AI Code Update

AI Code Update — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Teechart

TeeChart is a charting library for programmers, developed and managed by Steema Software of Girona, Catalonia, Spain. It is available as commercial and non-commercial software. TeeChart has been included in most Delphi and C++Builder products since 1997, and TeeChart Standard currently is part of Embarcadero RAD Studio 13 Florence. TeeChart Pro version is a commercial product that offers shareware releases for all of its formats. The TeeChart Charting Library offers charts, maps and gauges in versions for Delphi VCL/FMX, ActiveX, C# for Microsoft Visual Studio .NET. Full source code has always been available for all versions except the ActiveX version. TeeChart's user interface is translated into 38 languages. == History == The first version of TeeChart was authored in 1995 by David Berneda, co-founder of Steema, using the Borland Delphi Visual Component Library programming environment and TeeChart was first released as a shareware version and made available via Compuserve in the same year. It was written in the first version of Delphi VCL, as a 16-bit Charting Library named TeeChart version 1. The next version of TeeChart was released as a 32-bit library (Delphi 2 supported 32-bit compilation) but was badged as TeeChart VCL v3 to coincide with Borland's naming convention for inclusion on the toolbox palette of Borland Delphi v3 in 1997 and with C++ Builder v3 in 1998. It has been on the Delphi/C++ Builder toolbox palette ever since. The current version is Embarcadero RAD Studio 13 Florence. TeeChart's first ActiveX version named "version 3" too, to match the VCL version's nomenclature, was released in 1998. The version was optimised to work with Microsoft's Visual Studio v97 and v6.0 developer suites that include Visual Basic and Microsoft Visual C++ programming languages. Support for new programming environments followed with TeeChart's first native C# version for Microsoft Visual Studio .NET released in 2002 and TeeChart.Lite for .NET, a free charting component, released for Visual Studio.NET in 2003 and supporting too, Mono (programming). Steema Software released the first native TeeChart Java (programming language) version in 2006 and TeeChart's first native PHP version was released in 2009 and published as open-source in June 2010. Mobile versions of TeeChart, for Android (operating system) devices and Windows Phone 7 devices were released during the first half of 2011. In 2012 TeeChart extended functionality to iPhone/iPad and BlackBerry OS devices and a new JavaScript version was released in the same year to support HTML5 Canvas. In 2013 Steema launched TeeChart for .NET Chart for Windows Store applications and included support for Microsoft's Windows Phone 8 mobile platform. TeeChart for Xamarin.Forms written with 100% C# code and cross-platform support for .NET desktops, Windows Phone, iOS and Android was released in 2014. Also since 2014 Webforms charts now offers HTML5 interactivity. Steema launched TeeChart for Avalonia (software framework) in 2022 and in 2023 .NET_MAUI support was added to the TeeChart for .NET. == Usage == TeeChart is a general purpose charting component designed for use in differing ambits, offering a wide range of aesthetics to chart data. Generally TeeCharts published in the field, in areas where large amounts of data must be interpreted regularly, remain by designer choice in their simplest form to maximize the "data-ink ratio". Sloan Digital Sky Survey, SDSS Web Services' use for charting "Scientific .. plotting of online data" at The Virtual Observatory Spectrum Services reflects that approach. The SDSS chart authors choose to represent data using TeeChart's standard 2D line display. Speed is also a factor when choosing how to most effectively plot data. Realtime data, at frequencies of up to tens or hundreds of data points or more per second, require the most processor economic approach to charting. Computer processing time dedicated to the plotting of data needs to be as lightweight as possible, freeing-up computer tasks "to achieve real-time data acquisition, display and analysis". A critical and stated aspect of many data visualisation applications is the ability to offer interactivity to the user; NASA's document, the Orbital Debris Engineering Model Model ORDEM 3.0 - User's Guide, 2014, states that "The user may manipulate the graphs to zoom, pan, and copy to the clipboard and export to various file types" and Computer and Computing Technologies in Agriculture II, Volume 1, Daoliang, Li; Chunjiang, Zhao (2009), also using TeeChart, states "the properties at any point in the chart can be viewed moving the mouse over it". Writing about control education, Juha Lindfors states "The desired charting functionality (such as zooming and scaling) is achieved..". Charting applications have become increasingly 'onlined', made available either to a wider public or to a territorially remote userbase via networked applications. The World Wide Web (the Web) has become "by far, the most popular Internet protocol" to disseminate online applications. Most major IDEs now offer environments for web application developede aimed at browser hosted applications. Charting components, TeeChart among them, have adapted to provide models that work within a browser environment, often using static images and scripted layering techniques such as Ajax (programming) to offer a level of interactivity, improve response times and hide apparent delay from the user. Options to enrich client, browser-side processing flexibility are exploited by TeeChart libraries via modules that offer 'micro-environments' within the browser, such as the long established ActiveX technology, Adobe Flash, Microsoft Silverlight or Java Applets. Serverside environments offer too, a means to interact with browser based script to dynamically respond to charting requests. Joomla and CodeIgniter are host environments for TeeChart PHP and an example of an Embarcadero IntraWeb VCL designed application using TeeChart, is documented here. == Programmer reference == The Code Project includes a demo that uses TeeChart.Lite, called 'Self-Organizing Feature Maps (Kohonen maps)' written by Bashir Magomedovl and SourceForge includes a Database Stress and Monitor that also uses TeeChart.Lite. Books and information sources that include substantial sections about working with the Delphi version of TeeChart include "Mastering Delphi 6" by Marco Cantù, "C++ Builder 5 developer's guide", a video Delphi Tutorial on charting JPEG compression and support forums and reference pages at TeeChart Support Forums. Non-English language document sources include, in Czech "Myslíme v jazyku Delphi 7: knihovna zkušeného programátora" by Marco Cantù, and Chinese, Delphi 6, Delphi, and Delphi 5.
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Manufacture Modules Technologies

Manufacture Modules Technologies Sarl (MMT) is a Swiss company established in Geneva in 2015 which originally specialised in the development and commercialization of "Horological Smartwatch modules", firmware, apps and cloud. Located at Geneva's Skylab high-tech hub, it expanded into the development and manufacturing of "E-Straps" operated with a mobile application. Philippe Fraboulet is the CEO. == History == In June 2015, Fullpower Technologies and Union Horlogère Suisse (Swiss Watchmakers Corporation) formed MMT as a joint venture, which then launched the MotionX Horological Smartwatch Open Platform for the Swiss watch industry. The initial licensees were Frederique Constant, Alpina and Mondaine, brands owned by Union Horlogère Suisse. Fullpower created and managed the circuit design, firmware, smartphone applications (including sleep activity), as well as the cloud Infrastructure. MMT managed the Swiss watch movement development and production as well as licensing and support. In July 2016, Union Horlogere Holding and MMT were spun-out of the Frédérique Constant Group. Fullpower Technologies' 19.99% share was acquired by Union Horlogere Holding BV, giving it 100% of MMT's shares. == Business == The company offers firmware, a cloud, manufacturing, service and over-the-air facilities for upgrades. The company also offers its own apps, which bear the label “Swiss Made software”.
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Cancer Likelihood in Plasma

Cancer Likelihood in Plasma (CLiP) refers to a set of ensemble learning methods for integrating various genomic features useful for the noninvasive detection of early cancers from blood plasma. An application of this technique for early detection of lung cancer (Lung-CLiP) was originally described by Chabon et al. (2020) from the labs of Ash Alizadeh and Max Diehn at Stanford. This method relies on several improvements to cancer personalized profiling by deep sequencing (CAPP-Seq) for analysis of circulating tumor DNA (ctDNA). The CLiP technique integrates multiple distinctive genomic features of a cancer of interest findings within a machine-learning framework for cancer detection. For example, studies have shown that the majority of somatic mutations found in cell-free DNA (cfDNA) are not tumor derived, but instead reflect clonal hematopoeisis (also known as CHIP). Even though CHIP tends to target specific genes, it also involves many generally non-recurrent mutations that can be shed from leukocytes and detected in cfDNA, regardless of whether profiling patients with cancer and healthy adults. However, genuine tumor derived ctDNA mutations can be distinguished from CHIP-derived mutations. This is because unlike tumor-derived mutations, CHIP-derived mutations that are shed from leukocytes into plasma tend to occur on longer cfDNA fragments, and to lack specific mutational signatures such as those associated with tobacco smoking in lung cancer that are also found in tumor derived ctDNA molecules. CLiP integrates these features within hierarchical ensemble machine learning models that consider somatic mutations and copy number alternations, among other features. While the CLiP method is unique in relying exclusively on mutations and copy number alterations, it is related to a variety of other liquid biopsy methods being commercially developed for early cancer detection using ctDNA and proteins (e.g., CancerSEEK / DETECT-A ), cfDNA fragmentation patterns (e.g., DELFI), and DNA methylation (e.g., cfMeDIP-Seq, Grail). While the CLiP method has not yet been broadly applied for population-based cancer screening, it has been shown to distinguish discriminate early-stage lung cancers from risk-matched controls across multiple cohorts of patients enrolled across the US.
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EJB QL

EJB QL or EJB-QL is a portable database query language for Enterprise Java Beans. It was used in Java EE applications. Compared to SQL, however, it is less complex but less powerful as well. == History == The language has been inspired, especially EJB3-QL, by the native Hibernate Query Language. In EJB3 It has been mostly replaced by the Java Persistence Query Language. == Differences == EJB QL is a database query language similar to SQL. The used queries are somewhat different from relational SQL, as it uses a so-called "abstract schema" of the enterprise beans instead of the relational model. In other words, EJB QL queries do not use tables and their components, but enterprise beans, their persistent state, and their relationships. The result of an SQL query is a set of rows with a fixed number of columns. The result of an EJB QL query is either a single object, a collection of entity objects of a given type, or a collection of values retrieved from CMP fields. One has to understand the data model of enterprise beans in order to write effective queries.
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Clipmap

In computer graphics, clipmapping is a method of clipping a mipmap to a subset of data pertinent to the geometry being displayed. This is useful for loading as little data as possible when memory is limited, such as on a graphics processing unit. The technique is used for LODing in NVIDIA’s implementation of voxel cone tracing. The high-resolution levels of the mipmapped scene representation are clipped to a region near the camera, while lower resolution levels are clipped further away. == MegaTexture == MegaTexture is a clipmap implementation developed by id Software. It was introduced in their id Tech 4 engine and also appeared in id Tech 5 and id Tech 6 before being removed in id Tech 7. MegaTexture is a texture allocation technique that uses a single, extremely large texture rather than repeating multiple smaller textures. It is also featured in Splash Damage's game Enemy Territory: Quake Wars, and was developed by id Software former technical director John Carmack. MegaTexture employs a single large texture space for static terrain. The texture is stored on removable media or a computer's hard drive and streamed as needed, allowing large amounts of detail and variation over a large area with comparatively little RAM usage. Depending on the pixel resolution per square meter, covering a large area could require several gigabytes of memory. However, RAM is also filled by the rest of the game and the underlying operating system, limiting the amount available for texturing. As the player moves around the game, different sections of the MegaTexture are loaded into memory. They are then scaled to the correct size and applied to the 3D models of the terrain. Id has presented a more advanced technique that builds upon the MegaTexture idea and virtualizes both the geometry and the textures to obtain unique geometry down to the equivalent of the texel: the sparse voxel octree (SVO). It works by raycasting the geometry represented by voxels (instead of triangles) stored in an octree. The goal is to stream parts of the octree into video memory, going further down along the tree for nearby objects to give them more details, and to use higher level, larger voxels for farther objects, which give an automatic level of detail (LOD) system for both geometry and textures at the same time. The geometric detail that can be obtained using this method is nearly infinite, which removes the need for faking 3-dimensional details with techniques such as normal mapping. Despite that most voxel rendering tests use very large amounts of memory (up to several GB), Jon Olick of id Software claimed the technology is able to compress such SVO to 1.15 bits per voxel of position data. == Virtual texturing == Unlike clipmaps, which clip each mip level around a viewpoint-dependent clipcenter and therefore work best for terrain, virtual texturing preprocesses texture data into equally sized tiles that can be streamed for arbitrary textured geometry. Rage, powered by the id Tech 5 engine, uses a more advanced technique called virtual texturing. Textures can measure up to 128000×128000 pixels and are also used for in-game models and sprites, etc. and not just the terrain. Wolfenstein: The New Order and the 2016 version of Doom also use these. Carmageddon: Reincarnation also uses virtual texturing, though unlike id's virtual texturing system, which is designed for unique texture-mapping everywhere, their system is designed to use storage space sparingly while still offering good blend of texture variation and resolution.
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Information strategist

An information strategist analyses the information flow within an organisation and directs its information resources to better serve the organisation's strategic goals. They work with information technology or within a corporate library to direct high quality information from a variety of sources to users, based upon their profiles and needs. In warfare, information strategists not only seek to improve information flows for their own side but also try to disrupt the information flows of the enemy in order to demoralize and deceive them.
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Personal, Inc.

Personal (also referred to as Personal.com or Personal, Inc.) was a consumer personal data service and identity management system for individuals to aggregate, manage and reuse their own data. It merged with digi.me in August 2017, a business in Europe that has the same business model. The combined company is called digi.me. One of its product lines, a collaborative data management and information security solution for the workplace called TeamData, was spun off as a new company as a result of the merger. == History == Personal was founded in 2009 in Washington, DC by the management team that built The Map Network, a location data and mapping platform that was acquired by Nokia/NAVTEQ in 2006. Personal was the first online consumer-facing company to be named an Ambassador for Privacy by Design for its technical, business and legal commitments to providing users with control over the data they store in Personal's service. Called a “life management platform” by The Economist and a “personal encrypted cloud service” by TIME for its user-centric approach to data, the company has been associated with both the Infomediary model originated in 1999 by John Hagel III and Mark Singer, as well as the vendor relationship management (VRM) model developed by Doc Searls. Personal raised $30m in funding to develop its platform and products from such leading investors as Steve Case's Revolution Ventures, Grotech Ventures, Allen & Company, Ted Leonsis, Neil Ashe, Jonathan Miller, Bill Miller of Legg Mason, Esther Dyson of EDventures, and Eric C. Anderson. The company received recognition for its user agreement, called the Owner Data Agreement, which acted like a reverse license agreement when data was shared between registered parties and emphasized that data ownership resides with the user. Doc Searls wrote in The Intention Economy: When Customers Take Charge that the Owner Data Agreement “had no precedent and modeled a new legal position, both for vendors and for intermediaries.” Personal was early to embrace “small data,” which it defines as “big data for the benefit of individuals.” The term “small data” may have been originally coined by Jeremie Miller of Sing.ly, who mentioned it in a talk at the Web 2.0 Summit in November 2011 and is cited in The Intention Economy. In 2011, Personal was a part of the first group of companies to join the Personal Data Ecosystem Consortium's Startup Circle. A Small Data Meetup group has also formed in New York City, bringing together technology, legal and business experts to exchange ideas about user-centric and user-driven models for internet products and services. Personal has been included in case studies by Ctrl-Shift and Forrester regarding Personal Data Stores and Personal Identity Management. In 2011, Personal received the Innovator Spotlight Award at Privacy Identity Innovation Conference (pii2011) and participated in the Technology Showcase at pii2012. In 2012, TechHive named Personal as one of the top five apps or web services of SXSW. Personal won the 2013 Campus Technology Innovators Award with Lone Star College in July 2013. Personal was included in a list of Executive Travel Magazine's favorite travel apps for 2013 in its May/June issue. In 2013, Personal was also included as part of NYU GovLab's Open Data 500 and was named by J. Walter Thompson as one of 100 things to watch for in 2014. In 2015, the National Law Journal named Company Chief Policy Officer and General Counsel, Joshua P. Galper, as one of their 50 "Cybersecurity & Privacy Trailblazers." == Products and services == === Overview === The Personal Platform was a privacy- and security-by-design platform for individuals to manage and reuse their own data and information. The Fill It app was a 1-click form-filling solution for web and mobile logins, checkouts and forms, and the Data Vault app served as the main cloud-based repository for a user's data. Personal helped individuals take control and benefit from their information while knowing that the information in their Data Vault remained legally theirs and could not be used without their permission. === Data Vault with Cloud Sync === Personal spent two years building the Personal Platform before launching its Data Vault product in beta in November 2011. Following Privacy by Design principles, Personal only enabled users to see or share the sensitive data and all the files they stored in their Data Vault. Such information was encrypted, and could only be decrypted with a user's password. Only users could choose and know their passwords to their vault because Personal did not store user passwords – and therefore could not reset them without deleting a user's sensitive data and all files stored in their vault. All Personal apps and services were linked to a user's private Data Vault. The Data Vault featured automatic synchronization of data and files added on any device logged into Personal. It also featured a “Secure Share” function that created a live, private network, allowing registered users to share access to data and files through an exchange of encrypted keys without the risk of transmitting the data or files through non-secure, direct means. It also allowed users to immediately update data across their own network and revoke access to it when they choose. Fast Company called the Data Vault “a tool that will simplify our lives.” Personal launched its Android app on November 30, 2011. The iOS Data Vault app was released on May 7, 2012. Personal officially launched its application programming interface (APIs) on October 2, 2012 at the Mashery Business of APIs Conference. A review by CNET highlighted the challenges of getting people to trust such a new service with their sensitive data and spending the time required entering enough data to make it useful. === Fill It App and Form Index === When the Data Vault was launched in November 2011, Mashable posed the question: “Never Fill Out a Form Again?” The World Economic Forum in its February 2013 report highlighted the possibility of saving 10 billion hours globally “and improv[ing] the delivery of public and private sector services” through automated form-filling tools, specifically citing Personal's Fill It app. In January 2013, Personal launched Fill It in beta as a web bookmarklet for automatic form-filling. On June 11, 2014, Personal released Fill It as a web extension and announced that it was publishing an index of over 140,000 1-click online forms at www.fillit.com. The company also announced that a mobile version of the product will launch later in the year. According to a story in Tech Cocktail about the launch, Personal's “web extension and mobile app are able to support over 1,200 different types of reusable data, even enabling them to unlock more confidential information so they can complete longer forms, including patient registrations, job applications, event registrations, school admissions, insurance and bank applications, and government forms.” In November 2014, a mobile version of Fill It was launched that could autofill mobile forms using APIs. Personal's form portal ultimately indexed more than 500,000 forms with three components, which, together, allowed data to be captured and reused across any of the forms: (1) a form graph, which mapped individual form fields to the Personal ontology; (2) a semantic layer, which determined how data was required on a form (e.g. one field vs. three fields for a U.S. telephone number); and (3) a correlations graph, which helped individuals match their specific data to a form without looking at the data value (e.g. knowing which phone number is a mobile phone number, which address is a billing address, or that a person uses their middle name as a first name on most forms). === Monetizing personal data === With the initial public offering of Facebook in May 2012, there was media interest in the question of the monetary value of personal data and whether tools and services might emerge to help consumers monetize their own data. Personal was frequently cited as a company that could potentially offer such a service. Articles and pieces focusing on this subject have appeared in The New York Times, AdWeek, the MIT Technology Review, and on CNN and National Public Radio. Company Co-founder and CEO Shane Green was quoted as saying that “the average American consumer would soon be able to realize over $1,000 per year” by granting limited, anonymous access to their data to marketers, but that figure was never supported by Green or the company. === Launch of TeamData === In May 2016, Personal shifted its product focus to TeamData, which focuses on the problem of securing and collaboratively managing data in the workplace. It is now a separate business.
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Artificial intelligence in marketing

Artificial intelligence marketing (AI marketing) is a form of marketing that uses artificial intelligence concepts and models such as machine learning, natural language processing, and computer vision to achieve marketing goals. The main difference between AI marketing and traditional forms of marketing reside in the reasoning, which is performed through a computer algorithm rather than a human. Each form of marketing has a different technique to the core of the marketing theory. Traditional marketing directly focuses on the needs of consumers; meanwhile some believe the shift AI may cause will lead marketing agencies to manage consumer needs instead. AI is used in various digital marketing spaces, such as content marketing, email marketing, online advertisement (in combination with machine learning), social media marketing, affiliate marketing, and beyond. == Historical development == AI in marketing has a long history, which goes all the way back to the 1980s. At this time, AI research was focusing on expert systems and robotics. Despite the initial research and the studies that were carried out, AI adoption remained limited. Research on it came to a stop for a while, until research was revived two decades later with the advancement in technology, the rise of big data, and a significant increase in computational power. Eventually, AI became very popular in the marketing world, and caught the eyes of many researchers as well as professionals. A large‐scale bibliometric study covering 1,580 peer‑reviewed papers published between 1982 and 2020 confirms that scholarly output on AI in marketing has surged since 2017, with Expert Systems with Applications emerging as the most prolific outlet. Prior to the application of artificial Intelligence in marketing, there was something called "collaborative filtering". This was used as early as 1998 by Amazon, and one of the first ways companies predicted consumer behavior, which enabled millions of recommendations to different customers. Personalized recommender systems are now widely used, for example to suggest music on Spotify, or TV shows on Netflix. A big milestone in AI marketing happened in 2014, when programmatic ad buying gained much greater popularity. Marketing consists of numerous manual tasks such as researching target markets, insertion orders, and managing high budgets as well as prices. In order to cut costs, and remove the need for these tedious tasks, many companies started to automate the marketing process with AI. In 2015, Google introduced RankBrain, a machine learning component of its search algorithm designed to interpret the intent behind user queries. RankBrain was followed by further AI-based search updates, including BERT in 2019, which improved the understanding of conversational queries, and the Multitask Unified Model (MUM) in 2021, which is multimodal and processes information across 75 languages. These advances shifted search engine optimization practice away from keyword matching toward content that satisfies user intent. Artificial intelligence is increasingly used in marketing to personalize user experiences and automate decision-making. For example, Netflix uses AI algorithms to recommend content based on viewing history, while Sephora employs chatbots to assist customers with product selection and availability. Programmatic advertising platforms like Google Ads leverage machine learning to optimize bidding strategies and target audiences more effectively. These applications demonstrate how AI enhances efficiency, engagement, and conversion rates across digital channels. === Artificial neural networks === An artificial neural network is a form of computer program modeled on the brain and nervous system of humans. Neural networks are composed of a series of interconnected processing neurons that function in unison to achieve certain outcomes. Using “human-like trial and error learning methods neural networks detect patterns existing within a data set ignoring data that is not significant while emphasizing the data which is most influential”. From a marketing perspective, neural networks are a form of software tool used to assist in decision making. Neural networks are effective in gathering and extracting information from large data sources and have the ability to identify cause and effect within tha data. These neural nets through the process of learning, identify relationships and connections between databases. Once knowledge has been accumulated, neural networks can be relied on to provide generalizations and can apply past knowledge and learning to a variety of situations. Neural networks help fulfill the role of marketing companies through effectively aiding in market segmentation and measurement of performance while reducing costs and improving accuracy. Due to their learning ability, flexibility, adaption, and knowledge discovery, neural networks offer many advantages over traditional models. Neural networks can be used to assist in pattern classification, forecasting and marketing analysis. == Tools and uses == Classification of customers can be facilitated through the neural network approach allowing companies to make informed marketing decisions. An example of this was employed by Spiegel Inc., a firm dealing in direct-mail operations that used neural networks to improve efficiencies. Using software developed by NeuralWare Inc., Spiegel identified the demographics of customers who had made a single purchase and those customers who had made repeat purchases. Neural networks where then able to identify the key patterns and consequently identify the customers that were most likely to repeat purchase. Understanding this information allowed Spiegel to streamline marketing efforts, and reduced costs. Sales forecasting “is the process of estimating future events with the goal of providing benchmarks for monitoring actual performance and reducing uncertainty". Artificial intelligence techniques have emerged to facilitate the process of forecasting through increasing accuracy in the areas of demand for products, distribution, employee turnover, performance measurement, and inventory control. An example of forecasting using neural networks is the Airline Marketing Assistant/Tactician; an application developed by BehabHeuristics which allows for the forecasting of passenger demand and consequent seat allocation through neural networks. This system has been used by National air Canada and USAir. Neural networks provide a useful alternative to traditional statistical models due to their reliability, time-saving characteristics and ability to recognize patterns from incomplete or noisy data. Examples of marketing analysis systems includes the Target Marketing System developed by Churchull Systems for Veratex Corporation. This support system scans a market database to identify dormant customers allowing management to make decisions regarding which key customers to target. When performing marketing analysis, neural networks can assist in the gathering and processing of information ranging from consumer demographics and credit history to the purchase patterns of consumers. Predictive analytics is a form of analytics involving the use of historical data and artificial intelligence algorithms to predict future trends and outcomes. It serves as a tool for anticipating and understanding user behavior based on patterns found in data. Predictive analytics uses artificial intelligence machine learning algorithms to recognize and predict patterns within data. Machine learning algorithms analyze the data, recognize patterns, and make predictions through continuous learning and adaptation. Predictive analytics is widely used across businesses and industries as a way to identify opportunities, avoid risks, and anticipate customer needs based on information derived from the analysis of user data. By analyzing historical customer data, artificial intelligence algorithms can deliver relevant and targeted marketing content. Recent systematic reviews show that generative large‑language models such as GPT‑3 and GPT‑4 are now routinely embedded in predictive‑analytics pipelines to mine unstructured market data and anticipate customer intent with greater precision. Personalization engines use artificial intelligence and machine learning to provide content or advertisements that are relevant to the user. User data is gathered, which then gets processed with machine learning, and patterns and trends among the users are identified. Users with shared characteristics or behaviors are then segmented into groups, and the personalization engine adjusts content and advertisements to match each segment's preferences. By processing a large amount of data, personalization engines are able to match users to advertisements and recommendations that align with their interests or preferences. Field evidence from consumer‑goods and electronics firms indicates that AI‑driven personalization can raise
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Neural radiance field

A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance properties of the scene. Additional scene properties such as camera poses may also be jointly learned. First introduced in 2020, it has since gained significant attention for its potential applications in computer graphics and content creation. == Algorithm == The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location ( x , y , z ) {\displaystyle (x,y,z)} and viewing direction in Euler angles ( θ , Φ ) {\displaystyle (\theta ,\Phi )} of the camera. By sampling many points along camera rays, traditional volume rendering techniques can produce an image. === Data collection === A NeRF needs to be retrained for each unique scene. The first step is to collect images of the scene from different angles and their respective camera pose. These images are standard 2D images and do not require a specialized camera or software. Any camera is able to generate datasets, provided the settings and capture method meet the requirements for SfM (Structure from Motion). This requires tracking of the camera position and orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques. For such data, images (rendered through traditional non-learned methods) and respective camera poses are reproducible and error-free. === Training === For each sparse viewpoint (image and camera pose) provided, camera rays are marched through the scene, generating a set of 3D points with a given radiance direction (into the camera). For these points, volume density and emitted radiance are predicted using the multi-layer perceptron (MLP). An image is then generated through classical volume rendering. Because this process is fully differentiable, the error between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent model of the scene. == Variations and improvements == Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, many improvements have been made to the NeRF algorithm, with variations for special use cases. === Fourier feature mapping === In 2020, shortly after the release of NeRF, the addition of Fourier Feature Mapping improved training speed and image accuracy. Deep neural networks struggle to learn high frequency functions in low dimensional domains; a phenomenon known as spectral bias. To overcome this shortcoming, points are mapped to a higher dimensional feature space before being fed into the MLP. γ ( v ) = [ a 1 cos ⁡ ( 2 π B 1 T v ) a 1 sin ⁡ ( 2 π B 1 T v ) ⋮ a m cos ⁡ ( 2 π B m T v ) a m sin ⁡ ( 2 π B m T v ) ] {\displaystyle \gamma (\mathrm {v} )={\begin{bmatrix}a_{1}\cos(2{\pi }{\mathrm {B} }_{1}^{T}\mathrm {v} )\\a_{1}\sin(2\pi {\mathrm {B} }_{1}^{T}\mathrm {v} )\\\vdots \\a_{m}\cos(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\\a_{m}\sin(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\end{bmatrix}}} Where v {\displaystyle \mathrm {v} } is the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid convergence to high frequency functions, such as pixels in a detailed image. === Bundle-adjusting neural radiance fields === One limitation of NeRFs is the requirement of knowing accurate camera poses to train the model. Often times, pose estimation methods are not completely accurate, nor is the camera pose even possible to know. These imperfections result in artifacts and suboptimal convergence. So, a method was developed to optimize the camera pose along with the volumetric function itself. Called Bundle-Adjusting Neural Radiance Field (BARF), the technique uses a dynamic low-pass filter (DLPF) to go from coarse to fine adjustment, minimizing error by finding the geometric transformation to the desired image. This corrects imperfect camera poses and greatly improves the quality of NeRF renders. === Multiscale representation === Conventional NeRFs struggle to represent detail at all viewing distances, producing blurry images up close and overly aliased images from distant views. In 2021, researchers introduced a technique to improve the sharpness of details at different viewing scales known as mip-NeRF (comes from mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively anti-aliases across all viewing scales. mip-NeRF also reduces overall image error and is faster to converge at about half the size of ray-based NeRF. === Learned initializations === In 2021, researchers applied meta-learning to assign initial weights to the MLP. This rapidly speeds up convergence by effectively giving the network a head start in gradient descent. Meta-learning also allowed the MLP to learn an underlying representation of certain scene types. For example, given a dataset of famous tourist landmarks, an initialized NeRF could partially reconstruct a scene given one image. === NeRF in the wild === Conventional NeRFs are vulnerable to slight variations in input images (objects, lighting) often resulting in ghosting and artifacts. As a result, NeRFs struggle to represent dynamic scenes, such as bustling city streets with changes in lighting and dynamic objects. In 2021, researchers at Google developed a new method for accounting for these variations, named NeRF in the Wild (NeRF-W). This method splits the neural network (MLP) into three separate models. The main MLP is retained to encode the static volumetric radiance. However, it operates in sequence with a separate MLP for appearance embedding (changes in lighting, camera properties) and an MLP for transient embedding (changes in scene objects). This allows the NeRF to be trained on diverse photo collections, such as those taken by mobile phones at different times of day. === Relighting === In 2021, researchers added more outputs to the MLP at the heart of NeRFs. The output now included: volume density, surface normal, material parameters, distance to the first surface intersection (in any direction), and visibility of the external environment in any direction. The inclusion of these new parameters lets the MLP learn material properties, rather than pure radiance values. This facilitates a more complex rendering pipeline, calculating direct and global illumination, specular highlights, and shadows. As a result, the NeRF can render the scene under any lighting conditions with no re-training. === Plenoctrees === Although NeRFs had reached high levels of fidelity, their costly compute time made them useless for many applications requiring real-time rendering, such as VR/AR and interactive content. Introduced in 2021, Plenoctrees (plenoptic octrees) enabled real-time rendering of pre-trained NeRFs through division of the volumetric radiance function into an octree. Rather than assigning a radiance direction into the camera, viewing direction is taken out of the network input and spherical radiance is predicted for each region. This makes rendering over 3000x faster than conventional NeRFs. === Sparse Neural Radiance Grid === Similar to Plenoctrees, this method enabled real-time rendering of pretrained NeRFs. To avoid querying the large MLP for each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned feature vectors to encode view-dependent information. A lightweight, more efficient MLP is then used to produce view-dependent residuals to modify the color and opacity. To enable this compressive baking, small changes to the NeRF architecture were made, such as running the MLP once per pixel rather than for each point along the ray. These improvements make SNeRG extremely efficient, outperforming Plenoctrees. === Instant NeRFs === In 2022, researchers at Nvidia enabled real-time training of NeRFs through a technique known as Instant Neural Graphics Primitives. An innovative input encoding reduces computation, enabling real-time training of a NeRF, an improvement orders of magnitude above previous methods. The speedup stems from the use of spatial hash functions, which have O ( 1 ) {\displaystyle O(1)} access times, and parallelized architectures which run fast on modern GPUs. == Related techniques == === Plenoxels === Plen
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Operational system

An operational system is a term used in data warehousing to refer to a system that is used to process the day-to-day transactions of an organization. These systems are designed in a manner that processing of day-to-day transactions is performed efficiently and the integrity of the transactional data is preserved. == Synonyms == Sometimes operational systems are referred to as operational databases, transaction processing systems, or online transaction processing systems (OLTP). However, the use of the last two terms as synonyms may be confusing, because operational systems can be batch processing systems as well. Any enterprise must necessarily maintain a lot of data about its operation.
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Randomized rounding

In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). For such problems, randomized rounding can be used to design fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. The basic idea of randomized rounding is to convert an optimal solution of a relaxation of the problem into an approximately-optimal solution to the original problem. The resulting algorithm is usually analyzed using the probabilistic method. == Overview == The basic approach has three steps: Formulate the problem to be solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the ILP. Round the fractional solution x {\displaystyle x} of the LP to an integer solution x ′ {\displaystyle x'} of the ILP. (Although the approach is most commonly applied with linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) In the first step, the challenge is to choose a suitable integer linear program. Familiarity with linear programming, in particular modelling using linear programs and integer linear programs, is required. For many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm. In the third step, the fractional solution must be converted into an integer solution (and thus a solution to the original problem). This is called rounding the fractional solution. The resulting integer solution should (provably) have cost not much larger than the cost of the fractional solution. This will ensure that the cost of the integer solution is not much larger than the cost of the optimal integer solution. The main technique used to do the third step (rounding) is to use randomization, and then to use probabilistic arguments to bound the increase in cost due to the rounding (following the probabilistic method from combinatorics). Therein, probabilistic arguments are used to show the existence of discrete structures with desired properties. In this context, one uses such arguments to show the following: Given any fractional solution x {\displaystyle x} of the LP, with positive probability the randomized rounding process produces an integer solution x ′ {\displaystyle x'} that approximates x {\displaystyle x} according to some desired criterion. Finally, to make the third step computationally efficient, one either shows that x ′ {\displaystyle x'} approximates x {\displaystyle x} with high probability (so that the step can remain randomized) or one derandomizes the rounding step, typically using the method of conditional probabilities. The latter method converts the randomized rounding process into an efficient deterministic process that is guaranteed to reach a good outcome. == Example: the set cover problem == The following example illustrates how randomized rounding can be used to design an approximation algorithm for the set cover problem. Fix any instance ⟨ c , S ⟩ {\displaystyle \langle c,{\mathcal {S}}\rangle } of set cover over a universe U {\displaystyle {\mathcal {U}}} . === Computing the fractional solution === For step 1, let IP be the standard integer linear program for set cover for this instance. For step 2, let LP be the linear programming relaxation of IP, and compute an optimal solution x ∗ {\displaystyle x^{}} to LP using any standard linear programming algorithm. This takes time polynomial in the input size. The feasible solutions to LP are the vectors x {\displaystyle x} that assign each set s ∈ S {\displaystyle s\in {\mathcal {S}}} a non-negative weight x s {\displaystyle x_{s}} , such that, for each element e ∈ U {\displaystyle e\in {\mathcal {U}}} , x ′ {\displaystyle x'} covers e {\displaystyle e} —the total weight assigned to the sets containing e {\displaystyle e} is at least 1, that is, ∑ s ∋ e x s ≥ 1. {\displaystyle \sum _{s\ni e}x_{s}\geq 1.} The optimal solution x ∗ {\displaystyle x^{}} is a feasible solution whose cost ∑ s ∈ S c ( S ) x s ∗ {\displaystyle \sum _{s\in {\mathcal {S}}}c(S)x_{s}^{}} is as small as possible. Note that any set cover C {\displaystyle {\mathcal {C}}} for S {\displaystyle {\mathcal {S}}} gives a feasible solution x {\displaystyle x} (where x s = 1 {\displaystyle x_{s}=1} for s ∈ C {\displaystyle s\in {\mathcal {C}}} , x s = 0 {\displaystyle x_{s}=0} otherwise). The cost of this C {\displaystyle {\mathcal {C}}} equals the cost of x {\displaystyle x} , that is, ∑ s ∈ C c ( s ) = ∑ s ∈ S c ( s ) x s . {\displaystyle \sum _{s\in {\mathcal {C}}}c(s)=\sum _{s\in {\mathcal {S}}}c(s)x_{s}.} In other words, the linear program LP is a relaxation of the given set-cover problem. Since x ∗ {\displaystyle x^{}} has minimum cost among feasible solutions to the LP, the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover. === Randomized rounding step === In step 3, we must convert the minimum-cost fractional set cover x ∗ {\displaystyle x^{}} into a feasible integer solution x ′ {\displaystyle x'} (corresponding to a true set cover). The rounding step should produce an x ′ {\displaystyle x'} that, with positive probability, has cost within a small factor of the cost of x ∗ {\displaystyle x^{}} .Then (since the cost of x ∗ {\displaystyle x^{}} is a lower bound on the cost of the optimal set cover), the cost of x ′ {\displaystyle x'} will be within a small factor of the optimal cost. As a starting point, consider the most natural rounding scheme: For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( 1 , x s ∗ ) {\displaystyle \min(1,x_{s}^{})} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . With this rounding scheme, the expected cost of the chosen sets is at most ∑ s c ( s ) x s ∗ {\displaystyle \sum _{s}c(s)x_{s}^{}} , the cost of the fractional cover. This is good. Unfortunately the coverage is not good. When the variables x s ∗ {\displaystyle x_{s}^{}} are small, the probability that an element e {\displaystyle e} is not covered is about ∏ s ∋ e 1 − x s ∗ ≈ ∏ s ∋ e exp ⁡ ( − x s ∗ ) = exp ⁡ ( − ∑ s ∋ e x s ∗ ) ≈ exp ⁡ ( − 1 ) . {\displaystyle \prod _{s\ni e}1-x_{s}^{}\approx \prod _{s\ni e}\exp(-x_{s}^{})=\exp {\Big (}-\sum _{s\ni e}x_{s}^{}{\Big )}\approx \exp(-1).} So only a constant fraction of the elements will be covered in expectation. To make x ′ {\displaystyle x'} cover every element with high probability, the standard rounding scheme first scales up the rounding probabilities by an appropriate factor λ > 1 {\displaystyle \lambda >1} . Here is the standard rounding scheme: Fix a parameter λ ≥ 1 {\displaystyle \lambda \geq 1} . For each set s ∈ S {\displaystyle s\in {\mathcal {S}}} in turn, take x s ′ = 1 {\displaystyle x'_{s}=1} with probability min ( λ x s ∗ , 1 ) {\displaystyle \min(\lambda x_{s}^{},1)} , otherwise take x s ′ = 0 {\displaystyle x'_{s}=0} . Scaling the probabilities up by λ {\displaystyle \lambda } increases the expected cost by λ {\displaystyle \lambda } , but makes coverage of all elements likely. The idea is to choose λ {\displaystyle \lambda } as small as possible so that all elements are provably covered with non-zero probability. Here is a detailed analysis. ==== Lemma (approximation guarantee for rounding scheme) ==== Fix λ = ln ⁡ ( 2 | U | ) {\displaystyle \lambda =\ln(2|{\mathcal {U}}|)} . With positive probability, the rounding scheme returns a set cover x ′ {\displaystyle x'} of cost at most 2 ln ⁡ ( 2 | U | ) c ⋅ x ∗ {\displaystyle 2\ln(2|{\mathcal {U}}|)c\cdot x^{}} (and thus of cost O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} times the cost of the optimal set cover). (Note: with care the O ( log ⁡ | U | ) {\displaystyle O(\log |{\mathcal {U}}|)} can be reduced to ln ⁡ ( | U | ) + O ( log ⁡ log ⁡ | U | ) {\displaystyle \ln(|{\mathcal {U}}|)+O(\log \log |{\mathcal {U}}|)} .) ==== Proof ==== The output x ′ {\displaystyle x'} of the random rounding scheme has the desired properties as long as none of the following "bad" events occur: the cost c ⋅ x ′ {\displaystyle c\cdot x'} of x ′ {\displaystyle x'} exceeds 2 λ c ⋅ x ∗ {\displaystyle 2\lambda c\cdot x^{}} , or for some element e {\displaystyle e} , x ′ {\displaystyle x'} fails to cover e {\displaystyle e} . The expectation of each x s ′ {\displaystyle x'_{s}} is at most λ x s ∗ {\displaystyle \lambda x_{s
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MaPS S.A.

MaPS S.A. is a software editor founded in 2011 by Thierry Muller. The company is headquartered in Luxembourg. Its platform, called MaPS System, provides Data Management software for Multichannel Marketing. == History and funding == The first version of MaPS System was released under the agency Prem1um S.A. in 2005 in the partnership with Pingroom agency. In combination with MaPS System, Prem1um also provided various consulting services in Marketing, Publishing and Sales. This is where MaPS System takes its names (M stands for Marketing, P for Publishing and S for Sales). In 2011, after being successful, Prem1um S.A. decided to enable the software MaPS System to operate independently under MaPS S.A., as a separate company and editor of the software. The first financial supports were provided by Malta ICI, a Venture Capital firm, and the local partner Chameleon Invest, a seed-capital fund led by Business Angels, who invested €900,000. In a second investment round in 2014 led by Newion Investments, a Venture Capital firm, €1.4 Million were raised, thus amounting to total assets of €2.2 Million. In 2016, the company was taken over by three private investors. In 2018, after two years of continuous growth and European expansion in Belgium, Germany and Switzerland, MaPS S.A acquired Awevo, an e-commerce web agency. == Products == The services included in MaPS System range from the data centralization, Data Governance to an optimized Multichannel Marketing. The software currently includes more than 35 modules for Master Data Management, Product Information Management, Digital Asset Management, Business Process Management including catalogue Publishing features. == Certifications == In 2019, MaPS System and Awevo received "Made in Luxembourg" label, given to the companies whose services are entirely designed in Luxembourg, without any production or development offshoring. MaPS System is a member of ICT Cluster by Luxinnovation.
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Oculus Quill

Quill is a painting and animation software for virtual reality. It runs on Microsoft Windows with Oculus Rift headsets. It is used to create 3D paintings and animated cartoons. Quill was released on November 29, 2016, on the Oculus Store. Theater Elsewhere(formerly Quill Theater), an application for viewing creations made in Quill, was later made available following the release of the Oculus Quest. In September 2021, Facebook, now known as Meta Platforms, and the owner of Oculus, sold Quill to its original creator, who continues to develop and support the app. == Development == Quill was originally developed by Oculus Story Studio as an internal tool for the creative needs of the studio's project Dear Angelica directed by Saschka Unseld along with its art-director Wesley Allsbrook. == Controls == The software works on Oculus Rift utilizing its 6DoF motion controllers. Users can paint in 3D space using their hands naturally, and animate those paintings with keyframes. They can also capture videos and photos of their creations. == Reception == Dear Angelica, a VR story fully painted in Quill, was nominated for an Emmy Award in 2017.
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Enumeration algorithm

In computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems that take an input and produce a list of solutions, similarly to function problems. For each input, the enumeration algorithm must produce the list of all solutions, without duplicates, and then halt. The performance of an enumeration algorithm is measured in terms of the time required to produce the solutions, either in terms of the total time required to produce all solutions, or in terms of the maximal delay between two consecutive solutions and in terms of a preprocessing time, counted as the time before outputting the first solution. This complexity can be expressed in terms of the size of the input, the size of each individual output, or the total size of the set of all outputs, similarly to what is done with output-sensitive algorithms. == Formal definitions == An enumeration problem P {\displaystyle P} is defined as a relation R {\displaystyle R} over strings of an arbitrary alphabet Σ {\displaystyle \Sigma } : R ⊆ Σ ∗ × Σ ∗ {\displaystyle R\subseteq \Sigma ^{}\times \Sigma ^{}} An algorithm solves P {\displaystyle P} if for every input x {\displaystyle x} the algorithm produces the (possibly infinite) sequence y {\displaystyle y} such that y {\displaystyle y} has no duplicate and z ∈ y {\displaystyle z\in y} if and only if ( x , z ) ∈ R {\displaystyle (x,z)\in R} . The algorithm should halt if the sequence y {\displaystyle y} is finite. == Common complexity classes == Enumeration problems have been studied in the context of computational complexity theory, and several complexity classes have been introduced for such problems. A very general such class is EnumP, the class of problems for which the correctness of a possible output can be checked in polynomial time in the input and output. Formally, for such a problem, there must exist an algorithm A which takes as input the problem input x, the candidate output y, and solves the decision problem of whether y is a correct output for the input x, in polynomial time in x and y. For instance, this class contains all problems that amount to enumerating the witnesses of a problem in the class NP. Other classes that have been defined include the following. In the case of problems that are also in EnumP, these problems are ordered from least to most specific: Output polynomial, the class of problems whose complete output can be computed in polynomial time. Incremental polynomial time, the class of problems where, for all i, the i-th output can be produced in polynomial time in the input size and in the number i. Polynomial delay, the class of problems where the delay between two consecutive outputs is polynomial in the input (and independent from the output). Strongly polynomial delay, the class of problems where the delay before each output is polynomial in the size of this specific output (and independent from the input or from the other outputs). The preprocessing is generally assumed to be polynomial. Constant delay, the class of problems where the delay before each output is constant, i.e., independent from the input and output. The preprocessing phase is generally assumed to be polynomial in the input. == Common techniques == Backtracking: The simplest way to enumerate all solutions is by systematically exploring the space of possible results (partitioning it at each successive step). However, performing this may not give good guarantees on the delay, i.e., a backtracking algorithm may spend a long time exploring parts of the space of possible results that do not give rise to a full solution. Flashlight search: This technique improves on backtracking by exploring the space of all possible solutions but solving at each step the problem of whether the current partial solution can be extended to a partial solution. If the answer is no, then the algorithm can immediately backtrack and avoid wasting time, which makes it easier to show guarantees on the delay between any two complete solutions. In particular, this technique applies well to self-reducible problems. Closure under set operations: If we wish to enumerate the disjoint union of two sets, then we can solve the problem by enumerating the first set and then the second set. If the union is non disjoint but the sets can be enumerated in sorted order, then the enumeration can be performed in parallel on both sets while eliminating duplicates on the fly. If the union is not disjoint and both sets are not sorted then duplicates can be eliminated at the expense of a higher memory usage, e.g., using a hash table. Likewise, the cartesian product of two sets can be enumerated efficiently by enumerating one set and joining each result with all results obtained when enumerating the second step. == Examples of enumeration problems == The vertex enumeration problem, where we are given a polytope described as a system of linear inequalities and we must enumerate the vertices of the polytope. Enumerating the minimal transversals of a hypergraph. This problem is related to monotone dualization and is connected to many applications in database theory and graph theory. Enumerating the answers to a database query, for instance a conjunctive query or a query expressed in monadic second-order. There have been characterizations in database theory of which conjunctive queries could be enumerated with linear preprocessing and constant delay. The problem of enumerating maximal cliques in an input graph, e.g., with the Bron–Kerbosch algorithm Listing all elements of structures such as matroids and greedoids Several problems on graphs, e.g., enumerating independent sets, paths, cuts, etc. Enumerating the satisfying assignments of representations of Boolean functions, e.g., a Boolean formula written in conjunctive normal form or disjunctive normal form, a binary decision diagram such as an OBDD, or a Boolean circuit in restricted classes studied in knowledge compilation, e.g., NNF. == Connection to computability theory == The notion of enumeration algorithms is also used in the field of computability theory to define some high complexity classes such as RE, the class of all recursively enumerable problems. This is the class of sets for which there exist an enumeration algorithm that will produce all elements of the set: the algorithm may run forever if the set is infinite, but each solution must be produced by the algorithm after a finite time.
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Time Warp Edit Distance

In the data analysis of time series, Time Warp Edit Distance (TWED) is a measure of similarity (or dissimilarity) between pairs of discrete time series, controlling the relative distortion of the time units of the two series using the physical notion of elasticity. In comparison to other distance measures, (e.g. DTW (dynamic time warping) or LCS (longest common subsequence problem)), TWED is a metric. Its computational time complexity is O ( n 2 ) {\displaystyle O(n^{2})} , but can be drastically reduced in some specific situations by using a corridor to reduce the search space. Its memory space complexity can be reduced to O ( n ) {\displaystyle O(n)} . It was first proposed in 2009 by P.-F. Marteau. == Definition == δ λ , ν ( A 1 p , B 1 q ) = M i n { δ λ , ν ( A 1 p − 1 , B 1 q ) + Γ ( a p ′ → Λ ) d e l e t e i n A δ λ , ν ( A 1 p − 1 , B 1 q − 1 ) + Γ ( a p ′ → b q ′ ) m a t c h o r s u b s t i t u t i o n δ λ , ν ( A 1 p , B 1 q − 1 ) + Γ ( Λ → b q ′ ) d e l e t e i n B {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{p},B_{1}^{q})=Min{\begin{cases}\delta _{\lambda ,\nu }(A_{1}^{p-1},B_{1}^{q})+\Gamma (a_{p}^{'}\to \Lambda )&{\rm {delete\ in\ A}}\\\delta _{\lambda ,\nu }(A_{1}^{p-1},B_{1}^{q-1})+\Gamma (a_{p}^{'}\to b_{q}^{'})&{\rm {match\ or\ substitution}}\\\delta _{\lambda ,\nu }(A_{1}^{p},B_{1}^{q-1})+\Gamma (\Lambda \to b_{q}^{'})&{\rm {delete\ in\ B}}\end{cases}}} whereas Γ ( α p ′ → Λ ) = d L P ( a p ′ , a p − 1 ′ ) + ν ⋅ ( t a p − t a p − 1 ) + λ {\displaystyle \Gamma (\alpha _{p}^{'}\to \Lambda )=d_{LP}(a_{p}^{'},a_{p-1}^{'})+\nu \cdot (t_{a_{p}}-t_{a_{p-1}})+\lambda } Γ ( α p ′ → b q ′ ) = d L P ( a p ′ , b q ′ ) + d L P ( a p − 1 ′ , b q − 1 ′ ) + ν ⋅ ( | t a p − t b q | + | t a p − 1 − t b q − 1 | ) {\displaystyle \Gamma (\alpha _{p}^{'}\to b_{q}^{'})=d_{LP}(a_{p}^{'},b_{q}^{'})+d_{LP}(a_{p-1}^{'},b_{q-1}^{'})+\nu \cdot (|t_{a_{p}}-t_{b_{q}}|+|t_{a_{p-1}}-t_{b_{q-1}}|)} Γ ( Λ → b q ′ ) = d L P ( b p ′ , b p − 1 ′ ) + ν ⋅ ( t b q − t b q − 1 ) + λ {\displaystyle \Gamma (\Lambda \to b_{q}^{'})=d_{LP}(b_{p}^{'},b_{p-1}^{'})+\nu \cdot (t_{b_{q}}-t_{b_{q-1}})+\lambda } Whereas the recursion δ λ , ν {\displaystyle \delta _{\lambda ,\nu }} is initialized as: δ λ , ν ( A 1 0 , B 1 0 ) = 0 , {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{0},B_{1}^{0})=0,} δ λ , ν ( A 1 0 , B 1 j ) = ∞ f o r j ≥ 1 {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{0},B_{1}^{j})=\infty \ {\rm {{for\ }j\geq 1}}} δ λ , ν ( A 1 i , B 1 0 ) = ∞ f o r i ≥ 1 {\displaystyle \delta _{\lambda ,\nu }(A_{1}^{i},B_{1}^{0})=\infty \ {\rm {{for\ }i\geq 1}}} with a 0 ′ = b 0 ′ = 0 {\displaystyle a'_{0}=b'_{0}=0} === Implementations === An implementation of the TWED algorithm in C with a Python wrapper is available at TWED is also implemented into the Time Series Subsequence Search Python package (TSSEARCH for short) available at [1]. An R implementation of TWED has been integrated into the TraMineR, a R package for mining, describing and visualizing sequences of states or events, and more generally discrete sequence data. Additionally, cuTWED is a CUDA- accelerated implementation of TWED which uses an improved algorithm due to G. Wright (2020). This method is linear in memory and massively parallelized. cuTWED is written in CUDA C/C++, comes with Python bindings, and also includes Python bindings for Marteau's reference C implementation. ==== Python ==== Backtracking, to find the most cost-efficient path: ==== MATLAB ==== Backtracking, to find the most cost-efficient path:
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