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  Continuum robot

  A continuum robot is a type of robot that is characterised by infinite degrees of freedom and number of joints. These characteristics allow continuum manipulators to adjust and modify their shape at any point along their length, granting them the possibility to work in confined spaces and complex environments where standard rigid-link robots cannot operate. In particular, we can define a continuum robot as an actuatable structure whose constitutive material forms curves with continuous tangent vectors. This is a fundamental definition that allows to distinguish between continuum robots and snake-arm robots or hyper-redundant manipulators: the presence of rigid links and joints allows them to only approximately perform curves with continuous tangent vectors. The design of continuum robots is bioinspired, as the intent is to resemble biological trunks, snakes and tentacles. Several concepts of continuum robots have been commercialised and can be found in many different domains of application, ranging from the medical field to undersea exploration. == Classification == Continuum robots can be categorised according to two main criteria: structure and actuation. === Structure === The main characteristic of the design of continuum robots is the presence of a continuously curving core structure, named backbone, whose shape can be actuated. The backbone must also be compliant, meaning that the backbone yields smoothly to external loads. According to the design principles chosen for the continuum manipulator, we can distinguish between: single-backbone: these continuum manipulators have one central elastic backbone through which actuation/transmission elements can run. multi-backbone: the structure of these continuum robots has two or more elastic elements (either rods or tubes) parallel to each other and constrained with one another in some way. concentric-tube: the backbone is made of concentric tubes that are free to rotate and translate between each other, depending on the actuation happening at the base of the robot. === Actuation === The actuation strategy of continuum manipulators can be distinguished between extrinsic or intrinsic actuation, depending on where the actuation happens: extrinsic actuation: the actuation happens outside the main structure of the robot and the forces are transmitted via mechanical transmission; among these techniques, there are cable/tendon driven actuators and multi-backbone strategies. intrinsic actuation: the actuation mechanism operates within the structure of the robot; these strategies include pneumatic or hydraulic chambers and the shape memory effect. The Actuated Flexible Manifold (AFM), introduced by Medina, Shapiro, and Shvalb (2016), models flexible grid-based robots that approximate smooth manifolds using discrete segments, each contributing one degree of freedom. Their work provides forward and inverse kinematics for planar and spatial configurations, bridging hyper-redundant and continuum robotics. == Advantages == The particular design of continuum robots offers several advantages with respect to rigid-link robots. First of all, as already said, continuum robots can more easily operate in environments that require a high level of dexterity, adaptability and flexibility. Moreover, the simplicity of their structure makes continuum robots more prone to miniaturisation. The rise of continuum robots has also paved the way for the development of soft continuum manipulators. These continuum manipulators are made of highly compliant materials that are flexible and can adapt and deform according to the surrounding environment. The "softness" of their material grants higher safety in human-robot interactions. == Disadvantages == The particular design of continuum robots also introduces many challenges. To properly and safely use continuum robots, it is crucial to have an accurate force and shape sensing system. Traditionally, this is done using cameras that are not suitable for some of the applications of continuum robots (e.g. minimally invasive surgery), or using electromagnetic sensors that are however disturbed by the presence of magnetic objects in the environment. To solve this issue, in the last years fiber-Bragg-grating sensors have been proposed as a possible alternative and have shown promising results. It is also necessary to notice that while the mechanical properties of rigid-link robots are fully understood, the comprehension of the behaviour and properties of continuum robots is still subject of study and debate. This poses new challenges in developing accurate models and control algorithms for this kind of robots. == Modelling == Creating an accurate model that can predict the shape of a continuum robot allows to properly control the robot's shape. There are three main approaches to model continuum robots: Cosserat rod theory: this approach is an exact solution to the static of a continuum robot, as it is not subject to any assumption. It solves a set of equilibrium equations between position, orientation, internal force and torque of the robot. This method requires to be solved numerically and it is therefore computationally expensive, due to its high complexity. Constant curvature: this technique assumes the backbone to be made of a series of mutually tangent sections that can be approximated as arcs with constant curvature. This approach is also known as piecewise constant-curvature. This assumption can be applied to the entire segment of the backbone or to its subsegments. This model has shown promising results, however it must be taken into account that the segment/subsegments of the backbone may not comply to the constant curvature assumption and therefore the model's behaviour may not entirely reflect the behaviour of the robot. Rigid-link model: this approach is based on the assumption that the continuum robot can be divided in small segments with rigid links. This is a strong assumption, since if the number of segments is too low, the model hardly behaves like the continuum robot, while increasing the number of segments means increasing the number of variables, and thus complexity. Despite this limitation, rigid-link modelling allows the use of the standard control techniques that are well known for rigid-link robots. It has been proven that this model can be coupled with shape and force sensing to mitigate its inaccuracy and can lead to promising results. == Sensing == To develop accurate control algorithms, it is necessary to complement the presented modelling techniques with real time shape sensing. The following options are currently available: Electromagnetic (EM) sensing: shape is reconstructed thanks to the mutual induction between a magnetic field generator and a magnetic field sensor. The most common external EM tracking system is the commercially available NDI Aurora: small sensors can be placed on the robot and their position is tracked in an external generated magnetic field. The validity of this method has been extensively assessed, however its performance is hindered by the limited workspace, whose dimension depends on the magnetic field. Another alternative is to embed the sensors internally in the continuum robot, combining magnetic sensors with Hall effect sensors: the magnetic field is measured at the level of the Hall effect sensors in order to estimate the deflection of the robot. However, it has been noticed that the higher the bending of the manipulator, the higher is the estimation error, due to crosstalk between sensors and magnets. Optical sensing: fiber Bragg grating sensors incorporated in an optical fiber can be embedded into the backbone of the continuum robot to estimate its shape; these sensors can only reflect a small range of the input light spectrum depending on their strain; therefore, by measuring the strain on each sensor it is possible to obtain the shape of the robot. This type of sensor is however expensive and is more prone to breaking in case of excessive strain, and this can happen in robots that can perform high deflections. == Control strategies == The control strategies can be distinguished in static and dynamic; the first one is based on the steady-state assumption, while the latter also considers the dynamic behaviour of the continuum robot. We can also differentiate between model-based controllers, that depend on a model of the robot, and model-free, that learn the robot's behaviour from data. Model-based static controllers: they rely on one of the modelling approaches presented above; once the model is defined, the kinematics must be inverted to obtain the desired actuator or configuration space variables. There are several ways to do this, like differential inverse kinematics, direct inversion or optimization. Model-free static controllers: these approaches learn directly, via machine learning techniques (e.g. regression methods and neural networks), the inverse kinematic or the direct kinematic representation of the con

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  Hubert Dreyfus

  Hubert Lederer Dreyfus ( DRY-fəs; October 15, 1929 – April 22, 2017) was an American philosopher and a professor of philosophy at the University of California, Berkeley. His main interests included phenomenology, existentialism and the philosophy of both psychology and literature, as well as the philosophical implications of artificial intelligence. He was widely known for his exegesis of Martin Heidegger, which critics labeled "Dreydegger". Dreyfus was featured in Tao Ruspoli's film Being in the World (2010), and was among the philosophers interviewed by Bryan Magee for the BBC Television series The Great Philosophers (1987). The Futurama character Professor Hubert Farnsworth is partly named after him, writer Eric Kaplan having been a former student. == Life and career == Dreyfus was born on 15 October 1929, in Terre Haute, Indiana, to Stanley S. and Irene (Lederer) Dreyfus. He attended Harvard University from 1947. With a senior honors thesis on Causality and Quantum Theory (for which W. V. O. Quine was the main examiner) he was awarded a B.A. summa cum laude in 1951 and joined Phi Beta Kappa. He was awarded a M.A. in 1952. He was a Teaching Fellow at Harvard from 1952 to 1953 (as he was again in 1954 and 1956). Then, on a Harvard Sheldon traveling fellowship, Dreyfus studied at the University of Freiburg from 1953 to 1954. During this time he had an interview with Martin Heidegger. Sean D. Kelly records that Dreyfus found the meeting 'disappointing.' A brief mention of it was made by Dreyfus during his 1987 BBC interview with Bryan Magee in remarks that are revealing of both his and Heidegger's opinion of the work of Jean-Paul Sartre. Between 1956 and 1957, Dreyfus undertook research at the Husserl Archives at the University of Louvain on a Fulbright Fellowship. Towards the end of his stay, his first (jointly authored) paper "Curds and Lions in Don Quijote" would appear in print. After acting as an instructor in philosophy at Brandeis University (1957–1959), he attended the Ecole Normale Supérieure, Paris, on a French government grant (1959–1960). From 1960, first as an instructor, then as an assistant and then associate professor, Dreyfus taught philosophy at the Massachusetts Institute of Technology (MIT). In 1964, with his dissertation Husserl's Phenomenology of Perception, he obtained his Ph.D. from Harvard. (Due to his knowledge of Husserl, Dagfinn Føllesdal sat on the thesis committee but he has asserted that Dreyfus "was not really my student.") That same year, his co-translation (with his first wife) of Sense and Non-Sense by Maurice Merleau-Ponty was published. Also in 1964, and whilst still at MIT, he was employed as a consultant by the RAND Corporation to review the work of Allen Newell and Herbert A. Simon in the field of artificial intelligence (AI). This resulted in the publication, in 1965, of the "famously combative" Alchemy and Artificial Intelligence, which proved to be the first of a series of papers and books attacking the AI field's claims and assumptions. The first edition of What Computers Can't Do would follow in 1972, and this critique of AI (which has been translated into at least ten languages) would establish Dreyfus's public reputation. However, as the editors of his Festschrift noted: "the study and interpretation of 'continental' philosophers... came first in the order of his philosophical interests and influences." === Berkeley === In 1968, although he had been granted tenure, Dreyfus left MIT and became an associate professor of philosophy at the University of California, Berkeley, (winning, that same year, the Harbison Prize for Outstanding Teaching). In 1972 he was promoted to full professor. Though Dreyfus retired from his chair in 1994, he continued as professor of philosophy in the Graduate School (and held, from 1999, a joint appointment in the rhetoric department). He continued to teach philosophy at UC Berkeley until his last class in December 2016. Dreyfus was elected a fellow of the American Academy of Arts and Sciences in 2001. He was also awarded an honorary doctorate for "his brilliant and highly influential work in the field of artificial intelligence" and his interpretation of twentieth century continental philosophy by Erasmus University. Dreyfus died on April 22, 2017. His younger brother and sometimes collaborator, Stuart Dreyfus, is a professor emeritus of industrial engineering and operations research at the University of California, Berkeley. == Dreyfus' criticism of AI == Dreyfus' critique of artificial intelligence (AI) concerns what he considers to be the four primary assumptions of AI research. The first two assumptions are what he calls the "biological" and "psychological" assumptions. The biological assumption is that the brain is analogous to computer hardware and the mind is analogous to computer software. The psychological assumption is that the mind works by performing discrete computations (in the form of algorithmic rules) on discrete representations or symbols. Dreyfus claims that the plausibility of the psychological assumption rests on two others: the epistemological and ontological assumptions. The epistemological assumption is that all activity (either by animate or inanimate objects) can be formalized (mathematically) in the form of predictive rules or laws. The ontological assumption is that reality consists entirely of a set of mutually independent, atomic (indivisible) facts. It's because of the epistemological assumption that workers in the field argue that intelligence is the same as formal rule-following, and it's because of the ontological one that they argue that human knowledge consists entirely of internal representations of reality. On the basis of these two assumptions, workers in the field claim that cognition is the manipulation of internal symbols by internal rules, and that, therefore, human behaviour is, to a large extent, context free (see contextualism). Therefore, a truly scientific psychology is possible, which will detail the 'internal' rules of the human mind, in the same way the laws of physics detail the 'external' laws of the physical world. However, it is this key assumption that Dreyfus denies. In other words, he argues that we cannot now (and never will be able to) understand our own behavior in the same way as we understand objects in, for example, physics or chemistry: that is, by considering ourselves as things whose behaviour can be predicted via 'objective', context free scientific laws. According to Dreyfus, a context-free psychology is a contradiction in terms. Dreyfus's arguments against this position are taken from the phenomenological and hermeneutical tradition (especially the work of Martin Heidegger). Heidegger argued that, contrary to the cognitivist views (on which AI has been based), our being is in fact highly context-bound, which is why the two context-free assumptions are false. Dreyfus doesn't deny that we can choose to see human (or any) activity as being 'law-governed', in the same way that we can choose to see reality as consisting of indivisible atomic facts... if we wish. But it is a huge leap from that to state that because we want to or can see things in this way that it is therefore an objective fact that they are the case. In fact, Dreyfus argues that they are not (necessarily) the case, and that, therefore, any research program that assumes they are will quickly run into profound theoretical and practical problems. Therefore, the current efforts of workers in the field are doomed to failure. Dreyfus argues that to get a device or devices with human-like intelligence would require them to have a human-like being-in-the-world and to have bodies more or less like ours, and social acculturation (i.e. a society) more or less like ours. (This view is shared by psychologists in the embodied psychology (Lakoff and Johnson 1999) and distributed cognition traditions. His opinions are similar to those of robotics researchers such as Rodney Brooks as well as researchers in the field of artificial life.) Contrary to a popular misconception, Dreyfus never predicted that computers would never beat humans at chess. In Alchemy and Artificial Intelligence, he only reported (correctly) the state of the art of the time: "Still no chess program can play even amateur chess." Daniel Crevier writes: "time has proven the accuracy and perceptiveness of some of Dreyfus's comments. Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier." == Webcasting philosophy == When UC Berkeley and Apple began making a selected number of lecture classes freely available to the public as podcasts beginning around 2006, a recording of Dreyfus teaching a course called "Man, God, and Society in Western Literature – From Gods to God and Back" rose to the 58th most popular webcast on iTunes. These webcasts have attracted the attention of many, including non-academics, to Dreyfus and his

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  AI Dungeon

  AI Dungeon is a single-player/multiplayer text adventure game which uses artificial intelligence (AI) to generate content and allows players to create and share adventures and custom prompts. The game's first version was made available in May 2019, and its second version (initially called AI Dungeon 2) was released on Google Colaboratory in December 2019. It was later ported that same month to its current cross-platform web application. The AI model was then reformed in July 2020. == Gameplay == AI Dungeon is a text adventure game that uses artificial intelligence to generate random storylines in response to player-submitted stimuli. In the game, players are prompted to choose a setting for their adventure (e.g. fantasy, mystery, apocalyptic, cyberpunk, zombies), followed by other options relevant to the setting (such as character class for fantasy settings). After beginning an adventure, four main interaction methods can be chosen for the player's text input: Do: Must be followed by a verb, allowing the player to perform an action. Say: Must be followed by dialogue sentences, allowing players to communicate with other characters. Story: Can be followed by sentences describing something that happens to progress the story, or that players want the AI to know for future events. See: Must be followed by a description, allowing the player to perceive events, objects, or characters. Using this command creates an AI generated image, and does not affect gameplay. The game adapts and responds to most actions the player enters. Providing blank inputs can be used to prompt the AI to generate further content, and the game also provides players with options to undo or redo or modify recent events to improve the game's narrative. Players can also tell the AI what elements to "remember" for reference in future parts of their playthrough. === User-generated content === In addition to AI Dungeon's pre-configured settings, players can create custom "adventures" from scratch by describing the setting in text format, which the AI will then generate a setting from. These custom adventures can be published for others to play, with an interface for browsing published adventures and leaving comments under them. === Multiplayer === AI Dungeon includes a multiplayer mode in which different players each have their own character and take turns interacting with the AI within the same game session. Multiplayer supports both online play across multiple devices or local play using a shared device. The game's hosts are able to supervise the AI and modify its output. Unlike the single-player game, in which actions and stories use second person narration, multiplayer game stories are presented using third-person narration. === Worlds === AI Dungeon allows players to set their adventures within specific "Worlds" that give context to the broader environment where the adventure takes place. This feature was first released with two different worlds available for selection: Xaxas, a "world of peace and prosperity"; and Kedar, a "world of dragons, demons, and monsters". == Development == === AI Dungeon Classic (Early GPT-2) === The first version of AI Dungeon (sometimes referred to as AI Dungeon Classic) was designed and created by Nick Walton of Brigham Young University's "Perception, Control, and Cognition" deep learning laboratory in March 2019 during a hackathon. Before this, Walton had been working as an intern for several companies in the field of autonomous vehicles. This creation used an early version of the GPT-2 natural-language-generating neural network, created by OpenAI, allowing it to generate its original adventure narratives. During his first interactions with GPT-2, Walton was partly inspired by the tabletop game Dungeons & Dragons (D&D), which he had played for the first time with his family a few months earlier: I realized that there were no games available that gave you the same freedom to do anything that I found in [Dungeons & Dragons] ... You can be so creative compared to other games. This led him to wonder if an AI could function as a dungeon master. Unlike later versions of AI Dungeon, the original did not allow players to specify any action they wanted. Instead, it generated a finite list of possible actions to choose from. This first version of the game was released to the public in May 2019. It is not to be confused with another GPT-2-based adventure game, GPT Adventure, created by Northwestern University neuroscience postgraduate student Nathan Whitmore, also released on Google Colab several months after the public release of AI Dungeon. === AI Dungeon 2 (Full GPT-2) === In November 2019, a new, "full" version of GPT-2 was released by OpenAI. This new model included support for 1.5 billion parameters (which determine the accuracy with which a machine learning model can perform a task), compared with the 126 million parameter version used in the earliest stages of AI Dungeon's development. The game was recreated by Walton, leveraging this new version of the model, and temporarily rebranded as AI Dungeon 2. AI Dungeon 2's AI was given more focused training compared to its predecessor, using genre-specific text. This training material included approximately 30 megabytes of content web-scraped from chooseyourstory.com (an online community website of content inspired by interactive gamebooks, written by contributors of multiple skill levels, using logic of differing complexity) and multiple D&D rulebooks and adventures. The new version was released in December 2019 as open-source software available on GitHub. It was accessible via Google Colab, an online tool for data scientists and AI researchers that allows for free execution of code on Google-hosted machines. It could also be run locally on a PC, but in both cases, it required players to download the full model, around 5 gigabytes of data. Within days of the initial release, this mandatory download resulted in bandwidth charges of over $20,000, forcing the temporary shut-down of the game until a peer-to-peer alternative solution was established. Due to the game's sudden and explosive growth that same month, however, it became closed-source, proprietary software and was relaunched by Walton's start-up development team, Latitude (with Walton taking on the role of CTO). This relaunch constituted mobile apps for iOS and Android (built by app developer Braydon Batungbacal) on December 17. Other members of this team included Thorsten Kreutz for the game's long-term strategy and the creator's brother, Alan Walton, for hosting infrastructure. At this time, Nick Walton also established a Patreon campaign to support the game's further growth (such as the addition of multiplayer and voice support, along with longer-term plans to include music and image content) and turn the game into a commercial endeavor, which Walton felt was necessary to cover the costs of delivering a higher-quality version of the game. AI Dungeon was one of the only known commercial applications to be based upon GPT-2. Following its first announcement in December 2019, a multiplayer mode was added to the game in April 2020. Hosting a game in this mode was originally restricted to premium subscribers, although any players could join a hosted game. === Dragon model release (GPT-3) === In July 2020, the developers introduced a premium-exclusive version of the AI model, named Dragon, which uses OpenAI's API for leveraging the GPT-3 model without maintaining a local copy (released on June 11, 2020). GPT-3 was trained with 570 gigabytes of text content (approximately one trillion words, with a $12 million development cost) and can support 175 billion parameters, compared to the 40 gigabytes of training content and 1.5 billion parameters of GPT-2. The free model was also upgraded to a less-advanced version of GPT-3 and was named Griffin. Speaking shortly after this release, on the differences between GPT-2 and GPT-3, Walton stated: [GPT-3 is] one of the most powerful AI models in the world... It's just much more coherent in terms of understanding who the characters are, what they're saying, what's going on in the story and just being able to write an interesting and believable story. In the latter half of 2020, the "Worlds" feature was added to AI Dungeon, providing players with a selection of overarching worlds in which their adventures can take place. In February 2021, it was announced that AI Dungeon's developers, Latitude, had raised $3.3 million in seed funding (led by NFX, with participation from Album VC and Griffin Gaming Partners) to "build games with 'infinite' story possibilities." This funding intended to move AI content creation beyond the purely text-based nature of AI Dungeon as it existed at the time. After its announcement on August 20, a new "See" interaction mode was made available for all players and added to the game on August 30, 2022. AI Dungeon was retired from Steam on March 12, 2024. == Reception == Approximate

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  OpenNN

  OpenNN (Open Neural Networks Library) is a software library written in the C++ programming language which implements neural networks, a main area of deep learning research. The library is open-source, licensed under the GNU Lesser General Public License. == Characteristics == The software implements any number of layers of non-linear processing units for supervised learning. This deep architecture allows the design of neural networks with universal approximation properties. Additionally, it allows multiprocessing programming by means of OpenMP, in order to increase computer performance. OpenNN contains machine learning algorithms as a bundle of functions. These can be embedded in other software tools, using an application programming interface, for the integration of the predictive analytics tasks. In this regard, a graphical user interface is missing but some functions can be supported by specific visualization tools. == History == The development started in 2003 at the International Center for Numerical Methods in Engineering, within the research project funded by the European Union called RAMFLOOD (Risk Assessment and Management of FLOODs). Then it continued as part of similar projects. OpenNN is being developed by the startup company Artelnics. == Applications == OpenNN is a general purpose artificial intelligence software package. It uses machine learning techniques for solving predictive analytics tasks in different fields. For instance, the library has been applied in the engineering, energy, or chemistry sectors.

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  Adobe Encore

  Adobe Encore (previously Adobe Encore DVD) was a DVD authoring software tool produced by Adobe Systems and targeted at professional video producers. Video and audio resources could be used in their current format for development, allowing the user to transcode them to MPEG-2 video and Dolby Digital audio upon project completion. DVD menus could be created and edited in Adobe Photoshop using special layering techniques. Adobe Encore did not support writing to a Blu-ray Disc using AVCHD 2.0. Encore is bundled with Adobe Premiere Pro CS6. Adobe Encore CS6 was the last release. While Premiere Pro CC has moved to the Creative Cloud, Encore has now been discontinued. == Licensing == All forms of Adobe Encore used a proprietary licensing system from its developer, Adobe Systems. Versions 1.0 and 1.5 required a separate license fee (rather than making 1.5 available as a free update). Version 3, also known as CS3, was sold only in bundle with Premiere CS3. Encore CS4, CS5, CS5.5 and CS6 were only sold in the Premiere Pro CS4, CS5, CS5.5 and CS6 bundles, respectively. Adobe CC subscribers no longer have access to Adobe Encore CS6. Adobe Encore is not included with Premiere Pro CC. == Functionality == Adobe Encore allowed for creating interactive DVD menus from Photoshop documents, which could be tweaked from within Encore. Video and audio streams could be embedded in the DVD and be made to play when certain elements of the menu are interacted with. It had similar functionality to Adobe Flash and Premiere Pro, due to its ability to both edit video on a timeline and embed interactive content.

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  CatBoost

  CatBoost is an open-source software library developed by Yandex. It provides a gradient boosting framework which, among other features, attempts to solve for categorical features using a permutation-driven alternative to the classical algorithm. It works on Linux, Windows, macOS, and is available in Python, R, and models built using CatBoost can be used for predictions in C++, Java, C#, Rust, Core ML, ONNX, and PMML. The source code is licensed under Apache License and available on GitHub. InfoWorld magazine awarded the library "The best machine learning tools" in 2017. along with TensorFlow, Pytorch, XGBoost and 8 other libraries. Kaggle listed CatBoost as one of the most frequently used machine learning (ML) frameworks in the world. It was listed as the top-8 most frequently used ML framework in the 2020 survey and as the top-7 most frequently used ML framework in the 2021 survey. As of April 2022, CatBoost is installed about 100000 times per day from PyPI repository == Features == CatBoost has gained popularity compared to other gradient boosting algorithms primarily due to the following features Native handling for categorical features Fast GPU training Visualizations and tools for model and feature analysis Using oblivious trees or symmetric trees for faster execution Ordered boosting to overcome overfitting == History == In 2009 Andrey Gulin developed MatrixNet, a proprietary gradient boosting library that was used in Yandex to rank search results. Since 2009 MatrixNet has been used in different projects at Yandex, including recommendation systems and weather prediction. In 2014–2015 Andrey Gulin worked with a team of researchers to start a new project called Tensornet which was aimed at solving the problem of "how to work with categorical data". Their work resulted in several proprietary Gradient Boosting libraries with different approaches to handling categorical data. In 2016 the Machine Learning Infrastructure team led by Anna Dorogush started working on Gradient Boosting in Yandex, including Matrixnet and Tensornet. They implemented and open-sourced the next version of Gradient Boosting library called CatBoost, which has support for categorical and text data, GPU training, model analysis, and visualization tools. CatBoost was open-sourced in July 2017 and is under active development in Yandex and the open-source community. == Application == JetBrains uses CatBoost for code completion Cloudflare uses CatBoost for bot detection Careem uses CatBoost to predict future destinations of the rides

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  Automatic1111

  AUTOMATIC1111 Stable Diffusion Web UI (SD WebUI, A1111, or Automatic1111) is an open source generative artificial intelligence program that allows users to generate images from a text prompt. It uses Stable Diffusion as the base model for its image capabilities together with a large set of extensions and features to customize its output. == History == SD WebUI was released on GitHub on August 22, 2022, by AUTOMATIC1111, 1 month after the initial release of Stable Diffusion. At the time, Stable Diffusion could only be run via the command line. SD WebUI quickly rose in popularity and has been described as "the most popular tool for running diffusion models locally." SD WebUI is one of the most popular user interfaces for Stable Diffusion, together with ComfyUI. In February 2024, a book was published by ja:Gijutsu Hyoronsha on using Stable Diffusion with SD WebUI in Japanese. As of July 2024, the project had 136,000 stars on GitHub. == Features == SD WebUI uses Gradio for its user interface. Each parameter in the Stable Diffusion program is exposed via a UI interface within SD WebUI. SD WebUI contains additional parameters not included in Stable Diffusion itself, such as support for Low-rank adaptations, ControlNet and custom variational autoencoders. SD WebUI supports prompt weighting, image-to-image based generation, inpainting, outpainting and image scaling. It supports over 20 samplers including DDIM, Euler, Euler a, DPM++ 2M Karras, and UniPC. It is also used for its various optimizations over the base Stable Diffusion. == Stable Diffusion WebUI Forge == Stable Diffusion WebUI Forge (Forge) is a notable fork of SD WebUI started by Lvmin Zhang, who is also the creator of ControlNet and Fooocus. The initial goal of Forge was to improve the performance and features of SD WebUI with the intention to upstream changes back to SD WebUI. One of Forge's optimizations allowed users with low VRAM to generate images faster on some versions of Stable Diffusion. It improved generation speed for users with 8GB and 6GB VRAM by 30-45% and 60-75%, respectively. Forge also includes extra features such as support for more samplers than standard SD WebUI. Some of Forge's optimizations were borrowed from ComfyUI, and others were developed by the Forge team. In August 2024, Forge added support for the Flux diffusion model developed by Black Forest Labs, which is not yet supported by SD WebUI.

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  Buddhism and artificial intelligence

  The relationship between Buddhist philosophy and artificial intelligence (AI) includes how principles such as the reduction of suffering and ethical responsibility may influence AI development. Buddhist scholars and philosophers have explored questions such as whether AI systems could be considered sentient beings under Buddhist definitions, and how Buddhist ethics might guide the design and application of AI technologies. Some Buddhist scholars, including Somparn Promta and Kenneth Einar Himma, have analyzed the ethical implications of AI, emphasizing the distinction between satisfying sensory desires and pursuing the reduction of suffering. Other thinkers, such as Thomas Doctor and colleagues, have proposed applying the Bodhisattva vow—a commitment to alleviate suffering for all sentient beings—as a guiding principle for AI system design. Buddhist scholars and ethicists have examined Buddhist ethical principles, such as nonviolence, in relation to AI, focusing on the need to ensure that AI technologies are not used to cause harm. == Context == === Sentient beings === A major goal in Buddhist philosophy is the removal of suffering for all sentient beings, an aspiration often referred to in the Bodhisattva vow. Discussions about artificial intelligence (AI) in relation to Buddhist principles have raised questions about whether artificial systems could be considered sentient beings or how such systems might be developed in ways that align with Buddhist concepts. Buddhists have varying opinions about AI sentience, but if AI systems are determined to be sentient under Buddhist definitions, their suffering would also need to be addressed and alleviated in accordance with the principles of Buddhist thought. == Buddhist principles in AI system design == === Nonviolence and AI === The broadest ethical concern is that artificial intelligence should align with the Buddhist principle of nonviolence. From this perspective, AI systems should not be designed or used to cause harm. === Instrumental and transcendental goals === Scholars Somparn Promta and Kenneth Einar Himma have argued that the advancement of artificial intelligence can only be considered instrumentally good, rather than good a priori, from a Buddhist perspective. They propose two main goals for AI designers and developers: to set ethical and pragmatic objectives for AI systems, and to fulfill these objectives in morally permissible ways. Promta and Himma identify two potential purposes for creating AI systems. The first is to fulfill our sensory desires and survival instincts, similar to other tools. They suggest that many AI developers implicitly prioritize this goal by focusing on technicalities rather than broader functionalities. The second, and more important goal according to Buddhist teachings, is to transcend these desires and instincts. In texts like the Brahmajāla Sutta and minor Malunkya Sutta, the Buddha emphasizes that sensory desires and survival instincts confine beings to suffering, and that eliminating suffering is the primary goal of human life. Promta and Himma argue that AI has the potential to assist humanity in transcending suffering by helping individuals overcome survival-driven instincts. === Intelligence as care === Thomas Doctor, Olaf Witkowski, Elizaveta Solomonova, Bill Duane, and Michael Levin propose redefining intelligence through the concept of "intelligence as care," and promote it as a slogan. Inspired by the Bodhisattva vow, they suggest this principle could guide AI system design. The Bodhisattva vow involves a formal commitment to alleviate suffering for all sentient beings, with four primary objectives: Liberating all beings from suffering. Extirpating all forms of suffering. Mastering endless techniques of practicing Dharma (Pali: dhammakkhandha, Sanskrit: dharmaskandha). Achieving ultimate enlightenment (Sanskrit: अनुत्तर सम्यक् सम्बोधि, Romanized: anuttara-samyak-saṃbodhi). This approach positions AI as a tool for exercising infinite care and alleviating stress and suffering for sentient beings. Doctor et al. emphasize that AI development should align with these altruistic principles.

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  Tandem Money

  Tandem is one of the UK's original challenger banks. Tandem is a digital bank with a mobile app, and no branches. The acquisition of Harrods Bank in 2017 allowed the company to provide services using the former's banking licence. Tandem Bank Limited is authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority. Tandem has offices across the UK in Blackpool, Cardiff, Durham and London, employing over 500 people. == History == The company was founded by Ricky Knox, Matt Cooper and Michael Kent in 2014. In December 2016, Tandem announced that it had secured a £35 million investment from The Sanpower Group, the Chinese company that also owned the department store House of Fraser; however, £29 million of this investment was later revoked by Sanpower over concerns that the Chinese Government would object to the investment following increased restrictions on outbound investment in China. This resulted in a delay in the launch of Tandem's savings products, which, at the time of the revocation, was expected imminently and, more importantly, meant that Tandem volunteered the return of their banking license but retained all other permissions. In April 2018, Tandem launched fixed-term savings accounts, offering one-, two- and three-year terms through its app. === Acquisitions === In August 2017, it was announced that Tandem would fully acquire Harrods Bank, founded in 1893, in a deal that would bring a near-£200m loan book, over £300m of deposits and nearly £80 million of capital. Prior to its sale to Tandem Money, Harrods Bank catered for high-net-worth (HNW) individuals and operated from the Harrods store in Knightsbridge, London. It offered a variety of personal and business current and savings accounts, mortgages, foreign currency and gold bullion trading services. On 7 August 2017, Tandem Money Limited announced a deal to acquire 100% of Harrods Bank Limited shares. The purchase deal closed successfully on 11 January 2018. In March 2018, Tandem agreed to acquire Pariti Technologies Limited, developers of the Pariti money management application. In August 2020 Tandem acquired green home improvement loan specialists Allium Lending Group. It was announced on 8 February 2021 that Tandem had agreed to purchase the mortgage book from private bank Bank and Clients, consisting of 300 B&C customers for an undisclosed amount. In January 2022 Tandem Bank acquired consumer lender Oplo, creating a combined business with £1.2 billion of total assets. In April 2023, it was announced that Tandem had acquired money-sharing app Loop Money. At the time of the purchase, one of Loop's founders – Paul Pester – was also chairman at Tandem. == Features == Tandem Bank offers customers savings, mortgages, personal and secured loans, green home improvement loans and motor finance. In November 2022, the bank launched its new Tandem Marketplace, providing information and resources to help promote greener living.

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  Fifth Generation Computer Systems

  The Fifth Generation Computer Systems (FGCS; Japanese: 第五世代コンピュータ, romanized: daigosedai konpyūta) was a 10-year initiative launched in 1982 by Japan's Ministry of International Trade and Industry (MITI) to develop computers based on massively parallel computing and logic programming. The project aimed to create an "epoch-making computer" with supercomputer-like performance and to establish a platform for future advancements in artificial intelligence. Although FGCS was noted as ahead of its time, and its ambitious goals contributed significantly to the development of concurrent logic programming, it ultimately ended in commercial failure. The term "fifth generation" was chosen to emphasize the system's advanced nature. In the history of computing hardware, there had been four prior "generations" of computers: the first generation utilized vacuum tubes; the second, transistors and diodes; the third, integrated circuits; and the fourth, microprocessors. While earlier generations focused on increasing the number of logic elements within a single CPU, it was widely believed at the time that the fifth generation would achieve enhanced performance through the use of massive numbers of CPUs. == Background == In the late 1960s until the early 1970s, there was much talk about "generations" of computer hardware, then usually organized into three generations First generation: Thermionic vacuum tubes. Mid-1940s. IBM pioneered the arrangement of vacuum tubes in pluggable modules. The IBM 650 was a first-generation computer. Second generation: Transistors. 1956. The era of miniaturization begins. Transistors are much smaller than vacuum tubes, draw less power, and generate less heat. Discrete transistors are soldered to circuit boards, with interconnections accomplished by stencil-screened conductive patterns on the reverse side. The IBM 7090 was a second-generation computer. Third generation: Integrated circuits (silicon chips containing multiple transistors). 1964. A pioneering example is the ACPX module used in the IBM 360/91, which, by stacking layers of silicon over a ceramic substrate, accommodated over 20 transistors per chip; the chips could be packed together onto a circuit board to achieve unprecedented logic densities. The IBM 360/91 was a hybrid second and third-generation computer. Omitted from this taxonomy is the "zeroth-generation" computer based on metal gears (such as the IBM 407) or mechanical relays (such as the Mark I), and the post-third-generation computers based on Very Large Scale Integrated (VLSI) circuits. There was also a parallel set of generations for software: First generation: Machine language. Second generation: Low-level programming languages such as Assembly language. Third generation: Structured high-level programming languages such as C, COBOL and FORTRAN. Fourth generation: "Non-procedural" high-level programming languages (such as object-oriented languages). Throughout these multiple generations up to the 1970s, Japan built computers following U.S. and British leads. In the mid-1970s, the Ministry of International Trade and Industry stopped following western leads and started looking into the future of computing on a small scale. They asked the Japan Information Processing Development Center (JIPDEC) to indicate a number of future directions, and in 1979 offered a three-year contract to carry out more in-depth studies along with industry and academia. It was during this period that the term "fifth-generation computer" started to be used. Prior to the 1970s, MITI guidance had successes such as an improved steel industry, the creation of the oil supertanker, the automotive industry, consumer electronics, and computer memory. MITI decided that the future was going to be information technology. However, the Japanese language, particularly in its written form, presented and still presents obstacles for computers. As a result of these hurdles, MITI held a conference to seek assistance from experts. The primary fields for investigation from this initial project were: Inference computer technologies for knowledge processing Computer technologies to process large-scale data bases and knowledge bases High-performance workstations Distributed functional computer technologies Super-computers for scientific calculation == Project launch == The aim was to build parallel computers for artificial intelligence applications using concurrent logic programming. The project imagined an "epoch-making" computer with supercomputer-like performance running on top of large databases (as opposed to a traditional filesystem) using a logic programming language to define and access the data using massively parallel computing/processing. They envisioned building a prototype machine with performance between 100M and 1G LIPS, where a LIPS is a Logical Inference Per Second. At the time typical workstation machines were capable of about 100k LIPS. They proposed to build this machine over a ten-year period, 3 years for initial R&D, 4 years for building various subsystems, and a final 3 years to complete a working prototype system. In 1982 the government decided to go ahead with the project, and established the Institute for New Generation Computer Technology (ICOT) through joint investment with various Japanese computer companies. After the project ended, MITI would consider an investment in a new "sixth generation" project. Ehud Shapiro captured the rationale and motivations driving this project: "As part of Japan's effort to become a leader in the computer industry, the Institute for New Generation Computer Technology has launched a revolutionary ten-year plan for the development of large computer systems which will be applicable to knowledge information processing systems. These Fifth Generation computers will be built around the concepts of logic programming. In order to refute the accusation that Japan exploits knowledge from abroad without contributing any of its own, this project will stimulate original research and will make its results available to the international research community." === Logic programming === The target defined by the FGCS project was to develop "Knowledge Information Processing systems" (roughly meaning, applied Artificial Intelligence). The chosen tool to implement this goal was logic programming. Logic programming approach as was characterized by Maarten Van Emden – one of its founders – as: The use of logic to express information in a computer. The use of logic to present problems to a computer. The use of logical inference to solve these problems. More technically, it can be summed up in two equations: Program = Set of axioms. Computation = Proof of a statement from axioms. The Axioms typically used are universal axioms of a restricted form, called Horn-clauses or definite-clauses. The statement proved in a computation is an existential statement. The proof is constructive, and provides values for the existentially quantified variables: these values constitute the output of the computation. Logic programming was thought of as something that unified various gradients of computer science (software engineering, databases, computer architecture and artificial intelligence). It seemed that logic programming was a key missing connection between knowledge engineering and parallel computer architectures. == Results == After having influenced the consumer electronics field during the 1970s and the automotive world during the 1980s, the Japanese had developed a strong reputation. The launch of the FGCS project spread the belief that parallel computing was the future of all performance gains, producing a wave of apprehension in the computer field. Soon parallel projects were set up in the US as the Strategic Computing Initiative and the Microelectronics and Computer Technology Corporation (MCC), in the UK as Alvey, and in Europe as the European Strategic Program on Research in Information Technology (ESPRIT), as well as the European Computer‐Industry Research Centre (ECRC) in Munich, a collaboration between ICL in Britain, Bull in France, and Siemens in Germany. The project ran from 1982 to 1994, spending a little less than ¥57 billion (about US$320 million) total. After the FGCS Project, MITI stopped funding large-scale computer research projects, and the research momentum developed by the FGCS Project dissipated. However MITI/ICOT embarked on a neural-net project which some called the Sixth Generation Project in the 1990s, with a similar level of funding. Per-year spending was less than 1% of the entire R&D expenditure of the electronics and communications equipment industry. For example, the project's highest expenditure year was 7.2 million yen in 1991, but IBM alone spent 1.5 billion dollars (370 billion yen) in 1982, while the industry spent 2150 billion yen in 1990. === Concurrent logic programming === In 1982, during a visit to the ICOT, Ehud Shapiro invented Concurrent Prolog, a novel programming language t

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  Emospark

  EmoSpark is an artificial intelligence console created in London, United Kingdom by Patrick Levy-Rosenthal. The device uses facial recognition and language analysis to evaluate human emotion and convey responsive content according to the emotion. The console measures 90 mm x 90 mm x 90 mm and is cube shaped. It operates on an "Emotional Processing Unit", an emotion chip developed by Emoshape Inc. that enables the system to create emotional profile graphs of its surroundings. The emotional processing unit is a patent pending technology that is said to create synthesised emotional responses in machines. EmoSpark was funded through an Indiegogo campaign which aimed to raise $200,000. == Product overview == EmoSpark was created by French inventor Patrick Levy-Rosenthal, as an emotionally intelligent artificial life unit for the home that can interact with people. It is powered by Android and can communicate with users through typed input from a computer, tablet, smartphone or TV as well as through spoken commands. The EmoSpark's features are categorized into two types: functional and emotional. EmoSpark is said to have the ability to perform practical software-based tasks. Through the smartphone interface, it is able to gauge a person’s emotions and is reported to have a conversational library of over 2 million sentences. The face-tracking technology identifies users likes and dislikes to categorize their emotional responses to stimuli such as videos and music. The device has an emotional spectrum that is composed of eight emotions which are surprise, sadness, joy, trust, fear, disgust, anger and anticipation. EmoSpark monitors a person's facial expressions and emotions through images from an external camera, which are then processed through an emotion text analysis and content analysis. The New Scientist reported that EmoSpark had the ability to work on the best way to cheer up its users, emotionally. === Connectivity === EmoSpark is able to connect to Facebook and YouTube to present users with content designed to improve their mood, or to Wikipedia for collaborative knowledge that can be shared when users ask questions of it. Through Android OS, EmoSpark is able to be customized with Google Play store apps. The cube is expected to develop its own personality based on the communications it has had with the people using it. == EmoShape == The Emotion Chip (EPU) used in the cube is created by the US company Emoshape Inc, founded by Levy-Rosenthal. EmoShape Ltd (UK) was the company that developed EmoSpark cube. Patrick Levy-Rosenthal also received the IST Prize in 2005 from the European Council for Applied Science, Technology and Engineering.

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  Computational Intelligence (journal)

  Computational Intelligence Journal is a peer-reviewed scientific journal covering research on artificial intelligence and computer science. The journal published novel research as well as innovative applications in a broad range of AI, covering Computational Intelligence is an artificial intelligence journal publishing novel research on a broad range of experimental and theoretical topics in AI and computer science. With a broad scope, the journal covers machine learning, knowledge mining, web intelligence, AI language, and philosophical implications. The journal was established in 1985 and is published by Wiley-Blackwell. Currently, the editors-in-chief is Diane Inkpen. The quality of the journal as an academic publishing venue is evaluated according to public citation impact metrics. in 2022, the Computational Intelligence Journal CiteScore of Scopus was 5.3, while Clarivate's Web of Science gives it 0.39 in the Journal Citation Indicator and 2,8 in the Journal Impact Factor.

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  Moving object detection

  Moving object detection is a technique used in computer vision and image processing. Multiple consecutive frames from a video are compared by various methods to determine if any moving object is detected. Moving objects detection has been used for wide range of applications like video surveillance, activity recognition, road condition monitoring, airport safety, monitoring of protection along marine border, etc. == Definition == Moving object detection is to recognize the physical movement of an object in a given place or region. By acting segmentation among moving objects and stationary area or region, the moving objects' motion can be tracked and thus analyzed later. To achieve this, consider a video is a structure built upon single frames, moving object detection is to find the foreground moving target(s), either in each video frame or only when the moving target shows the first appearance in the video. == Traditional methods == Among all the traditional moving object detection methods, we could categorize them into four major approaches: Background subtraction, Frame differencing, Temporal Differencing, and Optical Flow. === Frame differencing === Instead of using traditional approach, to use image subtraction operator by subtracting second and images afterwards, the frame differencing method makes comparisons between two successive frames to detect moving targets. === Temporal differencing === The temporal differencing method identifies the moving object by applying pixel-wise difference method with two or three consecutive frames.

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  Yale shooting problem

  The Yale shooting problem is a conundrum or scenario in formal situational logic on which early logical solutions to the frame problem fail. The name of this problem comes from a scenario proposed by its inventors, Steve Hanks and Drew McDermott, working at Yale University when they proposed it. In this scenario, Fred (later identified as a turkey) is initially alive and a gun is initially unloaded. Loading the gun, waiting for a moment, and then shooting the gun at Fred is expected to kill Fred. However, if inertia is formalized in logic by minimizing the changes in this situation, then it cannot be uniquely proved that Fred is dead after loading, waiting, and shooting. In one solution, Fred indeed dies; in another (also logically correct) solution, the gun becomes mysteriously unloaded and Fred survives. Technically, this scenario is described by two fluents (a fluent is a condition that can change truth value over time): a l i v e {\displaystyle alive} and l o a d e d {\displaystyle loaded} . Initially, the first condition is true and the second is false. Then, the gun is loaded, some time passes, and the gun is fired. Such problems can be formalized in logic by considering four time points 0 {\displaystyle 0} , 1 {\displaystyle 1} , 2 {\displaystyle 2} , and 3 {\displaystyle 3} , and turning every fluent such as a l i v e {\displaystyle alive} into a predicate a l i v e ( t ) {\displaystyle alive(t)} depending on time. A direct formalization of the statement of the Yale shooting problem in logic is the following one: a l i v e ( 0 ) {\displaystyle alive(0)} ¬ l o a d e d ( 0 ) {\displaystyle \neg loaded(0)} t r u e → l o a d e d ( 1 ) {\displaystyle true\rightarrow loaded(1)} l o a d e d ( 2 ) → ¬ a l i v e ( 3 ) {\displaystyle loaded(2)\rightarrow \neg alive(3)} The first two formulae represent the initial state. The third formula formalizes the effect of loading the gun at time 1 {\displaystyle 1} . The fourth formula formalizes the effect of shooting at Fred at time 2 {\displaystyle 2} . This is a simplified formalization in which action names are neglected and the effects of actions are directly specified for the time points in which the actions are executed. See situation calculus for details. The formulae above, while being direct formalizations of the known facts, do not suffice to correctly characterize the domain. Indeed, ¬ a l i v e ( 1 ) {\displaystyle \neg alive(1)} is consistent with all these formulae, although there is no reason to believe that Fred dies before the gun has been shot. The problem is that the formulae above only include the effects of actions, but do not specify that all fluents not changed by the actions remain the same. In other words, a formula a l i v e ( 0 ) ≡ a l i v e ( 1 ) {\displaystyle alive(0)\equiv alive(1)} must be added to formalize the implicit assumption that loading the gun only changes the value of l o a d e d {\displaystyle loaded} and not the value of a l i v e {\displaystyle alive} . The necessity of a large number of formulae stating the obvious fact that conditions do not change unless an action changes them is known as the frame problem. An early solution to the frame problem was based on minimizing the changes. In other words, the scenario is formalized by the formulae above (that specify only the effects of actions) and by the assumption that the changes in the fluents over time are as minimal as possible. The rationale is that the formulae above enforce all effect of actions to take place, while minimization should restrict the changes to exactly those due to the actions. In the Yale shooting scenario, one possible evaluation of the fluents in which the changes are minimized is the following one. This is the expected solution. It contains two fluent changes: l o a d e d {\displaystyle loaded} becomes true at time 1 and a l i v e {\displaystyle alive} becomes false at time 3. The following evaluation also satisfies all formulae above. In this evaluation, there are still two changes only: l o a d e d {\displaystyle loaded} becomes true at time 1 and false at time 2. As a result, this evaluation is considered a valid description of the evolution of the state, although there is no valid reason to explain l o a d e d {\displaystyle loaded} being false at time 2. The fact that minimization of changes leads to wrong solution is the motivation for the introduction of the Yale shooting problem. While the Yale shooting problem has been considered a severe obstacle to the use of logic for formalizing dynamical scenarios, solutions to it have been known since the late 1980s. One solution involves the use of predicate completion in the specification of actions: in this solution, the fact that shooting causes Fred to die is formalized by the preconditions: alive and loaded, and the effect is that alive changes value (since alive was true before, this corresponds to alive becoming false). By turning this implication into an if and only if statement, the effects of shooting are correctly formalized. (Predicate completion is more complicated when there is more than one implication involved.) A solution proposed by Erik Sandewall was to include a new condition of occlusion, which formalizes the “permission to change” for a fluent. The effect of an action that might change a fluent is therefore that the fluent has the new value, and that the occlusion is made (temporarily) true. What is minimized is not the set of changes, but the set of occlusions being true. Another constraint specifying that no fluent changes unless occlusion is true completes this solution. The Yale shooting scenario is also correctly formalized by the Reiter version of the situation calculus, the fluent calculus, and the action description languages. In 2005, the 1985 paper in which the Yale shooting scenario was first described received the AAAI Classic Paper award. In spite of being a solved problem, that example is still sometimes mentioned in recent research papers, where it is used as an illustrative example (e.g., for explaining the syntax of a new logic for reasoning about actions), rather than being presented as a problem.

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  Tree (abstract data type)

  In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree, or sometimes only with the leaf nodes, which have no children nodes. The abstract data type (ADT) can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations (a specific type of adjacency list). Representations might also be more complicated, for example using indexes or ancestor lists for performance. Trees as used in computing are similar to but can be different from mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory. == Terminology == A node is a structure which may contain data and connections to other nodes, sometimes called edges or links. Each node in a tree has zero or more child nodes, which are below it in the tree (by convention, trees are drawn with descendants going downwards). A node that has a child is called the child's parent node (or superior). All nodes have exactly one parent, except the topmost root node, which has none. A node might have many ancestor nodes, such as the parent's parent. Child nodes with the same parent are sibling nodes. Typically siblings have an order, with the first one conventionally drawn on the left. Some definitions allow a tree to have no nodes at all, in which case it is called empty. An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has height −1. Each non-root node can be treated as the root node of its own subtree, which includes that node and all its descendants. Other terms used with trees: Neighbor Parent or child. Ancestor A node reachable by repeated proceeding from child to parent. Descendant A node reachable by repeated proceeding from parent to child. Also known as subchild. Degree For a given node, its number of children. A leaf, by definition, has degree zero. Degree of tree The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Complete tree A tree with every level filled, except the last. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of a tree Number of nodes in the tree. == Common operations == Enumerating all the items Enumerating a section of a tree Searching for an item Adding a new item at a certain position on the tree Deleting an item Pruning: Removing a whole section of a tree Grafting: Adding a whole section to a tree Finding the root for any node Finding the lowest common ancestor of two nodes === Traversal and search methods === Stepping through the items of a tree, by means of the connections between parents and children, is called walking the tree, and the action is a walk of the tree. Often, an operation might be performed when a pointer arrives at a particular node. A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk; a walk in which a node's left subtree, then the node itself, and finally its right subtree are traversed is called an in-order traversal. (This last scenario, referring to exactly two subtrees, a left subtree and a right subtree, assumes specifically a binary tree.) A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed. == Representations == There are many different ways to represent trees. In working memory, nodes are typically dynamically allocated records with pointers to their children, their parents, or both, as well as any associated data. If of a fixed size, the nodes might be stored in a list. Nodes and relationships between nodes might be stored in a separate special type of adjacency list. In relational databases, nodes are typically represented as table rows, with indexed row IDs facilitating pointers between parents and children. Nodes can also be stored as items in an array, with relationships between them determined by their positions in the array (as in a binary heap). A binary tree can be implemented as a list of lists: the head of a list (the value of the first term) is the left child (subtree), while the tail (the list of second and subsequent terms) is the right child (subtree). This can be modified to allow values as well, as in Lisp S-expressions, where the head (value of first term) is the value of the node, the head of the tail (value of second term) is the left child, and the tail of the tail (list of third and subsequent terms) is the right child. Ordered trees can be naturally encoded by finite sequences, for example with natural numbers. == Examples of trees and non-trees == == Type theory == As an abstract data type, the abstract tree type T with values of some type E is defined, using the abstract forest type F (list of trees), by the functions: value: T → E children: T → F nil: () → F node: E × F → T with the axioms: value(node(e, f)) = e children(node(e, f)) = f In terms of type theory, a tree is an inductive type defined by the constructors nil (empty forest) and node (tree with root node with given value and children). == Mathematical terminology == Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple path), with a distinguished root (one vertex is designated as the root), which determines the direction on the edges (arrows point away from the root; given an edge, the node that the edge points from is called the parent and the node that the edge points to is called the child), together with: an ordering on the child nodes of a given node, and a value (of some data type) at each node. Often trees have a fixed (more properly, bounded) branching factor (outdegree), particularly always having two child nodes (possibly empty, hence at most two non-empty child nodes), hence a "binary tree". Allowing empty trees makes some definitions simpler, some more complicated: a rooted tree must be non-empty, hence if empty trees are allowed the above definition instead becomes "an empty tree or a rooted tree such that ...". On the other hand, empty trees simplify defining fixed branching factor: with empty trees allowed, a binary tree is a tree such that every node has exactly two children, each of which is a tree (possibly empty). == Applications == Trees are commonly used to represent or manipulate hierarchical data in ap

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