AI Chatbot Quill

AI Chatbot Quill — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Morphological antialiasing

  Morphological antialiasing (MLAA) is a spatial anti-aliasing technique used in real-time computer graphics. It reduces artifacts, such as jaggies, when representing a high-resolution image at a lower resolution. MLAA is a post-process filtering which detects borders in the resulting image and then finds specific patterns in these. Anti-aliasing is achieved by blending pixels in these borders, according to the pattern they belong to and their position within the pattern. Introduced in 2009, MLAA was an early and influential example of anti-aliasing techniques done in post-processing, which makes them suitable for deferred shading. A similar method in this class is fast approximate anti-aliasing (FXAA). Temporal anti-aliasing, also a post-process, has become the most common anti-aliasing method for real-time rendering and video games. Enhanced subpixel morphological antialiasing, or SMAA, is an image-based GPU-based implementation of MLAA developed by Universidad de Zaragoza and Crytek.

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  Spatial computing

  Spatial computing refers to 3D human–computer interaction techniques that are perceived by users as taking place in the real world, in and around their bodies and physical environments, instead of constrained to and perceptually behind computer screens or in purely virtual worlds. This concept inverts the long-standing practice of teaching people to interact with computers in digital environments, and instead teaches computers to better understand and interact with people more naturally in the human world. This concept overlaps with and encompasses others including extended reality, augmented reality, mixed reality, natural user interface, contextual computing, affective computing, and ubiquitous computing. The usage for labeling and discussing these adjacent technologies is imprecise. Spatial computing devices include sensors—such as RGB cameras, depth cameras, 3D trackers, inertial measurement units, or other tools—to sense and track nearby human bodies (including hands, arms, eyes, legs, mouths) during ordinary interactions with people and computers in a 3D space. They further use computer vision to attempt to understand real world scenes, such as rooms, streets or stores, to read labels, to recognize objects, create 3D maps, and more. Quite often they also use extended reality and mixed reality to superimpose virtual 3D graphics and virtual 3D audio onto the human visual and auditory system as a way of providing information more naturally and contextually than traditional 2D screens. Spatial computing often refers to personal computing devices like headsets and headphones, but other human-computer interactions that leverage real-time spatial positioning for displays, like projection mapping or cave automatic virtual environment displays, can also be considered spatial computing if they leverage human-computer input for the participants. == History == The term "spatial computing" apparently originated in the field of GIS around 1985 or earlier to describe computations on large-scale geospatial information. Early examples of spatial computing in GIS include ArcInfo and its iterations, initially released in 1981, a part of ArcGIS along with ArcEditor, which together provide mapping, analysis, editing, and geoprocessing for geodatabases. This is somewhat related to the modern use, but on the scale of continents, cities, and neighborhoods. Modern spatial computing is more centered on the human scale of interaction, around the size of a living room or smaller. But it is not limited to that scale in the aggregate. In the early 1990s, as field of virtual reality was beginning to be commercialized beyond academic and military labs, a startup called Worldesign in Seattle used the term Spatial Computing to describe the interaction between individual people and 3D spaces, operating more at the human end of the scale than previous GIS examples may have contemplated. The company built a CAVE-like environment it called the Virtual Environment Theater, whose 3D experience was of a virtual flyover of the Giza Plateau, circa 3000 BC. Robert Jacobson, CEO of Worldesign, attributes the origins of the term to experiments at the Human Interface Technology Lab, at the University of Washington, under the direction of Thomas A. Furness III. Jacobson was a co-founder of that lab before spinning off this early VR startup. In 1997, an academic publication by T. Caelli, Peng Lam, and H. Bunke called "Spatial Computing: Issues in Vision, Multimedia and Visualization Technologies" introduced the term more broadly for academic audiences, focusing on a variety of topics such as image processing, dead reckoning navigation, object recognition, and visualizing spatial data. The specific term "spatial computing" was later referenced again in 2003 by Simon Greenwold, as "human interaction with a machine in which the machine retains and manipulates referents to real objects and spaces". MIT Media Lab alumnus John Underkoffler gave a TED talk in 2010 giving a live demo of the multi-screen, multi-user spatial computing systems being developed by Oblong Industries, which sought to bring to life the futuristic interfaces conceptualized by Underkoffler in the films Minority Report and Iron Man. Google Earth, initially released by Keyhole Inc. in 2001 and re-released by Google in 2005 can be considered a capable GIS and includes advanced geospatial tools and capabilities. == Notable instances of the use of spatial computing == In 2019, Microsoft HoloLens released a video outlining Airbus' partnership with Microsoft Azure to utilize the latter's mixed reality services for streamlining and improving the aircraft design process, as well as reducing the error in development. Airbus utilized the HoloLens 2 to this end, and the executive vice president of engineering claimed that their design process' validation phases were "hugely accelerated by 80 percent", as well as "strongly believe[d]" that up to 30% improvements in their industrial tasks could be attained with the HoloLens 2. During the presentational video, Airbus cited the maturity of Microsoft Azure services as "key" for their usage of the HoloLens 2. Also in 2019, the U.S. army partnered with Microsoft to produce a HoloLens based Integrated Visual Augmentation System (IVAS) to enhance infantry members by giving troops various abilities, including but not limited to using holographs to train, projecting 3D maps into their vision, and seeing through smoke and corners. Microsoft received tens of thousands of hours of feedback for their systems by 2021. Sergeant Marc Krugh at the time claimed that Microsoft's partnership has already caused the army to rethink some of its troops' operation strategy. == Products == === Apple Vision Pro === Apple announced Apple Vision Pro, a device it markets as a "spatial computer", on June 5, 2023. It includes several features such as Spatial Audio, two 4K micro-OLED displays, the Apple R1 chip and eye tracking, and released in the United States on February 2, 2024. In announcing the platform, Apple invoked its history of popularizing 2D graphical user interfaces that supplanted prior human-computer interface mechanisms such as the command line. Apple suggests the introduction of spatial computing as a new category of interactive device, on the same level of importance as the introduction of the 2D GUI. Apple Vision Pro runs on a new operating system called visionOS, which combines eye tracking, gesture recognition, and voice input to enable immersive interaction without physical controllers. The platform is aimed at productivity, entertainment, collaboration, and enterprise use cases. === Magic Leap === Magic Leap had also previously used the term “spatial computing” to describe its own devices. Its first headset, the Magic Leap 1, was released on August 8, 2018. Magic Leap’s technology enables the display of content into the real world using an optical see-through head-mounted display, which projects an overlay of a virtual world into the user’s field of view. This allows for an experience where the physical and digital worlds are perceived simultaneously. === Microsoft Hololens === On February 24, 2019, Microsoft released the HoloLens 2, which includes mixed reality tools and can generate interactable, manipulatable holograms in 3D space. The holograms in question can be related to a physical object or completely independent and free-floating. The Azure Spatial Anchors cloud service was released simultaneously, which gives the holograms capability to persist across time and many individuals' devices. === Meta Quest === The Meta Quest 3, a mixed reality gaming headset that includes spatial audio, two color cameras, and grants the ability to interact with virtual characters released on October 9, 2023, at a notably cheaper price than the Apple Vision Pro, but with reduced capabilities. === Snap Spectacles === Spectacles (product) are augmented reality glasses developed by Snap Inc.. The latest generation includes a 46-degree stereoscopic display, adjustable tint, and Snapdragon processors. Spectacles allow users to interact with a collection of augmented reality experiences designed for education, entertainment, and utility. Currently, the device is in the hands of selected developers and creators, as part of an experimental AR ecosystem focused on creativity, use case exploration and expression.

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  Algorism

  Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. == Etymology == The word algorism comes from the name Al-Khwārizmī (c. 780–850), a Persian mathematician, astronomer, geographer and scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the Algebra. In late medieval Latin, algorismus, the corruption of his name, simply meant the "decimal number system" that is still the meaning of modern English algorism. During the 17th century, the French form for the word – but not its meaning – was changed to algorithm, following the model of the word logarithm, this form alluding to the ancient Greek arithmos = number. English adopted the French very soon afterwards, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. In English, it was first used about 1230 and then by Chaucer in 1391. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. which translates as: This present art, in which we use those twice five Indian figures, is called algorismus. The word algorithm also derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts. == History == Starting with the integer arithmetic developed in India using base 10 notation, Al-Khwārizmī along with other mathematicians in medieval Islam, documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point. This system was popularized in Europe by Leonardo of Pisa, now known as Fibonacci.

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  Sparse identification of non-linear dynamics

  Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and sparse Bayesian inference) on a library of nonlinear candidate functions of the snapshots against the derivatives to find the governing equations. This procedure relies on the assumption that most physical systems only have a few dominant terms which dictate the dynamics, given an appropriately selected coordinate system and quality training data. It has been applied to identify the dynamics of fluids, based on proper orthogonal decomposition, as well as other complex dynamical systems, such as biological networks. == Mathematical Overview == First, consider a dynamical system of the form x ˙ = d d t x ( t ) = f ( x ( t ) ) , {\displaystyle {\dot {\textbf {x}}}={\frac {d}{dt}}{\textbf {x}}(t)={\textbf {f}}({\textbf {x}}(t)),} where x ( t ) ∈ R n {\displaystyle {\textbf {x}}(t)\in \mathbb {R} ^{n}} is a state vector (snapshot) of the system at time t {\displaystyle t} and the function f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} defines the equations of motion and constraints of the system. The time derivative may be either prescribed or numerically approximated from the snapshots. With x {\displaystyle {\textbf {x}}} and x ˙ {\displaystyle {\dot {\textbf {x}}}} sampled at m {\displaystyle m} equidistant points in time ( t 1 , t 2 , ⋯ , t m {\displaystyle t_{1},t_{2},\cdots ,t_{m}} ), these can be arranged into matrices of the form X = [ x T ( t 1 ) x T ( t 2 ) ⋮ x T ( t m ) ] = [ x 1 ( t 1 ) x 2 ( t 1 ) ⋯ x n ( t 1 ) x 1 ( t 2 ) x 2 ( t 2 ) ⋯ x n ( t 2 ) ⋮ ⋮ ⋱ ⋮ x 1 ( t m ) x 2 ( t m ) ⋯ x n ( t m ) ] , {\displaystyle {\bf {{X}={\begin{bmatrix}\mathbf {x} ^{\mathsf {T}}(t_{1})\\\mathbf {x} ^{\mathsf {T}}(t_{2})\\\vdots \\\mathbf {x} ^{\mathsf {T}}(t_{m})\end{bmatrix}}={\begin{bmatrix}x_{1}(t_{1})&x_{2}(t_{1})&\cdots &x_{n}(t_{1})\\x_{1}(t_{2})&x_{2}(t_{2})&\cdots &x_{n}(t_{2})\\\vdots &\vdots &\ddots &\vdots \\x_{1}(t_{m})&x_{2}(t_{m})&\cdots &x_{n}(t_{m})\end{bmatrix}},}}} and similarly for X ˙ {\displaystyle {\dot {\mathbf {X} }}} . Next, a library Θ ( X ) {\displaystyle \mathbf {\Theta } (\mathbf {X} )} of nonlinear candidate functions of the columns of X {\displaystyle {\textbf {X}}} is constructed, which may be constant, polynomial, or more exotic functions (like trigonometric and rational terms, and so on): Θ ( X ) = [ | | | | | | 1 X X 2 X 3 ⋯ sin ⁡ ( X ) cos ⁡ ( X ) ⋯ | | | | | | ] {\displaystyle \ \ \ {\bf {{\Theta }({\bf {{X})={\begin{bmatrix}\vline &\vline &\vline &\vline &&\vline &\vline &\\1&{\bf {X}}&{\bf {{X}^{2}}}&{\bf {{X}^{3}}}&\cdots &\sin({\bf {{X})}}&\cos({\bf {{X})}}&\cdots \\\vline &\vline &\vline &\vline &&\vline &\vline &\end{bmatrix}}}}}}} The number of possible model structures from this library is combinatorially high. f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} is then substituted by Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} and a vector of coefficients Ξ = [ ξ 1 ξ 2 ⋯ ξ n ] {\displaystyle {\bf {{\Xi }=\left[{\bf {{\xi }_{1}{\bf {{\xi }_{2}\cdots {\bf {{\xi }_{n}}}}}}}\right]}}} determining the active terms in f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} : X ˙ = Θ ( X ) Ξ {\displaystyle {\dot {\bf {X}}}={\bf {{\Theta }({\bf {{X}){\bf {\Xi }}}}}}} Because only a few terms are expected to be active at each point in time, an assumption is made that f ( x ( t ) ) {\displaystyle {\textbf {f}}({\textbf {x}}(t))} admits a sparse representation in Θ ( X ) {\displaystyle {\bf {{\Theta }({\textbf {X}})}}} . This then becomes an optimization problem in finding a sparse Ξ {\displaystyle {\bf {\Xi }}} which optimally embeds X ˙ {\displaystyle {\dot {\textbf {X}}}} . In other words, a parsimonious model is obtained by performing least squares regression on the system (4) with sparsity-promoting ( L 1 {\displaystyle L_{1}} ) regularization ξ k = arg ⁡ min ξ k ′ | | X ˙ k − Θ ( X ) ξ k ′ | | 2 + λ | | ξ k ′ | | 1 , {\displaystyle {\bf {{\xi }_{k}={\underset {\bf {{\xi }'_{k}}}{\arg \min }}\left|\left|{\dot {\bf {X}}}_{k}-{\bf {{\Theta }({\bf {{X}){\bf {{\xi }'_{k}}}}}}}\right|\right|_{2}+\lambda \left|\left|{\bf {{\xi }'_{k}}}\right|\right|_{1},}}} where λ {\displaystyle \lambda } is a regularization parameter. Finally, the sparse set of ξ k {\displaystyle {\bf {{\xi }_{k}}}} can be used to reconstruct the dynamical system: x ˙ k = Θ ( x ) ξ k {\displaystyle {\dot {x}}_{k}={\bf {{\Theta }({\bf {{x}){\bf {{\xi }_{k}}}}}}}}

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  Feature (machine learning)

  In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a data set. Choosing informative, discriminating, and independent features is crucial to producing effective algorithms for pattern recognition, classification, and regression tasks. Features are usually numeric, but other types such as strings and graphs are used in syntactic pattern recognition, after some pre-processing step such as one-hot encoding. The concept of "features" is related to that of explanatory variables used in statistical techniques such as linear regression. == Feature types == In feature engineering, two types of features are commonly used: numerical and categorical. Numerical features are continuous values that can be measured on a scale. Examples of numerical features include age, height, weight, and income. Numerical features can be used in machine learning algorithms directly. Categorical features are discrete values that can be grouped into categories. Examples of categorical features include gender, color, and zip code. Categorical features typically need to be converted to numerical features before they can be used in machine learning algorithms. This can be done using a variety of techniques, such as one-hot encoding, label encoding, and ordinal encoding. The type of feature that is used in feature engineering depends on the specific machine learning algorithm that is being used. Some machine learning algorithms, such as decision trees, can handle both numerical and categorical features. Other machine learning algorithms, such as linear regression, can only handle numerical features. == Classification == A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear predictor function (related to the perceptron) with a feature vector as input. The method consists of calculating the scalar product between the feature vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector include nearest neighbor classification, neural networks, and statistical techniques such as Bayesian approaches. == Examples == In character recognition, features may include histograms counting the number of black pixels along horizontal and vertical directions, number of internal holes, stroke detection and many others. In speech recognition, features for recognizing phonemes can include noise ratios, length of sounds, relative power, filter matches, logarithmic Mel-scale spectral vectors and Mel-frequency cepstral coefficients, which represent the frequency characteristics of audio signals. In spam detection algorithms, features may include the presence or absence of certain email headers, the email structure, the language, the frequency of specific terms, the grammatical correctness of the text. In computer vision, there are a large number of possible features, such as edges and objects. == Feature vectors == In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing images, the feature values might correspond to the pixels of an image, while when representing texts the features might be the frequencies of occurrence of textual terms. Feature vectors are equivalent to the vectors of explanatory variables used in statistical procedures such as linear regression. Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is used to determine a score for making a prediction. The vector space associated with these vectors is often called the feature space. In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed. Higher-level features can be obtained from already available features and added to the feature vector; for example, for the study of diseases the feature 'Age' is useful and is defined as Age = 'Year of death' minus 'Year of birth' . This process is referred to as feature construction. Feature construction is the application of a set of constructive operators to a set of existing features resulting in construction of new features. Examples of such constructive operators include checking for the equality conditions {=, ≠}, the arithmetic operators {+,−,×, /}, the array operators {max(S), min(S), average(S)} as well as other more sophisticated operators, for example count(S, C) that counts the number of features in the feature vector S satisfying some condition C or, for example, distances to other recognition classes generalized by some accepting device. Feature construction has long been considered a powerful tool for increasing both accuracy and understanding of structure, particularly in high-dimensional problems. Applications include studies of disease and emotion recognition from speech. == Selection and extraction == The initial set of raw features can be redundant and large enough that estimation and optimization is made difficult or ineffective. Therefore, a preliminary step in many applications of machine learning and pattern recognition consists of selecting a subset of features, or constructing a new and reduced set of features to facilitate learning, and to improve generalization and interpretability. Extracting or selecting features is a combination of art and science; developing systems to do so is known as feature engineering. It requires the experimentation of multiple possibilities and the combination of automated techniques with the intuition and knowledge of the domain expert. Automating this process is feature learning, where a machine not only uses features for learning, but learns the features itself.

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  Documentation

  Documentation is any communicable material that is used to describe, explain, or instruct regarding some attributes of an object, system, or procedure, such as its parts, assembly, installation, maintenance, and use. As a form of knowledge management and knowledge organization, documentation can be provided on paper, online, or on digital or analog media, such as audio tape or CDs. Examples of such resources include user guides, white papers, online help, and quick-reference guides. Paper or hard-copy documentation has become less common. Contemporary documentation is often distributed through websites, software products, and other online applications. Documentation, understood as a set of instructional materials, should not be confused with documentation science, which is the study of the recording and retrieval of information. == Principles for producing documentation == While associated International Organization for Standardization (ISO) standards are not easily available publicly, a guide from other sources for this topic may serve the purpose. Documentation development may involve document drafting, formatting, submitting, reviewing, approving, distributing, reposting and tracking, etc., and are convened by associated standard operating procedure in a regulatory industry. It could also involve creating content from scratch. Documentation should be easy to read and understand. If it is too long and too wordy, it may be misunderstood or ignored. Clear, concise words should be used, and sentences should be limited to a maximum of 15 words. Documentation intended for a general audience should avoid gender-specific terms and cultural biases. In a series of procedures, steps should be clearly numbered. == Producing documentation == Technical writers and corporate communicators are professionals whose field and work is documentation. Ideally, technical writers have a background in both the subject matter and also in writing, managing content, and information architecture. Technical writers more commonly collaborate with subject-matter experts, such as engineers, technical experts, medical professionals, etc. to define and then create documentation to meet the user's needs. Corporate communications includes other types of written documentation, for example: Market communications (MarCom): MarCom writers endeavor to convey the company's value proposition through a variety of print, electronic, and social media. This area of corporate writing is often engaged in responding to proposals. Technical communication (TechCom): Technical writers document a company's product or service. Technical publications can include user guides, installation and configuration manuals, and troubleshooting and repair procedures. Legal writing: This type of documentation is often prepared by attorneys or paralegals. Compliance documentation: This type of documentation codifies standard operating procedures, for any regulatory compliance needs, as for safety approval, taxation, financing, and technical approval. Healthcare documentation: This field of documentation encompasses the timely recording and validation of events that have occurred during the course of providing health care. == Documentation in computer science == === Types === The following are typical software documentation types: Request for proposal Requirements/statement of work/scope of work Software design and functional specification System design and functional specifications Change management, error and enhancement tracking User acceptance testing Manpages The following are typical hardware and service documentation types: Network diagrams Network maps Datasheet for IT systems (server, switch, e.g.) Service catalog and service portfolio (Information Technology Infrastructure Library) === Software Documentation Folder (SDF) tool === A common type of software document written in the simulation industry is the SDF. When developing software for a simulator, which can range from embedded avionics devices to 3D terrain databases by way of full motion control systems, the engineer keeps a notebook detailing the development "the build" of the project or module. The document can be a wiki page, Microsoft Word document or other environment. They should contain a requirements section, an interface section to detail the communication interface of the software. Often a notes section is used to detail the proof of concept, and then track errors and enhancements. Finally, a testing section to document how the software was tested. This documents conformance to the client's requirements. The result is a detailed description of how the software is designed, how to build and install the software on the target device, and any known defects and workarounds. This build document enables future developers and maintainers to come up to speed on the software in a timely manner, and also provides a roadmap to modifying code or searching for bugs. === Software tools for network inventory and configuration === These software tools can automatically collect data of your network equipment. The data could be for inventory and for configuration information. The Information Technology Infrastructure Library requests to create such a database as a basis for all information for the IT responsible. It is also the basis for IT documentation. Examples include XIA Configuration. == Documentation in criminal justice == "Documentation" is the preferred term for the process of populating criminal databases. Examples include the National Counterterrorism Center's Terrorist Identities Datamart Environment, sex offender registries, and gang databases. == Documentation in early childhood education == Documentation, as it pertains to the early childhood education field, is "when we notice and value children's ideas, thinking, questions, and theories about the world and then collect traces of their work (drawings, photographs of the children in action, and transcripts of their words) to share with a wider community". Thus, documentation is a process, used to link the educator's knowledge and learning of the child/children with the families, other collaborators, and even to the children themselves. Documentation is an integral part of the cycle of inquiry - observing, reflecting, documenting, sharing and responding. Pedagogical documentation, in terms of the teacher documentation, is the "teacher's story of the movement in children's understanding". According to Stephanie Cox Suarez in "Documentation - Transforming our Perspectives", "teachers are considered researchers, and documentation is a research tool to support knowledge building among children and adults". Documentation can take many different styles in the classroom. The following exemplifies ways in which documentation can make the research, or learning, visible: Documentation panels (bulletin-board-like presentation with multiple pictures and descriptions about the project or event). Daily log (a log kept every day that records the play and learning in the classroom) Documentation developed by or with the children (when observing children during documentation, the child's lens of the observation is used in the actual documentation) Individual portfolios (documentation used to track and highlight the development of each child) Electronic documentation (using apps and devices to share documentation with families and collaborators) Transcripts or recordings of conversations (using recording in documentation can bring about deeper reflections for both the educator and the child) Learning stories (a narrative used to "describe learning and help children see themselves as powerful learners") The classroom as documentation (reflections and documentation of the physical environment of a classroom). Documentation is certainly a process in and of itself, and it is also a process within the educator. The following is the development of documentation as it progresses for and in the educator themselves: Develop(s) habits of documentation Become(s) comfortable with going public with recounting of activities Develop(s) visual literacy skills Conceptualize(s) the purpose of documentation as making learning styles visible, and Share(s) visible theories for interpretation purposes and further design of curriculum.

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  Applied Information Science in Economics

  The Applied Information Science in Economics (Russian: Прикладная информатика в Экономике) or Applied Computer Science in Economics is a professional qualification generally awarded in Russian Federation. The degree inherited from the U.S.S.R. education system also known as Specialist degree. The degree is awarded after five years of full-time study and includes several internships, course-works, thesis writing and defense. The degree has similarities with German Magister Artium or Diplom degree. However, due to the Bologna Process number of such degrees are declining. Degree focuses on applying mathematical methods in economics involving maximum information technology. It is very close to applied mathematics, but includes also major part of computer science. == List of specialty codes in the education system == 080801 - Applied computer science in economics 351400 - Applied computer science == Fields of activity == Organization and management; Project design; Experimental research; Marketing; Consulting; Operational and Maintenance. == Major == Information Science and Programming. High Level Methods of Information Science and Programming. Information Technologies in Economics. Computer Systems, Networks and Telecommunications Services. Operational Environments, Systems and Shells. Architecture and Design of Information Systems for Companies. Data Bases. Information security. Information Management. Imitative Simulation.

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  Sikidy

  Sikidy is a form of algebraic geomancy practiced by Malagasy peoples in Madagascar. It involves algorithmic operations performed on random data generated from tree seeds, which are ritually arranged in a tableau called a toetry and divinely interpreted after being mathematically operated on. Columns of seeds, designated "slaves" or "princes" belonging to respective "lands" for each, interact symbolically to express vintana ('fate') in the interpretation of the diviner. The diviner also prescribes solutions to problems and ways to avoid fated misfortune, often involving a sacrifice. The centuries-old practice derives from Islamic influence brought to the island by medieval Arab traders. The sikidy is consulted for a range of divinatory questions pertaining to fate and the future, including identifying sources of and rectifying misfortune, reading the fate of newborns, and planning annual migrations. The mathematics of sikidy involves Boolean algebra, symbolic logic and parity. == History == The practice is several centuries old, and is influenced by Arab geomantic traditions of Arab Muslim traders on the island. Most writers link the origins of sikidy to the "sea-going trade involving the southwest coast of India, the Persian Gulf, and the east coast of Africa in the 9th or 10th century C.E." Stephen Ellis and Solofo Randrianja describe sikidy as "probably one of the oldest components of Malagasy culture", writing that it most likely the product of an indigenous divinatory art later influenced by Islamic practice. Umar H. D. Danfulani writes that the integration of Arabic divination into indigenous divination is "clearly demonstrated" in Madagascar, where the Arabic astrological system was adapted to the indigenous agricultural system and meshed with Malagasy lunar months by "adapting indigenous months, volana, to the astrological months, vintana". Danfulani also describes the concepts in sikidy of "houses" (lands) and "kings in their houses" as retained from medieval Arabic astrology. Chemillier et al. say the practice's spread across Madagascar likely originated with the southeastern Antemoro people, among whom Arab influence was the strongest. Though the etymology of sikidy is unknown, it has been posited that the word derives from the Arabic sichr ('incantation' or 'charm'). Sikidy was of central importance to pre-Christian Malagasy religion, with one practitioner quoted in 1892 as calling sikidy "the Bible of our ancestors". A missionary report from 1616 describes one form of sikidy using tamarind seeds, and another using fingered markings in the sand. The early colonial French governor of Madagascar Étienne de Flacourt documented sikidy in the mid-17th century: Matatane country in southeastern Madagascar [...] where the Antemoro [...] live was a center of astrological study as early as the fourteenth century [...]. This area was also the site of early Arab settlements, although strict Islamic observances were lost centuries ago [...]. Historical evidence shows that Antemoro diviners, bearers of the astrological system, infiltrated nearly all the ancient kingdoms of Madagascar beginning in the sixteenth century. [...] Today, although many persons claim to be ombiasy [diviners], only the Antemoro diviners are considered true professionals. The area is still a famous place of learning where specialists go for training and then return to their home communities with a certain body of knowledge. Now we can better understand the degree of similarity of divination forms found throughout Madagascar. For centuries Matitanana has remained a training center for diviners who have migrated widely, usually attaining important positions in their home communities and with various royal families. Comparison of contemporary rites with centuries-old texts show that sikidy has been remarkably unchanged throughout its history. The "infiltration" of Malagasy kingdoms by Antemoro diviners, and Matitanana's role as a place for astrological and divinatory learning, help to explain the relatively uniform practicing of sikidy across Madagascar. Chemallier et al. write that the mathematical construction of the arrangement of seeds is procedurally consistent across all of Madagascar, with variations in practice between groups and regions being limited to more minor aspects, such as the alignment of figures according to cardinal directions. One exception is the simplified Merina sikidy joria. === Origin myths === Mythic tradition relating to the origin of sikidy "links [the practice] both to the return by walking on water of Arab ancestors who had intermarried with Malagasy but then left, and to the names of the days of the week" and holds that the art was supernaturally communicated to the ancestors, with Zanahary (the supreme deity of Malagasy religion) giving it to Ranakandriana, who then gave it to a line of diviners (Ranakandriana to Ramanitralanana to Rabibi-andrano to Andriambavi-maitso (who was a woman) to Andriam-bavi-nosy), the last of whom terminated the monopoly by giving it to the people, declaring: "Behold, I give you the sikidy, of which you may inquire what offerings you should present in order to obtain blessings; and what expiation you should make so as to avert evils, when any are ill or under apprehension of some future calamity". A mythic anecdote of Ranakandriana says that two men observed him one day playing in the sand. In fact he was practicing a form of sikidy worked in sand called sikidy alanana. The two men seized him, and Ranakandriana promised that he would teach them something if they released him. They agreed, and Ranakandriana taught them in depth how to work the sikidy. The two men then went to their chief and told him that they could tell him "the past and the future—what was good and what was bad—what increased and what diminished." The chief asked them to tell him how he could obtain plenty of cattle. The two men worked their sikidy and told the chief to kill all of his bulls, and that "great numbers would come to him" on the following Friday. The chieftain, doubting, asked what would happen if their prediction didn't come true, and the two men promised they would pay with their lives. The chief agreed and killed his bulls. On Thursday, thinking he'd been duped, he prematurely killed the first man of the two who'd told him about the divinatory art. On Friday, however, "vast herds" came amidst heavy rain, actually filling an immense plain in their crowd. The chieftain lamented the mpisikidy's wrongful execution and ordered for him a pompous funeral. The chieftain took the second man as his close adviser and friend, and trusted the sikidy forever afterwards. The British missionary William Ellis recorded in 1839 two idiomatic expressions used in Madagascar that come from this story: "Tsy mahandry andro Zoma" (lit. 'He cannot wait 'til Friday') is said of someone extremely impatient, and heavy rainshowers falling in rapid succession are called "sese omby" (lit. 'a crowding together of cattle'). == Rites and arrangement of seeds == The divination is performed by a practitioner called an mpisikidy, ny màsina (lit. 'sacred one'), ombiasy, or ambiàsa (derived from the Arabic anbia, meaning 'prophet') who guides the client through the process and interprets the results in the context of the client's inquiries and desires. As part of an mpisikidy's formal initiation into the art, which includes a long period of apprenticeship, the initiate (called a mianatsy) must gather 124 and 200 fàno (Entada sp.) or kily (tamarind) tree seeds for his subsequent ritual use in sikidy. Raymond Decary writes that, at least among the Sakalava, a man must be 40 years old before learning and practicing sikidy, or he risks death. Before beginning to study, a student practitioner must make incisions at the tips of his index finger, his middle finger, and his tongue, and put within the incisions a paste containing red pepper and crushed wasp. This paste impregnates the fingers that will move the seeds of the sikidy and the tongue that will speak their revelations with the power to decipher the sikidy. Once this is done, he leaves at dawn to search for a fano (Entada chrysostachys) tree. Upon finding it, he throws his spear at its branches, shaking the tree and causing its large seed pods to fall. During this act, some initiates say: "When you were on the steep peak and in the dense forest, on you the crabs climbed, from you the crocodiles made their bed, with their paws the birds trod on you. Whether you are suspended in the trees or buried, you are never dried up nor rotten." In his study (written in 1941 and revised in 1948), Decary reported that the salary paid by a mianatsy to his master is "not very high": up to five francs, plus a red rooster's feather. The mpisikidy ritually arranges his seeds into a sixteen-column table consisting of four columns of randomly-generated data (representing fate) and eight columns of data derived from logical ope

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  Dynamic texture

  Dynamic texture ( sometimes referred to as temporal texture) is the texture with motion which can be found in videos of sea-waves, fire, smoke, wavy trees, etc. Dynamic texture has a spatially repetitive pattern with time-varying visual pattern. Modeling and analyzing dynamic texture is a topic of images processing and pattern recognition in computer vision. Extracting features that describe the dynamic texture can be utilized for tasks of images sequences classification, segmentation, recognition and retrieval. Comparing with texture found within static images, analyzing dynamic texture is a challenging problem. It is important that the extracted features from dynamic texture combine motion and appearance description, and also be invariance to some transformation such as rotation, translation and illumination. == Analysis methods of dynamic texture == The methods of dynamic texture recognition can categorized as follows: Methods based on optical flow: by applying optical flow to the dynamic texture, velocity with direction and magnitude can be detected and used to recognize the dynamic texture. Due to simplicity of its computation, it is currently the most popular method. Methods computing geometric properties: this methods track the surfaces of motion trajectories in spatiotemporal domain. Methods based on local spatiotemporal filtering : this methods analyze the local spatiotemporal patterns and its orientation and energy and employ them as feature used for classification. Methods based on global spatiotemporal transform: this method characterize the motion at different scale using wavelets that can decompose the motion into local and global. Model-based methods : These methods aims at generating a model to describe the motion by a set of parameters. == Applications == - Segmenting the sequence images of natural scenes. This helps on differentiate between streets and grass alongside these streets which could be used in the application of navigations. - Motion detection : Dynamic texture features extracted from footage videos can be exploited to detect abnormal crowd activities. - Video classification: video of natural scenes or other scenes that exhibit dynamic textures. - Video retrieval : Dynamic textures can be employed as a feature retrieve videos that contain, for example, sea-waves, smoke, clouds, wavy trees.

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  Browsing

  Browsing is a kind of orienting strategy. It is supposed to identify something of relevance for the browsing organism. In context of humans, it is a metaphor taken from the animal kingdom. It is used, for example, about people browsing open shelves in libraries, window shopping, or browsing databases or the Internet. In library and information science, it is an important subject, both purely theoretically and as applied science aiming at designing interfaces which support browsing activities for the user. == Definition == In 2011, Birger Hjørland provided the following definition: "Browsing is a quick examination of the relevance of a number of objects which may or may not lead to a closer examination or acquisition/selection of (some of) these objects. It is a kind of orienting strategy that is formed by our "theories", "expectations" and "subjectivity". == Controversies == As with any kind of human psychology, browsing can be understood in biological, behavioral, or cognitive terms on the one hand or in social, historical, and cultural terms on the other hand. In 2007, Marcia Bates researched browsing from "behavioural" approaches, while Hjørland (2011a+b) defended a social view. Bates found that browsing is rooted in our history as exploratory, motile animals hunting for food and nesting opportunities. According to Hjørland (2011a), on the other hand, Marcia Bates' browsing for information about browsing is governed by her behavioral assumptions, while Hjørland's browsing for information about browsing is governed by his socio-cultural understanding of human psychology. In short: Human browsing is based on our conceptions and interests. === Is browsing a random activity? === Browsing is often understood as a random activity. Dictionary.com, for example, has this definition: "to glance at random through a book, magazine, etc.". Hjørland suggests, however, that browsing is an activity that is governed by our metatheories. We may dynamically change our theories and conceptions but when we browse, the activity is governed by the interests, conceptions, priorities and metatheories that we have at that time. Therefore, browsing is not totally random. == Browsing versus analytical search strategies == In 1997, Gary Marchionini wrote: "A fundamental distinction is made between analytical and browsing strategies [...]. Analytical strategies depend on careful planning, the recall of query terms, and iterative query reformulations and examinations of results. Browsing strategies are heuristic and opportunistic and depend on recognizing relevant information. Analytic strategies are batch oriented and half duplex (turn talking) like human conversation, whereas browsing strategies are more interactive, real-time exchanges and collaborations between the information seeker and the information system. Browsing strategies demand a lower cognitive load in advance and a steadier attentional load throughout the information-seeking process. When it comes to Browsing, giblets are amazing." == Orienting strategies == Some sociologists, such as Berger and Zelditch in 1993, Wagner in 1984, and Wagner & Berger in 1985, have used the term "orienting strategies". They find that orienting strategies should be understood as metatheories: "Consider the very large proportion of sociological theory that is in the form of metatheory. It is discussion about theory: about what concepts it should include, about how those concepts should be linked, and about how theory should be studied. Similar to Kuhn’s paradigms, theories of this sort provide guidelines or strategies for understanding social phenomena and suggest the proper orientation of the theorist to these phenomena; they are orienting strategies. Textbooks in theory frequently focus on orienting strategies such as functionalism, exchange, or ethnomethodology." Sociologists thus use metatheories as orienting strategies. We may generalize and say that all people use metatheories as orienting strategies and that this is what direct our attention and also our browsing – also when we are not conscious about it.

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  Driver scheduling problem

  The driver scheduling problem (DSP) is type of problem in operations research and theoretical computer science. The DSP consists of selecting a set of duties (assignments) for the drivers or pilots of vehicles (e.g., buses, trains, boats, or planes) involved in the transportation of passengers or goods, within the constraints of various legislative and logistical criteria. == Criteria and modelling == This very complex problem involves several constraints related to labour and company rules and also different evaluation criteria and objectives. Being able to solve this problem efficiently can have a great impact on costs and quality of service for public transportation companies. There is a large number of different rules that a feasible duty might be required to satisfy, such as Minimum and maximum stretch duration Minimum and maximum break duration Minimum and maximum work duration Minimum and maximum total duration Maximum extra work duration Maximum number of vehicle changes Minimum driving duration of a particular vehicle Operations research has provided optimization models and algorithms that lead to efficient solutions for this problem. Among the most common models proposed to solve the DSP are the Set Covering and Set Partitioning Models (SPP/SCP). In the SPP model, each work piece (task) is covered by only one duty. In the SCP model, it is possible to have more than one duty covering a given work piece. In both models, the set of work pieces that needs to be covered is laid out in rows, and the set of previously defined feasible duties available for covering specific work pieces is arranged in columns. The DSP resolution, based on either of these models, is the selection of the set of feasible duties that guarantees that there is one (SPP) or more (SCP) duties covering each work piece while minimizing the total cost of the final schedule.

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  Operational historian

  In manufacturing, an operational historian is a time-series database application that is developed for operational process data. Historian software is often embedded or used in conjunction with standard DCS and PLC control systems to provide enhanced data capture, validation, compression, and aggregation capabilities. Historians have been deployed in almost every industry and contribute to functions such as supervisory control, performance monitoring, quality assurance, and, more recently, machine learning applications which can learn from vast quantities of historical data. These systems were originally developed to capture instrumentation and control data, which led many to use the term "tag" for a stream of process data, referring to the physical "tags" which had been placed on instrumentation for manually capturing data. Raw data may be accessed via OPC HDA, SQL, or REST API interfaces. == Operational Support == Operational historians are typically used within the manufacturing facility by engineers and operators for supervisory functions and analysis. An operational historian will typically capture all instrumentation and control data, whereas an enterprise historian that is deployed to support business functions will capture only a subset of the plant data. Typically, these applications offer data access through dedicated APIs (Application Programming Interfaces) and SDKs (Software Development Kits) which offer high-performance read and write operations. These operate through vendor-specific or custom applications. Front-end tools for trending process data over time are the most common interfaces to these databases. Because these applications are typically deployed next to or near the source of their process data, they are often marketed and sold as 'real-time database systems.' This distinction varies among vendors, who often have to make tradeoffs in performance between data capture and presentation, and application and analysis functionality. The following is a list of typical challenges for operational historians: data collection from instrumentation and controls storage and archiving of very large volumes of data organization of data in the form of "tags" or "points" limiting of monitoring (alarms) and validation aggregation and interpolation manual data entry (MDE) == Data access == As opposed to enterprise historians, the data access layer in the operational historian is designed to offer sophisticated data fetching modes without complex information analysis facilities. The following settings are typically available for data access operations: Data scope (single point or tag, history based on time range, history based on sample count) Request modes (raw data, last-known value, aggregation, interpolation) Sampling (single point, all points without sampling, all points with interval sampling) Data omission (based on the sample quality, based on the sample value, based on the count) Even though the operational historians are rarely relational database management systems, they often offer SQL-based interfaces to query the database. In most of such implementations, the dialect does not follow the SQL standard in order to provide syntax for specifying data access operations parameters.

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  AstroPay

  AstroPay is a global digital wallet that provides users with a way to pay, send, and receive money. The app provides online payments, virtual and physical debit cards, peer-to-peer money transfers, and more. == History == AstroPay was founded in Uruguay in 2009 as a payment processing company. Over time, it expanded its services across Latin America, EMEA, and APAC. A significant milestone occurred in 2016, when AstroPay spun off dLocal, focusing on cross-border payments for emerging markets. dLocal became Uruguay's first unicorn and eventually went public through a successful IPO. In 2020, AstroPay spun off its payment processing services into a new entity, D24, to focus on mobile wallet for cross border. Between 2023 and 2024 the Company brought new leadership to guide its transition towards becoming a fully focused global digital multicurrency wallet where users save, send, and spend globally. This shift introduced enhanced features, including loyalty prepaid cards and multicurrency accounts. == Services == AstroPay offers three main products: AstroPay Wallet, AstroPay check-out, and AstroPay Platform. AstroPay Wallet is a digital wallet for consumers, where they have multicurrency accounts, prepaid card and marketplace. With AstroPay check-out, businesses can tap into AstroPay's wallet user base by accepting AstroPay as a payment method in their check-out options. Lastly, AstroPay Platform enables other businesses to use the AstroPay network to launch their own global wallet. == Brand endorsements, partnerships == AstroPay's marketing strategy has included the development of co-branded products with sports teams and other brand. The company sponsored Burnley Football Club during the 2018–19 Premier League season, renewing the partnership for the 2021–22 Premier League season when it became the club's official payment service partner. In August 2021, AstroPay entered into a partnership with the Wolverhampton Wanderers for the 2021-22 Premier League season, and the following year, became the team's shirt sponsor. Later, in September 2021, AstroPay expanded its partnership with Wolverhampton Wanderers, which included becoming the team's official payment partner and later, in 2023, co-launching a co-branded card. Other partnerships include Newcastle United in 2021 in the English Premier League. AstroPay made arrangements to ensure that branding and logo would be visible on the pitch-side LED advertising during Premier League matches. Furthermore, in June 2022, the company renewed it's partnership with Wolverhampton Wanderers for the 2022-23 Premier League season and launched its Wolves debit card in February 2023. Some other notable partnerships include: Universidad de Chile in 2024, Tottenham Hotspurs in 2023-25, and even a collaboration with Lionel Messi across all of Latin America. == Recent developments == AstroPay has refocused its strategy since 2023, pivoting from payment processing to concentrate on its global digital wallet. This move reflects a broader effort to redefine the company's market positioning by emphasizing global user-friendly financial services, while separating its identity from previous operations managed by dLocal and D24.

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  Retention period

  A retention period (associated with a retention schedule or retention program) is an aspect of records and information management (RIM) and the records life cycle that identifies the duration of time for which the information should be maintained or "retained", irrespective of format (paper, electronic, or other). Retention periods vary with different types of information, based on content and a variety of other factors, including internal organizational need, regulatory requirements for inspection or audit, legal statutes of limitation, involvement in litigation, and taxation and financial reporting needs, as well as other factors as defined by local, regional, state, national, and/or international governing entities. Once an applicable retention period has elapsed for a given type or series of information, and all holds/moratoriums have been released, the information is typically destroyed using an approved and effective destruction method, which renders the information completely and irreversibly unusable via any means. Alternatively, it may be converted from one form to another (e.g. from paper to electronic), depending on the defined retention period per format. Information with historical value beyond its "usable value" may be accessioned to the custody of an archive organization for permanent or extended long-term preservation. == Defensible disposition == Defensible disposition refers to the ability of an identified and applied retention period to effectively provide for the defense of the record, and its eventual destruction or accessioning when scrutinized within a court of law or by other review. It is commonly advised by records and information management (RIM) professionals that any and all retention periods applied to organizational information should be reviewed and approved for use by competent legal counsel, which represents the organization, and is familiar with the specific business needs and legal and regulatory requirements of the organization. Additionally, a practical approach to information assessment/classification, proper documentation of the disposition program, strategic review of disposition policy over time for efficacy are required for proper defensible disposition. == Guidance and education organizations == ARMA International Information and Records Management Society filerskeepers records retention FAQ

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  Sardinas–Patterson algorithm

  In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. The algorithm carries out a systematic search for a string which admits two different decompositions into codewords. As Knuth reports, the algorithm was rediscovered about ten years later in 1963 by Floyd, despite the fact that it was at the time already well known in coding theory. == Idea of the algorithm == Consider the code { a ↦ 1 , b ↦ 011 , c ↦ 01110 , d ↦ 1110 , e ↦ 10011 } {\displaystyle \{\,{\texttt {a}}\mapsto {\texttt {1}},{\texttt {b}}\mapsto {\texttt {011}},{\texttt {c}}\mapsto {\texttt {01110}},{\texttt {d}}\mapsto {\texttt {1110}},{\texttt {e}}\mapsto {\texttt {10011}}\,\}} . This code, which is based on an example by Berstel, is an example of a code which is not uniquely decodable, since the string 011101110011 can be interpreted as the sequence of codewords 01110 – 1110 – 011, but also as the sequence of codewords 011 – 1 – 011 – 10011. Two possible decodings of this encoded string are thus given by cdb and babe. In general, a codeword can be found by the following idea: In the first round, we choose two codewords x 1 {\displaystyle x_{1}} and y 1 {\displaystyle y_{1}} such that x 1 {\displaystyle x_{1}} is a prefix of y 1 {\displaystyle y_{1}} , that is, x 1 w = y 1 {\displaystyle x_{1}w=y_{1}} for some "dangling suffix" w {\displaystyle w} . If one tries first x 1 = 011 {\displaystyle x_{1}={\texttt {011}}} and y 1 = 01110 {\displaystyle y_{1}={\texttt {01110}}} , the dangling suffix is w = 10 {\displaystyle {\texttt {w}}={\texttt {10}}} . If we manage to find two sequences x 2 , … , x p {\displaystyle x_{2},\ldots ,x_{p}} and y 2 , … , y q {\displaystyle y_{2},\ldots ,y_{q}} of codewords such that x 2 ⋯ x p = w y 2 ⋯ y q {\displaystyle x_{2}\cdots x_{p}=wy_{2}\cdots y_{q}} , then we are finished: For then the string x = x 1 x 2 ⋯ x p {\displaystyle x=x_{1}x_{2}\cdots x_{p}} can alternatively be decomposed as y 1 y 2 ⋯ y q {\displaystyle y_{1}y_{2}\cdots y_{q}} , and we have found the desired string having at least two different decompositions into codewords. In the second round, we try out two different approaches: the first trial is to look for a codeword that has w as prefix. Then we obtain a new dangling suffix w, with which we can continue our search. If we eventually encounter a dangling suffix that is itself a codeword (or the empty word), then the search will terminate, as we know there exists a string with two decompositions. The second trial is to seek for a codeword that is itself a prefix of w. In our example, we have w = 10 {\displaystyle w={\texttt {10}}} , and the sequence 1 is a codeword. We can thus also continue with w = 0 {\displaystyle w={\texttt {0}}} as the new dangling suffix. == Precise description of the algorithm == The algorithm is described most conveniently using quotients of formal languages. In general, for two sets of strings D and N, the (left) quotient N − 1 D {\displaystyle N^{-1}D} is defined as the residual words obtained from D by removing some prefix in N. Formally, N − 1 D = { y ∣ x y ∈ D and x ∈ N } {\displaystyle N^{-1}D=\{\,y\mid xy\in D~{\textrm {and}}~x\in N\,\}} . Now let C {\displaystyle C} denote the (finite) set of codewords in the given code. The algorithm proceeds in rounds, where we maintain in each round not only one dangling suffix as described above, but the (finite) set of all potential dangling suffixes. Starting with round i = 1 {\displaystyle i=1} , the set of potential dangling suffixes will be denoted by S i {\displaystyle S_{i}} . The sets S i {\displaystyle S_{i}} are defined inductively as follows: S 1 = C − 1 C ∖ { ε } {\displaystyle S_{1}=C^{-1}C\setminus \{\varepsilon \}} . Here, the symbol ε {\displaystyle \varepsilon } denotes the empty word. S i + 1 = C − 1 S i ∪ S i − 1 C {\displaystyle S_{i+1}=C^{-1}S_{i}\cup S_{i}^{-1}C} , for all i ≥ 1 {\displaystyle i\geq 1} . The algorithm computes the sets S i {\displaystyle S_{i}} in increasing order of i {\displaystyle i} . As soon as one of the S i {\displaystyle S_{i}} contains a word from C or the empty word, then the algorithm terminates and answers that the given code is not uniquely decodable. Otherwise, once a set S i {\displaystyle S_{i}} equals a previously encountered set S j {\displaystyle S_{j}} with j < i {\displaystyle j Read more →