undermine social stability. The measures also require providers of public-facing generative AI services to undergo security assessments and register their algorithms with the CAC. As of December 2025, 748 generative AI services had completed the filing process at the national level. == Background == The Interim Measures build on two earlier sets of regulations targeting specific algorithm applications. The Administrative Provisions on Algorithm Recommendation for Internet Information Services, effective from March 2022, established China's algorithm registry and required providers of recommendation algorithms with "public opinion properties or social mobilization capabilities" to file with the CAC and undergo security assessments. The Administrative Provisions on Deep Synthesis of Internet Information Services, effective from January 2023, extended similar requirements to algorithms used for generating synthetic media such as deepfakes. In April 2023, the CAC released a draft of the generative AI regulation for public comment. The draft included several requirements that attracted attention, including that generated content should "embody Core Socialist Values" and that training data should be "true and accurate". The public consultation period ran until May 2023. The final version, published in July 2023, was substantially revised from the draft. According to an analysis by the Future of Privacy Forum, changes appeared to reflect feedback from industry stakeholders including Baidu, Xiaomi, SenseTime, and others, as well as input from government-affiliated research institutes. The final measures adopted a more permissive tone, with the CAC describing its approach as "inclusive and prudent" (包容审慎) and emphasising "classified and graded" (分类分级) supervision. == Scope == The measures apply to services that use generative AI technology to provide text, images, audio, video, or other content to the public within mainland China (Article 2). They do not apply to organisations that develop or use generative AI internally without offering services to the domestic public, such as industry associations, enterprises, and research institutions. Overseas providers whose services are accessible to users in China are also subject to the measures. == Key provisions == === Content requirements === Article 4 sets out the core content obligations. Providers and users of generative AI services must uphold the Core Socialist Values. The measures prohibit generating content that incites subversion of national sovereignty or the socialist system, endangers national security or the nation's image, incites separatism, promotes terrorism or extremism, promotes ethnic hatred or discrimination, or contains violence, obscenity, or false information prohibited by law. These content prohibitions largely mirror those in Article 12 of the Cybersecurity Law and in prior regulations governing online content. Article 4 also requires that models be designed and trained to avoid discrimination, that services respect intellectual property rights, and that providers take effective measures to improve the transparency and accuracy of generated content. === Training data and labelling === Article 7 requires providers to ensure that training data is of high quality and legitimately sourced, and that it does not infringe upon intellectual property rights. Where personal information is used, consent must be obtained. The final version of this provision removed language from the draft that would have held providers responsible for the "legitimacy" of all pretraining data, replacing it with a requirement to "employ effective measures to improve the quality of training data". Article 8 requires providers to establish labelling rules for training data and to conduct quality assessments of data annotations. Article 12 requires that generated images, videos, and other synthetic content be labelled as AI-generated. === User rights and privacy === Article 11 requires providers to protect user privacy, to minimise the collection and retention of personal data, and to refrain from unlawfully sharing user information. Users have the right to request review, correction, or deletion of their personal information. Article 10 requires providers to take measures to prevent excessive dependence on or addiction to generative AI services by minors. === Security assessment and algorithm filing === Article 17 requires that providers of generative AI services with "public opinion properties or the capacity for social mobilization" (具有舆论属性或者社会动员能力) carry out security assessments and complete algorithm filing procedures in accordance with the Administrative Provisions on Algorithm Recommendation for Internet Information Services. == Implementation == === Algorithm filing process === In practice, the filing requirements under the Interim Measures have developed into a two-tier process. The first tier is the standard algorithm filing (算法备案) under the pre-existing Algorithm Recommendation Provisions, which involves submitting information about an algorithm's design, purpose, and data sources to the CAC. This process is primarily a registration mechanism. For public-facing generative AI products, there is an additional, more rigorous process commonly referred to as the "large model filing" (大模型备案). This involves submitting a security self-assessment report, data annotation rules, a keyword blocking list, and evaluation test question sets. The process includes technical testing at the provincial level, followed by review at the national CAC level. The algorithm filing targets specific algorithms, while the large model filing evaluates the broader system architecture, training data, model parameters, and potential social impact. The CAC publishes lists of generative AI services that have successfully completed the filing process. The first such list was published on 2 April 2024. According to the CAC's year-end announcements, 302 generative AI services had completed national-level filing by the end of 2024 (of which 238 were new that year), alongside 105 applications that completed local-level registration. By the end of 2025, the cumulative total had risen to 748 national-level filings and 435 local-level registrations. === Content compliance and testing === According to the Carnegie Endowment, the CAC has conducted compliance audits of generative AI services with a particular focus on ensuring appropriate responses to queries about politically sensitive topics. The large model filing process requires providers to pass both provincial-level and national-level technical testing before their services can be made available to the public. On 1 March 2024, the National Technical Committee 260 on Cybersecurity (TC260) published TC260-003, the Basic Security Requirements for Generative AI Services (生成式人工智能服务安全基本要求), a technical standard that provides detailed guidance on the security assessments required under the Interim Measures. The standard covers requirements for training data safety, model security, and content safety evaluation, and is used as a reference for the filing process. == Analysis == === Relationship to broader Chinese internet regulation === The content requirements in the Interim Measures extend China's existing framework for online information control to generative AI. Legal scholars have noted that the "Core Socialist Values" provision and the specific content prohibitions are consistent with longstanding requirements imposed on internet platforms under the Cybersecurity Law and related regulations. The Asia Society Policy Institute has described the Chinese government's highest regulatory priority in this area as retaining control of information, noting that content-related obligations receive stricter enforcement than other provisions. === Nature of the filing system === The character of the filing system has been debated by scholars. Angela Huyue Zh

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  Instance-based learning

  In machine learning, instance-based learning (sometimes called memory-based learning) is a family of learning algorithms that, instead of performing explicit generalization, compare new problem instances with instances seen in training, which have been stored in memory. Because computation is postponed until a new instance is observed, these algorithms are sometimes referred to as "lazy." It is called instance-based because it constructs hypotheses directly from the training instances themselves. This means that the hypothesis complexity can grow with the data: in the worst case, a hypothesis is a list of n training items and the computational complexity of classifying a single new instance is O(n). One advantage that instance-based learning has over other methods of machine learning is its ability to adapt its model to previously unseen data. Instance-based learners may simply store a new instance or throw an old instance away. Examples of instance-based learning algorithms are the k-nearest neighbors algorithm, kernel machines and RBF networks. These store (a subset of) their training set; when predicting a value/class for a new instance, they compute distances or similarities between this instance and the training instances to make a decision. To battle the memory complexity of storing all training instances, as well as the risk of overfitting to noise in the training set, instance reduction algorithms have been proposed.

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  Flux (text-to-image model)

  Flux (also known as FLUX.1 and FLUX.2) is a text-to-image model developed by Black Forest Labs (BFL), based in Freiburg im Breisgau, Germany. Black Forest Labs was founded by former employees of Stability AI. As with other text-to-image models, Flux generates images from natural language descriptions, called prompts. == History == Black Forest Labs (BFL) was founded in 2024 by Robin Rombach, Andreas Blattmann, and Patrick Esser, former employees of Stability AI. All three founders had previously researched the artificial intelligence image generation at LMU Munich as research assistants under Björn Ommer. They published their research results on image generation in 2022, which resulted in creation of Stable Diffusion. Investors in BFL included venture capital firm Andreessen Horowitz, Brendan Iribe, Michael Ovitz, Garry Tan, and Vladlen Koltun. The company received an initial investment of US$31 million. In August 2024, Flux was integrated into the Grok chatbot developed by xAI and made available as part of premium feature on X (formerly Twitter). Grok later switched to its own text-to-image model Aurora in December 2024. On 18 November 2024, Mistral AI announced that its Le Chat chatbot had integrated Flux Pro as its image generation model. On 21 November 2024, BFL announced the release of Flux.1 Tools, a suite of editing tools designed to be used on top of existing Flux models. The tools consisting of Flux.1 Fill for inpainting and outpainting, Flux.1 Depth for control based on extracted depth map of input images and prompts, Flux.1 Canny for control based on extracted canny edges of input images and prompts, and Flux.1 Redux for mixing existing input images and prompts. Each tools are available in both Pro and Dev models. In January 2025, BFL announced a partnership with Nvidia for inclusion of Flux models as foundation models for Nvidia's Blackwell microarchitecture. The company also announced the release of Flux Pro Finetuning API, designed for customisation and fine-tuning of Flux-generated images and a partnership with German media company Hubert Burda Media for usage of Flux Pro as part of content creation. On 29 May 2025, BFL announced Flux.1 Kontext, a suite of models that enable in-context image generation and editing, allowing users to prompt with both text and images. Alongside this, BFL Playground, an interface for testing Flux models was released. On 31 July 2025, BFL announced Flux.1 Krea Dev, a model developed in collaboration with Krea AI that trained to achieve better performance, more varied aesthetics, and better realism compared to existing text-to-image models. In September 2025, Adobe Inc. announced that Photoshop (beta) users can use Flux.1 Kontext Pro as a model for its generative fill tool. BFL collaborated with Meta on Vibes, a video-generation app. On 25 November 2025, BFL announced the release of Flux.2 model series, consisting of Pro, Flex, Dev, and Apache 2.0-licensed Klein (meaning Little or Small in German language) models along with Flux.2 variational autoencoder which also released as open-source software under Apache 2.0 licence. This series claimed improvements for image reference, photorealism, typography, and prompt understanding. == Models == Flux is a series of text-to-image models. The models are based on rectified flow transformer blocks scaled to 12 billion parameters. Flux.1 models were released under different licences with Schnell (meaning Fast or Quick in German language) released as open-source software under Apache License, Dev released as source-available software under a non-commercial licence (users can obtain a self-serving commercial licence for Dev from BFL), and Pro released as proprietary software and only available as API that can be licensed by third-party users. Users retained the ownership of resulting output regardless of models used. An improved flagship model, Flux 1.1 Pro was released on 2 October 2024. Two additional modes were added on 6 November, Ultra which can generate image at four times higher resolution and up to 4 megapixel without affecting generation speed and Raw which can generate hyper-realistic image in the style of candid photography. Flux.1 Kontext is a series with in-context image generation and editing capabilities. It is available in Max, Pro, and Dev models. Max is the highest quality model and can be used to iteratively modify an existing image by using prompt while Pro is optimized to balance quality and speed of generation. Dev is an open-weight model released under non-commercial license, same as Flux.1 Dev. Flux.2 models are based on latent flow matching architecture with Mistral AI's Mistral-3 model (24 billion parameters) for its vision-language model. As with Flux.1, Flux.2 models were also released under different licences with Klein released as open-source software under Apache License, Dev released as source-available software under a non-commercial licence (users can obtain a self-serving commercial licence from BFL), and both Flex and Pro released as proprietary software and only available as API. The models can be used either online or locally by using generative AI user interfaces such as ComfyUI, Recraft Studio and Stable Diffusion WebUI Forge (a fork of Automatic1111 WebUI). Related to Flux is a text-to-video model by Black Forest Labs, under development as of February 2026. == Reception == According to a test performed by Ars Technica, the outputs generated by Flux.1 Dev and Flux.1 Pro are comparable with DALL-E 3 in terms of prompt fidelity, with the photorealism closely matched Midjourney 6 and generated human hands with more consistency over previous models such as Stable Diffusion XL. Flux has been criticised for its very realistic generated images. According to media reports, depictions ranged from an image of Donald Trump posing with guns to disturbing scenes, which triggered discussions about ethical implications of Flux models. After the release of the model, social media platform X was flooded with Flux-generated images. Black Forest Labs has not provided exact details of the data used to train the model. Ars Technica suspected that Flux is based on a large, unauthorised collection of images scraped from the internet, a controversial practice with potential legal consequences. According to a test performed by Japanese technology news website Gigazine for Flux.1 Kontext, the model series has a good understanding of the English language and can easily transfer style of the image from photorealistic into anime-style according to prompts given by the user; however, its ability to understand Japanese is quite poor. == Availability == In addition to the official BFL Playground on its website, the Flux models are also widely available through various third-party platforms for creative and professional use. These include repositories on platforms like Hugging Face and Replicate. == Further readings == FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space (29 May 2025) FLUX.2: Analyzing and Enhancing the Latent Space of FLUX – Representation Comparison (25 November 2025)

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  Evolutionary computation

  Evolutionary computation (EC) from computer science is a family of algorithms for global optimization inspired by biological evolution, and a subfield of computational intelligence and soft computing studying these algorithms. In technical terms, they are a family of population-based trial and error problem solvers with a metaheuristic or stochastic optimization character. In evolutionary computation, an initial set of candidate solutions is generated and iteratively updated. Each new generation is produced by stochastically removing less desired solutions, and introducing small random changes as well as, depending on the method, mixing parental information. In biological terminology, a population of solutions is subjected to natural selection (or artificial selection), mutation and possibly recombination. These biological functions serve as role models for the genetic operators - mutation, crossover, and selection - used in the EC procedures. As a result, the population will gradually evolve to increase in fitness, in this case the chosen fitness function of the algorithm. Evolutionary computation techniques can produce highly optimized solutions in a wide range of problem settings, making them popular in computer science. Many variants and extensions exist, suited to more specific families of problems and data structures. Evolutionary computation is also sometimes used in evolutionary biology as an in silico experimental procedure to study common aspects of general evolutionary processes. == History == The concept of mimicking evolutionary processes to solve problems originates before the advent of computers, such as when Alan Turing proposed a method of genetic search in 1948 . Turing's B-type u-machines resemble primitive neural networks, and connections between neurons were learnt via a sort of genetic algorithm. His P-type u-machines resemble a method for reinforcement learning, where pleasure and pain signals direct the machine to learn certain behaviors. However, Turing's paper went unpublished until 1968, and he died in 1954, so this early work had little to no effect on the field of evolutionary computation that was to develop. Evolutionary computing as a field began in earnest in the 1950s and 1960s. There were several independent attempts to use the process of evolution in computing at this time, which developed separately for roughly 15 years. Three branches emerged in different places to attain this goal: evolution strategies, evolutionary programming, and genetic algorithms. A fourth branch, genetic programming, eventually emerged in the early 1990s. These approaches differ in the method of selection, the permitted mutations, and the representation of genetic data. By the 1990s, the distinctions between the historic branches had begun to blur, and the term 'evolutionary computing' was coined in 1991 to denote a field that exists over all four paradigms. In 1962, Lawrence J. Fogel initiated the research of Evolutionary Programming in the United States, which was considered an artificial intelligence endeavor. In this system, finite state machines are used to solve a prediction problem: these machines would be mutated (adding or deleting states, or changing the state transition rules), and the best of these mutated machines would be evolved further in future generations. The final finite state machine may be used to generate predictions when needed. The evolutionary programming method was successfully applied to prediction problems, system identification, and automatic control. It was eventually extended to handle time series data and to model the evolution of gaming strategies. In 1964, Ingo Rechenberg and Hans-Paul Schwefel introduce the paradigm of evolution strategies in Germany. Since traditional gradient descent techniques produce results that may get stuck in local minima, Rechenberg and Schwefel proposed that random mutations (applied to all parameters of some solution vector) may be used to escape these minima. Child solutions were generated from parent solutions, and the more successful of the two was kept for future generations. This technique was first used by the two to successfully solve optimization problems in fluid dynamics. Initially, this optimization technique was performed without computers, instead relying on dice to determine random mutations. By 1965, the calculations were performed wholly by machine. John Henry Holland introduced genetic algorithms in the 1960s, and it was further developed at the University of Michigan in the 1970s. While the other approaches were focused on solving problems, Holland primarily aimed to use genetic algorithms to study adaptation and determine how it may be simulated. Populations of chromosomes, represented as bit strings, were transformed by an artificial selection process, selecting for specific 'allele' bits in the bit string. Among other mutation methods, interactions between chromosomes were used to simulate the recombination of DNA between different organisms. While previous methods only tracked a single optimal organism at a time (having children compete with parents), Holland's genetic algorithms tracked large populations (having many organisms compete each generation). By the 1990s, a new approach to evolutionary computation that came to be called genetic programming emerged, advocated for by John Koza among others. In this class of algorithms, the subject of evolution was itself a program written in a high-level programming language (there had been some previous attempts as early as 1958 to use machine code, but they met with little success). For Koza, the programs were Lisp S-expressions, which can be thought of as trees of sub-expressions. This representation permits programs to swap subtrees, representing a sort of genetic mixing. Programs are scored based on how well they complete a certain task, and the score is used for artificial selection. Sequence induction, pattern recognition, and planning were all successful applications of the genetic programming paradigm. Many other figures played a role in the history of evolutionary computing, although their work did not always fit into one of the major historical branches of the field. The earliest computational simulations of evolution using evolutionary algorithms and artificial life techniques were performed by Nils Aall Barricelli in 1953, with first results published in 1954. Another pioneer in the 1950s was Alex Fraser, who published a series of papers on simulation of artificial selection. As academic interest grew, dramatic increases in the power of computers allowed practical applications, including the automatic evolution of computer programs. Evolutionary algorithms are now used to solve multi-dimensional problems more efficiently than software produced by human designers, and also to optimize the design of systems. == Techniques == Evolutionary computing techniques mostly involve metaheuristic optimization algorithms. Broadly speaking, the field includes: Agent-based modeling Ant colony optimization Particle swarm optimization Swarm intelligence Artificial immune systems Artificial life Digital organism Cultural algorithms Differential evolution Dual-phase evolution Estimation of distribution algorithm Evolutionary algorithm Genetic algorithm Evolutionary programming Genetic programming Gene expression programming Grammatical evolution Evolution strategy Learnable evolution model Learning classifier system Memetic algorithms Neuroevolution Self-organization such as self-organizing maps, competitive learning Over recent years many dubious algorithms have been proposed, that are often just copies of existing algorithms (frequently Particle Swarm Optimization), where only the metaphor changed, but the algorithm itself is not new at all. A thorough catalogue with many of these dubious algorithms has been published in the Evolutionary Computation Bestiary. It is also important to note that many of these dubiously 'novel' algorithms have poor experimental validation. == Evolutionary algorithms == Evolutionary algorithms form a subset of evolutionary computation in that they generally only involve techniques implementing mechanisms inspired by biological evolution such as reproduction, mutation, recombination and natural selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the cost function determines the environment within which the solutions "live" (see also fitness function). Evolution of the population then takes place after the repeated application of the above operators. In this process, there are two main forces that form the basis of evolutionary systems: Recombination (e.g. crossover) and mutation create the necessary diversity and thereby facilitate novelty, while selection acts as a force increasing quality. Many aspects of such an evolutionary process are stochastic. Changed pieces of information due to recombination and mutati

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